mathewhe/aqua_rat huggingface dataset:
Question: A man invested Rs. 1552 in a stock at 97 to obtain an income of Rs. 200. The dividend from the stock is :
(A) 7.5 %
(B) 8 %
(C) 12.5 %
(D) None of these
(E) Cannot be determined
Rationale: Solution
By investing Rs. 1552,income = Rs. 200.
By investing Rs. 97, income = Rs. (200/1552x97)= Rs.12.5
âˆ´ Dividend =12.5%.
Answer C
Answer: (C) 12.5 %
Question: Rick deposited $700 to his bank account using $5 and $15 dollar bills only. If Rick came to the bank with 70 bills and left with 10 bills only, how many $15 dollar billsმ did he deposit?
(A) 40.
(B) 25.
(C) 50.
(D) 55.
(E) 65.
Rationale: 5x+15y=700 --1
x+y=60 ---2
multiply eq 2 with 5 and subtract from eq 1
5x+15y=700
5x+5y=300
10y= 400
y=40 and x = 20
therefore $15 bills = 40
Answer A
Answer: (A) 40.
Question: The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 35% profit?
(A) 2080
(B) 2778
(C) 2299
(D) 2778
(E) 2771
Rationale: Let C.P. be Rs. x.
Then, (1920 - x)/x * 100 = (x - 1280)/x * 100
1920 - x = x - 1280
2x = 3200 => x = 1600
Required S.P. = 130 % of Rs. 1600 = 130/100 * 1600 = Rs. 2080.
Answer:A
Answer: (A) 2080
Question: A computer manufacturer produces a certain electronic component at a cost of $100 per component. Shipping costs for delivering the components are $2 per unit. Further, the manufacturer has costs of $10,000 a month related to the electronic component regardless of how many it produces. If the manufacturer produces and sells 1000 components a month, what is the lowest price it can sell them for such that the costs don't exceed the revenues?
(A) 122
(B) 112
(C) 134
(D) 108
(E) 101
Rationale: $10000 is a fixed cost
Each component is $102 ($100 to produce, $2 to ship)
Manufacturer will be producing and selling 1000 components
so therefore the equation to find price would be
1000*p = 10000+(1000*100)+(1000*2)
p = (10000+100000+2000)/1000
p = 112
Answer: B
Answer: (B) 112
Question: A train 800 metres long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel (in meters) is:
(A) 400
(B) 450
(C) 500
(D) 520
(E) 550
Rationale: Speed of train: 78km/hr=78*(5/18)=21.67m/sec
Distance=800m
Time=60sec
d=s*t
800+x=21.67*60
x=1300.2-800=500
ANSWER :C
Answer: (C) 500
Question: A tank contains 10,000 gallons of a solution that is 5 percent sodium chloride by volume. If 3,000 gallons of water evaporate from the tank, the remaining solution will be approximately what percent sodium chloride?
(A)  1.25%
(B)  3.75%
(C)  6.25%
(D)  6.67%
(E)  7.14%
Rationale: The remaining solution will be approximately what percent sodium chloride?means:what percent of the remaining solution is sodium chloride. Now, since the remaining solution is 10,000-3,000=7,000 gallons and sodium chloride is 500 gallons (5% of initial solution of 10,000 gallons) then sodium chloride is 500/7,000*100=~7.14% of the remaining solution of 7,000 gallons.
Answer: E.
Answer: (E)  7.14%
Question: A worker is paid a regular rate of Rs.10 for completing a survey. The worker completes 100 surveys per week. For any survey involving the use of her cellphone, she is paid at a rate of that is 30% higher than her regular rate. If she completed 60 surveys involving the use of her cellphone, how much did she get that week?
(A) 180
(B) 1180
(C) 280
(D) 580
(E) 2080
Rationale: Amount earned using her cell phone = 60 * 13 = 780
earned for remaining surveys = 40 * 10 = 400
Total earning = 1180
Answer : B
Answer: (B) 1180
Question: 10 camels cost as much as 24 horses, 16 horses cost as much as 4 oxen and 6 oxen as much as 4 elephants. If the cost of 10 elephants is Rs.170000, find the cost of a camel?
