Bunuel PS questions with Explanations
1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5.
Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With
Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers'
Dozen
Tough and Tricky Questions:
1. THE SUM OF EVEN INTEGERS:
The sum of the even numbers between 1 and k is 79*80, where k is an odd number, then k=?
(A) 79
(B) 80
(C) 81
(D) 157
(E) 159
The solution given in the file was 79, which is not correct. Also the problem was solved with AP formula
thus was long and used the theory rarely tested in GMAT. Here is my solution and my notes about AP.
Some may be useful:
The number of terms in this set would be: n=(k-1)/2 (as k is odd)
Last term: k-1
Average would be first term+last term/2=(2+k-1)/2=(k+1)/2
Also average: sum/number of terms=79*80/((k-1)/2)=158*80/(k-1)
(k+1)/2=158*80/(k-1) --> (k-1)(k+1)=158*160 --> k=159
Answer E.
MY NOTES ABOUT AP:
ARITHMETIC PROGRESSION
Sequence a1, a2,…an, so that a(n)=a(n-1)+d (constant)
nth term an = a1 + d ( n – 1 )
Sn=n*(a1+an)/2 or Sn=n*(2a1+d(n-1))/2
Special cases:
I. 1+2+…+n=n(1+n)/2 (Sum of n first integers)
II. 1+3+5+… (n times)=n^2 (Sum of n first odd numbers). nth term=2n-1
III. 2+4+6+… (n times)=n(n+1) (Sum of n first even numbers) nth term=2n
SOLUTION WITH THE AP FORMULA:
Sequence of even numbers
First term a=2, common difference d=2 since even number
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materials. ---ASAX
Bunuel PS questions with Explanations
Sum to first n numbers of AP:
Sn=n*(a1+an)/2=n(2*2+2(n-1))/2=n(n+1)=79*80
n=79 (odd)
Number of terms n=(k-1)/2=79 k=159
OR
Sum of n even numbers n(n+1)=79*80
n=79
k=2n+1=159
2. THE PRICE OF BUSHEL:
The price of a bushel of corn is currently $3.20, and the price of a peck of wheat is $5.80. The price of
corn is increasing at a constant rate of
cents per day while the price of wheat is decreasing at a
constant rate of
cents per day. What is the approximate price when a bushel of corn costs the
same amount as a peck of wheat?
(A) $4.50
(B) $5.10
(C) $5.30
(D) $5.50
(E) $5.60
Note that we are not asked in how many days prices will cost the same.
Let
be the # of days when these two bushels will have the same price.
First let's simplify the formula given for the rate of decrease of the price of wheat:
, this means that the price of wheat decreases by
day, in
days it'll decrease by
As price of corn increases
Set the equation:
The cost of a bushel of corn in
will be
cents per
cents;
cents per day, in
days it'll will increase by
, solve for
-->
cents;
;
days (the # of days when these two bushels will have the same price)
or $5.6.
Answer: E.
3. LEAP YEAR:
How many randomly assembled people are needed to have a better than 50% probability that at least 1
of them was born in a leap year?
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materials. ---ASAX
Bunuel PS questions with Explanations
A. 1
B. 2
C. 3
D. 4
E. 5
Probability of a randomly selected person NOT to be born in a leap year=3/4
Among 2 people, probability that none of them was born in a leap = 3/4*3/4=9/16. The probability at
least one born in leap = 1- 9/16=7/16<1/2
So, we are looking for such n (# of people), when 1-(3/4)^n>1/2
n=3 --> 1-27/64=37/64>1/2
Thus min 3 people are needed.
4. ADDITION PROBLEM:
AB + CD = AAA, where AB and CD are two-digit numbers and AAA is a three digit number; A, B, C, and D
are distinct positive integers. In the addition problem above, what is the value of C?
(A) 1
(B) 3
(C) 7
(D) 9
(E) Cannot be determined
AB and CD are two digit integers, their sum can give us only one three digit integer of a kind of AAA it's
111.
So, A=1. 1B+CD=111
C can not be less than 9, because no to digit integer with first digit 1 (mean that it's<20) can be added to
two digit integer less than 90 to have the sum 111 (if CD<90 meaning C<9 CD+1B<111).
C=9
Answer: D.
5. RACE:
A and B ran, at their respective constant rates, a race of 480 m. In the first heat, A gives B a head start of
48 m and beats him by 1/10th of a minute. In the second heat, A gives B a head start of 144 m and is
beaten by 1/30th of a minute. What is B’s speed in m/s?
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materials. ---ASAX
Bunuel PS questions with Explanations
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20
Let x be the speed of B.
Write the equation:
(480-48)/x (time of B for first heat) - 6 (seconds, time B lost to A first heat) = TIME OF A (in both heats A
runs with constant rate, so the time for first and second heats are the same)=(480-144)/x (time of B for
second heat) + 2 (seconds, time B won to A second heat)
(480-48)/x-6=(480-144)/x+2
x=12
Answer: A.
6. PROBABILITY OF DRAWING:
A bag contains 3 red, 4 black and 2 white balls. What is the probability of drawing a red and a white ball
in two successive draws, each ball being put back after it is drawn?
(A) 2/27
(B) 1/9
(C) 1/3
(D) 4/27
(E) 2/9
This is with replacement case (and was solved incorrectly by some of you):
We are multiplying by 2 as there are two possible wining scenarios RW and WR.
Answer: D.
7. THE DISTANCE BETWEEN THE CIRCLE AND THE LINE:
What is the least possible distance between a point on the circle x^2 + y^2 = 1 and a point on the line y =
3/4*x - 3?
A) 1.4
B) sqrt (2)
C) 1.7
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materials. ---ASAX
Bunuel PS questions with Explanations
D) sqrt (3)
E) 2.0
This is tough:
First note that min distance from the circle to the line would be: length of perpendicular from the origin
to the line (as the circle is centered at the origin) - the radius of a circle (which is 1).
Now we can do this by finding the equation of a line perpendicular to given line
(we know
it should cross origin and cross given line, so we can write the formula of it), then find the croos point of
these lines and then the distance between the origin and this point. But it's very lengthy way.
There is another, shorter one. Though I've never seen any GMAT question requiring the formula used in
it.
We know the formula to calculate the distance between two points
and
:
BUT there is a formula to calculate the distance between the point (in
our case origin) and the line:
DISTANCE BETWEEN THE LINE AND POINT:
Line:
, point
DISTANCE BETWEEN THE LINE AND ORIGIN:
As origin is
-->
So in our case it would be:
So the shortest distance would be:
Answer: A.
OR ANOTHER APPROACH:
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materials. ---ASAX
Bunuel PS questions with Explanations
In an x-y Cartesian coordinate system, the circle with center (a, b) and radius r is the set of all points (x,
y) such that:
If the circle is centered at the origin (0, 0), then the equation simplifies to:
So, the circle represented by the equation
.
is centered at the origin and has the radius of
Then note that min distance from the circle to the line would be: length of perpendicular from the
origin to the line (as the circle is centered at the origin) - the radius of a circle (which is 1).
