Percentage Exercises B
1. The price of a prestigious kitchen knife had a 40% discount in April, and later became
10% more expensive in May. David bought the knife in May for $99. What was the
original price of the knife in dollars?
(A) 150
(B) 100
(C) 90
(D) 80
(E) 120
2. Lital loses 20% of her weight during spring, and later gains 5% of her weight during
summer. At the end of the process her weight is 84 kg. What was her weight before
the changes?
(A) 150 kg
(B) 200 kg
(C) 120 kg
(D) 110 kg
(E) 100
3. The price of a ticket for a soccer game between Israel and Macedonia was
discounted a month before the game by 40% and was $72. On the day of the game
tickets were sold for only 30% off (from the original price), and so the price of one
ticket was $_______.
(1) 104
(B) 84
(C) 100
(D) 96
(E) 90
4. A barrel of liquor has 25% alcohol, and the rest is water. What is the percentage of
alcohol after two thirds of the water in the barrel was vaporized?
(1) 25%
(B) 52%
(C) 3333%
(D) 75%
(E) 20%
5. Chewing gum is 20% more expensive than a piece of candy. A piece of candy is 40%
more expensive than a can of Coke. By what percentage is chewing gum more
expensive than a can of Coke?
(1) 55%
(B) 35%
(C) 33%
(D) 86%
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(E) 75%
6. Quantitative questions constitute 40% of all questions in the SATs. Verbal questions
constitute 10% of all quantitative questions. Percentage questions constitute 5% of all
verbal questions. The test has a total of 2 percentage questions. Therefore, the entire
test has a total of ________ questions.
(1) 520
(B) 300
(C) 2000
(D) 1500
(E) 1000
7. X percent of X equals X. if it is known that X is different than zero, what is the value of
X?
(1) 1
(B) 200
(C) 5.5
(D) 10
(E) 100
8. The ratio of the number of blonds in the Israeli population in relation to the number of
non-blonds is 1:3. Therefore the percentage of blonds in the Israeli population is
(1) 3333%
(B) 52%
(C) 52%
(D) 8838%
(E) 50%
9. A percent of A equals one eighth of A. What is the value of A?
(B) 6532
(1) 8
(C) 66
(D) 68
(E) 14
10. The price of an oil barrel goes down by 40% during a trading day. How many times
does the barrel price need to go up during the night in order to start the next trading
day with a price 20% higher than the price in the beginning of the previous trading
day?
(1) 1.5 times
(B) 1 time
(C) 0.5 times
(D) 2 times
(E) 3 times
11. The price of an off-road vehicle is P dollars. What would be its price after a D%
discount?
(1) D 2
p
100
(B) D 
PD
100
(C) p 
DP
100
(D) p 
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DP
100
(E) p 
D
100
12. The music store has D CDs of only two artists: the band Pintzeta and the singer
Kylie. If we know that K% of the CDs are Kylie’s, how many CDs are of the band
Pintzeta?
(1)
D2
100
(B)
K 

(C) D 1 

 100 
DK
100
K 

(D) D 1 

 100 
(E)
k2
100
13. The price of a plot of land in Neveh Savyon B rises each year by 20%. By how much
would the plot’s price go up in two years compared to its price today?
(1) 33%
(B) 35%
(C) 55%
(D) 25%
(E) 75%
14. Three quarters of the basketball players in Maccabi Netanya are foreign players.
One third of the remaining players, which are 11, are shorter than 2 meters. How
many total players are in Maccabi Netanya?
(1) 636
(B) 656
(C) 99
(D) 666
(E) 132
15. A bottle of 1 liter of tequila has 40% alcohol. The bottle was diluted with 1 liter of
water (with no alcohol). The percentage of alcohol in the new drink is:
(1) 55%
(B) 52%
(C) 25%
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(D) Cannot be
determined
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Percentage Exercises B - Solutions
Question
1.
2.
3.
4.
5.
Answer
(A)
(E)
(B)
(A)
(D)
Question
6.
7.
8.
9.
10.
Answer
(E)
(E)
(B)
(B)
(D)
Question
11.
12.
13.
14.
15.
Answer
(C)
(C)
(A)
(E)
(A)
Explanations:
1. The correct answer is (A). Explanation:
Let’s define the starting price of a knife is $X. So after the first discount its price will
60
60
110
be
. This expression equals $99
 X . After a 10% rise its price will be
X 
100
100
100
60
110
and so
X 
 99 . We’ll calculate and find that X  150 .
100
100
2. The correct answer is (E). Explanation:
This question is algebraically similar to the previous question, and here too we can
105 80
create an equation

