mathewhe/aqua_rat huggingface dataset:
Question: A man takes 3 hours 45 minutes to row a boat 30 km downstream of a river and 2 hours 30 minutes to cover a distance of 5 km upstream. Find the speed of the current.
(A) 1 km/hr
(B) 2 km/hr
(C) 3 km/hr
(D) 4 km/hr
(E) None of these
Rationale: Explanation:
First of all, we know that
speed of current = 1/2(speed downstream - speed upstream) [important]
So we need to calculate speed downstream and speed upstream first.
Speed = Distance / Time [important]
Speed upstream =(30/3 3/4)km/hr
=8 km/hr
Speed Downstream = (5/2 1/2)km/hr
=2km/hr
So speed of current = 1/2(8−2)
=3 km/hr
Option C
Answer: (C) 3 km/hr
Question: There are 7 man and 5 women sitting in a circle, find the all possible way so that two women wont sit together?
(A) 6!*7P5
(B) 6!*7P4
(C) 6!*7P3
(D) 5!*7P5
(E) 4!*7P5
Rationale: 7 men can sit in a circle in (7-1)!= 6! ways
no two women sit together,so woman have to sit alternate to men
there will be 7 places,in which 5 women have to sit
so women can sit in 7 places as 7P5 ways
reqd ways= 6!*7P5
ANSWER:A
Answer: (A) 6!*7P5
Question: In a stockpile of products produced by three machines M1, M2 and M3, 40% and 30% were manufactured by M1 and M2 respectively. 3% of the products of M1 are defective, 1% of products of M2 defective, while 90% of the products of M3 III are not defective. What is the percentage of defective in the stockpile?
(A) 3%
(B) 5%
(C) 4.5%
(D) 4%
(E) 6%
Rationale: Explanation :
Let there be 100 products in the stockpile. 40% and 30% were manufactured by M1 and M2 respectively. So, 30% are manufactured by M3.
Products from M1 = 40, from M2 = 30 and from M3 = 30.
Number of defective products from M1 = 0.03 x 40 = 1.2, from M2 = 0.01 x 30 = 0.3 and from M3 = 0.1 x 30 = 3
Therefore, total number of defective products = 4.5.
Answer : C
Answer: (C) 4.5%
Question: Convert the 8/36 m/s into kilometers per hour?
(A) 0.8 kmph
(B) 9.9 kmph
(C) 1.3 kmph
(D) 1.2 kmph
(E) 5.7 kmph
Rationale: 8/36 m/s = 8/36 * 18/5 = 8/10
= 0.8 kmph.
Answer: A
Answer: (A) 0.8 kmph
Question: Bill made a profit of 10% by selling a product. If he had purchased that product for 10% less and sold it at a profit of 30%, he would have received $42 more. What was his original selling price?
(A) $480
(B) $570
(C) $660
(D) $720
(E) $850
Rationale: Let P be the original purchase price of the product.
Bill originally sold the product for 1.1*P.
In the second scenario, the purchase price is 0.9*P.
A 30% profit means the selling price would be 1.3*0.9*P = 1.17*P
Thus, according to the information in the question, 1.17P - 1.1P = 42
0.07 = 42
P = 600
The original selling price was 600*1.1 = 660.
The correct answer is C.
Answer: (C) $660
Question: How many times does a clock from a right angle in 24 hours?
(A) 44
(B) 24
(C) 22
(D) 40
(E) 48
Rationale: the minute hand makes one full 360 rotation wrt the hour hand every hour, and so it passes through all of the angles, including 90 degrees and 270 degrees wrt the hour hand every hour. Both 90 and 270 degrees are right angles. Since there are 24 hours in a day, that would be 48 right angles
Answer E
Answer: (E) 48
Question: If X is the set of prime single-digit numbers and Y is a set containing each of the numbers in set X raised to the power of 2, how much greater is the median of set Y than the median of set X?