So we should find the length of perpendicular, or the height of the right triangle formed by the X and Y
axis and the line
.
The legs would be the value of x for y=0 (x intercept) --> y=0, x=4 -->
and the value of y for x=0 (y intercept) --> x=0, y=-3 -->
.
.
So we have the right triangle with legs 4 and 3 and hypotenuse 5. What is the height of this triangle
(perpendicular from right angle to the hypotenuse)? As perpendicular to the hypotenuse will always
divide the triangle into two triangles with the same properties as the original triangle:
-->
-->
.
Answer: A.
8. THE AVERAGE TEMPERATURE:
The average of temperatures at noontime from Monday to Friday is 50; the lowest one is 45, what is the
possible maximum range of the temperatures?
A. 20
B. 25
C. 40
D. 45
E. 75
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materials. ---ASAX
Bunuel PS questions with Explanations
Average=50, Sum of temperatures=50*5=250
As the min temperature is 45, max would be 250-4*45=70 --> The range=70(max)-45(min)=25
Answer: B.
9. PROBABILITY OF INTEGER BEING DIVISIBLE BY 8:
If n is an integer from 1 to 96 (inclusive), what is the probability for n*(n+1)*(n+2) being divisible by 8?
A. 25%
B 50%
C 62.5%
D. 72.5%
E. 75%
N=n*(n+1)*(n+2)
N is divisible by 8 in two cases:
When n is even:
No of even numbers (between 1 and 96)=48
AND
When n+1 is divisible by 8. -->n=8p-1 --> 8p-1<=96 --> p=12.3 --> 12 such nembers
Total=48+12=60
Probability=60/96=0.62
Answer: C
10. SUM OF INTEGERS:
If the sum of five consecutive positive integers is A, then the sum of the next five consecutive integers in
terms of A is:
A. A+1 inquiry
B. A+5
C A+25
D 2A
E. 5A
Sum=A, next 5 consecutive will gain additional 5*5=25, so sum of the next five consecutive integers in
terms of A is: A+25
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materials. ---ASAX
Bunuel PS questions with Explanations
Answer: C.
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Hard Questions:
1. A family consisting of one mother, one father, two daughters and a son is taking a road trip in
a sedan. The sedan has two front seats and three back seats. If one of the parents must drive
and the two daughters refuse to sit next to each other, how many possible seating
arrangements are there?
(A) 28
(B) 32
(C) 48
(D) 60
(E) 120
As most of the combination problems this one can be solved in more than 1 way:
Sisters sit separately:
1. one of them is on the front seat (2 ways). Others (including second sister) can be arranged in:
2 (drivers seat)*3! (arrangements of three on the back seat)=12 ways. Total for this case:
2*12=24
Or
2. both by the window on the back seat (2 ways). Others can be arranged in: 2 (drivers seat)*2
(front seat)*1(one left to sit between the sisters on the back seat)=4 ways. Total for this case=8.
Total=24+8=32.
Another way: Total number of arrangements-arrangements with sisters sitting together=2*4*3!2*2(sisters together)*2*2*1(arrangement of others)=48-16=32
Answer: B.
2. What is the probability that a 3-digit positive integer picked at random will have one or
more "7" in its digits?
(A) 271/900
(B) 27/100
(C) 7/25
(D) 1/9
(E) 1/10
Total 3 digit numbers 900, 3 digit number with no 7 =8*9*9=648, P(at least one 7)=1-P(no 7)=1All contents have been taken form www.gmatclub.com . I do not own the copyright of the any of the
materials. ---ASAX
Bunuel PS questions with Explanations
648/900=252/900=7/25
Answer: C.
3. A sphere is inscribed in a cube with an edge of 10. What is the shortest possible distance
from one of the vertices of the cube to the surface of the sphere?
(A)
(B)
(C)
(D)
(E)
Shortest distance=(diagonal of cube-diameter of sphere)/2=
Answer: D.
4. A contractor estimated that his 10-man crew could complete the construction in 110 days if
there was no rain. (Assume the crew does not work on any rainy day and rain is the only
factor that can deter the crew from working). However, on the 61-st day, after 5 days of rain,
he hired 6 more people and finished the project early. If the job was done in 100 days, how
many days after day 60 had rain?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
This one was solved incorrectly:
Days to finish the job for 10 people 110 days.
On the 61-st day, after 5 days of rain --> 5 days was rain, 55 days they worked, thus completed
1/2 of the job, 1/2 is left (55 days of work for 10 people).
Then 6 more people was hired --> speed of construction increased by 1.6, days needed to finish
55/1.6=34.375, BUT after they were hired job was done in 100-60=40 days --> so 5 days rained.
They needed MORE than 34 days to finish the job, so if it rained for 6 days they wouldn't be able
to finish the job in 100(40) days.
Answer: B.
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materials. ---ASAX
Bunuel PS questions with Explanations
5. If s and t are positive integer such that s/t=64.12, which of the following could be the
remainder when s is divided by t?
(A) 2
(B) 4
(C) 8
(D) 20
(E) 45
divided by yields the remainder of can always be expressed as:
same as
(which is the
), where is the quotient and is the remainder.
Given that
, so according to the above
, which
means that must be a multiple of 3. Only option E offers answer which is a multiple of 3
Answer: E.
6. A committee of 6 is chosen from 8 men and 5 women so as to contain at least 2 men and 3
women. How many different committees could be formed if two of the men refuse to serve
together?
(A) 3510
(B) 2620
(C) 1404
(D) 700
(E) 635
Committee can have either: 2 men and 4 women OR 3 men and 3 women (to meet the condition
of at least 2 men and 3 women).
Ways to chose 6 members committee without restriction (two men refuse to server together):
Ways to chose 6 members committee with two particular men serve together:
700-65 = 635
Answer: E.
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materials. ---ASAX
Bunuel PS questions with Explanations
7. If x is positive, which of the following could be the correct ordering of 1/x,2x and x^2 ?
I. x^2<2x<1/x
II. x^2<1/x<2x
III. 2x<x^2<1/x
(A) None
(B) I only
(C) III only
(D) I and II only
(E) I II and III
First note that we are asked "which of the following COULD be the correct ordering" not MUST
be.
Basically we should determine relationship between
, and
in three areas:
When
-->
is the greatest and no option is offering this, so we know that x<2.
If
-->
is greatest then comes
So, we are left with
and no option is offering this.
:
In this case
is least value, so we are left with:
I.
positive for
--> can
? Can
, the expression
can be negative or
. (You can check it either algebraically or by picking numbers)
II.
--> can
negative or positive for
.
? The same here
, the expression
can be
. (You can check it either algebraically or by picking numbers)
Answer: D.
8. In the xy plane, Line k has a positive slope and x-intercept 4. If the area of the triangle
formed by line k and the two axes is 12, What is the y-intercept of line K ?