(A) Rs.9800
(B) Rs.3800
(C) Rs.9800
(D) Rs.6800
(E) Rs.6880
Rationale: Cost of the camel = P
10 camels = 24 horses
16 horses = 4 oxen
6 oxen = 4 elephants
10 elephants = Rs.170000
P = Rs.[(24 * 4 * 4 * 170000)/(10 * 16 * 6 * 10)]
P = Rs.(65280000/9600) => P = Rs.6800
Answer:D
Answer: (D) Rs.6800
Question: If 4 boys can color 60 m long cloth in 3 days, then 6 boys can color 36 m long cloth in
(A) day
(B) days
(C) days
(D) days
(E) days
Rationale: The length of cloth painted by one boy in one day = 60 / 4 × 3 =5 m
No. of days required to paint 36 m cloth by 6 boys = 36/ 5 × 6 = 6/5 day.
A)
Answer: (A) day
Question: If k^3 is divisible by 180, what is the least possible value of integer k?
(A) 12
(B) 30
(C) 60
(D) 90
(E) 120
Rationale: 180 = 2^2*3^2*5
Therefore k must include at least 2 * 3 * 5 = 30.
The answer is B.
Answer: (B) 30
Question: An automobile financier claims to be lending money at S.I., but he includes the interest every six months for calculating the principal. If he is charging an interest of 10%, the effective rate of interest becomes?
(A) 10.26%
(B) 10.25%
(C) 10.85%
(D) 17.25%
(E) 10.35%
Rationale: Let the sum be Rs. 100. Then,
S.I. for first 6 months = (100 * 10 *1) / (100 * 2) = Rs. 5
S.I. for last 6 months = (105 * 10 * 1) / (100 * 2) = Rs. 5.25
So, amount at the end of 1 year = (100 + 5 + 5.25) = Rs. 110.25
Effective rate = (110.25 - 100) = 10.25%.
Answer:B
Answer: (B) 10.25%
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 123
(B) 166
(C) 240
(D) 157
(E) 198
Rationale: Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 36 = 15
x + 300 = 540
x = 240 m.
Answer: C
Answer: (C) 240
Question: The average weight of A, B and C is 45 kg. If the average weight of A and B be 41 kg and that of B and C be 43 kg, then the weight of B is:
(A) 33 kg
(B) 31 kg
(C) 32 kg
(D) 36 kg
(E) 37 kg
Rationale: A
33 kg
Let A, B, C represent their respective weights.
Then, we have: A + B + C = (45 x 3) = 135 .... (i)
A + B = (41 x 2) = 82 .... (ii)
B + C = (43 x 2) = 86 ....(iii)
Adding (ii) and (iii), we get: A + 2B + C = 168 .... (iv)
Subtracting (i) from (iv), we get : B = 33.
B's weight = 33 kg.
A
Answer: (A) 33 kg
Question: reema has 25 mangoes.srujana has 13 mangoes. Totally how many mangoes they have in all?
(A) 20
(B) 38
(C) 30
(D) 25
(E) 15
Rationale: 25+13=38. Answer is B
Answer: (B) 38
Question: A drama group that must consists of 7 members is to be formed from a pool of 10 candidates. How many different groups are possible?
(A) 112
(B) 120
(C) 40
(D) 56
(E) 336
Rationale: Note that the drama group must consist of 7 members, not at least 7 members. Hence, all you have to do is 10C7 = 120
Answer (B)
Answer: (B) 120
Question: If a number is chosen at random from the set {1, 2, 3, ...., 100}, then the probability that the chosen number is a perfect cube is
(A) 1/25
(B) 1/29
(C) 1/26
(D) 1/24
(E) 1/21
Rationale: We have 1, 8, 27 and 64 as perfect cubes from 1 to 100.