(A) 2
(B) 4
(C) 9
(D) 13
(E) 17
Rationale: set X={2,3,5,7} set of prime single digit numbers
set Y={4,9.25.49} each of the numbers in set X raised to the power of 2
Median set X= (3+5)/2= 4
Median set Y= (9+25)/2= 17
Required set Y - set X= 13
ANSWER:D
Answer: (D) 13
Question: A merchant marks his goods up by 20% and then offers a discount of 10% on the marked price. What % profit does the merchant make after the discount?
(A) 8%
(B) 10%
(C) 21%
(D) 15%
(E) 17%
Rationale: Let the price be 100.
The price becomes 120 after a 20% markup.
Now a discount of 10% on 120.
Profit=108-100
8%
answer A
Answer: (A) 8%
Question: A started a business with an investment of Rs. 70000 and after 3 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 43000, then the share of B is?
(A) 33888
(B) 36000
(C) 27778
(D) 27772
(E) 81122
Rationale: Ratio of investments of A and B is (70000 * 12) : (120000 * 9) = 7 : 36
Total profit = Rs. 43000
Share of B = 36/43 (43000) = Rs. 36000
Answer: B
Answer: (B) 36000
Question: If 3x+y=40, 2x-y=20, for integers of x and y, 3y^2=?
(A) 2
(B) 48
(C) 0
(D) 10
(E) 3
Rationale: 3x+y = 40
2x-y = 20
5x = 60
x = 12
y = 4
3y^2 = 3*16=48
Answer is B
Answer: (B) 48
Question: At a certain fast food restaurant, Brian can buy 3 burgers, 7 shakes and 1 order of fries for exactly Rs 120. At the same place it would cost Rs 164.5 for 4 burgers, 10 shakes and 1 order of fries. How much would it cost for an ordinary meal of 1burgers, 1 shakes and 1 order of fries ?
(A) Rs. 31
(B) Rs 41
(C) Rs 21
(D) Cannot be determined
(E) None of these
Rationale: Explanation :
Let the cost of 1 burger, 1 shake and 1 fries be x, y
and z.
Then
3x + 7y + z = 120 ... (i)
4x + 10y + z = 164.5 ... (ii)
x + 3y = 44.5 ... (iii) [ After subtracting (i) from (ii) ]
Multiplying (iii) by 4 and subtracting (ii) from it, we find
2y – z = 13.5 ...(iv)
Subtracting (iv) from (iii), we get x + y + z = 31.
Answer : A
Answer: (A) Rs. 31
Question: If 0.764 B = 1.236 A, then what is the value of (B - A)/(B + A) ?
(A) 0.764
(B) 0.236
(C) 2
(D) 0.472
(E) None
Rationale: Answer
Given, 0.764 B = 1.236 A
⇒ B/A = 1.236 / 0.764
Now, (B - A)/(B + A) = (B/A - 1) / (B/A + 1)
= (1.236/0.764 - 1) / (1.236/0.764 + 1)
= (1.236 - 0.764)/(1.236 + 0.764)
= 0.472/2.000
= 0.236
Correct Option: B
Answer: (B) 0.236
Question: A certain car dealership offers its newest model in ten exterior and ten interior colors. If the ten interior colors are identical to the ten exterior colors, and the dealership sells every pair of colors except those that would result in a car with an identically colored interior and exterior, how many different color combinations are possible?
(A) 45
(B) 81
(C) 90
(D) 10!/2!
(E) 10!
Rationale: The question says there are 10 different colors.
Since interior and exterior are to be painted with different colors, the order is important while counting the color combination.
Therefore, the number of possible ways can be found out by permutation of 2 colors out of 10 colors.
10P2 = 10!/(10-2)! = 10!/8! = 90 [10P2 = 10C2*2!]
Answer: (C
Answer: (C) 90
Question: The average of six numbers is 3.65. The average of two of them is 3.4, while the average of the other two is 3.85. What is the average of the remaining two numbers ?