(A) 3
(B) 6
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materials. ---ASAX
Bunuel PS questions with Explanations
(C) -3
(D) -6
(E) -4
Positive slope, positive (4) x-intercept --> negative y-intercept. --> 1/2*4*|y|=12 --> |y|=6. -->
y=-6
Answer: D
9. Of the applicants passes a certain test, 15 applied to both college X and Y. If 20 % of the
applicants who applied college X and 25% of the applicants who applied college Y applied both
college X and Y, how many applicants applied only college X or college Y?
(A) 135
(B) 120
(C) 115
(D) 105
(E) 90
20%X=X&Y=15 --> X=75 --> Only X=75-15=60
25%Y=X&Y=15 --> Y=60 --> Only Y=60-15=45
Only X or Y=60+45=105
Answer: D.
10. What is the lowest positive integer that is divisible by each of the integers 1 through 7,
inclusive.
(A) 420
(B) 840
(C) 1260
(D) 2520
(E) 5040
The integer should be divisible by: 2, 3, 4(=2^2), 5, 6(=2*3), and 7. LCM=2^2*3*5*7=420
Answer: A.
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Another Set of Hard questions:
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materials. ---ASAX
Bunuel PS questions with Explanations
1. ABCDE is a regular pentagon with F at its center. How many different triangles can be
formed by joining 3 of the points A,B,C,D,E and F?
(A) 10
(B) 15
(C) 20
(D) 25
(E) 30
Answer: C.
2. The function f is defined for all positive integers n by the following rule: f(n) is the number
of positive integers each of which is less than n and has no positive factor in common with n
other than 1. If p is prime, then f(p) =
(A) P-1
(B) P-2
(C) (P+1)/2
(D) (P-1)/2
(E) 2
Answer: A.
3. How many numbers that are not divisible by 6 divide evenly into 264,600?
(A) 9
(B) 36
(C) 51
(D) 63
(E) 72
Answer: D.
4.A certain quantity is measured on two different scales, the R-scale and the S-scale, that are
related linearly. Measurements on the R-scale of 6 and 24 correspond to measurements on
the S-scale of 30 and 60, respectively. What measurement on the R-scale corresponds to a
measurement of 100 on the S-scale?
(A) 20
(B) 36
(C) 48
(D) 60
(E) 84
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materials. ---ASAX
Bunuel PS questions with Explanations
Answer: C.
5. Mrs. Smith has been given film vouchers. Each voucher allows the holder to see a film
without charge. She decides to distribute them among her four nephews so that each nephew
gets at least two vouchers. How many vouchers has Mrs. Smith been given if there are 120
ways that she could distribute the vouchers?
(A) 13
(B) 14
(C) 15
(D) 16
(E) more than 16
Answer: C.
6. This year Henry will save a certain amount of his income, and he will spend the rest. Next
year Henry will have no income, but for each dollar that he saves this year, he will have 1 + r
dollars available to spend. In terms of r, what fraction of his income should Henry save this
year so that next year the amount he was available to spend will be equal to half the amount
that he spends this year?
(A) 1/(r+2)
(B) 1/(2r+2)
(C) 1/(3r+2)
(D) 1/(r+3)
(E) 1/(2r+3)
Answer: E.
7. Before being simplified, the instructions for computing income tax in Country Rwere to add
2 percent of one's annual income to the average(arithmetic mean)of 100units of Country R's
currency and 1 percent of one's annual income. Which of the following represents the
simplified formula for computing the income tax in Country R's currency, for a person in that
country whose annual income is I?
(A) 50+I/200
(B) 50+3I/100
(C) 50+I/40
(D) 100+I/50
(E) 100+3I/100
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materials. ---ASAX
Bunuel PS questions with Explanations
Answer: C.
8. How many positive integers less than 10,000 are such that the product of their digits is 210?
(A) 24
(B) 30
(C) 48
(D) 54
(E) 72
Answer: D.
9. Find the number of selections that can be made taking 4 letters from the word"ENTRANCE".
(A) 70
(B) 36
(C) 35
(D) 72
(E) 32
Answer:B.
Find in the above word, the number of arrangements using the 4 letters.
Answer:606.
10. How many triangles with positive area can be drawn on the coordinate plane such that the
vertices have integer coordinates (x,y) satisfying 1≤x≤3 and 1≤y≤3?
(A) 72
(B) 76
(C) 78
(D) 80
(E) 84
Answer: B.
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Standard Deviation Questions:
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materials. ---ASAX
Bunuel PS questions with Explanations
Please note the following:
A. I was assured MANY TIMS, by various GMAT tutors, that GMAT won't ask you to actually
calculate SD, but rather to understand the concept of it. Though KNOWING how it's calculated
helps in understanding the concept.
B. During the real GMAT it's highly unlikely to get more than one ot two question on SD (as on
combinatorics), actually you may see none, so do not spend too much of your preparation time
on it, it's better to concentrate on issues you'll definitely face on G-day.
Many questions below are easy, some are tough, but anyway they are good to master in solving
SD problems. I'll post OA after some discussions. Please provide your way of thinking along with
the answer. Thanks.
1. A set of data consists of the following 5 numbers: 0,2,4,6, and 8. Which two numbers, if
added to create a set of 7 numbers, will result in a new standard deviation that is close to
the standard deviation for the original 5 numbers?
(A) -1 and 9
(B) 4 and 4
(C) 3 and 5
(D) 2 and 6
(E) 0 and 8
Answer: D.
2. A certain list of 100 data has an average of 6 and standard deviation of d where d is
positive. Which of the following pairs of data, when added to the list must result in a list
of 102 data with the standard deviation less than d?
(A) 0 and 6
(B) 0 and 12
(C) 0 and 0
(D) -6 and 0
(E) 6 and 6
Answer: E.
3. For a certain examination, a score of 58 was 2 standard deviations below the mean, and
a score of 98 was 3 standard deviations above the mean. What was the mean score for the
examination?
(A) 74
(B) 76
(C) 78
(D) 80
(E) 82
Answer: A.
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materials. ---ASAX
Bunuel PS questions with Explanations
4. Which of the following distribution of numbers has the greatest standard deviation?
(A) {-3, 1, 2}
(B) {-2, -1, 1, 2}
(C) {3, 5, 7}
(D) {-1, 2, 3, 4}
(E) {0, 2, 4}
Answer: A.
5. Which of the following has the same standard deviation as {s,r,t}?
I. {r-2, s-2, t-2}
II. {0, s-t, s-r}
III. {|r|, |s|, |t|}
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only
Answer: D.
6. A certain characteristic in a large population has a distribution that is symmetric about
the mean m. If 68% of the distribution lies one standard deviation d of the mean, what
percent of the distribution is less than m+d?
(A) 16%
(B) 32%
(C) 48%
(D) 84%
(E) 92%
Answer: D.
7. Which of the following data sets has the third largest standard deviation?
(A) {1, 2, 3, 4, 5}
(B) {2, 3, 3, 3, 4}
(C) {2, 2, 2, 4, 5}
(D) {0, 2, 3, 4, 6}
(E) {-1, 1, 3, 5, 7}
Answer: A.
