divelab/Sys2Bench huggingface dataset:
Question: The ratio of the volumes of two cubes is 1331 : 2197. What is the ratio of their total surface areas?
Options:
A)121 : 169
B)169 : 122
C)81 : 124
D)81 : 126
E)81 : 129
Rationale: Ratio of the sides = 3√1331 : 3√2197 = 11 : 13
Ratio of surface areas = 11^2 : 13^2 = 121 : 169
Answer: Option A
Answer: A
Question: A circular garden is surrounded by a fence of negligible width along the boundary. If the length of the fence is 1/5 of th area of the garden. What is the radius of the circular garden?
Options:
A)1
B)2
C)10
D)8
E)16
Rationale: as per the question-- width is negligible
now,
let L be the length of the fence =2pir
L=1/5(pir^2)
pir^2=10pir
r=10
Answer : C
Answer: C
Question: 38, 69, 22,73, 31,47, 90, 82
Which of the following numbers is greater than three-fourth of the numbers but less than one-fourth of the numbers in the list above?
Options:
A)a- 56
B)b- 68
C)c- 69
D)d- 71
E)e- 77.5
Rationale: Important:- Arrange the numbers in ascending order first.
22, 31, 38, 47, 69, 73, 82, 90
3/4th of the number list represents- 73 (6th number)
remaining 1/4th list represents 82 (7 th number)
77.5 fits in between above 2
Answer:- E
Answer: E
Question: Of the 3,600 employees of Company X, 3/4 are clerical. If the clerical staff were to be reduced by 4/5, what percent of the total number of the remaining employees would then be clerical?
Options:
A)37%
B)22.2%
C)20%
D)12.5%
E)11.1%
Rationale: Let's see, the way I did it was
3/4 are clerical out of 3600 so 2700 are clerical
2700 reduced by 4/5 is 2700*4/5
so it reduced 2160 people , so there is 540 clerical people left
but since 2160 people left, it also reduced from the total of 3600 so there are 1440 people total
since 540 clerical left / 1440 people total
you get (A) 37%
Answer: A
Question: A die is thrown three times. Events X and Y are defined as below:
X : 4 on the third throw
Y : 6 on the first and 5 on the second throw
What is the probability of X given that Y has already occurred.
Options:
A)1/5
B)1/6
C)2/7
D)3/7
E)3/11
Rationale: The sample space has 216 outcomes.
Now X =
(1,1,4) (1,2,4) ... (1,6,4) (2,1,4) (2,2,4) ... (2,6,4)
(3,1,4) (3,2,4) ... (3,6,4) (4,1,4) (4,2,4) ...(4,6,4)
(5,1,4) (5,2,4) ... (5,6,4) (6,1,4) (6,2,4) ...(6,5,4) (6,6,4)
Y = {(6,5,1), (6,5,2), (6,5,3), (6,5,4), (6,5,5), (6,5,6)}
and X n Y = {(6,5,4)}.
Now P(Y) = 6/216
and P (X n Y) = 1/216
Then P(X|Y) = (1/216)/(6/216) = 1/6.
B)
Answer: B
Question: There have 12 basket,7 red balls and 5 white balls,find the probability of getting at least 1 red ball and 1 blue ball, if 8 balls are to be drawn ?
Options:
A)505
B)495
C)425
D)548
E)525
Rationale: (7c3*5c5)+(7c4*5c4)+(7c5*5c3)+(7c6)5c2)+(7c1*5c1)=495
ANSWER:B
Answer: B
Question: The sum of two numbers is 40 and their product is 375. What will be the sum of their reciprocals?
Options:
A)1/40
B)8/75
C)75/4
D)75/8
E)75/6
Rationale: (1/a)+(1/b)=(a+b)/ab=40/375=8/75
ANSWER:B
Answer: B
Question: According to a recent student poll, 3/4 out of 20 members of the finance club are interested in a career in investment banking. If two students are chosen at random, what is the probability that at least one of them is interested in investment banking?