(A) 4.7
(B) 4.6
(C) 4.2
(D) 4.1
(E) 3.7
Rationale: Explanation:
Sum of the remaining two numbers = (3.65 * 6) - [(3.4 * 2) + (3.85 * 2)]
= 21.90 - (6.8 + 7.7) = 21.90 - 14.5 = 7.4.
Required average = (7.4 / 2) = 3.7.
Answer: E) 3.7
Answer: (E) 3.7
Question: A and B rent a pasture for 10 months. A put in 80 cows for 7 months. How many can B put in for the remaining 3 months, if he pays half as much again as A?
(A) 2: 7
(B) 2: 0
(C) 2: 4
(D) 2: 3
(E) 2: 1
Rationale: 80* 7: x* 3 = 1:1 1/2
560: 3x = 2: 3
x = 280.Answer:D
Answer: (D) 2: 3
Question: On a certain day, Tim invested $500 at 10 percent annual interest, compounded annually, and Lana invested 900 at 5 percent annual interest, compounded annually.The total amount of interest earned by Tim’s investment in the first 2 years was how much greater than the total amount of interest earned by Lana’s investment in the first 2 years?
(A) $5
(B) $12.75
(C) $51.75
(D) $100.75
(E) $105
Rationale: Compounded annually means that the interest is applied once per year. One can have 10% annual interest compounded monthly - in this case 10%/12 would be applied each month, or 10% annual interest compounded daily etc.
With respect to the problem at hand, at the end of two years, Tim would have
500(1.10)^2 = 500(1.21) = 605
and Lana would have
900(1.05)^2 = 900(1.1025) = 992.25
Thus, Tim earned 105 dollars, while Lana earned 92.25 dollars
The difference is $12.75 and the answer is B.
Answer: (B) $12.75
Question: If the sum of a set of 5 different positive prime numbers is 94, what is the difference between smaller 2 prime numbers between them?
(A) 6
(B) 4
(C) 5
(D) 9
(E) 11
Rationale: All prime numbers apart from 2 are odd.
Even + Even = Even
Odd + Even = Odd
Odd + Odd = Even
We are given 5 different prime numbers, whose sum is 94 i.e even
If we include 2, we will have 4 odd prime numbers and one even.
This sum would be odd
If we exclude 2, we will have 5 odd numbers.
This sum would be even
Hence 2 is included.
The possible 5 no. are = 11+7+2+43+31 = 94
difference between smaller 2 prime numbers between them = 7 - 2 = 5
Ans - C
Answer: (C) 5
Question: If 6 (A's capital) = 8 (B's capital) = 12 (C's capital). Then the ratio of their capitals is?
(A) 20:15:16
(B) 4:3:1
(C) 4:3:2
(D) 20:15:11
(E) 20:15:19
Rationale: 6A = 8B = 12 C
A:B:C = 1/6:1/8:1/12
= 4:3:2
Answer: C
Answer: (C) 4:3:2
Question: How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
(A) 22
(B) 30
(C) 88
(D) 26
(E) 12
Rationale: Speed of train relative to man = 63 - 3 = 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 500 * 3/50
= 30 sec.
Answer: B
Answer: (B) 30
Question: The ratio of two numbers is 3:4 and their sum is 35. The greater of the two numbers is?
(A) 12
(B) 20
(C) 16
(D) 17
(E) 19
Rationale: 3:4
Total parts = 7
= 7 parts --> 35 (7 Ã— 5 = 35)
= 1 part ---->5 (1 Ã— 5 = 5)
= The greater of the two number is = 4
= 4 parts ----> 20 (4 Ã— 5 = 20)
B)
Answer: (B) 20
Question: Tough and Tricky questions: Exponents.
If a and b are positive integers and x = 26^a and y = 9^b, which of the following is a possible units digit of xy?
(A) 1
(B) 6
(C) 5
(D) 7
(E) 8
Rationale: Only Units digit of X and Y contribute to the Units digit of XY.
Finding all values ofXfor positive values ofa
When,
a=1; X=26
a=2; X=676
a=3; X=17576........ Units digit repeat in a cycle of 6,6,6,6......