8. The table below represents three sets of numbers with their respective medians, means
and standard deviations. The third set, Set [A+B], denotes the set that is formed by
combining Set A and Set B.
Median Mean StandardDeviation
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materials. ---ASAX
Bunuel PS questions with Explanations
Set A: X, Y, Z.
Set B: L, M, N.
Set [A + B]: Q, R, S.
If X – Y > 0 and L – M = 0, then which of the following must be true?
I. Z > N
II. R > M
III. Q > R
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) None
Answer: E
9. E is a collection of four odd integers and the greatest difference between any two
integers in E is 4. The standard deviation of E must be one of how many numbers?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Answer: B
10. If a certain sample of data has a mean of 20.0 and a standard deviation of 3.0, which of
the following values is more than 2.5 standard deviations from the mean?
(A) 12.0
(B) 13.5
(C) 17.0
(D) 23.5
(E) 26.5
Answer: A.
11. Arithmetic mean and standard deviation of a certain normal distribution are 13.5 and
1.5. What value is exactly 2 standard deviations less than the mean?
(A) 10.5
(B) 11
(C) 11.5
(D) 12
(E) 12.5
Answer: A.
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materials. ---ASAX
Bunuel PS questions with Explanations
Exponents and roots problems are very common on the GMAT. So, it's extremely
important to know how to manipulate them, how to factor out, take roots, multiply,
divide, etc. Below are 11 problems to test your skills. Please post your thought
process/solutions along with the answers.
I'll post OA's with detailed solutions tomorrow. Good luck.
Exponents and Roots Questions:
1. What is the value of
A.
B.
C.
D. 50
E. 60
?
Solution: tough-and-tricky-exponents-and-roots-questions-125956-40.html#p1029216
2. What is the units digit of
A. 0
B. 2
C. 4
D. 6
E. 8
?
Solution: tough-and-tricky-exponents-and-roots-questions-125956-40.html#p1029219
3. If
A. 14/5
B. 5
C. 28/5
D. 13
E. 14
and
what is the value of
?
Solution: tough-and-tricky-exponents-and-roots-questions-125956-40.html#p1029221
4. What is the value of
A. 5^6
B. 5^7
C. 5^8
?
All contents have been taken form www.gmatclub.com . I do not own the copyright of the any of the
materials. ---ASAX
Bunuel PS questions with Explanations
D. 5^9
E. 5^10
Solution: tough-and-tricky-exponents-and-roots-questions-125956-40.html#p1029222
5. If
and is a multiple of
integer, then what is the value of
A. -26
B. -25
C. -1
D. 0
E. 1
, where
is a non-negative
?
Solution: tough-and-tricky-exponents-and-roots-questions-125956-40.html#p1029223
6. If
A.
B. x>-2
C. x^2<4
D. x^3<-8
E. x^4>32
then which of the following must be true?
Solution: tough-and-tricky-exponents-and-roots-questions-125956-40.html#p1029224
7. If
following must be true:
A. x<6
B. 6<x<8
C. 8<x<10
D. 10<x<12
E. x>12
, then which of the
Solution: tough-and-tricky-exponents-and-roots-questions-125956-40.html#p1029227
8. If is a positive number and equals to
, where the given
expression extends to an infinite number of roots, then what is the value of x?
A.
B. 3
C.
D.
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materials. ---ASAX
Bunuel PS questions with Explanations
E. 6
Solution: tough-and-tricky-exponents-and-roots-questions-125956-40.html#p1029228
9. If is a positive integer then the value of
following?
is closest to which of the
A.
B.
C.
D.
E.
Solution: tough-and-tricky-exponents-and-roots-questions-125956-40.html#p1029229
10. Given that
and
, then what is the value
of
?
A. 5
B. 10
C. 15
D. 20
E. Can not be determined
Solution: tough-and-tricky-exponents-and-roots-questions-125956-40.html#p1029231
11. If
A. 2
B. 2^(11)
C. 2^(32)
D. 2^(37)
E. 2^(64)
,
and
then what is the value of
?
Solution: tough-and-tricky-exponents-and-roots-questions-125956-40.html#p1029232
Tough and Tricky Exponents and roots questions: Answers by Bunuel:
1. What is the value of
A.
B.
C.
D. 50
?
All contents have been taken form www.gmatclub.com . I do not own the copyright of the any of the
materials. ---ASAX
Bunuel PS questions with Explanations
E. 60
Square the given expression to get rid of the roots, though don't forget to un-square the value
you get at the end to balance this operation and obtain the right answer:
Must know fro the GMAT:
(while
).
So we get:
.
Note that sum of the first and the third terms simplifies to
so we have
,
-->
.
Also must know for the GMAT:
, thus
.
Recall that we should un-square this value to get the right the answer:
.
Answer: C.
2. 2. What is the units digit of
A. 0
B. 2
C. 4
D. 6
E. 8
?
Must know for the GMAT:
I. The units digit of
is the same as that of
is that same as that of
, which means that the units digit of
and the units digit of
is that same as that of
.
II. If exponentiation is indicated by stacked symbols, the rule is to work from the top down, thus:
and not
, which on the other hand equals to
.
So:
All contents have been taken form www.gmatclub.com . I do not own the copyright of the any of the
materials. ---ASAX
Bunuel PS questions with Explanations
;
.
Thus,
and
.
III. The units digit of integers in positive integer power repeats in specific pattern (cyclicity): The
units digit of 7 and 3 in positive integer power repeats in patterns of 4:
1. 7^1=7 (last digit is 7)
2. 7^2=9 (last digit is 9)
3. 7^3=3 (last digit is 3)
4. 7^4=1 (last digit is 1)
5. 7^5=7 (last digit is 7 again!)
...
1. 3^1=3 (last digit is 3)
2. 3^2=9 (last digit is 9)
3. 3^3=27 (last digit is 7)
4. 3^4=81 (last digit is 1)
5. 3^5=243 (last digit is 3 again!)
...
Thus th units digit of
the units digit of
will be 1 (4th in pattern, as 12 is a multiple of cyclicty number 4) and
will be 3 (first in pattern, as 9=4*2+1).
So, we have that the units digit of
is 1 and the units digit of
is 3. Also notice that the second number is much larger then the first one, thus their difference
will be negative, something like 11-13=-2, which gives the final answer that the units digit of
is 2.
Answer B.
3. 3. If
A. 14/5
B. 5
C. 28/5
D. 13
and
what is the value of
?
All contents have been taken form www.gmatclub.com . I do not own the copyright of the any of the
materials. ---ASAX
Bunuel PS questions with Explanations
E. 14
First thing one should notice here is that and must be some irrational numbers (4,900 has
other primes then 5 in its prime factorization and 25 doesn't have 2 as a prime at all), so we
should manipulate with given expressions rather than to solve for x and y.
-->
-->
Answer: E.
4. 4. What is the value of
A. 5^6
B. 5^7
C. 5^8
D. 5^9
E. 5^10
?
