mathewhe/aqua_rat huggingface dataset:
Question: A person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 16km?
(A) 3
(B) 6
(C) 8
(D) 9
(E) 7
Rationale: M = 4
S = 2
US = 4 - 2 = 2
D = 16
T = 16/2 = 8
Answer:C
Answer: (C) 8
Question: A train 600 m long can cross an electric pole in 20 sec and then find the speed of the train?
(A) 987
(B) 271
(C) 108
(D) 27
(E) 28
Rationale: Length = Speed * time
Speed = L/T
S = 600/20
S = 30M/Sec
Speed= 30*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 108 Kmph
Answer:C
Answer: (C) 108
Question: The average age of students of a class is 15.8 years. The average age of boys in the class is 16.4 years and that of the girls is 15.3 years. The ration of the number of boys to the number of girls in the class is?
(A) 5:6
(B) 2:3
(C) 2:5
(D) 2:1
(E) 2:4
Rationale: Let the ratio be k : 1. Then,
k * 16.4 + 1 * 15.3 = (k + 1) * 15.8
= (16.4 - 15.8)k = (15.8 - 15.3)
= k = 0.5/0.6 = 5/6
Required ratio = 5/6 : 1 = 5:6.
Answer:A
Answer: (A) 5:6
Question: Line J has a y-intercept of 11 and passes through point (a,b). What is the slope of Line J in terms of a and b?
(A) (a−6)/b
(B) (a−b)/6
(C) (6−a)/b
(D) (6−b)/a
(E) (b-11)/a
Rationale: You know that the line goes through point (a,b) and the y-intercept of 11 tells you that the line also goes through point (0,11).
slope m = (y-y1)/(x-x1) = (b-11)/(a-0)= (b-11)/a
E
Answer: (E) (b-11)/a
Question: The sum of three consecutive integers is 102. Find the lowest of the three?
(A) 40
(B) 53
(C) 29
(D) 33
(E) 35
Rationale: Explanation:
Three consecutive numbers can be taken as (P - 1), P, (P + 1).
So, (P - 1) + P + (P + 1) = 102
3P = 102 => P = 34.
The lowest of the three = (P - 1) = 34 - 1 = 33.
ANSWER IS D
Answer: (D) 33
Question: By selling 150 mangoes, a fruit-seller gains the selling price of 30 mangoes. Find the gain percent?
(A) 25%
(B) 20%
(C) 18%
(D) 30%
(E) 40%
Rationale: SP = CP + g
150 SP = 150 CP + 30 SP
120 SP = 150 CP
120 --- 30 CP
100 --- ? => 25%
ANSWER A
Answer: (A) 25%
Question: A ribbon is cut into three smaller strips in the ratio 2:3:5. If the shortest of the three strips is 30 inches in length, what was the length, in inches, of the ribbon before it was cut?
(A) 60
(B) 75
(C) 90
(D) 150
(E) 170
Rationale: Given 2x = 30 so x =15
Have to find 2x+3x+5x = 30+45+75= 150
Ans D
Answer: (D) 150
Question: The average daily wages of A, B and C is Rs 120. If B earns Rs 40 more than C per day and ,A earns double of what C earns per day, the wage of A per day is?
(A) Rs 80
(B) Rs 120
(C) Rs 160
(D) Rs 100
(E) Rs 140
Rationale: Let daily wages of C = X
Then, daily wages of A = 2X
and daily wages of B = X + 40
Hence, average daily wages of A, B and C
= (X + 2X + X + 40) / 3 = (4X + 40)/3
Thus, (4X + 40)/3 =120
=>4X + 40 = 360
=>4X = 320
X = 80.
Therefore, Wages of A per day = 2 x 80 = Rs 160.
ANSWER:C
Answer: (C) Rs 160
Question: A political candidate collected $1,749 from a fund raising dinner. If each supporter contributed at least $50, what is the greatest possible number of contributors at the dinner?