Similarly, Finding all values of Y for positive values of b
When,
b=1; Y=9
b=2; Y= 81
b=3; Y= 729....... Units digit repeat in cycle of 9,1,9,1....
So, possible value of Units digit of XY can be found by considering all possibilities of Units digit of X and Y
When X=6 and Y=9: Units digit of XY = 4
When X=6 and Y=1: Units digit of XY = 6
When X=6 and Y=9: Units digit of XY = 4
When X=6 and Y=1: Units digit of XY = 6
Only two possibilities for Units digit of XY i.e. 4 and 6.
Only 6 is given in answer choices, therefore answer is B
Answer: (B) 6
Question: A coin is tossed live times. What is the probability that there is at the least one tail?
(A) 31/32
(B) 31/37
(C) 31/67
(D) 31/17
(E) 31/31
Rationale: Let P(T) be the probability of getting least one tail when the coin is tossed five times.
= There is not even a single tail.
i.e. all the outcomes are heads.
= 1/32 ; P(T) = 1 - 1/32
= 31/32
Answer: A
Answer: (A) 31/32
Question: A train 108 m long moving at a speed of 50 km/hr crosses a train 112 m long coming from opposite direction in 6 seconds. What is the speed of the second train ?
(A) 48 km/hr
(B) 54 km/hr
(C) 66 km/hr
(D) 82 km/hr
(E) 89 km/hr
Rationale: Let speed of d second train= xkm/hr
Distance covered=(108+112)=220m=0.22km
Time=6sec= 6/3600hr =1/600hr
So
1/600hr= 0.22km/(50+x)
x=82km/hr
answer :D
Answer: (D) 82 km/hr
Question: The average of first five multiples of 7 is?
(A) 6
(B) 8
(C) 9
(D) 5
(E) 21
Rationale: Average = 7(1 + 2 + 3 + 4 + 5)/5
= 105/5
= 21.
Answer:E
Answer: (E) 21
Question: The length of the bridge, which a train 140 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 328
(B) 279
(C) 235
(D) 288
(E) 211
Rationale: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (140 + X)/30 = 25/2 ==> 2(140 + X) = 750 ==> X = 235 m.Answer: C
Answer: (C) 235
Question: If 2^x + 2^y = x^2 + y^2, where x and y are non negative and non zero integers, what is the greatest possible value of x + y possible from options below?
(A) 4
(B) 5
(C) 2
(D) 3
(E) none of these
Rationale: x + y for x and y 2^x + 2^y = x^2 + y^2
A. x= y x=y=2 4 + 4 = 4 + 4 right
B. x=2, y=3 4 + 8 = 4 + 9 wrong
C. x=1, y=1 2 + 2 = 1 + 1 wrong
D. x=2, y =1 4 + 2 = 4 + 1 wrong
E. as option A is correct E is wrong
My answer is A.
Answer: (A) 4
Question: A jar contains only red, yellow, and orange marbles. If there are 1 red, 5 yellow, and 4 orange marbles, and 3 marbles are chosen from the jar at random without replacing any of them, what is the probability that 2 yellow, 1 red, and no orange marbles will be chosen?
(A) 1/60
(B) 1/45
(C) 2/45
(D) 3/22
(E) 5/22
Rationale: I started by finding the 2 probabilities, without calculation, like this:
P(YYR)
P(YRY)
P(RYY)
I calculated the first one and ended in 1/22. I looked at the answer choices at this point and saw answer D: 1/45.
This helped me realise that for the 3 possible orderings the probabbility is the same. So, it should be (1/45)*(1), which indeed is 1/45.
B
Answer: (B) 1/45
Question: The average age of husband, wife and their child 3 years ago was 25 years and that of wife and the child 5 years ago was 18 years. The present age of the husband is:
(A) 34 Years
(B) 36 Years
(C) 38 Years
(D) 39 Years
(E) 40 Years
Rationale: Sum of the present ages of husband, wife and child = (25 x 3 + 3 x 3) years = 84 years.