This question can be solved in several ways:
Traditional approach:
Note that we
have the sum of geometric progression in brackets with first term equal to 5 and common ratio
also equal to 5. The sum of the first terms of geometric progression is given by:
, where is the first term,
# of terms and is a common ratio
So in our case:
.
.
30 sec approach based on answer choices:
We have the sum of 6 terms. Now, if all terms were equal to the largest term 4*5^5 we would
have:
5^7, thus the answer must be A: 5^6.
, so the actual sum must be less than
Answer: A.
5. 5. If
then what is the value of
A. -26
and is a multiple of
, where
is a non-negative integer,
?
All contents have been taken form www.gmatclub.com . I do not own the copyright of the any of the
materials. ---ASAX
Bunuel PS questions with Explanations
B. -25
C. -1
D. 0
E. 1
so
it to be a multiple of
is an odd number. The only way
(even number in integer power) is when
and 1 is a factor of every integer. Thus
, in this case
-->
. Must know for the GMAT:
, for
- any
nonzero number to the power of 0 is 1. Important note: the case of 0^0 is not tested on the
GMAT.
Answer: C.
6. 6. If
A.
B. x>-2
C. x^2<4
D. x^3<-8
E. x^4>32
then which of the following must be true?
Must know for the GMAT: Even roots from negative number is undefined on the GMAT (as
GMAT is dealing only with Real Numbers):
, for example
.
Odd roots have the same sign as the base of the root. For example,
and
.
Back to the original question:
As
then
must be a little bit less than -2 -->
. Thus
, so option D must be true.
As for the other options:
A.
B.
C.
,
is not true.
, thus x>-2 is also not true.
, thus x^2<4 is also not true.
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materials. ---ASAX
Bunuel PS questions with Explanations
E.
also not true.
, (2^4=16, so anyway -2.1^4 can not be more than 32) thus x^4>32 is
Answer: D.
7. 7. If
must be true:
A. x<6
B. 6<x<8
C. 8<x<10
D. 10<x<12
E. x>12
, then which of the following
Here is a little trick: any positive integer root from a number more than 1 will be more than 1.
For example:
Now,
.
(as 3^2=9) and
(2^3=8). Thus
Answer: E.
8. 8. If is a positive number and equals to
, where the given
expression extends to an infinite number of roots, then what is the value of x?
A.
B. 3
C.
D.
E. 6
Given:
and
-->
, as the
expression under the square root extends infinitely then expression in brackets would equal to
itself and we can safely replace it with
Square both sides:
then:
.
-->
and rewrite the given expression as
-->
or
, but since
Answer: B.
All contents have been taken form www.gmatclub.com . I do not own the copyright of the any of the
materials. ---ASAX
.
Bunuel PS questions with Explanations
9. 9. If is a positive integer then the value of
following?
is closest to which of the
A.
B.
C.
D.
E.
Note that we need approximate value of the given expression. Now,
number than
. Hence
will be very close to
negligible in this case. The same way
is much larger
itself, basically
will be very close to
is
itself.
Thus .
You can check this algebraically as well:
. Again, -1, both in
denominator and nominator is negligible value and we'll get the same expression as above:
Answer: D.
10. 10. Given that
and
, then what is the value of
?
A. 5
B. 10
C. 15
D. 20
E. Can not be determined
Rearranging both expressions we'll get:
Denote
as and
So we have that
and
as .
and
. Now,
then
with two unknowns:
.
-->
and
and as
. Thus we get two equations
--> solving for -->
-->
Solving for -->
Finally,
.
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materials. ---ASAX
.
Bunuel PS questions with Explanations
Answer: B.
11. 11. If
A. 2
B. 2^(11)
C. 2^(32)
D. 2^(37)
E. 2^(64)
that
,
-->
).
and
then what is the value of
(note that
?
is not a valid solution as given
Second step:
-->
OR second step:
-->
--> since
.
then
.
Answer: D.
12 Easy Pieces or not:
After posting some 700+ questions, I've decided to post the problems which are not that hard. Though
each question below has a trap or trick so be careful when solving. I'll post OA's with detailed
solutions after some discussion. Good luck.
1. There are 5 pairs of white, 3 pairs of black and 2 pairs of grey socks in a drawer. If four socks are
picked at random what is the probability of getting two socks of the same color?
A. 1/5
B. 2/5
C. 3/4
D. 4/5
E. 1
Solution: 12-easy-pieces-or-not-126366.html#p1033919
2. If x is an integer and 9<x^2<99, then what is the value of maximum possible value of x minus
minimum possible value of x?
A. 5
B. 6
C. 7
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materials. ---ASAX
Bunuel PS questions with Explanations
D. 18
E. 20
Solution: 12-easy-pieces-or-not-126366.html#p1033921
3. Fanny and Alexander are 360 miles apart and are traveling in a straight line toward each other at a
constant rate of 25 mph and 65 mph respectively, how far apart will they be exactly 1.5 hours before
they meet?
A. 25 miles
B. 65 miles
C. 70 miles
D. 90 miles
E. 135 miles
Solution: 12-easy-pieces-or-not-126366.html#p1033924
4. If -3<x<5 and -7<y<9, which of the following represent the range of all possible values of y-x?
A. -4<y-x<4
B. -2<y-x<4
C. -12<y-x<4
D. -12<y-x<12
E. 4<y-x<12
Solution: 12-easy-pieces-or-not-126366.html#p1033925
5. The angles in a triangle are x, 3x, and 5x degrees. If a, b and c are the lengths of the sides opposite
to angles x, 3x, and 5x respectively, then which of the following must be true?
I. c>a+b
II. c^2>a^2+b^2
III. c/a/b=10/6/2
A. I only
B. II only
C. III only
D. I and III only
E. II and III only
Solution: 12-easy-pieces-or-not-126366.html#p1033930
6. Anna has 10 marbles: 5 red, 2 blue, 2 green and 1 yellow. She wants to arrange all of them in a row
so that no two adjacent marbles are of the same color and the first and the last marbles are of
different colors. How many different arrangements are possible?
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materials. ---ASAX
Bunuel PS questions with Explanations
A. 30
B. 60
C. 120
D. 240
E. 480
Solution: 12-easy-pieces-or-not-126366.html#p1033932
7. After 2/9 of the numbers in a data set A were observed, it turned out that 3/4 of those numbers
were non-negative. What fraction of the remaining numbers in set A must be negative so that the
total ratio of negative numbers to non-negative numbers be 2 to 1?
A. 11/14
B. 13/18
C. 4/7
D. 3/7
E. 3/14
Solution: 12-easy-pieces-or-not-126366.html#p1033933
8. There are 15 black chips and 5 white chips in a jar. What is the least number of chips we should pick
to guarantee that we have 2 chips of the same color?
A. 3
B. 5
C. 6
D. 16
E. 19
Solution: 12-easy-pieces-or-not-126366.html#p1033935
9. Julie is putting M marbles in a row in a repeating pattern: blue, white, red, green, black, yellow,
pink. If the row begins with blue marble and ends with red marble, then which of the following could
be the value of M?
