mathewhe/aqua_rat huggingface dataset:
Question: A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
(A) 239
(B) 240
(C) 288
(D) 282
(E) 238
Rationale: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 20 = 300 m.
Let the length of the platform be x m . Then,
(x + 300)/36 = 15 => x = 240 m.
Answer: B
Answer: (B) 240
Question: Vijay sells a cupboard at 12% below cost price. Had he got Rs.1650 more, he would have made a profit of 12%. What is the cost price of the cupboard?
(A) 7450
(B) 14900
(C) 7400
(D) 6875
(E) None of these
Rationale: Explanation:
Cost price = 1650/(0.12 + 0.12) = 2086/0.24
= Rs.6875
ANSWER D
Answer: (D) 6875
Question: A worker can load one truck in 6 hours. A second worker can load the same truck in 8 hours. If both workers load one truck simultaneously while maintaining their constant rates, approximately how long, in hours, will it take them to fill one truck?
(A) 2.6
(B) 2.8
(C) 3.0
(D) 3.2
(E) 3.4
Rationale: The workers fill the truck at a rate of 1/6 + 1/8 = 14/48 = 7/24 of the truck per hour.
Then the time to fill one truck is 24/7 which is about 3.4 hours.
The answer is E.
Answer: (E) 3.4
Question: From a bunch of four keys, three particular keys have to be used to open a combination lock, such that the second key can be used only after the first key and the third key can be used only after the second key. What are the chances of opening the lock in a random selection of three keys?
(A) 1/24
(B) 1/36
(C) 1/60
(D) 1/80
(E) 1/120
Rationale: The probability is 1/4*1/3*1/2 = 1/24.
The answer is A.
Answer: (A) 1/24
Question: A contractor is engaged for 30days on the condition thathe receives Rs.25 for each day he works &is fined Rs.7.50 for each day is absent. He gets Rs.360 in all. For how many days was he absent?
(A) 8
(B) 12
(C) 15
(D) 17
(E) 19
Rationale: 30 * 25 = 750
360
-----------
380
25 + 7.50 = 32.5
390/32.5 = 12
B
Answer: (B) 12
Question: On a certain transatlantic crossing, 10 percent of a ship's passengers held round-trip tickets and also took their cars aboard the ship. If 60 percent of the passengers with round-trip tickets did not take their cars aboard the ship, what percent of the ship's passengers held round-trip tickets?
(A) 33 1/3%
(B) 40%
(C) 50%
(D) 25%
(E) 66 2/3%
Rationale: On a certain transatlantic crossing, 20 percent of a ship’s passengers held round-trip tickets and also took their cars abroad the ship. If 60 percent of the passengers with round-trip tickets did not take their cars abroad the ship, what percent of the ship’s passengers held round-trip tickets?
Solution: Let total number of passengers be 100
According to Q stem 40% of passengers who had round-trip tics have taken cars - let number of passengers with round trip be X then
40% of X = 10 => X= 25.
Answer D
Answer: (D) 25%
Question: If a number is subtracted from its square we get 272. Find the number?
(A) 22
(B) 29
(C) 17
(D) 29
(E) 11
Rationale: Explanation:
x2 â€“ x = 272 => x =17
Answer: C
Answer: (C) 17
Question: The ages of Patrick and Michael are in the ratio of 3 : 5 and that of Michael and Monica are in the ratio of 3 : 5. If the sum of their ages is 245, what is the difference between the ages of Patrick and Monica?
(A) 27
(B) 48
(C) 80
(D) 72
(E) 18
Rationale: Ages of P and Mi=3x:5x
Ages of Mi and Mo=3x:5x
Rationalizing their ages. ratio of their ages will be 9x:15x:25x
Sum=49x=245
x=5
Difference if ages of Pa and Mo=25x-9x=16x=16*5=80
Answer C
Answer: (C) 80
Question: What is the next number of the following sequence
108,58,50,8,?
(A) 40
(B) 50
(C) 30
(D) 42
(E) 35
Rationale: 108-58=50
58-50=8
50-8=42
therefore next no. is 42
ANSWER:D
Answer: (D) 42
Question: In 10 years, A will be twice as old as B was 10 years ago. If A is now 9 years older than B the present age of B is
(A) 37
(B) 38
(C) 39
(D) 40
(E) 41
Rationale: let present age of A be a and B be b
a+10 = 2*(b-10)
=> 2b-a = 30 ......(i)
a = b+9
=>2b-b-9 = 30
b=39
so the present age of b is 39 years
ANSWER:C
Answer: (C) 39
Question: A store sells two kinds of birdseed. If brand a is 40% millet and 60% sunflower and brand b is 65% millet and 35% sunflower . A customers purchases a mix of the two types that is 50% millet. What percent is brand A
(A) 30
(B) 40
(C) 50
(D) 60
(E) 70
Rationale: Let "a" and "b" be the amount of brand A and brand B respectively in the mixture.