Thus, the probability of picking a perfect cube is
4/100 = 1/25.
Answer:A
Answer: (A) 1/25
Question: What is the sum of all the multiples of 3 between 30 and 80?
(A) 2103
(B) 2106
(C) 1053
(D) 1252
(E) 1535
Rationale: You first have to know all the multiples of 3 between 30 and 80. They are 3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,60,63,66,69,72,75,and78. If you add all these numbers together, you get1053.
Final Answer:C
Answer: (C) 1053
Question: A manâ€™s current age is (2/5) of the age of his father. After 6 years, he will be (1/2) of the age of his father. What is the age of father at now?
(A) 40
(B) 45
(C) 38
(D) 50
(E) 30
Rationale: Let, fatherâ€™s current age is A years.
Then, Manâ€™s current age =[ (2/5)A ]years.
Therefore, [ (2/5)A + 6 ]= (1/2)(A + 6)
2(2A + 30) = 5(A + 6)
A = 30
E
Answer: (E) 30
Question: How much is 80% of 40 is greater than 4/5 of 25?
(A) 15
(B) 57
(C) 16
(D) 12
(E) 73
Rationale: (80/100) * 40 – (4/5) * 25
32 - 20 = 12
Answer: D
Answer: (D) 12
Question: There are 18 teams in the hockey league, and each team faces all the other teams 10 times each. How many games are played in the season?
(A) 1370
(B) 1530
(C) 1790
(D) 1950
(E) 2110
Rationale: The number of ways to choose two teams is 18C2 = 18*17/2 = 153
The total number of games in the season is 10*153 = 1530.
The answer is B.
Answer: (B) 1530
Question: A freight elevator can carry a maximum load of 1100 pounds. Sean, who weighs 200 pounds, is in the elevator with two packages weighing 150 pounds and 280 pounds. If he needs to fit three more packages in the elevator that weigh as much as possible without exceeding the elevator limit, what is the difference between their average and the average of the two packages already in the elevator?
(A) 59
(B) 85
(C) 190
(D) 215
(E) 210
Rationale: The average of existing 2 package is150 + 280/2 = 430/2 = 215
Remaining allowed weight = 1100 - 200 - 430 = 470.
allowed per package = 470 / 3 = 156
So difference in average of existing and allowable = 215 - 156 = 59
Hence A
Answer: (A) 59
Question: If A and B can do a piece of work in 7.5 days. If B works 1/2 of work and remaining work was completed by A, taking total time of 20 days to complete the work. If b is more efficient then B can do work in how many days?
(A) 9 days
(B) 10 days
(C) 11 days
(D) 12 days
(E) 13 days
Rationale: 1/A + 1/B = 2/15 or (A+B)/AB= 2/15 ----(i)
(1/2)/(1/A) + (1/2)/(1/B) = 20 or A/2 + B/2 = 20 or A+B= 40 ----(ii)
Substituting A+B= 40 from (ii) in (i), we get AB= 300
Now finding the factors of 300, whose sum is 40, we have 10 and 30
As B is more efficient than A, B can do the work in 10 days.
ANSWER:B
Answer: (B) 10 days
Question: There are three different hoses used to fill a pool: hose x, hose V, and hose z. Hose x can fill the pool in a days, hose V in b days, and hose z in c days, where a > b > c. When all three hoses are used together to fill a pool, it takes d days to fill the pool. Which of the following must be true?
