Ripdos, Eul Mark T.
BSEE 3-9
16.1) Which one of the following is not an irrational number?
A. sqrt of 2
B. sq rt of 4 C. sq rt of 3 D. sqrt of 5
The irrational number is a number that cannot
𝑎
be expressed as a simple fraction (ex., 𝑏 ). The
choices
√2 , √3 , 𝑎𝑛𝑑 √5 are irrational
number except for √4 = 2 , 𝑤ℎ𝑒𝑟𝑒 2 can be
2
expressed into fraction ( ).
1
16.2) At what distance from the 250-pound weight and a 300-pound weight balance
when placed on each end of an 11-foot bar?
A. 4 ft
B. 5 ft
C. 6 ft
D. 7 ft
250𝑑1 = 3300 − 300𝑑1
Let 𝑑1 = Distance 1
300𝑑1 + 250𝑑1 = 3300
𝑑2 = Distance 2
550𝑑1 = 3300
𝑑2 = 11 − 𝑑1
250𝑑1 = 300𝑑2
𝑑1 =
250𝑑1 = 300(11 − 𝑑1 )
𝑑1= 5ft
41.1) Given the function, f(x) = x² + 2x, find f(f(3)).
A. 15
B. 225
C.255
𝑓(3) = (3)2 + 2(3)
= 15
𝑓(15) = (15)2 + 2(5)
= 255
3300
550
D. 275
41.2) Find the sum of 10 terms of the arithmetic progression 2, 5, 8...
A. 140
B. 188
C. 155
𝑟 = 5−2=3
D. 220
𝑆=
𝑎𝑛 = 𝑎1 + (𝑛 − 1)(𝑟)
(𝑎1 + 𝑎𝑛 )𝑛
2
𝑆=
𝑎10 = 2 + (10 − 1)(3)
(2+29)10
2
= 155
= 29
66.1) Peter and John working together can finish painting a house in 6 days. Peter
working alone can finish it in 5 days less than John. How long will it take Peter to finish
the work alone?
A. 15 days
B. 18 days
C. 12 days
D. 10 days
6𝑥 + 30 + 6𝑥 = 𝑥 2 + 5𝑥
Let: Peter
2
𝑥 = 7𝑥 + 30
𝑥 2 = 12𝑥 + 30 − 5𝑥
=x
𝑥 2 = 7𝑥 + 30
John = x+5
(𝑥 − 10)(𝑥 + 3) = 0
6
6
+
=1
𝑥 𝑥+5
𝑥 = 10 𝑑𝑎𝑦𝑠
6𝑥 + 30 + 6𝑥 = 𝑥 2 + 5𝑥
𝑥 2 = 12𝑥 + 30 − 5𝑥
66.2) Find the sum of three arithmetic means between 1 and 9.
𝑥 2 = 7𝑥 + 30
A. 15
B. 16
C. 13
𝑆=
(𝑎1 + 𝑎𝑛 )𝑛
2
𝑆=
(9 + 1)(3)
2
𝑆 = 15
D. 14
91.1) If 10𝑘 = 1/2 what is the value of 10k + 3?
A. 400
B. 200
10𝑘 =
1
2
C. 300
D. 500
10k + 3 =?
1
𝑘 × 𝑙𝑛(10) = ln ( )
2
𝑘=
ln(0.5)
ln (10)
𝑘 = −0.3010299957
10k + 3 = 500
91.2) A farmer bought 20 chickens consisting of roosters, hens and chicks for $20. Each
rooster cost $3 each, each hen at $1.50 each and each chick at $0.50 each. How many
chicks did he buy?
A. 11
B.13
C. 12
D. 14
𝑅 = $3, 𝐻 = $1.2, 𝐶 = $0.5
1.5(18 − 𝐶) + 0.5𝐶 = 14
Assume he only bought two roasters
total cost of $6
𝐶 = 13
𝐻 + 𝐶 = 18
1.5𝐻 + 0.5𝐶 = 14
116.1) A three-person maintenance crew could clean a certain building in 4 hours,
whereas a four-person crew could do the job in 3 hours. If one worker of the four-person
crew was an hour late, how long did the job take?
A. 3.25 hrs.
B. 4.55 hrs.
C. 2.2h hrs.
D 3.55 hrs.
Considering that 1 person from the 4-person crew is late by 1 hour, the work is
done for 1 hr. by a 3-person crew. the 3-person crew completes 100% of the job in
4 hrs., hence, in 1 hr. it completes 25 % of the job. Now when 75% of the job is
unfinished, the 4th member joins, so now it is a 4-person crew to do 75% of the
job. If they can complete 100% job in 3hrs, they would complete the 75% job in
2.25 hrs.
75×3
.
100
Hence total time required for completion of the job = 2.25 + 1= 3.25 hrs.
116.2) The 1st term of an arithmetic sequence is -15 and the 5th term is 13. Find the
40th term.
A. 258
B. 245
𝑑=
C. 188
13 − (−15)
4
D. 196
𝑎𝑛 = 𝑎1 + (𝑛 − 1)𝑑
𝑎40 = −15 + (−1)7
𝑑=7
𝑎40 =285
141.1) John and Peter are linemen. John can string 10 miles of line in 3 days, while
together they can string it in 1 day. How long in days would it take Peter alone to string
the same line?