Total amount of the mixture = a+b
Amount of millet in the mixture = 40% of a + 65 % b . This is also equal to 50% of the mixture as per the question i.e (a+b)/2
.4 a + .65 b = (a+b)/2 => .8a +1.3 b = a+b => .3b =.2 a => b =(2/3)a
We have to find the percent of brand A in the total mixture i.e (a/(a+b)) * 100 = (a/(a+(2/3)a))*100 = (3/5)*100 = 60%
ANSWER:D
Answer: (D) 60
Question: Stuart bought a sweater on sale for 30% off the original price and another 25% off the discounted price. If the original price of the sweater was $120, what was the final price of the sweater?
(A) $25.75
(B) $35.75
(C) $63
(D) $ 45.75
(E) $15.75
Rationale: The price with 30% off
120 - 30% of 120 = 120 - (30 / 100) *120 = 84
The price with another 25% off
84 - 25% of 84 = 84 - (25/100)* 84 = $63
correct answer C
Answer: (C) $63
Question: The list price of an article is Rs.68. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?
(A) 3.23%
(B) 4.23%
(C) 5.23%
(D) 7.23%
(E) 8.23%
Rationale: 68*(90/100)*((100-x)/100) = 56.16
x = 8.23%
ANSWER:E
Answer: (E) 8.23%
Question: There are 48 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) 1) 4
(B) 2) 7
(C) 3) 17
(D) 4) 18
(E) 5) 27
Rationale: x -> Golf Club
2x -> Tennis Club
y -> both
x+2x-y = 48
3x - y =48
multiples of 3 greater than 48
51
54
57
60
63
66 - 18= 48
IMO (D)
Answer: (D) 4) 18
Question: A professional janitor can clean a certain high school in 8 hours, working at a constant rate. A student sentenced to detention can clean that same high school in (10*2) hours, also working at a constant rate. If the student is paid $7 total per hour and the janitor is paid $21 per hour, how much more would it cost the school to pay the janitor to do the job himself than it would to pay the student and the janitor to do the job together?
(A) -$56
(B) -$6
(C) $0
(D) $6
(E) $8
Rationale: A professional janitor can clean a certain high school in 8 hours
So (applying rule #1), the janitor can clean 1/8 of the school in ONE HOUR
A student sentenced to detention can clean that same high school in (10*2) or 20 hours
So (applying rule #1), the student can clean 1/20 of the school in ONE HOUR
So, COMBINED, the student and janitor can clean (1/8 + 1/20) of the school in ONE HOUR
1/8 + 1/20 = 5/40 + 2/40 = 7/40
So, in ONE HOUR they can clean 7/40 of the school.
Applying rule #2, it will takethem40/7 hoursto clean the ENTIRE school.
The janitor earns $21/hour and the student earns $7/hour, so their combined rate is$28/hour.
Theircombined wages= (pay rate)(time) = ($28/hour)(40/7 hours) =$160
Working ALONE, the janitor takes 8 hours and earns $21/hour
So, working alone, the janitor's earnings = (pay rate)(time) = ($21/hour)(8 hours) =$168
$168-$160= $8, so the answer is E
Answer: (E) $8
Question: If the average (arithmetic mean) of five consecutive integers is k + 2, then the product of the greatest and least integer is
(A) k^2 - 9
(B) k^2 - 2k + 1
(C) k^2 + 4k
(D) k^2 + 6k + 9
(E) k^2 + 4k - 12
Rationale: n = smallest number
n+4 = largest number
(n + n + 4)/2 = k+2
=> (2n+4)/2 = k+ 2
=> n + 2 = k + 2
=> n = k
So Product of n and n+4 = (k)(k+4)
= k^2 + k
= k^2 + 4k
Answer - C
Answer: (C) k^2 + 4k
Question: If 313,252 football shoes need to be placed in boxes and each box can contain at most 11 pair of football shoes. How many pair of football shoes will be in the last unfilled box?