I. d<c
II. d>b
III. c/3<d<a/3
(A) I
(B) III
(C) II
(D) I&II
(E) II&III
Rationale: Name T = full pool
X fills a pool in a days ==> 1 day X fills: T/a
V fills a pool in b days ==> 1 day Y fills: T/b
Z fills a pool in c days ==> 1 day Z fills: T/c
1 day (X+V+Z) together fill: T(1/a + 1/b + 1/c)
d days (X+V+Z) together fill: T
==> d = Tx1 / T(1/a+1/b+1/c) = abc/(ab+bc+ca)
==>d = abc/(ab+bc+ca)
d cannot be greater than c ; d is greater than b ; d is greater than c/3 but not less than a/3
C
Answer: (C) II
Question: Rs. 9800 are invested partly in 9% stock at 75 and 10% stock at 80 to have equal amount of incomes. The investment in 9% stock is:
(A) Rs. 4800
(B) Rs. 5000
(C) Rs. 5400
(D) Rs. 5600
(E) Rs. 6600
Rationale: let investment is x... den remaining investment is (9800-x)
x*9/75= (9800-x)*10/80
x=4800
9800-x=5000
ANSWER:B
Answer: (B) Rs. 5000
Question: A man bought an article and sold it at a gain of 5 %. If he had bought it at 5% less and sold it for Re 5 less, he would have made a profit of 10%. The C.P. of the article was
(A) 960
(B) 980
(C) 900
(D) 970
(E) 1000
Rationale: Explanation:
Let original Cost price is x
Its Selling price = (105/100) * x = 21x/20
New Cost price = (95/100) * x = 19x/20
New Selling price = (110/100 )* (19x/20 )= 209x/200
[(21x/20) - (209x/200)] = 1
=> x = 1000
Answer: E) Rs 1000
Answer: (E) 1000
Question: If A speaks the truth 40% of the times, B speaks the truth 80% of the times. What is the probability that at least one will tell the truth
(A) 0.18
(B) 0.12
(C) 1.02
(D) 1.2
(E) 1.3
Rationale: probability of A speaks truth p(A)=4/10;false=6/10
probability of B speaks truth p(B)=8/10;false=2/10.For given qtn
Ans=1-(neither of them tell truth).Because A & B are independent events
=1-[(6/10)*(2/10)]=1-12/100=1-0.88=0.12
ANSWER:B
Answer: (B) 0.12
Question: Three coins are tossed. What is the probability of getting at most two tails?
(A) 7/9
(B) 7/7
(C) 3/3
(D) 7/8
(E) 7/2
Rationale: Explanation:
It is given that 3 coins are tossed simultaneously.
=>Total outcomes when one coin is tossed=2
=>Total outcomes when 3 coins are tossed= 2n = 2 X 2 X 2
=8 outcomes
Favourable outcomes: TTH, THT, HTT, THH, THT,HHT,HHH=7
Therefore, Probability= 7/8
ANSWER: D
Answer: (D) 7/8
Question: The greatest possible length which can be used to measure exactly the length 6m, 4m 30cm, 4 m is
(A) 10
(B) 27
(C) 35
(D) 87
(E) 98
Rationale: Explanation:
Required Length = H.C.F of 600 cm, 430 cm and 400 c
= 10 cm.
Answer: A) 10 cm
Answer: (A) 10
Question: Set A consists of all the prime numbers between 62 and 85. What is the range of set A?
(A) 12
(B) 13
(C) 16.6
(D) 16
(E) 23
Rationale: The range of a set of data is the difference between the highest and lowest values in the set
In this set,
Highest number = 83
Lowest number = 67
Range = Highest - Lowest = 83 - 67= 16
Option D
Answer: (D) 16
Question: For a certain exam,a score of 58 was 2 standard deviations below mean and a score of 98 was 3 standard deviations above mean.What was the mean score T for the exam?
(A) 74
(B) 76
(C) 78
(D) 80
(E) 82
Rationale: A score of 58 was 2 standard deviations below the mean --> 58 = Mean - 2d
A score of 98 was 3 standard deviations above the mean --> 98 = Mean + 3d
Solving above for Mean T= 74.
Answer: A.
Answer: (A) 74
Question: How many gallons of milk that is 10 percent butter-fat must be added to 8 gallons of milk that is 25 percent butterfat to obtain milk that is 20 percent butterfat?