(A) 33
(B) 34
(C) 35
(D) 36
(E) 37
Rationale: Nearest to 1749≈1750
175/50=35 (Caution: Collection is 1750 - 1 = 1749)
Counting 1 less = 50*34 = 1700 >> 49 remains which will be adjusted with the 34 members
51* 34 = 1734 >> 15 remains which will be adjusted with 15 members
52 * 15 + 51 * 19 = 780 + 969 = 1749
Answer = B
Answer: (B) 34
Question: The age of Somu is one-third his father's. 7 years back he was one-fifth of his father's age. What is his persent age ?
(A) 11
(B) 13
(C) 14
(D) 12
(E) 10
Rationale: Explanation :
Let Somu's age be x and that of his father be 3x.
So, x - 7 = 3x - 7/5 = x = 14
Answer : Option C
Answer: (C) 14
Question: The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:
(A) 200m
(B) 225m
(C) 245m
(D) 250m
(E) 300m
Rationale: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30 = 25/2 => 2(130 + x) = 750 => x = 245 m.
ANSWER C
Answer: (C) 245m
Question: The “length of integer x” refers to the number of prime factors, not necessarily distinct, that x has. (If x = 60, the length of x would be 4 because 60 = 2 × 2 × 3 × 5.) What is the greatest possible length of integer z if z < 800?
(A) 13
(B) 10
(C) 9
(D) 7
(E) 6
Rationale: To maximize the length of z, we should minimize its prime base. The smallest prime is 2 and since 2^9 = 512 < 800, then the greatest possible length of integer z is 9.
The answer is C.
Answer: (C) 9
Question: The rate of failure in an examination is 39.25%. Find the least number of total candidates appeared in the examination.
(A) 100
(B) 200
(C) 300
(D) 400
(E) 500
Rationale: if 100 student appear then failure=39.25 ......... which is not possible because number of student can not be fraction,like wise in 200 student,failure=78.5, so we have to make the failure percentage into a unit digit failure not fraction...so min no of student =400 so that no of failure=157..........so least no of student appeared in the exam= 400.
ANSWER:D
Answer: (D) 400
Question: In the word CONTRACTUAL, the positions of the first and the eleventh letters are interchanged. Similarly, the positions of the second and the tenth letters are interchanged, and so on, up to the positions of fifth and seventh letters are interchanged, keeping the position of sixth letter unchanged. Which letter will be the third to the right of the sixth letter from the left end?
(A) U
(B) N
(C) T
(D) A
(E) None of these
Rationale: New word will be LAUTCARTNOC
6th letter from the left end is A,and and 3rd to the righ of thet letter is N.
ANSWER:B
Answer: (B) N
Question: In an examination, 35% of students failed in quants and 42% of students failed in verbal while 14% failed in both the topics. If 222 students passed in both the topics, how many students appeared to write the examination?
(A) 500
(B) 600
(C) 700
(D) 800
(E) 900
Rationale: DETAILED SOLUTION
Percent of students failing quants = 35
Percent of students failing verbal = 42
Sum = 35 + 42 = 77
Percent of students failing both = 14
= ) Percent of students failing either one = 77 – 14 = 63. Thus, 37% students passed in both the topics
= ) 37% of x = 222 = ) x = 600
Correct Answer: B
Answer: (B) 600
Question: Three coins are tossed. What is the probability of getting at most two tails?
(A) 7/8
(B) 1/8
(C) 1/2
(D) 1/7
(E) 1/3
Rationale: Total number of outcomes possible when a coin is tossed = 2 (âˆµ Head or Tail)
Hence, total number of outcomes possible when 3 coins are tossed, n(S) = 2 Ã— 2 Ã— 2 = 8
(âˆµ i.e., S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH})
E = event of getting at most two Tails = {TTH, THT, HTT, THH, HTH, HHT, HHH}
Hence, n(E) = 7
P(E) = n(E)/n(S)=7/8
Answer:A
Answer: (A) 7/8
Question: A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, the how old is B?
(A) 7 years.
(B) 8 years.
(C) 9 years.
(D) 10 years.
(E) 11 years.
Rationale: EXPLANATION
Let C’s age be x years. Then, B’s age = 2x years. A’s age = (2x + 2) years.