Options:
(A) 5 football shoes
(B) 3 football shoes
(C) 4 football shoes
(D) 7 football shoes
(E) 9 football shoes
Rationale: The number of football shoes that can be placed in boxes of 11 football shoes is the first number that is divisible by 11 that occurs before 313,252
In order to divide the sum in 11 parts, the amount must be divisible by 11
Divisibility rule of 11: Subtract the last digit from the remaining leading truncated number. If the result is divisible by 11, then so was the first number 313,252->31325-2=>3132-3=3129->312-9=303->30-3=27
Hence, we need to remove 5 to this number for it to be divisible by 11
Correct Option: A
Answer: (A) 5 football shoes
Question: In the equation ax^2 + bx + c = 0 a, b, and c are constants, and abc # 0. If one root of the equation is -2, and b = 6a then which of the following is c equal to?
(A) a/12
(B) a/8
(C) 6a
(D) 8a
(E) 12a
Rationale: The sum of the roots is = -b/a = -6a/a = -6. Let the other root be x. Thus, x-2 = -6
x = -4. Again, the product of the roots is -2*-4 = 8. Thus, c/a = 8. c = 8a.
D.
Answer: (D) 8a
Question: A car during its journey travels 30 minutes at a speed of 40 kmph, another 45 minutes at a speed of 80 kmph, and 2 hours at a speed of 50 kmph.The average speed of the car is
(A) 60.07 kmph
(B) 55.38 kmph
(C) 50.02 kmph
(D) 44.02 kmph
(E) None of these
Rationale: First car travels 30 min at speed of 40 kmph
distance = 40 x 1/2 = 20 m
Then car travels 45 min at a speed of 80 kmph
distance = 45 min at speed of 80 kmph
distance = 80 x 3/4 = 60 m
at last it travels 2 hours at speed of 50 kmph
distance = 50 x 2 = 100 m
Total distance = 20 + 60 + 100 = 180
Total time= 1/2 + 3/4 + 2 = 3.25
Average speed of the car = 180/3.25 = 55.38
ANSWER:B
Answer: (B) 55.38 kmph
Question: A tourist purchased a total of $1,550 worth of traveler’s checks in $10 and $50 denominations, During the trip the tourist cashed 7 checks and then lost all of the rest. If the number of $10 checks cashed was one more or one less than the number of $50 checks cashed, what is the minimum possible value of the checks that were lost?
(A) $1,430
(B) $1,320
(C) $1,290
(D) $1,270
(E) $1,150
Rationale: since total cashed checks = 7 ans $10 check cashed = one less or more than $50 checks
Therefore either $10 checks = 3 and $50 checks = 4 OR $10 checks = 4 and $50 checks = 3
using this information 1st option gives us the maximum cashed value therefore if we negate this value from total value we will get minimum value of which checks have lost
Therfore 1550 - 230 = 1320 hence answer is B
Answer: (B) $1,320
Question: Two persons A and B can complete a piece of work in 40 days and 60 days respectively. If they work together, what part of the work will be completed in 6 days?
(A) 1/8
(B) 1/3
(C) 1/6
(D) 1/2
(E) 1/4
Rationale: A's one day's work = 1/40
B's one day's work = 1/60
(A + B)'s one day's work = 1/40 + 1/60 = 1/24
The part of the work completed in 6 days = 6 (1/24) = 1/4.
Answer:E
Answer: (E) 1/4
Question: Find the no.of ways of arranging the boy and 8 guests at a circular table so that the boy always sits in a particular seat?
(A) 5!
(B) 8!
(C) 9!
(D) 11!
(E) 12!
Rationale: Ans.(B)
Sol. Total number of persons = 9 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 8 places in 8P8 = 8! Ways ... The number of required arrangements = 8! x 1= 8! = 8! ways
Answer: (B) 8!
Question: A trader has 60 kg of rice, a part of which he sells at 14% profit and rest at 6% loss. On the whole his loss is 4% . What is the quantity sold at 14% profit and that at 6% loss?
(A) 6 and 54 kg
(B) 10 and 40 kg
(C) 15 and 35 kg
(D) 20 and 30 kg
(E) 40 and 30 kg
Rationale: Alligation Method
I PART II PART
14 (x1) -6 (x2)
\ /
x
/ \
(x2-x) (x-x1)
2 18
1 9
Ratio of quantities sold at 14% profit and 6% loss = 1: 9
Quantity sold at 14% profit = 60/1+9 *1 = 6 kg
Quantity sold at 6% loss = 60/1+9 *9 = 54kg
ANSWER:A
Answer: (A) 6 and 54 kg
Question: Sum of products of three numbers taken two at a time is 131. Sum of squares of the three numbers is 138. What is the sum of the three numbers?