Sum of the present ages of wife and child = (18 x 2 + 5 x 2) years = 46years.
Husband's present age = (84 - 46) years = 38 years.
answer : C
Answer: (C) 38 Years
Question: a person travels from his house to office from 11:10am to 12:10 am and covers a distence of 20km. find the average speed of the person.
(A) 20.1km/h
(B) 20.5km/h
(C) 21.1km/h
(D) 22.1km/h
(E) 20km/h
Rationale: time=12:10-11:10=1 hour
distance=20km
speed=20*1=20km/h
ANSWER:E
Answer: (E) 20km/h
Question: When processing flower-nectar into honey bees' extract, a considerable amount of water gets reduced. How much flower-nectar must be processed to yield 1kg of honey, if nectar contains 50% water, and the honey obtained from this nectar contains 25% water?
(A) 1.2 kg
(B) 1.5 kg
(C) 1.7 kg
(D) 1.9 kg
(E) None of these
Rationale: Explanation :
Flower-nectar contains 50% of non-water part.
In honey this non-water part constitutes 75% (100-25).
Therefore 0.5 X Amount of flower-nectar = 0.75 X Amount of honey = 0.75 X 1 kg
Therefore amount of flower-nectar needed =
(0.75/0.51)kg=1.5 kgs
Answer : B
Answer: (B) 1.5 kg
Question: Calculate the number of bricks, each measuring 25 cm * 15 cm * 8 cm required to construct a wall of dimensions 10 m * 4 m * 5 m when 10% of its volume is occupied by mortar?
(A) 3388
(B) 27678
(C) 6000
(D) 2977
(E) 27681
Rationale: 10 * 4/100 * 5 * 90/100 = 25/100 * 15/100 * 8/100 * x
10 * 20 * 90 = 15 * 2 * x => x = 6000
Answer:C
Answer: (C) 6000
Question: A sum of money is sufficient to pay C's wages for 12 days and D's wages for 4 days. The same money is sufficient to pay the wages of both for?
(A) 3
(B) 4
(C) 5
(D) 2
(E) 1
Rationale: Let the total money be $x
C's 1day work = $ x/12
D's 1day work = $ x/4
C+D 1day work = $ x/3
Money is sufficient to pay the wages of both for 3days
Answer is A
Answer: (A) 3
Question: what is the next term of this series6,10,9,15,12,20,15,25,18...?
(A) 9
(B) 10
(C) 11
(D) 12
(E) 30
Rationale: 3&2=6;
5*2=10;
3*3=9;
3*5=15
3*4=12
5*4=20
3*5=15
5*5=25
3*6=18
5*6=30.
ANSWER:E
Answer: (E) 30
Question: A beekeeper has 300,000 bees living in seven beehives. Among these beehives, the sizes of the beehives are proportional to the numbers of bees living in them. No beehive has less than 80% the number of bees of any other beehive. What is the maximum possible number of bees that the greatest beehive could have?
(A) 40,000
(B) 51724
(C) 60,000
(D) 80,000
(E) 90,000
Rationale: x be the # of bees in the hive with the max # of bees. Let other hives have same # of bees. So, x+6*(0.8)*x = 300,000 => 5.8x = 300,000 => x = 51724.
B is the answer.
Answer: (B) 51724
Question: Surekha started a business investing Rs.25,000 in 1999. In 2000, he invested an additional amount of Rs. 10,000 and Rajesh joined him with an amount of Rs. 35,000. In 2001, Surekha invested another additional amount of Rs.10,000 and Jay joined them with an amount of Rs.35,000. What will be Rajesh's share in the profit of Rs.2,40,000 earned at the end of 3 years from the start of the business in 1999?
(A) Rs 45000
(B) Rs 50000
(C) Rs 70000
(D) Rs 80000
(E) None
Rationale: Surekha:Rajesh:Jay= (25000×12+35000×12+45000×12):(35000×24) : (35000×12) = 1260000 : 840000 : 420000 = 3 : 2 : 1. Rajesh's share =Rs.(240000×2/6) = Rs.80000.