 X  84 and minimize until we find x. Only here the
100 100
minimization can be more complicated, so we would prefer trying the answers:
We’ll start with answer (C) since its value is 100 (easy to calculate). If Lital’s starting
weight is 100 and she loses 20%, her new weight is 80, and now she gains 5% of her
new weight, which is 4 kg. Her weight now is 84 kg, as asked in the question. This is
the correct answer and there is no need to check the others.
3. The correct answer is (B). Explanation:
Before the game: percent = 60%, part = $72 and so the whole is
72 72 100

 120
60
60
100
At the day of the game: percent = 70%, whole = 120. Therefore the part =
70
120  84
100
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4. The correct answer is (A). Explanation:
In this question there are no actual numbers given so we can put an easy number
instead of the total of each amount in a barrel. If every barrel has 100 cc, and in the
beginning the distribution of the barrel was 75% water and 25% alcohol, there were
exactly 75 cc water and exactly 25 cc alcohol. After the vaporization only a third of the
original amount of water was left – which means 25 cc water, and exactly the same
amount of alcohol – 25 cc. now we see that the total liquid in cc is 25  25  50 and so
the alcohol constitutes exactly a half – meaning exactly 50% of the barrel content.
The correct answer is (A).
5. The correct answer is (D). Explanation:
Since there are no actual numbers given regarding the whole, we can use an easy
number. We can decide that the price of a Coke can is $100, and as a result the price
120
of a piece of candy is $140, the price of a piece of gum is
140  168 , meaning
100
68% higher than a can of Coke.
6. The correct answer is (E). Explanation:
total number of questions X
/
\
not quantitative 85%
quantitative 35%
/
\
not verbal 05%
verbal 65%
/
\
not percentage 02%
5 questions = percentage 2%
In order to climb up the tree we need to divide by each and every branch:
2
 1000
5
10 40


100 100 100
7. The correct answer is (E). Explanation:
Let’s translate the question into an equation:
and find that X  100 .
X
 X  X . We’ll solve the equation
100
8. The correct answer is (B). Explanation:
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According to the ratio we’ll define that the number of blonds = X, and the number of
non-blonds = 3X. The entire population is 4X, therefore the part of blonds in the
X
1
population is
  25%
4X 4
9. The correct answer is (B). Explanation:
Let’s translate the question into an equation:
that A 
A
1
 A   A . We’ll solve it and find
100
8
100
 12.5 .
8
10. The correct answer is (D). Explanation:
Let’s assume that the original price of a barrel is $100. The price goes down by 40%
and is now $60. The price we need to reach is $120 (20% more than the original
price), which means times 2. The correct answer is (D).
11. The correct answer is (C). Explanation:
Whole = P, percentage
100  D
D
D
PD
therefore the part = P(1 
 1
) P
100
100
100
100
12. The correct answer is (C). Explanation:
K
The number of Kylie CDs is
 D , therefore the number of Pintzeta CDs is
100
K
K
D
 D  D(1 
)
100
100
13. The correct answer is (A). Explanation:
Since there is no actual number as the whole in the question, we should (and it is
easy) to put a number. We shall decide that the price of the plot in the beginning of
the process is $100. After the first year its price will be $120 and after the second year
120
it will be 120 
 144 , which means an increase of 44%.
100
14. The correct answer is (C). Explanation:
Let’s define the number of players in the team is X. the number of the players who
1
are not foreign is  X , the number of players who are shorter than 2 meters is
4
1 1
1 1
  X . This expression equals 11 players, therefore:   X  11 . We’ll calculate
4 3
4 3
and find that X  132 .
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15. The correct answer is (A). Explanation:
The original drink, in 1 liter, contained 40% alcohol. Therefore, 400 ml of alcohol and
600 ml of something else. After the addition of a liter of water we get a new drink, a
total of 2000 ml, out of which 400 ml are still alcohol. We can see that the alcohol
constitutes one fifth of the entire drink, or in other words, 20% of the entire drink.
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