A. 22
B. 30
C. 38
D. 46
E. 54
Solution: 12-easy-pieces-or-not-126366.html#p1033936
10. If
is an integer and
, then what is the value of n?
All contents have been taken form www.gmatclub.com . I do not own the copyright of the any of the
materials. ---ASAX
Bunuel PS questions with Explanations
A. 1
B. 2
C. 3
D. 4
E. 5
Solution: 12-easy-pieces-or-not-126366.html#p1033938
11. The numbers {1, 3, 6, 7, 7, 7} are used to form three 2-digit numbers. If the sum of these three
numbers is a prime number p, what is the largest possible value of p?
A. 97
B. 151
C. 209
D. 211
E. 219
Solution: 12-easy-pieces-or-not-126366-20.html#p1033939
12. If
A. -1/100
B. -1/50
C. -1/36
D. -1/18
E. -1/6
and
, what is the least value of
possible?
Solution: 12-easy-pieces-or-not-126366-20.html#p1033949
12 Easy Pieces or not – Solutions by Bunuel:
1. There are 5 pairs of white, 3 pairs of black and 2 pairs of grey socks in a drawer. If four socks
are picked at random what is the probability of getting two socks of the same color?
A. 1/5
B. 2/5
C. 3/4
D. 4/5
E. 1
No formula is need to answer this one. The trick here is that we have only 3 different color socks
but we pick 4 socks, which ensures that in ANY case we'll have at least one pair of the same
color (if 3 socks we pick are of the different color, then the 4th sock must match with either of
previously picked one). P=1.
All contents have been taken form www.gmatclub.com . I do not own the copyright of the any of the
materials. ---ASAX
Bunuel PS questions with Explanations
Answer: E.
_________________
2. 2. If x is an integer and 9<x^2<99, then what is the value of maximum possible value of x
minus minimum possible value of x?
A. 5
B. 6
C. 7
D. 18
E. 20
Also tricky. Notice that can take positive, as well as negative values to satisfy
hence can be: -9, -8, -7, -6, -4, 4, 5, 6, 7, 8, or 9. We asked to find the value of
, ans since
and
,
then
.
Answer: D.
3. 3. Fanny and Alexander are 360 miles apart and are traveling in a straight line toward each
other at a constant rate of 25 mph and 65 mph respectively, how far apart will they be exactly
1.5 hours before they meet?
A. 25 miles
B. 65 miles
C. 70 miles
D. 90 miles
E. 135 miles
Make it simple! The question is: how far apart will they be exactly 1.5 hours before they meet?
As Fanny and Alexander's combined rate is 25+65 mph then 1.5 hours before they meet they'll
be (25+65)*1.5=135 miles apart.
Answer: E.
_________________
4. 4. If -3<x<5 and -7<y<9, which of the following represent the range of all possible values of yx?
A. -4<y-x<4
B. -2<y-x<4
C. -12<y-x<4
D. -12<y-x<12
E. 4<y-x<12
All contents have been taken form www.gmatclub.com . I do not own the copyright of the any of the
materials. ---ASAX
Bunuel PS questions with Explanations
To get max value of y-x take max value of y and min value of x: 9-(-3)=12;
To get min value of y-x take min value of y and max value of x: -7-(5)=-12;
Hence, the range of all possible values of y-x is -12<y-x<12.
Answer: D.
5. 5. The angles in a triangle are x, 3x, and 5x degrees. If a, b and c are the lengths of the sides
opposite to angles x, 3x, and 5x respectively, then which of the following must be true?
I. c>a+b
II. c^2>a^2+b^2
III. c/a/b=10/6/2
A. I only
B. II only
C. III only
D. I and III only
E. II and III only
According to the relationship of the sides of a triangle: the length of any side of a triangle must
be larger than the positive difference of the other two sides, but smaller than the sum of the
other two sides. Thus I and III can never be true: one side (c) can not be larger than the sum of
the other two sides (a and b). Note that III is basically the same as I: if c=10, a=6 and b=2 then
c>a+b, which can never be true. Thus even not considering the angles, we can say that only
answer choice B (II only) is left.
Answer: B.
Now, if interested why II is true: as the angles in a triangle are x, 3x, and 5x degrees then
x+3x+5x=180 --> x=20, 3x=60, and 5x=100. Next, if angle opposite c were 90 degrees, then
according to Pythagoras theorem c^2=a^+b^2, but since the angel opposite c is more than 90
degrees (100) then c is larger, hence c^2>a^+b^2.
6. 6. Anna has 10 marbles: 5 red, 2 blue, 2 green and 1 yellow. She wants to arrange all of them
in a row so that no two adjacent marbles are of the same color and the first and the last
marbles are of different colours. How many different arrangements are possible?
A. 30
B. 60
C. 120
D. 240
E. 480
All contents have been taken form www.gmatclub.com . I do not own the copyright of the any of the
materials. ---ASAX
Bunuel PS questions with Explanations
Seems tough and complicated but if we read the stem carefully we find that the only way both
conditions to be met for 5 red marbles, which are half of total marbles, they can be arranged
only in two ways: R*R*R*R*R* or *R*R*R*R*R.
Here comes the next good news, in these cases BOTH conditions are met for all other marbles as
well: no two adjacent marbles will be of the same color and the first and the last marbles will be
of different colors.
Now, it's easy: 2 blue, 2 green and 1 yellow can be arranged in 5 empty slots in 5!/(2!*2!)=30
ways (permutation of 5 letters BBGGY out of which 2 B's and 2 G' are identical). Finally as there
are two cases (R*R*R*R*R* and *R*R*R*R*R. ) then total # of arrangement is 30*2=60.
Answer: B.
______________
7. 7. After 2/9 of the numbers in a data set A were observed, it turned out that 3/4 of those
numbers were non-negative. What fraction of the remaining numbers in set A must be
negative so that the total ratio of negative numbers to non-negative numbers be 2 to 1?
A. 11/14
B. 13/18
C. 4/7
D. 3/7
E. 3/14
If choose variable for set A there will be too many fractions to manipulate with, so pick some
smart #: let set A contain 18 numbers.
"2/9 of the numbers in a data set A were observed" --> 4 observed and 18-4=14 numbers left to
observe;
"3/4 of those numbers were non-negative" --> 3 non-negative and 1 negative;
Ratio of negative numbers to non-negative numbers to be 2 to 1 there should be total of
18*2/3=12 negative numbers, so in not yet observed part there should be 12-1=11 negative
numbers. Thus 11/14 of the remaining numbers in set A must be negative.
Answer: A.
8. 8. There are 15 black chips and 5 white chips in a jar. What is the least number of chips we
should pick to guarantee that we have 2 chips of the same color?
A. 3
B. 5
C. 6
D. 16
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materials. ---ASAX
Bunuel PS questions with Explanations
E. 19
Worst case scenario would be if the first two chips we pick will be of the different colors. But the
next chip must match with either of two, so 3 is the answer.
Answer: A.