Answer D
Answer: (D) Rs 80000
Question: Rahul can do a work in 3 days while Rajesh can do the same work in 2days. Both of them finish the work together and get $105. What is the share of Rahul?
(A) $50
(B) $42
(C) $60
(D) $100
(E) $90
Rationale: Rahul's wages: Rajesh's wages = 1/3 : 1/2 = 2:3
Rahul's share = 105*2/5 = $42
Answer is B
Answer: (B) $42
Question: The odds against ram solving the problem are 5 to 3 and the odds in favour of krishna solving the same are 7 to 5. What is the chance that it will be solved when they both try?
(A) 1/4
(B) 5/21
(C) 16/21
(D) 23/28
(E) 71/96
Rationale: Odds against Ram are 5:3 so probability that he will solve the problem is 3/8.
Odds in favor of Krishna are 7:5 so probability that he will solve it is 7/12
It will be solved means that either Ram or Krishna or both will be able to solve it.
P(A or B) = P(A) + P(B) - P(A and B) = 3/8 + 7/12 - (3/8)*(7/12) = 71/96
E
Answer: (E) 71/96
Question: A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 54 years now, the son's age five years back was?
(A) 18years
(B) 19years
(C) 20years
(D) 21years
(E) 22years
Rationale: Let the son's present age be x years. Then, (54 - x) = x
2x = 54.
x = 27.
Son's age 5 years back (27 - 5) = 22 years.
E
Answer: (E) 22years
Question: The distance between Station Atena and Station Barcena is 90 miles. A train starts from Atena towards Barcena. A bird starts at the same time from Barcena straight towards the moving train. On reaching the train, it instantaneously turns back and returns to Barcena. The bird makes these journeys from Barcena to the train and back to Barcena continuously till the train reaches Barcena. The bird finally returns to Barcena and rests. Calculate the total distance in miles the bird travels in the following two cases:
(a) The bird flies at 90 miles per hour and the speed of the train is 60 miles per hour.
(b) the bird flies at 60 miles per hour and the speed of the train is 90 miles per hour
(A) 135miles,60miles
(B) 134miles,60miles
(C) 135miles,70miles
(D) 136miles,60miles
(E) 135miles,80miles
Rationale: A) There is no need to consider their meeting pointt at all.
The train has been running for 90miles/(60miles/hr)=1.5hrs.
bird flies till train reaches destination from starting point.so bird flies for1.5hrs at the vel given(90).so distance=1.5*90=135miles
b) time of train=1hr.so distance of bird=60*1=60miles
Answer A
Answer: (A) 135miles,60miles
Question: At what rate percent of simple interest will a sum of money double itself in 11 years?
(A) 9.09 %
(B) 4.54 %
(C) 8 .2 %
(D) 4.94 %
(E) 5.54 %
Rationale: Let sum = x. Then, S.I. = x.
Rate = (100 * S.I.) / (P * T) = (100 * x) / (x * 11)
= 100/11 = 9.09 %
ANSWER:A
Answer: (A) 9.09 %
Question: The population of a city is 415600.It increased by 25% in the first year and decreased by 30% in the second year.What is the population of the city at the end of second year?
(A) 367300
(B) 363580
(C) 363650
(D) 373650
(E) 386750
Rationale: As per given data, P = 415600, R1= 25% incresed, R2 = 30% decreased
Population of the city at the end of the second year= P (1+R1/100) (1-R2/100)
= 415600 (1+25/100) (1-30/100)
=363650
ANSWER:C
Answer: (C) 363650
Question: Evaluate: 1222343 - 12*3*2 =?
(A) 122336
(B) 145456
(C) 122347
(D) 126666
(E) 383838
Rationale: According to order of operations, 12?3?2 (division and multiplication) is done first from left to right
12**2 = 4* 2 = 8
Hence
1222343 - 12*3*2 = 122343 - 8 = 122336
correct answer A
Answer: (A) 122336
Question: Jo's collection contains US, Indian and British stamps. If the ratio of US to Indian stamps is 5 to 2 and the ratio of Indian to British stamps is 5 to 1, what is the ratio of US to British stamps?