A. 1 1/2 days
B. 1 4/5 days
C. 2 days
D. 2 3/4 days
1 1
+ =1
3 𝑋
𝑥 + 3 = 3𝑥
𝑥=
3
1
= 1.5 𝑜𝑟 1 𝑑𝑎𝑦𝑠
2
2
141.2) A ball is dropped from a height of 100 ft. On each rebound, the ball rises to one
half of the height from which it last fell. Find the total distance the ball has traveled, up
to the instant it hits the ground for the 12th time. s time t is 5 hours After the w in
A. 290 ft
B. 280 ft
𝑠=
𝑠=
𝑎1 (1 − 𝑟 2 )
,
1−𝑟
1 2
100 (1 − (2) )
1
1 − (2)
C. 270 ft
𝑟=
D. 300 ft
1
2
= 150
𝑠 = 150𝑥2 = 300𝑓𝑡
166.1) Simplify:
A. x + y
𝑥 −1 +𝑦 −1
𝑥 −1 𝑦 −1
B. x-y
C. x/y
D. 2xy
𝑥 −1 + 𝑦 −1
𝑥 −1 𝑦 −1
1 1
1 1
𝑥𝑦 𝑥𝑦
𝑥+𝑦
=
= ( + ) 𝑥𝑦 =
+
11
𝑥 𝑦
𝑥
𝑦
𝑥𝑦
= 𝑦+𝑥
166.2) Jonathan has $1 and 15 cents worth of change in his pocket. He has three more
dimes than quarters and two more dimes than nickels. How many quarters he has?
A. 2
B. 4
C. 3
D. 5
Q= quarters, D = dimes, N = nickels
0.4𝑄 = 1.15 − 0.35
0.25𝑄 + 0.05𝐷 + 0.1𝑁 = 1.15
𝑄=2
𝐷 = 𝑄 + 3,
𝐷 = 𝑁+2
Therefore, 𝑁 = 𝑄 + 1
0.25𝑄 + 0.05(𝑄 + 3) + 0.1( 𝑄 + 1 ) = 1.15
191.1) Find the numerical value of the Roman numeral MMDCCCLIX.
A. 2859
B. 2649
C. 2354
D. 2599
M=1000, D=500, C=100, L=50, X=10, I=1
2000 +500+300+50+10-1= 2859
191.2) A and B start at the same time from two places 136 km apart and travel toward
each other. A travel 10 kph and B at 8 kph. If B rests 1 hour on the way, in how many
hours will they meet?
A. 10 hours B. 8 hours
C. 7 hours
10𝑥 + 8 (𝑥 − 1) = 136
10𝑥 + 8𝑥 = 136 + 8
18𝑥 = 144
𝑥=8
D. 9 hour
216.1) There are three consecutive integers. The sum of the smallest and largest is 36.
Find the largest number.
A. 16
B. 18
C. 17
D. 19
By trial and error let z = highest integer and x = lowest integer
Let’s assume that the numbers are 17, 18, 19
Z=19 and x =17 , 19 + 17 = 36 , therefore 19 is the highest integer
216.2) Find the 37th term of an AP if the 4th term is 6 and common difference is 5.
A. 172
B. 174
C. 171
D. 173
𝑎1 = 64 − 53 − 52 − 51 = −91
𝑎𝑛 = 𝑎1 + (𝑛 − 1)(𝑑)
𝑎37 = −9 + (37 − 1)(5)
𝑎37 = 171
241.1) One student can solve a math problem in 6 minutes. Another student can solve a
math problem in 5 minutes. How long can they solve 110 problems?
A. 300 minutes
B. 270 minutes
𝑠1 =
1
,
6
𝑠2 =
C. 330 minutes
1
5
1
1
𝑡 + 𝑡 = 110
6
5
11
𝑡 = 110 ,
30
𝑡 = 300 𝑚𝑖𝑛𝑢𝑡𝑒𝑠
D. 240 minutes
241.2) A box contains beetles (with 6 legs) spiders (with 8 legs), and centipedes (with
100 legs). The box contains 78 heads, 1656 legs and 6 more spiders than twice the
number of centipedes, how many beetles are there in the box?
A. 30
B. 36
C. 27
D. 12
𝑙𝑒𝑡; 𝑥 = 𝑏𝑒𝑒𝑡𝑙𝑒𝑠, 𝑦 = 𝑠𝑝𝑖𝑑𝑒𝑟𝑠 , 𝑧 = 𝑐𝑒𝑛𝑡𝑖𝑝𝑒𝑑𝑒𝑠
𝑒𝑞1 . 6𝑥 + 8𝑦 + 100𝑧 = 1656
And,
𝑒𝑞2 . 𝑥 + 𝑦 + 𝑧 = 100
𝑥 + (6 + 2𝑧) + 𝑧 = 100
𝑒𝑞3 . 𝑦 = 6 + 2𝑧
𝑥 + 3𝑧 = 72
Substituting equations we get,
Solving these two equations
𝑥 + 3𝑧 = 72
6𝑥 + 8(6 + 2𝑧) + 100𝑧 = 1656
6𝑥 + 16𝑧 + 100𝑧 = 1656 − 48
6𝑥 + 116𝑧 = 1608
And
6𝑥 + 116𝑧 = 1608
we get z= 12 and x =36 beetles