(2x + 2) + 2x + x = 27
5x = 25
x = 5.
Hence, B’s age = 2x = 10 years.
Answer D
Answer: (D) 10 years.
Question: A can do a work in 12 days. B is 60% more efficient than A. How many days does B alone take to do the same job?
(A) 15/2
(B) 10
(C) 7/2
(D) 12
(E) 6
Rationale: Ratio of times taken by A and B = 160:100 = 8:5
suppose B alone to take x days to do the work
then, 8:5::12:x
8x= 5*12
x=15/2 days
correct option is A
Answer: (A) 15/2
Question: In a 1000 m race, A beats B by 200 meters or 24 seconds. Find the speed of B?
(A) 6
(B) 8.3
(C) 7
(D) 5
(E) 2
Rationale: Since A beats B by 200 m or 24 seconds, i
t implies that B covers 200 m in 24 seconds.
Hence speed of B = 200/24 = 8.3 m/s.
Answer: B
Answer: (B) 8.3
Question: The current of a stream at 1 kmph. A motor boat goes 35 km upstream and back to the starting point in 12 hours. The speed of the motor boat in still water is?
(A) 6
(B) 7
(C) 8
(D) 65
(E) 4
Rationale: S = 1
M = x
DS = x + 1
US = x - 1
35/(x + 1) + 35/(x - 1) = 12
x = 6
Answer: A
Answer: (A) 6
Question: In a recent head-to-head run-off election, 12,000 absentee ballets were cast. 1/6 of the absentee ballets were thrown out and 3/5 of the remaining absentee ballets were cast for Candidate A. How many absentee votes did Candidate B receive?
(A) 2,000
(B) 3,000
(C) 4,000
(D) 8,000
(E) 9,000
Rationale: 5/6 * 2/5 (total absentee votes) = 1/3 (total votes)=1/3*12000=4000
Answer is C
Answer: (C) 4,000
Question: The average height of 15 girls out of a class of 30 is 152 cm. and that of the remaining girls is 156 cm. The average height of the whole class is :
(A) 150 cms
(B) 151 cms
(C) 152 cms
(D) 154 cms
(E) 156 cms
Rationale: Explanation:
Average height of the whole class =(15×152+15×156/30)=154 cms
Answer D
Answer: (D) 154 cms
Question: 10^25 - 360 is divisible by all of the following except:
(A) A.7
(B) B.8
(C) C.5
(D) D.4
(E) E.2
Rationale: The last three digits ( 1000 - 360 ) 640
640 is divisible by 2,4,8,5
640 is not evenly divisible by 7 so the answer is A) 7
Answer: (A) A.7
Question: Present ages of Kiran and Syam are in the ratio of 5:4 respectively. Three years hence, the ratio of their ages will become 11:9 respectively. What is Syam's present age in years?
(A) 21
(B) 22
(C) 23
(D) 25
(E) 24
Rationale: Ratio of the present age of Kiran and Syam =5:4
Let present age of Kiran =5x
Present age of Syam =4x
After 3 years, ratio of their ages =11:9
⇒(5x+3):(4x+3)=11:9⇒9(5x+3)=11(4x+3)⇒45x+27=44x+33⇒x=33−27=6
Syam's present age =4x=4×6=24
Answer is E.
Answer: (E) 24
Question: The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ?
(A) 150
(B) 250
(C) 270
(D) 280
(E) 290
Rationale: Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 6x + 15
5x = 1350
x = 270
Smaller number = 270.
Answer C)270.
Answer: (C) 270
Question: A, B and C started a shop by investing Rs. 10,000, Rs. 20,000 and Rs. 30,000 respectively. At the end of the year, the profits were distributed among them. If Câ€™s share of profit be Rs. 9,000, then the total profit was :
(A) 30,000
(B) 60,000
(C) 18,000
(D) 120,000
(E) None
Rationale: Sol.
A : B : C = 10000 :20000 : 30000 = 1: 2 : 3. so, Câ€™s share : Total Profit = 3 : 6
Let the total profit be Rs. x. Then, 3/6 = 9000/x
x = 9000 * 6 / 3 = 18000.