(A) 4
(B) 12
(C) 14
(D) 16
(E) 28
Rationale: Equate the fat:
0.1x + 0.25*8 = 0.2(x + 8) --> x = 4.
Answer: A.
Answer: (A) 4
Question: A security guard at a certain store is instructed to check the receipt of one out of every five customers as they are leaving the store. If, on the guard's shift, 16 customers leave the store, how many different samples of customers could have been selected to have their receipts checked?
(A) 20
(B) 120
(C) 59
(D) 90
(E) 100
Rationale: to choose the sample of 2 customers from 16. it can be done 16C2 possible ways.
So the answer is B. 120
Answer: (B) 120
Question: The average salary of all the 60 employees in an office is Rs. 12,000 per month. if the number of executives is twice the number of non executives employees, then the average salary of all the non executives employees is
(A) Rs. 9000
(B) Rs. 8000
(C) Rs. 6000
(D) can't be determined
(E) None
Rationale: Answer
No. of executives / No. of non- executives
= 2 / 1
Therefore
Number of executives = 40
and number of non executives employees = 20
now , go through the options
Total salary = 40 x salary of executives + 20 x salary of non-executives
60 x 12000 = 40 x k + 20 x l, here k, l are unknowns
so we con't determine the required average salary
Correct Option: D
Answer: (D) can't be determined
Question: A is a working partner and B is a sleeping partner in a business. A puts in 80,000 and B 70,000. A gets 25% of the profit for managing the business, and the rest is divided in proportion to their capitals. Find the profit if B get 14000.
(A) 42000
(B) 46000
(C) 54000
(D) 40000
(E) None of these
Rationale: Let amount distributed between A and B is x
Ratio of capital between A and B is 8:7
If B get 14000 Then
x*7/15 = 14000
x*7 = 210000
x = 30000
Let total profit = y
y*75/100 = 30000
y = 40000
Answer D
Answer: (D) 40000
Question: What is the least whole number that should be added to 625573 if it is to be divisible by 3?
(A) 6
(B) 1
(C) 4
(D) 3
(E) 2
Rationale: A number is divisible by 3 if the sum of the digits is divisible by 3..
Here, 6+2+5+5+7+3=28, the next multiple of 3 is 30.
2 must be added to 625574 to make it divisible by 3
E
Answer: (E) 2
Question: Seven fencers participate in a fencing championship. Assuming all competitors have an equal chance of winning, how many possibilities are there with respect to how a first-place and second-place medal can be awarded?
(A) 30
(B) 36
(C) 42
(D) 48
(E) 49
Rationale: 7*6 = 42
The answer is C.
Answer: (C) 42
Question: In 1995, the Johnsons spent $800 on the family’s water bills. Anticipating that water rates would increase in 1996 by 50%, the Johnsons cut back their water usage. By how much must the Johnsons have reduced their 1996 water usage to pay exactly the same amount R in 1996 as they paid in 1995?
(A) 33 1⁄3%
(B) 40%
(C) 50%
(D) 66 2⁄3%
(E) 100%
Rationale: water rate increases by 50 % in 1996 means 150% of rate in 1995. to pay exactly the same amount R in 1996 as they paid in 1995, water use should decrease in the same ratio
150-> 100 means 1/3 rd= 33(1/3) %.A
Answer: (A) 33 1⁄3%
Question: In how many ways can you seat 5 people on a bench if one of them, Rohit, does not want to sit on the middle seat or at either end?
(A) 48
(B) 1720
(C) 2880
(D) 5040
(E) 10080
Rationale: Since Rohit does not want to sit on the middle seat or at either end (3 chairs), then he can choose 2 chairs to sit. The remaining 4 people can sit in 4! ways. Thus the # of arrangements is 2*4! = 48.
Answer: A.
Answer: (A) 48
Question: In a class of 50 students, 18 take Chorus, 26 take Band, and 2 take both Chorus and Band. How many students in the class are not enrolled in either Chorus or Band?