(A) 25
(B) 30
(C) 20
(D) 22
(E) 21
Rationale: Explanation:
All the data given in the question points to the equation mentioned below:
Considering the three numbers to be a,b and c:
(a+b+c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
Accordingly, substitute for a, b and c and solve:
=> a2+b2+c2= 138, ab+bc+ac = 131. Thus, 2(ab+bc+ac)= 2*131= 262
(a+b+c)2= 138+262= 400.
Therefore, a+b+c= 20
ANSWER: C
Answer: (C) 20
Question: What annual payment will discharge a debt of Rs. 1025 due in 2 years at the rate of 5% compound interest?
(A) Rs. 551.29
(B) Rs. 551.25
(C) Rs. 551.21
(D) Rs. 551.22
(E) Rs. 551.23
Rationale: Explanation:
Let each installment be Rs. x. Then,
x/(1 + 5/100) + x/(1 + 5/100)2 = 1025
820x + 1025 * 441
x = 551.25
So, value of each installment = Rs. 551.25
Answer:B
Answer: (B) Rs. 551.25
Question: P is a prime number. If 6p is between 15 and 95, which of the following Y can be a value of 7p + 2?
(A) 15
(B) Y=79
(C) 121
(D) 65
(E) 21
Rationale: [3,5,7,11,13] are prime numbers that fits this equation 15< 6X <95. Afterwards subtract 2 from all the answer n see if it's divisible by 7. Therefore A and E are out. Leaves out with B C D.
B =11
C =17
D = 9
Only 11 is the set of prime numbers that fit between 15 and 95. Therefore 79 is the answer.B
Answer: (B) Y=79
Question: If a trader sold two cars each at Rs. 325475 and gains 12% on the first and loses 12% on the second, then his profit or loss percent on the whole is?
(A) 1.44%
(B) 1.74%
(C) 1.84%
(D) 1.54%
(E) 1.24%
Rationale: SP of each car is Rs. 325475, he gains 12% on first car and losses 12% on second car.
In this case, there will be loss and percentage of loss is given by
= [(profit%)(loss%)]/100
= (12)(12)/100 % = 1.44%
Answer:A
Answer: (A) 1.44%
Question: Peter rolls three dice at the same time. What is the probability that all the dices will show the same number?
(A) a) 1/12
(B) b) 1/36
(C) c) 1/6
(D) d) 1/36
(E) e) 1/3
Rationale: We can have 6 different outcomes on a dice.
Total outcomes on two dices = 6*6*6 = 216
We need only the cases when Peter the same number with all the dices, that means only the outcomes in which the numbers on all three dices are same
They can be {1, 1, 1}, {2, 2, 2}, {3, 3, 3}, {4, 4, 4}, {5, 5, 5}, {6, 6, 6}.
A total of 6 outcomes
Probability = favorable outcomes/ total outcomes = 6/216 = 1/36.
Option D
Answer: (D) d) 1/36
Question: A man leaves a point P at 6 a.m. and reaches the point Q at 10 a.m. another man leaves the point give at 8 a.m. and reaches the point P at 12 noon. At what time do they meet?
(A) 7 a.m.
(B) 10 a.m.
(C) 9 a.m.
(D) 3 a.m.
(E) 6 a.m.
Rationale: Explanation:
9 a.m.
Answer: Option C
Answer: (C) 9 a.m.
Question: Before leaving home for the town of Madison, Pete checks a map which shows that Madison is 5 inches from his current location, Gardensquare. Pete arrives in Madison 1.5 hours later and drove at an average speed of 60 miles per hour. At what scale, in inches per mile, is the map drawn?
(A) 1/3
(B) 1/18
(C) 1/10
(D) 2
(E) 30
Rationale: Pete covered 1.5*60=90 miles which correspond to 5 inches on the map --> scale in inches per mile is 5/90=1/18.
Answer: B.
Answer: (B) 1/18
Question: Vijay invested Rs.50,000 partly at 10% and partly at 15%. His total income after a year was Rs.7000. How much did he invest at the rate of 10%?
(A) Rs.40,000
(B) Rs.40,000
(C) Rs.12,000
(D) Rs.20,000
(E) None
Rationale: Solution:
The best way to solve this problem is by using the concept in Mixtures and Alligation.
Vijay earned a total income of Rs.7000 for his investment of 50,000.