Options:
A)1/14
B)4/49
C)18/19
D)45/49
E)13/14
Rationale: 15 students are interested, 5 are not interested
Prob = 1 - 5C2/20C2 = 1 - (5*4/(20*19))=1 - 1/19 = 18/19
Answer :C
Answer: C
Question: 2,5,10,17,26,__
Options:
A)31
B)35
C)39
D)56
E)37
Rationale: 2=1*1 +1
5=2*2 +1
10=3*3+1
17=4*4+1
26=5*5+1
Similarly 6*6+1=37
ANSWER:E
Answer: E
Question: If the ratio of a to b is 4 to 3 and the ratio of b to c is 1 to 5, what is the ratio of a to c?
Options:
A)4/15
B)1/3
C)2/5
D)4/5
E)7/6
Rationale: a:b = 4:3 -- 1
b:c = 1:5
=>b:c = 3 :15 --2
From 1 and 2 , we get
a:c = 4:15
Answer A
Answer: A
Question: In a 100 member association consisting of men and women, exactly 20% of men and exactly 25 % women are homeowners. What is the least number of members who are homeowners?
Options:
A)21
B)47
C)45
D)43
E)41
Rationale: Solution simple
Out of 100 20% are male i.e 20 and 25% are female i.e 25 , so total homeowner is 45.
Now min number homeowner is 20 and max is 45 so question ask us to find least and 21 has least value among all option.
So ans is 21.
Answer : A
Answer: A
Question: A letter lock consists of three rings each marked with twelve different letters. The number of distinct unsuccessful attempts to open the lock is at the most?
Options:
A)1762
B)1783
C)1727
D)1728
E)1298
Rationale: Since each ring consists of twelve different letters, the total number of attempts possible with the three rings is
= 12 * 12 * 12= 1728. Of these attempts, one of them is a successful attempt.
Maximum number of unsuccessful attempts
= 1728 - 1 = 1727.
Answer: C
Answer: C
Question: The smallest number which when diminished by 7, is divisible 12, 16, 18, 21 and 28 is:
Options:
A)3665
B)1015
C)2676
D)287
E)2667
Rationale: Required number = (L.C.M. of 12,16, 18, 21, 28) + 7 = 1008 + 7
= 1015
Answer: B
Answer: B
Question: The length of minute hand of a clock is 5.4 cm. What is the area covered by this in 5 minutes
Options:
A)15.27
B)16.27
C)17.27
D)7.27
E)7.63
Rationale: area of circle is pi*r^2
but in 5 minutes area covered is (5/60)*360=30 degree
so formula is pi*r^2*(angle/360)=3.14*(5.4^2)*(30/360)=7.63 cm^2
ANSWER:E
Answer: E
Question: Of the 200 students at University XYZ majoring in one or more of the engineering disciplines, 130 are majoring in electrical and 150 are majoring in mechanical. If at least 30 of the students are not majoring in either electrical or mechanical, then the number of students majoring in both electrical and mechanical could be any number from
Options:
A)30 to 70
B)70 to 100
C)110 to 130
D)130 to 150
E)150 to 170
Rationale: lower point = Sum in each - total possible = 150+130- (200-30) = 280-170 =110...
higher point = entire 130 majoring in electrical major in mechanical too , so = 130..
range = 110 to 130
ANSWER:C
Answer: C
Question: A lady goes to a bank near her newly possessed home. The bank's policies are weird, but she decides to open the account anyhow with a certain amount. The policy is that at the end of each year, the total amount gets doubled and Rs. 65 is deducted from that amount. After 6 years, when the lady checks her account, the total amount is 0.
Can you find out what was the original amount that she had deposited in the bank?
Options:
A)70.853813
B)33.659045
C)70.361982
D)65.443567
E)63.984375
Rationale: E
Explanation:
This question is hypothetical because you cannot transact in fractions in bank account. The following is the solution:
Year	Amount	Interest and Deduction
Start	63.984375
Y1 End	62.968750	63.984375 * 2 - 65
Y2 End	60.937500	62.96875* 2 - 65
Y3 End	56.875000	60.9375 * 2 - 65
Y4 End	48.750000	56.875 * 2 - 65
Y5 End	32.500000	48.75 * 2 - 65
Y6 End	0.000000	32.5 * 2 - 65 = 0
Answer: E
Question: Certain loan amount was repaid in two annual installments of Rs.1331/- each. If the rate of interest be 10% per annum Compounded annually the sum borrowed was?