(A) 8
(B) 12
(C) 15
(D) 16
(E) 18
Rationale: 16 + 2 + 24 + x = 50
42 + x = 50
x = 8 students
A)
Answer: (A) 8
Question: The average age of a husband, wife and their child 19 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is?
(A) 3 years
(B) 5 years
(C) 16 years
(D) 4 years
(E) 14 years
Rationale: Sum of the present ages of husband, wife and child
= (23 * 2 + 5 * 2) = 57 years.
Required average
= 57/19
= 3 years.
Answer:A
Answer: (A) 3 years
Question: It is currently 7:16 PM. At what time in the morning was it exactly 19,443 minutes earlier?
(A) 7:11
(B) 7:13
(C) 7:17
(D) 7:19
(E) 7:21
Rationale: Converting 19,443 minutes to hours, we get 19,443/60 = 324 R 3; that is 324 hours and 3 minutes. All of the answers are during the same hour of the morning, thus the hours can be assumed to bring us into the 7 AM hour evenly from 7:16 PM. Thus 324 hours ago was 7:16 AM. Take an extra 3 minutes off, and it was 7:13 AM. B
Answer: (B) 7:13
Question: A man has some hens and cows. If the number of heads be 46 and the number of feet equals 140, then the number of hens will be:
(A) 22
(B) 23
(C) 24
(D) 26
(E) 28
Rationale: let hens be x and cows be y
now,
feet: x*2+y*4=140
heads: x*1+y*1=46
implies, 2x+4y=140 and x+y=46
solving these two equations, we get x=22 and y=24
Therefore, hens are 22.
ANSWER:A
Answer: (A) 22
Question: Sony and Johnny caught 60 fishes. Sony caught four times as many as Johnny. How many fishes did Johnny catch?
(A) 12
(B) 16
(C) 34
(D) 38
(E) 42
Rationale: s+j=60
s=4*j
j=12
ANSWER:A
Answer: (A) 12
Question: Set M contains number that satisfy the condition that, if integer x is in the set then x + 1 will also be in the set M. If -4 is one value in the set, which of the following values must also be present in the set M? I) -6 II) -2 III) 2
(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II and III
Rationale: Since -4 is in the set, then the set must also include -3, -2, -1, 0, 1, 2, 3, 4, etc...
Depending on whether -4 is the starting element in the set or not, we can have -6...or not.
The answer is D.
Answer: (D) II and III only
Question: 3 candidates in an election and received 2136, 7636 and 11628 votes respectively. What % of the total votes did the winningcandidate got in that election?
(A) 45%
(B) 49%
(C) 54%
(D) 59%
(E) 61%
Rationale: Total number of votes polled = (2136 + 7636 + 11628) = 21260
So, Required percentage = 11628/21260 * 100 = 54%
C
Answer: (C) 54%
Question: A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 650 m long?
(A) 11
(B) 89
(C) 77
(D) 66
(E) 22
Rationale: Speed = 240/24 = 10 m/sec.
Required time = (240 + 650)/10 = 89 sec.
Answer:B
Answer: (B) 89
Question: In one year, the population, of a village increased by 12% and in the next year, it decreased by 12%. If at the end of 2nd year, the population was 14784, what was it in the beginning?
(A) 7787
(B) 8000
(C) 15000
(D) 1277
(E) 2081
Rationale: x*112/100 * 88/100 = 14784
X*0.9856=14784
X=14784/0.9856
=> 15000
Answer:C
Answer: (C) 15000
Question: How much time will a train of length 200 m moving at a speed of 72 kmph take to cross another train of length 300 m, moving at 36 kmph in the same direction?
(A) 50 sec
(B) 26 sec
(C) 80 sec
(D) 82 sec
(E) 81 sec
Rationale: The distance to be covered = Sum of their lengths = 200 + 300 = 500 m.
Relative speed = 72 -36 = 36 kmph = 36 * 5/18 = 10 mps.
Time required = d/s = 500/10 = 50 sec.