Answer C
Answer: (C) 18,000
Question: problemsolvingproblemsolvingprob . . . . . . Find the 2015th term in the series?
(A) 23
(B) 26
(C) 13
(D) 76
(E) 18
Rationale: Sol.
Problemsolving = 14 letter word. So divide 2015 by 14 and find the remainder. Here remainder is 13. so 13th letter in problemsolving is 'n'
Answer:C
Answer: (C) 13
Question: If the area of circle is 1520 sq cm then its circumference?
(A) 221
(B) 138
(C) 166
(D) 116
(E) 112
Rationale: 22/7 r2 = 1520 => r = 22
2 * 22/7 * 22 = 138
Answer: B
Answer: (B) 138
Question: In how many ways can the letters of word EMULATION be arranged such that NO two vowels appear together?
(A) 9!
(B) 5!*4!
(C) 4!*5!
(D) 5!*4!*2!
(E) 6!*4!
Rationale: No 2 vowels together = the only arrangement possible will be V C V C V C V C V (with V=vowel, C=consonant). This is true as we have 5 vowels and 4 consonants and any other combination will force us to pair 2 vowels together.
Thus, the number of arrangements possible : 5 *4 *4 *3 *3 *2 *2*1 = 5!*4! ----> C is the correct answer.
Answer: (C) 4!*5!
Question: Sum of two numbers is 80. Greater number exceeds by 5 from four times of the smaller. Find the numbers?
(A) 65, 15
(B) 64, 16
(C) 62, 18
(D) 60, 20
(E) 61, 30
Rationale: Explanation:
x + y = 80
x – 4y = 5
x = 65 y = 15
ANSWER IS A
Answer: (A) 65, 15
Question: How many prime numbers are between 78/14 and 55/4?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: 78/14= 39/7 = 6-
55/4 = 14-
Prime numbers between 6 and 14 are 7, 11 and 13
- sign signifies that the number is marginally less .
Answer B
Answer: (B) 3
Question: 5 pears and 2 apples cost $16. 3 pears and 3 apples cost $15. How much does one apple cost?
(A) 3.5
(B) 3.25
(C) 3
(D) 2.5
(E) 2
Rationale: Let cost of 1 pear = x, let cost of 1 apple = y
5x + 2y = 16
y = (16 - 5x)/2
Again,
3x + 3y = 15
3x + 3((16 - 5x)/2) = 15
3x + 24 - 7.5x = 15
3x + 24 = 15 + 7.5x
9 = 4.5x
x = 2
Now plug this value into one of the initial equations:
5x + 2y = 16
5(2) + 2y = 16
10 + 2y = 16
2y = 6
y = 3
Answer: C
ANSWER:C
Answer: (C) 3
Question: Which of the following is the lowest positive integer that is divisible by 6, 7, 8, 9, and 10?
(A) 2140
(B) 2520
(C) 2980
(D) 3260
(E) 3680
Rationale: The number needs to be divisible by 2*3, 7, 2^3, 3^2, and 2*5.
The lowest positive integer is 7 * 2^3 * 3^2 * 5 = 2520
The answer is B.
Answer: (B) 2520
Question: A lighting store is stocked with 410 fixtures. Some of the fixtures are floor lamps and the rest are table lamps. If 5% of the floor lamps and 30% of the table lamps are imported, what is the smallest possible number L of imported lamps stocked at the store?
(A) 3
(B) 10
(C) 13
(D) 20
(E) 23
Rationale: We want to minimize not maximize the expression,.
L=x/20+(410-x)*3/10=123+x/20-3x/10=123-5x/20 --> maximize x to minimize the expression --> x must be the greatest multiple of 20 less than 410, so 400 --> 123-5*400/20=23.
But i'm guessing 123-5x/20 can be written as 123- x/4
if x has to be the greatest multiple of 4 less then 410, then it would be 408.