Options:
A)Rs.2310/-
B)Rs.2400/-
C)Rs.2420/-
D)Rs.2430/-
E)Rs.2450/-
Rationale: Principal = (P.W of Rs. 1331/- due 1 year hence) + (P.W of Rs. 1331/- due 2 years hence)
= [1331/(1 + 10/100) + 1331/(1 + 10/100)2]
= [1331/(110/100) + 1331/(110/100 × 110/100)]
= 13310/11 + 133100/121 = 1210 + 1100 = Rs.2310/-
A
Answer: A
Question: The ratio of the present age of two brothers is 1:2 and 5 years back, the ratio was 1:3. What will be the ratio of their ages after 5 years?
Options:
A)3:6
B)3:2
C)3:5
D)3:1
E)3:2
Rationale: Let the present ages of the two brothers be x and 2x years respectively.
Then, (x - 5)/(2x - 5) = 1/3
3(x - 5) = (2x - 5) => x = 10
Required ratio = (x + 5) : (2x + 5) = 15 : 25
= 3:5
Answer:C
Answer: C
Question: If 7^e is a factor of the product of the integers from 1 to 100, inclusive, what is the largest value of e?
Options:
A)12
B)13
C)14
D)15
E)16
Rationale: So the question just means that we have to find all the multiples e of 7 between 1 to 100
So there are 14 multiples of 7 ( 7 - 98)
But 49 and 98 contain two 7's as factors
so we have to add 14 + 2 = 16
E
Answer: E
Question: A bike covers a certain distance at the speed of 65km/h in 8 hrs. If the bike was to cover the same distance in approximately 6 hrs, at what approximate speed should the bike travel?
Options:
A)85 km/h
B)85.34 km/h
C)86.66 km/h
D)90.25 km/h
E)90.64 km/h
Rationale: Ans.(C)
Sol. Total distance = 65 × 8 = 520 km
Now speed = 520/6 = 86.66 km/h
Answer: C
Question: John Purchased 1325 large bottles at $1.89 per bottle and 750 small bottles at $1.38 per bottle. What was the approximate average price paid per bottle?
Options:
A)$1.63
B)$1.71
C)$1.68
D)$1.72
E)$1.76
Rationale: (1325*1.89+750*1.38)/(1325+750) =~1.71
Option (B)
Answer: B
Question: There were two candidates in an election. Winner candidate received 62% of votes and won the election by 348 votes. Find the number of votes casted to the winning candidate?
Options:
A)456
B)744
C)899
D)1200
E)1400
Rationale: W = 62% L = 38%
62% - 38% = 24%
24% -------- 348
62% -------- ? => 899
ANSWER:C
Answer: C
Question: The C.P of 10 pens is equal to the S.P of 12 pens. Find his gain % or loss%?
Options:
A)16 2/6%
B)16 2/8%
C)16 2/3%
D)19 2/3%
E)16 2/5%
Rationale: 10 CP = 12 SP
12 --- 2 CP loss
100 --- ? => 16 2/3%
Answer: C
Answer: C
Question: A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 20%?
Options:
A)600
B)2277
C)297
D)972
E)121
Rationale: Cost price = Rs.500
profit = 20% of 500 = Rs.100
Selling price = Cost price + Profit
= 500 + 100 = 600
Answer: A
Answer: A
Question: Dimitri weighs 4x-3x pounds more than Allen weighs. Together, Allen and Dimitri weigh a total of y pounds. Which of the following represents Allen’s weight?
Options:
A)y - x/2
B)2x - y/2
C)(y - x)/2
D)y - 2x
E)2x - y
Rationale: These type of multi-variable story problems are usually perfect for TESTing VALUES.
Here, we're told that Dimitri weighs 4X-3X or X pounds more than Allen weighs and that they weight a combined TOTAL of Y pounds.
IF....
Dimitri = 30
Allen = 20
X = 10
Y = 50
We're asked for Allen's weight, so we're looking for an answer that equals 20 when X = 10 and Y = 50.