Therefore, his average rate of return = 7000/50000 * 100
By rule of alligation, if the value of one of the products is 10 (cheaper) and the other is 15 (dearer) and if the two are mixed such that the average value of the mixture is 14 (mean price), then the two products have been mixed in the following ratio.
The ratio of
Cheaper product : Dearer product
(Dearer product price - mean price) : (Mean price - cheaper product price)
In our example, the cheaper product is the investment at 10%, the dearer product is the investment at 15% and the mean price is the average return of 14%.
Therefore, the amount invested @10% interest = 1/5 * 50,000 = 10,000.
Answer B
Answer: (B) Rs.40,000
Question: From a pack of 52 cards, 1 card is drawn at random. What is the probability that a red king is drawn?
(A) 1/2
(B) 1/4
(C) 1/13
(D) 1/26
(E) 1/52
Rationale: The total number of cards is 52.
The number of red kings is 2.
P(red king) = 2/52 = 1/26
The answer is D.
Answer: (D) 1/26
Question: A person borrowed Rs.600 @ 3% per annum S.I and Rs.800 @ 4½ % per annum on the agreement that the whole sum will be returned only when the total interest becomes Rs.246. The number of years, after which the borrowed sum is to be returned, is
(A) 2 years
(B) 3years
(C) 4 years
(D) 5 years
(E) 6 years
Rationale: Let the time be x years. Then (600 *3* x)/100 + (800*9*x)/(2*100) = 24
18x+ 36x = 246 ; x = 246/54 = 4 years
Required time = 4 years
ANSWER:C
Answer: (C) 4 years
Question: In a class exactly 10% students get 70 marks, exactly 25% get 80 marks, exactly 15% get 85 marks, exactly 25% get 90 marks and remaining get 95 marks.what is the minimum number of students in the class if the avg. of sum of marks is an even no.
(A) 20
(B) 80
(C) 100
(D) 120
(E) 200
Rationale: Let total no. of students be x
(x(10*70 + 25*80 + 15*85 + 25* 90 + 25*90)/100)/ x = 86
Hence the avg is always 86 and does not depend upon the no. of students.
Hence the answer is the minimum value that is 20
ANSWER:A
Answer: (A) 20
Question: What is the largest 4 digit number exactly divisible by 88
(A) 9900
(B) 9999
(C) 9988
(D) 9944
(E) 9966
Rationale: Explanation:
Largest 4 digit number is 9999
After doing 9999 ÷ 88 we get remainder 55
Hence largest 4 digit number exactly divisible by 88 = 9999 - 55 = 9944
Answer: Option D
Answer: (D) 9944
Question: If m is a positive integer, and m/15 = 8.2, what is the remainder T when m is divided by 15?
(A) A.1
(B) B.2
(C) C.3
(D) D.4
(E) E.8
Rationale: If m were a multiple of 15, the quotient m/15 would be an integer. The fact that it's a decimal tells us that 15 goes into m eight whole times and some decimal part of a time. This decimal part, 0.2 is the remainder divided by the divisor. Let T be the remainder.
T/15 = 0.2 = 1/5
T = (15)*(1/5) = 3
Answer =(C)
Answer: (C) C.3
Question: The greatest common divisor of two positive integers is 25. If the sum of the integers is 350, then how many such pairs are possible?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: 350 = 25 * 14
To have the GCD of two numbers to be 25, we need to split 14 into two co-prime numbers. Such pairs of numbers are: (1,13), (3,11), and (5,9).
Answer:C
Answer: (C) 3
Question: If an amount of Rs 41,910 is distributed equally
amongst 22 persons, how much amount would each
person get?
(A) Rs 1905
(B) Rs 2000
(C) Rs 745
(D) Rs 765
(E) None
Rationale: Required amount =41910/22 = Rs 1905
Answer A
Answer: (A) Rs 1905
Question: Rajan buys an old scooter for Rs. 7400 and spends Rs. 600 on its repairs. If he sells the scooter for Rs. 8800, his gain percent is :
(A) 20%
(B) 12%
(C) 10%
(D) 5%
(E) None of these
Rationale: Explanation :
Solution: C.P. =Rs. (7400+600) =Rs. 8000; S.P. = Rs. 9600.
Gain% = (1600*100/8000) = 20%.