Hence 123-408/4 --> 123-102 -->21
Yes, you cannot reduce in this case. If x=408, then 5/100*x and (410-x)*3/10 won't be integers.E
Answer: (E) 23
Question: If a coin is tossed three times, what is the probability that on the first toss the coin lands on tails and then lands on heads the next two tosses?
(A) 1/8
(B) 1/3
(C) 1/4
(D) 1/2
(E) 1
Rationale: P(THH) = 1/2*1/2*1/2=1/8
The answer is A.
Answer: (A) 1/8
Question: By selling 99 pens, a trader gains the cost of 9 pens. Find his gain percentage?
(A) 9 1/3%
(B) 9 7/3%
(C) 9 1/8%
(D) 9 1/3%
(E) 9 1/11%
Rationale: Let the CP of each pen be Rs. 1.
CP of 99 pens = Rs. 99
Profit = Cost of 9 pens
= Rs. 9
Profit% = 9/99 * 100
= 9 1/11%
Answer: E
Answer: (E) 9 1/11%
Question: About the number of pairs which have 16 as their HCF and 121 as their LCM, the conclusion can be
(A) only one such pair exists
(B) only two such pairs exist
(C) many such pairs exist
(D) many such pairs exist
(E) such pair did not exists
Rationale: Explanation:
HCF is always a factor of LCM. ie., HCF always divides LCM perfectly.
Correct Option: E
Answer: (E) such pair did not exists
Question: A certain research group plans to create computer models of x% of a list of 10,000 bacterial species known to inhabit the human body. After a budget cut, the group finds it must reduce this selection by (x − 6)%. In terms of x, how many species of bacteria will the group be able to model?
(A) (x)*(106 - x)
(B) (x)(105 – x)
(C) (100)(105 – x)
(D) (100)(95 – x)
(E) (x-5)/100
Rationale: Initial: (x/100)*10000 = 100x (bacterial species)
After reduce BY (x - 6)%, the percentage of bacterial species = 1 - (x - 6)% = 1 - (x - 6)/100 = (106 - x)/100
Note: Difference between reduce to[means: the remain] and reduce by[means: the remain = 1 -reduce by]
So, the number of bacterial species after reducing: 100x*(106 - x)/100 = (x)*(106 - x)
Ans is A.
Answer: (A) (x)*(106 - x)
Question: In Township K each property is taxed at 8 percent of its assessed value. If the assessed value of a property in Township K is increased from $18,000 to $28,000, by how much will the property tax increase?
(A)  $320
(B)  $800
(C)  $320
(D)  $600
(E)  $850
Rationale: Increase in house value = $28,000 - $18,000 =$10000
So, tax increase = 8% of$10000=$800
Answer: B
Answer: (B)  $800
Question: The difference between C.I. and S.I. on an amount of Rs. 15,000 for 2 years is Rs. 24. What is the rate of interest per annum?
(A) 8
(B) 2
(C) 9
(D) 4
(E) 6
Rationale: Explanation:
[15000 * (1 + R/100)2 - 15000] - (15000 * R * 2)/100 = 104
15000[(1 + R/100)2 - 1 - 2R/100] = 24
15000[(100 + R)2 - 10000 - 200R]/10000 = 24
R2 = (24 * 2)/3 = 16 => R = 4
Rate = 4%
Answer: Option D
Answer: (D) 4
Question: A sum of Rs. 2691 is lent into two parts so that the interest on the first part for 8 years at 3% per annum may be equal to the interest on the second part for 3 years at 5% per annum. Find the second sum?
(A) 1629
(B) 1656
(C) 1277
(D) 6298
(E) 1279
Rationale: (x*8*3)/100 = ((2691 - x)*3*5)/100
24x/100 = 40365/100 - 15x/100
39x = 40365 => x = 1035
Second sum = 2691 â€“ 1035 = 1656
Answer:B
Answer: (B) 1656
Question: Find the area of a rhombus whose side is 25 cm and one of the diagonals is 30 cm?