Answer A: 50 - (10/2) = 45 NOT a match
Answer B: 20 - (50/2) = -5 NOT a match
Answer C: (50-10)/2 = 20 This IS a match
Answer D: 50 - 20 = 30 NOT a match
Answer E: 20 - 50 = -30 NOT a match
Final Answer:
C
Answer: C
Question: The largest natural number which exactly divides the product of any four consecutive natural numbers is
Options:
A)6
B)12
C)24
D)120
E)100
Rationale: Solution
Required numbers	= 1×2×3×4
‹=›24.
Answer C
Answer: C
Question: Today Jim is twice as old as Fred, and Sam is 4 years younger than Fred. Four years ago Jim was 8 times as old as Sam. How old is Jim now?
Options:
A)8
B)12
C)16
D)20
E)24
Rationale: We're asked how old Jim is NOW. We're given three facts to work with:
1) Today, Jim is TWICE as old as Fred
2) Today, Sam is 4 years younger than Fred
3) Four years ago, Jim was 8 times as old as Sam.
let's TEST Answer D: 20
IF....Jim is currently 20 years old....
Fred is 10 years old
Sam is 6 years old
4 years ago, Jim was 16 and Sam was 2, so Jim WAS 8 times Sam's age. This is an exact MATCH for what we were told, so this MUST be the answer.
D
Answer: D
Question: A train traveling at 72 kmph crosses a platform in 32 seconds and a man standing on the platform in 18 seconds. What is the length of the platform in meters?
Options:
A)280 meters
B)360 meters
C)420 meters
D)600 meters
E)Cannot be determined
Rationale: Speed of train = 72 * (5/18) = 20 m/s
Lets consider the man as a stationery point on the platform.
Crossing the point gives us the length of the train.
Lt = 20 * 18 = 360 m.
Crossing the platform gives us the length of trainlength of platform.
L(t+p) = 20 * 32 = 640 m.
So, length of platform = 640 - 360 = 280 m
IMO, Answer
A
Answer: A
Question: If TIER is written as 7193 and BRAIN is written as 23415, how is RENT coded ?
Options:
A)3653
B)3657
C)2977
D)3957
E)2711
Rationale: Explanation:
Given :
Letter : T I E R B A N
Code : 7 1 9 3 2 4 5
Thus, the code for RENT is 3957.
ANSWER:D
Answer: D
Question: There is a baseball tournament that is single elimination meaning that after one loss the team is out. There are 40 teams in this tournament. How many games are played?
Options:
A)20
B)10
C)39
D)40
E)15
Rationale: C
The number of games always adds up to one less than the number of teams in a single elimination tournament. You may calculate it any way. Therefore, 39 games were played.
Answer: C
Question: In the recent, climate conference in New York, out of 500 men, 300 women, 500 children present inside the building premises, 10% of the men, 60% of the women and 70% of the children were Indians. Find the percentage of people who were not Indian?
Options:
A)59.54%
B)66.25%
C)55.39%
D)63.21%
E)64.22%
Rationale: Solution: Number of Indians men present there = 500*10/100 = 50
Indian women = 300*60/100 = 180
Indian children = 500*70/100 = 350.
Total member present in climate conference = 500+300+500 = 1300
Total Indian = 50+180+350 = 580
Hence, % of Indian present there = 580*100/1300 = 44.61%
% of people who were not Indian = 100-44.61 = 55.39%.
Answer C
Answer: C
Question: What will come in place of the x in the following Number series? 5,28,57,88
Options:
A)156
B)159
C)166
D)125
E)180
Rationale: 28=23+5
57=29+28
88=31+57
125=37+88
D
Answer: D
Question: Caleb won Bruce in a 100 m race by 0.35 m. If Bruce had given Caleb a 6 m head start how many meters more will it take for Bruce to overtake Caleb?
Options:
A)7.2m
B)5.2m
C)8.2m
D)4.2m
E)6.2m
Rationale: Distance Bruce ran before completion of race---100 m-0.35m=99.65m
Distance gained on Caleb over 99.65m---6m-0.35m=5.65
then Bruce gains 99.65/5.65m = 1m on Kelly every 17.64 meters.