Answer: A
Answer: (A) 50 sec
Question: In a certain match all the teams were to play with each other. If there are 15 teams, how many matches will have to be played?
(A) 120
(B) 105
(C) 110
(D) 90
(E) None of the above
Rationale: 15c2
=105
ANSWER:B
Answer: (B) 105
Question: The area of a circle is increased by 1500%. By what percent has the diameter of the circle increased?
(A)  100%
(B)  500%
(C)  300%
(D)  600%
(E)  800%
Rationale: The area of the circle is increased by 1500%, thus the area is increased 16 times.
The area of a circle it proportional to the square of the diameter (area=πd^2/4), therefore the diameter must increase 4 times (diameter increase 4 times = area increase 16 times), which is increase by 500%.
Answer: B.
Answer: (B)  500%
Question: If a and b are positive even integers, and the least common multiple of a and b is expressed as a*b/w, which of the following statements could be false?
(A) n is a factor of both a and b
(B) (a*b)/n < ab
(C) ab is multiple of 2.
(D) (a*b)/n is a multiple of 2.
(E) w is a multiple of 4.
Rationale: If we divide bynand get a multiple ofaand ofb, then w must be a common factor. Answer A must be true.
Ifaandbare even integers, dividing by a factor (also an integer) results in something smaller than the productab. Answer B must be true.
If eitheraorbis even, then ab must be even. Answer C must be true.
If both are even, the smallest either number can be is 2. Thus, the smallest common factor must be 2. Answer D must be true.
Ifbis 6 andais 2,nwould be 6, which is not 4. E can be false.
Answer: (E) w is a multiple of 4.
Question: Solve the inequality
{(x^2)-7|x|+10}/{(x^2)-6x+9}
(A) -3
(B) -5
(C) 3
(D) 5
(E) 0
Rationale: taking one time |x| as +ve we get x=5 while
taking |x| as -ve we get x= -5
ANSWER:B
Answer: (B) -5
Question: A's salary is 40% of B's salary which is 25% of C's salary. What percentage of C's salary is A's salary ?
(A) 10
(B) 93
(C) 78
(D) 76
(E) 28
Rationale: Explanation:
A's Salary = 40% of B = 40% of (25% of C) = % of C = 10% of C.
Answer: A) 10
Answer: (A) 10
Question: There are 66 people in a certain community who belong to the local golf club, tennis club or both clubs. If twice as many people belong to the tennis club as belong to the golf club, what could be the number of people who belong to both clubs?
(A) 4
(B) 31
(C) 17
(D) 21
(E) 27
Rationale: let's find the range of Both and hence the range of x.66 = x + 2xx = 22In this case Both = 0 Maximum value of Both: Say there is maximum overlap between the two sets. One set has x so it could be a subset of the set 2x.66 = 2xX=33 So Both lies between 0 and 33 Only option (B) satisfies this condition. ANSWER:B
Answer: (B) 31
Question: In a class, there are 18 boys who are over 160 cm tall. If these constitute three-fourths of the boys and the total number of boys is two-thirds of the total number of students in the class, what is the number of girls in the class ?
(A) 6
(B) 12
(C) 18
(D) 24
(E) 26
Rationale: Explanation:
Let the number of boys be x. Then, (3/4)x = 18 or x = 18 x(4/3) = 24.
If total number of students is y, then (2/3) y = 24 or y = 24 x (3/2) = 36.
Therefore Number of girls in the class = (36 - 24) = 12.
Answer: B
Answer: (B) 12
Question: A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 350 m long platform?
(A) 18 min
(B) 16 min
(C) 19 min
(D) 47 min
(E) 12 min
Rationale: Let the length of the train be x m.
When a train crosses an electric pole, the distance covered is its own length.
So, x = 12 * 36 * 5 /18 m = 120 m.
Time taken to cross the platform = (120 +350)/ 36 * 5/18 = 47 min.
Answer:D
Answer: (D) 47 min