(A) 876
(B) 268
(C) 269
(D) 600
(E) 278
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:D
Answer: (D) 600
Question: There are 4 runners on a track team who run an average of 4.5 seconds per 40 yards. If another runner joins their team who runs 4.3 seconds per 40 yards, what will the new average 40 yard time be?
(A) 4.46
(B) 4.39
(C) 4.42
(D) 4.49
(E) 4.33
Rationale: (sum of the 4 times)/4 = 4.5
sum of the 4 times = 18
new sum = 18+4.3 = 22.3
new average = 22.3/5 = 4.46
ans: A
Answer: (A) 4.46
Question: Carol and Jordan draw rectangles of equal area. If Carol's rectangle measures 15 inches by 20 inches and Jordan's rectangle is 6 inches long, how wide is Jordan's rectangle, in inches?
(A) 20
(B) 30
(C) 40
(D) 50
(E) 60
Rationale: Area of first rectangle is 15*20=300 hence area of second would be 6x=300x
x=50
answer is D
Answer: (D) 50
Question: A cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 7 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?
(A) 2.9 hrs
(B) 8.9 hrs
(C) 9.3 hrs
(D) 7.2 hrs
(E) 8.6 hrs
Rationale: Net part filled in 1 hour = (1/4 - 1/7)
= 3/28
The cistern will be filled in 28/3 hrs i.e., 9.3 hrs.
Answer:C
Answer: (C) 9.3 hrs
Question: The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water?
(A) 6 kmph
(B) 9 kmph
(C) 8 kmph
(D) 10 kmph
(E) 1 kmph
Rationale: S = 4
M = x
DS = x + 4
US = x - 4
6/(x + 4) + 6/(x - 4) = 2
x = 8
Answer:C
Answer: (C) 8 kmph
Question: On his drive to work, Leo listens to one of three radio stations A, B or W. He first turns to A. If A is playing a song he likes, he listens to it; if not, he turns it to B. If B is playing a song he likes, he listens to it; if not, he turns it to W. If W is playing a song he likes, he listens to it; if not, he turns off the radio. For each station, the probability is 0.30 that at any given moment the station is playing a song Leo likes. On his drive to work, what is the probability that Leo will hear a song he likes?
(A) 0.027
(B) 0.09
(C) 0.417
(D) 0.657
(E) 0.9
Rationale: Probability he hears a song is like:
Tune to A and likes what he is hearing = 0.3
Tune to A, don't find he like what they are airing, then tune to B and likes what he finds there = 0.7 * 0.3 = 0.21
Tune to A, finds crap there, Tune to B, hears a similar crap, Tune to W and finally falls in love with the program = 0.7^2 * 0.3 = 0.147
Total = 0.657
Ans D
Answer: (D) 0.657
Question: is twice as fast as B. If B alone can do a piece of work in 30 days, in what time can A and B together complete the work?
(A) 13 days
(B) 10 days
(C) 16 days
(D) 11 days
(E) 18 days
Rationale: B
10 days
A can do the work in 30/2 i.e., 15 days.
A and B's one day's work = 1/15 + 1/30 = (2 + 1)/30 = 1/10
So A and B together can do the work in 10 days.
Answer: (B) 10 days
Question: What will be the vulgar fraction of 0.70
(A) 3/5
(B) 7/10
(C) 3/2
(D) 3/7
(E) 3/8
Rationale: Explanation:
0.70 = 70/100 = 7/10
Option B
Answer: (B) 7/10
Question: 220, 218, 214, 208, 200, 190, ?
(A) 120
(B) 140
(C) 147
(D) 178
(E) 189
Rationale: 220
220 - 2 = 218
218 - 4 = 214
214 - 6 = 208
208 - 8 = 200
200 - 10 = 190
190 - 12 = 178
Answer is D
Answer: (D) 178
Question: If the President and Vice President must sit next to each other in a row with 6 other members of the Board, how many different seating arrangements are possible?
(A) 120
(B) 240
(C) 300
(D) 10080
(E) 720
Rationale: We need to take President and VP as one unit. Therefore we have 7 people to arrange=7! ways
Also, we both President and VP can be arranged in 2 ! ways.