Therefore 17.64 divided by 0.35 of 1 meter.
ANSWER: E. 6.2m
Answer: E
Question: If (5)(x^2) has four different prime factors, at most how many different prime factors does x have?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: x can have at most 4 prime factors, namely the prime factor 5 plus 3 others.
If x had more than this number of prime factors, then (5)(x^2) would have more than 4 prime factors.
The answer is D.
Answer: D
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
Options:
A)872 m
B)278 m
C)267 m
D)150 m
E)287 m
Rationale: Speed=(60 * 5/18) m/sec
= (50/3) m/sec Length of the train
= (Speed x Time) = (50/3 * 9) m
= 150 m.
Answer: D
Answer: D
Question: In the xy-plane the point (-2 -3) is the centre of a circle, the point (-2, 0) lies inside the circle and the point (2, -3) lies outside the circle. If the radius r of the circle r is an integer then r=
Options:
A)6
B)5
C)4
D)3
E)2
Rationale: Can be solved without much calculations.
You are given that (-2,-3) is the center of the circle. Point (2,-3) lies inside the circle ---> the radius is lesser than distance of (-2,-3) from (2,-3) ---> lesser than 5 units but the radius will also be greater than the distance of (-2,-3) from (-2,0) ----> greater than 3 units.
Thus the radius is >3 but <5and as it is an integer, the only possible value of radius = 4 units.
C is the correct answer.
Answer: C
Question: A can do a piece of work in 12 days. He worked for 15 days and then B completed the remaining work in 10 days. Both of them together will finish it in.
Options:
A)2 days
B)6 days
C)3 days
D)4 days
E)5 days
Rationale: 15/25 + 5/x = 1 => x = 25/4
1/25 + 4/25 = 5/25=1/5
5 days
ANSWER:E
Answer: E
Question: Find the area of a rhombus whose side is 25 cm and one of the diagonals is 30 cm?
Options:
A)656 sq.cm
B)517 sq.cm
C)657 sq.cm
D)826 sq.cm
E)600 sq.cm
Rationale: Consider the rhombus ABCD. Let the diagonals intersect at E. Since diagonals bisect at right angles in a rhombus.
BE2 + AE2 = AB2
252 = 152 + AE2 AE = √(625 - 225) = √400 = 20,
AC = 20 + 20 = 40 cm.
Area of a rhombus = 1/2 * d1d2
= 1/2 * 40 * 30 = 600 sq.cm.
Answer: E
Answer: E
Question: Suppose we have six marbles: 3 blue marbles, 2 red marbles, and one green marble. Suppose we are going to put them into three cups: a black cup, a white cup, and a orange cup. We could put all six in any cup and leave two cups empty; or we could put marbles in two cups and leave one cup empty; or we could put some marbles in each of the three cups. How many combinations are possible?
Options:
A)120
B)140
C)150
D)160
E)180
Rationale: # ways to distribute Blue marbels(3) is :
1 in each cup= 1
2 in one cup and 1 in other=6
all 3 in one cup = 3
total 1+6+3=10 possibilities
# ways to distribute Red marbels(2) is :
1 in each cup = 3 ways
all in one cup = 3ways
total 6ways.
# ways to distribute Green marbels(1) is :
3 ways
total number of ways = 10*6 *3 = 180
E
Answer: E
Question: If 45% of z is 120% of y and y is 75% of x, what percent of x is z?
Options:
A)200
B)160
C)100
D)65
E)50
Rationale: (45/100)z = (120/100)y
and y = (75/100)x i.e. y = (3/4)x
i.e. (45/100)z = (120/100)*(3/4)x
i.e. z = (120*3)x/(45*4)
i.e. z = (2)x = (200/100)x
i.e. z is 200% of x
Answer: Option A
Answer: A
Question: A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 38 years now, the son's age fourteen years back was?