(A) 25 : 8
(B) 25 : 0
(C) 25 : 8
(D) 25 : 2
(E) 25 : 9
Rationale: Indian stamps are common to both ratios. Multiply both ratios by factors such that the Indian stamps are represented by the same number.
US : Indian = 5 : 2, and Indian : British = 5 : 1. Multiply the first by 5, and the second by 2.
Now US : Indian = 25 : 10, and Indian : British = 10 : 2
Hence the two ratios can be combined and US : British = 25 : 2
Answer:D
Answer: (D) 25 : 2
Question: A completes a work in 12 days and B complete the same work in 24 days. If both of them work together, then the number of days required to complete the work will be?
(A) 8 days
(B) 9 days
(C) 11 days
(D) 13 days
(E) 14 days
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days
Therefore, here, the required number of days = 12 × 24/ 36 = 8 days
A)
Answer: (A) 8 days
Question: Of the 50 researchers in a workgroup, 40 percent will be assigned to Team A and the remaining 60 percent to Team B. However, 60 percent of the researchers prefer Team A and 30 percent prefer Team B. What is the lowest possible number of researchers who will NOT be assigned to the team they prefer?
(A)  10
(B)  17
(C)  20
(D)  25
(E)  30
Rationale: I solved it by assuming 100 people and then dividing my answer in two to save time on calculations. (percentage equals number of people) In that case
40 will be in team A
60 will be in team B
The larger diff is
70 want team A so diff is 60-40=20. At least 20 people will NOT get their wish, so for 50 researchers the same number is 10.
Answer choice A
Answer: (A)  10
Question: Rs. 2600 is divided into three parts A, B and C. How much A is more than C if their ratio is 1/2:1/3:1/4?
(A) 187
(B) 187
(C) 300
(D) 600
(E) 555
Rationale: 1/2:1/3:1/4
= 6:4:3
3/13*2600
= 300
Answer: D
Answer: (D) 600
Question: A dishonest dealer professes to sell goods at the cost price but uses a weight of 600 grams per kg, what is his percent?
(A) 28%
(B) 66.7%
(C) 55%
(D) 28%
(E) 55%
Rationale: 600 --- 400
100 --- ? => 66.7%
Answer: B
Answer: (B) 66.7%
Question: A trader bought a car at 20% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price?
(A) 12%
(B) 15 %
(C) 86 %
(D) 42 %
(E) 16%
Rationale: Explanation:
Original price = 100
CP = 80
S = 80*(140/100) = 112
100 - 112 = 12%
Answer:A
Answer: (A) 12%
Question: A cistern has a leak which would empty the cistern in 20 minutes. A tap is turned on which admits 4 liters a minute into the cistern, and it is emptied in 24 minutes. How many liters does the cistern hold?
(A) 480
(B) 488
(C) 882
(D) 269
(E) 298
Rationale: 1/x - 1/20 = -1/24
x = 120
120 * 4 = 480
Answer: A
Answer: (A) 480
Question: The length of a train and that of a platform are equal.If with a speed of 90 kmph the train crosses the platform in one minute,then the length of the train in metres is
(A) 500
(B) 600
(C) 750
(D) 900
(E) 950
Rationale: 2x will be the distance travelled by the train if the length of the train= the length of the platform = x as distance= speed*time
distance=2x
speed in kmph=90
speed in mps=90*5/18
as dist=speed*time
2x=(90*5/18)*(60sec)
on solving x=900mts
ANSWER:D
Answer: (D) 900
Question: A and B started a business with their capitals Rs. 3,00,000 and 18,00,000 respectively. Annual profit will be distributed between them in the ratio
(A) 2:5
(B) 2:3
(C) 1:3
(D) 1:6
(E) 1:9
Rationale: 3,00,000:18,00,000
Ans. 1:6
ANSWER:D
Answer: (D) 1:6