Reqd no of ways=7!*2!=10080 ways
Answer D
Answer: (D) 10080
Question: Of the science books in a certain supply room, 50 are on botany, 62 are on zoology, 83 are on physics. 50 are on geology, and 110 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same science?
(A) 321
(B) 159
(C) 166
(D) 285
(E) 324
Rationale: First, you can take all 50 Botany books, all 62 zoology books and all 50 geology books because you're sure to never pick 80 of them.
There are still 83 on physics and 110 on chemistry
The worst case could be that we pick 79 physics and 79 chemistry. So that the next book picked will necessary complete 80 books picked, either in physics or chemistry.
Minimum number of books picked to reach 80 in the same science should be : 50 + 62 + 50 + 79 +79 + 1 = 321
A
Answer: (A) 321
Question: The present worth of Rs.169 due in 2 years at 4% per annum compound interest is
(A) Rs 155.25
(B) Rs 156.25
(C) Rs 157.25
(D) Rs 158.25
(E) None of these
Rationale: Explanation:
In this type of question we apply formula
Amount=P /(1+R/100)n
Amount=169 /(1+4/100)2
Amount=169∗25∗25/26∗26
Amount=156.25
Option B
Answer: (B) Rs 156.25
Question: For prime numbers x and y, x^3*y^5=z^4. How many positive factors does positive integer z have?
(A) One
(B) Two
(C) Three
(D) Four
(E) Five
Rationale: Solution: given x^3*y^5=z^4; here if x and y are two different prime numbers then z = x^3/4 * y^5/4
in this case z can not be and integer.
now to make z = (x^3*y^5)^1/4 an integer it is required to have x=y then equation will become z=x^2 or z=y^2
hence total positive factors will be 3.	ANSWER:C
Answer: (C) Three
Question: A dealer purchases 15 articles for Rs. 25 and sells 12 articles for Rs. 30. Find the profit percentage?
(A) 20%
(B) 40%
(C) 50%
(D) 80%
(E) 30%
Rationale: C
50%
L.C.M of 15 and 12 = 60
CP of 60 articles = Rs. 100 (25 * 4)
SP of 60 articles = Rs. 150 (30 * 5)
Profit percentage = (150 - 100)/100 * 100 = 50%
Answer: (C) 50%
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?
(A) 10 days
(B) 11 days
(C) 15 days
(D) 20 days
(E) None of these
Rationale: B's 1 day's work=(1/12-1/20)=2/60=1/30
Now, (A+B)'s 1 day's work=(1/20+1/60)=4/60=1/15
So, A and B together will complete the work in 15 days.
Correct Option: C
Answer: (C) 15 days
Question: Mike has forty-five cents. If mike gives away two nickles and a dime, how much money does he have left?
(A) 10 cents
(B) 16 cents
(C) 35 cents
(D) 25 cents
(E) 40 cents
Rationale: Nickle = 5 cents
Dime = 10 cents
45-(2)5-10 = 25
D.25 cents
Answer: (D) 25 cents
Question: The value of a 10.5% stock, in which an income of Rs.756 is derived by investing Rs.9000, brokerage being% is :
(A) Rs. 113.5
(B) Rs. 119.7
(C) Rs. 124.75
(D) Rs. 130.75
(E) Rs. 134.45
Rationale: For an income of Rs.756, investment = Rs.9000
For an income of Rs., investment = = Rs.125
For a Rs.100 stock, investment = Rs.125.
Market value of Rs. 100 stock = = Rs. 124.75
C
Answer: (C) Rs. 124.75
Question: Life expectancy is defined by the formula 2SB/G, where S = shoe size, B = average monthly electric bill in dollars, and G = GMAT score. If Melvin's GMAT score is twice his monthly electric bill, and his life expectancy is 60, what is his shoe size?
(A) 25
(B) 60
(C) 35
(D) 40
(E) 50
Rationale: Solution -
Given that, G = 2B and Life expectancy(L) = 60
L=2SB/G -> 60 = 2SB/2B --> S=60.
ANS B
Answer: (B) 60