Options:
A)5yr
B)15yr
C)20yr
D)25yr
E)30yr
Rationale: Let the son's present age be x years
Then, 38-x = x
x = 19
Son's age 14 years back = 19-14 = 5 years
Answer is A
Answer: A
Question: A bag contains 5 green balls and 8 white balls. If two balls are drawn simultaneously, what is the probability that both balls are the same colour?
Options:
A)3/7
B)6/11
C)12/21
D)19/39
E)29/49
Rationale: The total number of ways to draw two balls is 13C2 = 78
The number of ways to draw two green balls is 5C2 = 10
The number of ways to draw two white balls is 8C2 = 28
P(two balls of the same colour) = 38/78 = 19/39
The answer is D.
Answer: D
Question: If x, y, and z are positive integers such that x^2 - y^2 + z^2 = 36, which of the following could be the values of x, y, and z?
I)x=122,y=157,z=99
II)x=125,y=160,z=102
III)x=100,y=150,z=167
Options:
A)I only
B)II only
C)III only
D)I​ and II
E)I and III
Rationale: 10 sec answer if you know how to find the units digit of a number
The number given is of the form of square, so calculate the units digit - Here your objective is to find the sum where last digit is 0
x = 122, so x^2 will have units digit 4
y = 157, so y^2 will have units digit 9
z = 99, so z^2 will have units digit 1
Calculate the units digit , the units digit will be 0
Test with options II and III, only option I will satisfy the condition , hence this will be our answer is option A.
Answer: A
Question: If u r genius solve it:-
40 * 14 = 11
30 * 13 = 12
20 * 12 = ?
Options:
A)2
B)4
C)6
D)8
E)10
Rationale: Logic :
40*14=560=5+6+0=11
30*13=390=3+9+0=12
So 20*12=240=2+4+0=6
Answer : C
Answer: C
Question: A customer asks the clerk for a paintbrush and a bucket of whitewash for a total price of B dollars. If the paintbrush costs 300 cents less than twice the price of a bucket of whitewash, what is the price of half a bucket of whitewash in dollars?
Options:
A)(B + 200)/2.
B)(B + 2)/6.
C)(2B + 200)/3.
D)(B + 2)/3.
E)(B - 2)/6.
Rationale: P = 2w - 200
thus total price in cents as given should be
2w-200 +w = 100B
3w - 200 = 100 B
3w = 100 B+200
3w =b+2 (in dollars)
w/2 = (b+2)/6
Ans:D
Answer: D
Question: A manufacturer sells a pair of plastics to a wholesale dealer at a profit of 18%. The wholesaler sells the same to retailer at a profit of 20%. The retailer in turn sells them to a customer for Rs. 30.09, there by earning a profit of 25%. The cost price for the manufacturer is:
Options:
A)23
B)16
C)17
D)45
E)28
Rationale: C
Let the cost price for the manufacturer be Rs. x. Then, 125% of 120% of 118% of x = 30.09.
125/100 * 120/100 * 118/100 * x = 3009/100
177/100 x = 3009/100 => x = 17
Answer: C
Question: In a certain sequence, the first term is 1, and each successive term is 1 more than the reciprocal of the term that immediately precedes it. What is the fifth term in this sequence?
Options:
A)13/8
B)21/13
C)8/5
D)5/8
E)8/13
Rationale: let five terms in the sequence be a,b,c,d,e
a=1
b= 1+1/1=2/1
c=1+1/2= 3/2
d= 1+2/3 = 5/3
e= 1+3/5 = 8/5
hence answer should be C.
Answer: C
Question: What is difference between biggest and smallest fraction among 2/3, 3/4, 4/5 and 5/3
Options:
A)2/5
B)3/5
C)1/6
D)1
E)None of these
Rationale: Explanation:
2/3 = .66, 3/4 = .75, 4/5 = .8 and 5/3 = 1.66
So biggest is 5/3 and smallest is 2/3
Their difference is 5/3 - 2/3 = 3/3 = 1
Option D
Answer: D
Question: Find the 25% of Rs. 400.
Options:
A)s. 50
B)s. 70
C)s. 100
D)s. 80
E)s. 60
Rationale: Explanation :
25% of 400
=> 25/100 *400 = Rs. 100
Answer : C
Answer: C
Question: Which of the following numbers must be added to 5678 to give a remainder of 35 when divided by 460?