9. 9. Julie is putting M marbles in a row in a repeating pattern: blue, white, red, green, black,
yellow, pink. If the row begins with blue marble and ends with red marble, then which of the
following could be the value of M?
A. 22
B. 30
C. 38
D. 46
E. 54
There are total of 7 different color marbles in a pattern. Now, as the row begins with blue
marble and ends with red marble (so ends with 3rd marble in a pattern) then M=7k+3. The only
answer choice which is multiple of 7 plus 3 is 38=35+3.
Answer: C.
10. 10. If
A. 1
B. 2
C. 3
D. 4
E. 5
is an integer and
, then what is the value of n?
Also no need for algebraic manipulation. 1/10^(n+1) is 10 times less than 1/10^n, and both
when expressed as decimals are of a type 0.001 (some number of zeros before 1) --> so the
given expression to hold true we should have: 0.001<0.00737<0.01, which means that n=2
(1/10^n=0.01 --> n=2).
Answer: B.
11. 11. The numbers {1, 3, 6, 7, 7, 7} are used to form three 2-digit numbers. If the sum of these
three numbers is a prime number p, what is the largest possible value of p?
A. 97
B. 151
C. 209
D. 211
All contents have been taken form www.gmatclub.com . I do not own the copyright of the any of the
materials. ---ASAX
Bunuel PS questions with Explanations
E. 219
What is the largest possible sum of these three numbers that we can form? Maximize the first
digit: 76+73+71=220=even, so not a prime. Let's try next largest sum, switch digits in 76 and
we'll get: 67+73+71=211. Question is it a prime number? If you notice 210=2*3*5*7=the
product of the first four primes. So, 210+1=211 must be a prime. For example: 2+1=3=prime,
2*3+1=7=prime, 2*3*5+1=31=prime.
Answer: D.
12. 12. If
A. -1/100
B. -1/50
C. -1/36
D. -1/18
E. -1/6
and
To get the least value of
of
it is).
, what is the least value of
possible?
, which obviously will be negative, try to maximize absolute value
, as more is the absolute value of a negative number "more" negative it is (the smallest
To maximize
pick largest absolute values possible for and :
Notice that: -1/18<-1/36<-1/50<-1/100, so -1/100 is the largest number and -1/18 is the
smallest number (we cannot obtain -1/6 from x^2*y or else it would be the correct answer).
.
Answer: D.
BaKers Dozen:
1. A password on Mr. Wallace's briefcase consists of 5 digits. What is the probability that
the password contains exactly three digit 6?
A. 860/90,000
B. 810/100,000
C. 858/100,000
D. 860/100,000
E. 1530/100,000
Solution: baker-s-dozen-128782-20.html#p1057502
All contents have been taken form www.gmatclub.com . I do not own the copyright of the any of the
materials. ---ASAX
Bunuel PS questions with Explanations
2. If
A. 6^4
B. 62^2
C. 65^2
D. 15^4
E. 52^4
, then y is NOT divisible by which of the following?
Solution: baker-s-dozen-128782-20.html#p1057503
3. For the past k days the average (arithmetic mean) cupcakes per day that Liv baked
was 55. Today Bibi joined and together with Liv they baked 100 cupcakes, which raises
the average to 60 cupcakes per day. What is the value of k?
A. 6
B. 8
C. 9
D. 10
E. 12
Solution: baker-s-dozen-128782-20.html#p1057504
4. What is the smallest positive integer
integer?
A. 14
B. 36
C. 144
D. 196
E. 441
such that
is the square of a positive
Solution: baker-s-dozen-128782-20.html#p1057505
5. There are 7 red and 5 blue marbles in a jar. In how many ways 8 marbles can be
selected from the jar so that at least one red marble and at least one blue marble to
remain in the jar?
A. 460
B. 490
C. 493
D. 455
E. 445
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materials. ---ASAX
Bunuel PS questions with Explanations
Solution: baker-s-dozen-128782-20.html#p1057507
6. A pool has two water pumps A and B and one drain C. Pump A alone can fill the
whole pool in x hours, and pump B alone can fill the whole pool in y hours. The drain
can empty the whole pool in z hours, where z>x. With pumps A and B both running
and the drain C unstopped till the pool is filled, which of the following represents the
amount of water in terms of the fraction of the pool which pump A pumped into the
pool?
A.
B.
C.
D.
E.
Solution: baker-s-dozen-128782-20.html#p1057508
7. Metropolis Corporation has 4 shareholders: Fritz, Luis, Alfred and Werner. Number
of shares that Fritz owns is 2/3 rd of number of the shares of the other three
shareholders, number of the shares that Luis owns is 3/7 th of number of the shares of
the other three shareholders and number of the shares that Alfred owns is 4/11 th of
number of the shares of the other three shareholders. If dividends of $3,600,000 were
distributed among the 4 shareholders, how much of this amount did Werner receive?
A. $60,000
B. $90,000
C. $100,000
D. $120,000
E. $180,000
Solution: baker-s-dozen-128782-20.html#p1057509
8. A set A consists of 7 consecutive odd integers. If the sum of 5 largest integers of set
A is -185 what is the sum of the 5 smallest integers of set A?
A. -165
B. -175
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materials. ---ASAX
Bunuel PS questions with Explanations
C. -195
D. -205
E. -215
Solution: baker-s-dozen-128782-20.html#p1057512
9. If x and y are negative numbers, what is the value of
A. 1+y
B. 1-y
C. -1-y
D. y-1
E. x-y
?
Solution: baker-s-dozen-128782-20.html#p1057514
10. If x^2<81 and y^2<25, what is the largest prime number that can be equal to x-2y?
A. 7
B. 11
C. 13
D. 17
E. 19
Solution: baker-s-dozen-128782-20.html#p1057515
11. In an infinite sequence 1, 3, 9, 27, ... each term after the first is three times the
previous term. What is the difference between the sum of 13th and 15th terms and
the sum of 12th and 14th terms of the sequence?
A. 10*3^11
B. 20*3^11
C. 10*3^12
D. 40*3^11
E. 20*3^12
Solution: baker-s-dozen-128782-40.html#p1057517
12. x, y and z are positive integers such that when x is divided by y the remainder is 3
and when y is divided by z the remainder is 8. What is the smallest possible value of
x+y+z?
A. 12
B. 20
C. 24
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materials. ---ASAX
Bunuel PS questions with Explanations
D. 29
E. 33
Solution: baker-s-dozen-128782-40.html#p1057519
13. If
, what is the product of the tens and the units digits of
?
A. 0
B. 6
C. 7
D. 12
E. 14
Solution: baker-s-dozen-128782-40.html#p1057520
Bakers Dozen Solution by Bunuel:
1. A password on Mr. Wallace's briefcase consists of 5 digits. What is the probability that
the password contains exactly three digit 6?
A. 860/90,000
B. 810/100,000
C. 858/100,000
D. 860/100,000
E. 1530/100,000
Total # of 5 digit codes is 10^5, notice that it's not 9*10^4, since in a code we can have
zero as the first digit.
# of passwords with three digit 6 is
6) has 9 choices, thus we have 9*9 and
out of 5 digits we have.
: each out of two other digits (not
is ways to choose which 3 digits will be 6's
Answer: B.
All contents have been taken form www.gmatclub.com . I do not own the copyright of the any of the
materials. ---ASAX
Bunuel PS questions with Explanations
2. 2. If
A. 6^4
B. 62^2
C. 65^2
D. 15^4
E. 52^4
, then y is NOT divisible by which of the following?
.
Now, if you analyze each option you'll see that only
, since the power of 13 in it is higher than the power of 13 in
is not a factor of
.
Answer: E.
3. 3. For the past k days the average (arithmetic mean) cupcakes per day that Liv baked
was 55. Today Bibi joined and together with Liv they baked 100 cupcakes, which raises
the average to 60 cupcakes per day. What is the value of k?
A. 6
B. 8
C. 9
D. 10
E. 12
Total cupcakes for k days was 55k, which means that total cupcakes for k+1 days was
55k+100. The new average is (55k+100)/(k+1)=60 --> 55k+100=60k+60 --> k=8
Answer: B.
4. 4. What is the smallest positive integer
integer?
A. 14
B. 36
C. 144
D. 196
E. 441
, so in order
such that
is the square of a positive
to be a square of an integer
the powers of 2 and 7 to even number, so the least value of
which makes the leas value of equal to 14^2=196.
must complete
must equal to 2*7=14,
All contents have been taken form www.gmatclub.com . I do not own the copyright of the any of the
materials. ---ASAX
Bunuel PS questions with Explanations
Answer: D.
5. 5. There are 7 red and 5 blue marbles in a jar. In how many ways 8 marbles can be
selected from the jar so that at least one red marble and at least one blue marble to
remain in the jar?
A. 460
B. 490
C. 493
D. 455
E. 445
Total ways to select 8 marbles out of 7+5=12 is
;
Ways to select 8 marbles so that zero red marbles is left in the jar is
Ways to select 8 marbles so that zero blue marbles is left in the jar is
;
;
Hence ways to select 8 marbles so that at least one red marble and at least one blue
marble to remain the jar is
.
Answer: D.
6. 6. A pool has two water pumps A and B and one drain C. Pump A alone can fill the
whole pool in x hours, and pump B alone can fill the whole pool in y hours. The drain
can empty the whole pool in z hours, where z>x. With pumps A and B both running
and the drain C unstopped till the pool is filled, which of the following represents the
amount of water in terms of the fraction of the pool which pump A pumped into the
pool?
A.
B.
C.
D.
E.
All contents have been taken form www.gmatclub.com . I do not own the copyright of the any of the
materials. ---ASAX
Bunuel PS questions with Explanations
With pumps A and B both running and the drain unstopped the pool will be filled in a
rate
pool/hour. So, the pool will be filled in
hours (time is reciprocal of rate).
In
hours A will pump
water into the pool.
amount of the
Answer: B.
7. 7. Metropolis Corporation has 4 shareholders: Fritz, Luis, Alfred and Werner. Number
of shares that Fritz owns is 2/3 rd of number of the shares of the other three
shareholders, number of the shares that Luis owns is 3/7 th of number of the shares of
the other three shareholders and number of the shares that Alfred owns is 4/11 th of
number of the shares of the other three shareholders. If dividends of $3,600,000 were
distributed among the 4 shareholders, how much of this amount did Werner receive?
A. $60,000
B. $90,000
C. $100,000
D. $120,000
E. $180,000
Fritz owns is rd of the shares of the other three shareholders --> Fritz owns
of all shares;
th
Luis owns is th of the shares of the other three shareholders --> Luis owns
of all shares;
th
Alfred owns is
th of the shares of the other three shareholders --> Alfred owns
th of all shares;
Together those three own
owns
.
th of all shares, which means that Werner
. Hence from $3,600,000 Werner gets
Answer: D.
_________________
8. 8. A set A consists of 7 consecutive odd integers. If the sum of 5 largest integers of set
A is -185 what is the sum of the 5 smallest integers of set A?
All contents have been taken form www.gmatclub.com . I do not own the copyright of the any of the
materials. ---ASAX
Bunuel PS questions with Explanations
A. -165
B. -175
C. -195
D. -205
E. -215
Say 7 consecutive odd integers are:
,
,
,
,
,
,
.
Question:
Given:
-->
-->
-->
Answer: D.
9. 9. If x and y are negative numbers, what is the value of
A. 1+y
B. 1-y
C. -1-y
D. y-1
E. x-y
Note that
. Next, since
and
then
?
and
.
So,
Answer: D.
10. 10. If x^2<81 and y^2<25, what is the largest prime number that can be equal to x-2y?
A. 7
B. 11
C. 13
D. 17
E. 19
Notice that we are not told that
means that
and
and
are integers.
means that
. Now, since the
All contents have been taken form www.gmatclub.com . I do not own the copyright of the any of the
materials. ---ASAX
Bunuel PS questions with Explanations
largest value of
is almost 9 and the largest value of
), then the largest value of
is almost 10 (for example if
is almost 9+10=19, so the actual value is
less than 19, which means that the largest prime that can be equal to
example:
and
is 17. For
.
Answer: D.
11. 11. In an infinite sequence 1, 3, 9, 27, ... each term after the first is three times the
previous term. What is the difference between the sum of 13th and 15th terms and
the sum of 12th and 14th terms of the sequence?
A. 10*3^11
B. 20*3^11
C. 10*3^12
D. 40*3^11
E. 20*3^12
You don't need to know geometric progression formula to solve this question. All you
need is to find the pattern:
;
;
;
;
...
;
Answer: B.
12. 12. x, y and z are positive integers such that when x is divided by y the remainder is 3
and when y is divided by z the remainder is 8. What is the smallest possible value of
x+y+z?
A. 12
B. 20
C. 24
D. 29
E. 33
All contents have been taken form www.gmatclub.com . I do not own the copyright of the any of the
materials. ---ASAX
Bunuel PS questions with Explanations
Given
, where is a quotient, an integer
. Which means that the least
value of is when
, in that case
. This basically means that
. For example 3 divided by 4 yields remainder of 3.
is less than
Thus we have that:
is divided by the remainder is 3 --> minimum value of is 3;
is divided by the remainder is 8 --> minimum value of is 8 and minimum value of
is one more than 8, so 9 (8 divided by 9 yields the remainder of 8);
So, the smallest possible value of
is 3+8+9=20.
Answer: B.
13. 13. If
, what is the product of the tens and the units digits of
?
A. 0
B. 6
C. 7
D. 12
E. 14
Apply
:.
Next, .
Now, since
has 2 and 5 as its multiples, then it will have 0 as the units digit, so
will have two zeros in the end, which means that
last digits: 6*2=12.
will have 00-38=62 as the
Answer: D.
All contents have been taken form www.gmatclub.com . I do not own the copyright of the any of the
materials. ---ASAX