Options:
A)955
B)980
C)797
D)618
E)718
Rationale: (5678+x)=(460*y)+35
5678-35+x=460*y
5643+x=460*y
so in x last digit must be 7 so ans should be c
ANSWER:C
Answer: C
Question: The total surface area of a solid hemisphere of diameter 14 cm is
Options:
A)308 cm2
B)462 cm2
C)1232 cm2
D)1848 cm2
E)None
Rationale: Solution
Total surface area	= 3ΠR2
= (3 x 22/7 x 7 x 7)cm2
= 462 cm2.
Answer B
Answer: B
Question: When positive integer x is divided by 7, the quotient is y and the remainder is 3. When 2x is divided by 6, the quotient is 3y and the remainder is 2. What is the value of 11y – x?
Options:
A)4
B)3
C)2
D)1
E)0
Rationale: (1) x = 7y+3
(2) 2x = 18y+2
(2)-(1): x=11y-1
11y-x=1
The answer is D.
Answer: D
Question: Pipe A can fill a tank in 30 minutes. Pipe B can fill the same tank 6 times faster than pipe A. If both the pipes are connected to the tank so that they fill the tank simultaneously, how long will it take for the empty tank to overflow?
Options:
A)4 minutes
B)15/4 minutes
C)192/7 minutes
D)224/7 minutes
E)28 minutes
Rationale: Pipe A can fill a tank in 30 minutes --> the rate of A = 1/30tank/minute;
Pipe B can fill the same tank6 times fasterthan pipe A --> the rate of B = 1/30 + 6/30 = 7/30 tank/minute.
Their combined rate = 1/30 + 7/30 = 4/15 tank/minute;
Therefore, A and B can fill the tank in 15/4 minutes.
Answer: B
Answer: B
Question: What is the area inscribed by the lines y =3, x = 2, y = x+3 on an xy-coordinate plane?
Options:
A)a) 1
B)b) 2
C)c) 4
D)d) 6
E)e) 10
Rationale: First, let's graph the lines y = 3 and x = 2
At this point, we need to find the points where the line y = x+3 INTERSECTS the other two lines.
For the vertical line, we know that x = 2, so we'll PLUG x = 2 into the equation y = x+3 to get y = 2+3 = 5
Perfect, when x = 2, y = 5, so one point of intersection is (2,5)
For the horizontal line, we know that y = 3, so we'll PLUG y = 3 into the equation y = x+3 to get 3 = x+3. Solve to get: x = 0
So, when y = 3, x = 0, so one point of intersection is (0,3)
Now add these points to our graph and sketch the line y = x+3
At this point, we can see that we have the following triangle.
The base has length 2 and the height is 2
Area = (1/2)(base)(height)
= (1/2)(2)(2)
= 2
Answer:
B
Answer: B
Question: John makes $60 a week from his job. He earns a raise andnow makes $70 a week. What is the % increase?
Options:
A)16%
B)16.66%
C)18%
D)21%
E)23%
Rationale: Increase = (10/60)*100 = (1/6)*100 = 16.66%.
B
Answer: B
Question: A and B together can complete a work in 12 days. A alone can complete it in 20 days. If B does the work only for half a day daily, then in how many days A and B together will complete the work?
Options:
A)65 days
B)85 days
C)15 days
D)45 days
E)13 days
Rationale: B's 1 day work = (1/12 - 1/20) = 1/30
Now, (A + B)'s 1 day work = (1/20 + 1/60) = 1/15
So, A and B together will complete the work in 15 days.
Answer:C
Answer: C
Question: The average age of 6 men increases by 2 years when two women are included in place of two men of ages 10 and 12 years. Find the average age of the women?
Options:
A)87
B)12
C)30
D)28
E)17
Rationale: 10 + 12 + 6 * 2
= 34/2
= 17
Answer:E
Answer: E
Question: If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 5 years the amount to be paid is?
Options:
A)3377
B)2688
C)2688
D)9125
E)1268
Rationale: A = 7500(26/25)^5 = 9125
Answer: D
Answer: D