Answer : A
Answer: (A) 20%
Question: Find the slope of the line perpendicular to the line y = (1/6)x - 7
(A) 1
(B) 2
(C) -6
(D) 4
(E) 5
Rationale: Two lines are perpendicular if the product of their slopes is equal to -1. The slope of the given line is equal to 1 / 6. If m is the slope of the line perpendicular to the given line, then
m × (1/6) = -1
Solve for m
m = - 6
correct answer C) -6
Answer: (C) -6
Question: If two dies are thrown simultaneously what is the prob. of one of the dice getting face 6 ?
(A) 11/36
(B) 1/3
(C) 12/35
(D) 1/36
(E) 5/36
Rationale: Sample space for two dice = 36
Probability of getting one of the dice 6 is,
n={(1,6)(2,6)(3,6)(4,6)(5,6)(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)}=11
n=11
Probability = Total possibilities(n)/Sample space
P = 11/36
ANSWER:A
Answer: (A) 11/36
Question: The sector of a circle has radius of 21 cm and central angle 225o. Find its perimeter?
(A) 91.5
(B) 92
(C) 93
(D) 94
(E) 124.5
Rationale: Perimeter of the sector = length of the arc + 2(radius)
= (225/360 * 2 * 22/7 * 21) + 2(21)
= 124.5 cm
Answer: Option E
Answer: (E) 124.5
Question: If the productivity of a brigade grows by 5% when the number of the workers in the brigade is increased by one, then which of the following is closest to the ratio of the productivity of a 12-person brigade to that of a 10-person brigade?
(A) 0.21
(B) 0.82
(C) 1.155
(D) 1.21
(E) 1.44
Rationale: B = 10-men brigade
p = increase in the productivity = 5%
Solution: B x p = B x 1.05 = 1.05B -------> the productivity of 11 men brigade
1.05B x p = 1.05B x 1.1 = 1.155B -----> the productivity of 12 men brigade
The ratio of the productivity of a 12-men brigade to that of a 10-men brigade = 1.155B/B = 1.155
C
Answer: (C) 1.155
Question: Set S contains exactly 10 numbers and has an average (arithmetic mean) of 6.2. If one of the numbers in Set S is increased by 4, while all other numbers remain the same, what is the new average of Set S?
(A) 6.6
(B) 6.7
(C) 6.8
(D) 6.85
(E) 6.9
Rationale: Old set S - Total is avg * no of elements = 6.2*10 = 62
If one number is increased by 4 then total increased to 62+4=66
New avg - 66/10 = 6.6.
Hence answer is A.
Answer: (A) 6.6
Question: There are 12 people in a room. If each person shakes hands with exactly 3 other people, what is the total number of handshakes?
(A) 12
(B) 18
(C) 24
(D) 36
(E) 48
Rationale: Note that each handshake includes two people.
The total number of handshakes is 12*3/2 = 18
The answer is B.
Answer: (B) 18
Question: A number whose fifth part increased by 4 is equal to its fourth part diminished by 10, is :
(A) 240
(B) 260
(C) 270
(D) 280
(E) 290
Rationale: Let the number be x. Then,
((1/5)x+4)=((1/4)x−10)
<=>
x/20
<=> x = 14 * 20 = 280.
ANSWER :D
Answer: (D) 280
Question: If the compound interest on a certain sum for 2 years at 12% p.a. is Rs.1590, What would be the simple interest for same rate and same period?
(A) Rs.1500
(B) Rs.1450
(C) Rs.1550
(D) Rs.1650
(E) Rs.1750
Rationale: Let principal be P.
Then Amount = P + 1590
According to formula, Amount = P*[1 + 0.12]^2
Hence, we get, P+ 1590 = P*[1.12]^2
So, P + 1590 = 1.2544P
So, 0.2544P = 1590
So, P = 6250
Hence, simple interest on â�¹6250 @ 12% for 2 years = 6250*12/100*2 = 1500
ANSWER :A
Answer: (A) Rs.1500
Question: If in a certain sequence of consecutive multiples of 50, the median is 825, and the greatest term is 1050, how many terms that are smaller than 825 are there in the sequence?
(A) 6
(B) 5
(C) 8
(D) 12
(E) 13
Rationale: Since the median is 825 we know there must be a even number of integers because 50 is not a multiple of 825.
So the list around 625 must go. 750 800 (825) 850 900 950 1000 1050
Since we know there are 5 numbers greater than 825 then there must be 5 numbers less then 825.
answer:B
Answer: (B) 5
Question: In a class, there are 15 boys and 10 girls. Three students are selected at random. The probability that 1 girl and 2 boys are selected, is:
(A) 21/46
(B) 25/117
(C) 1/50
(D) 3/25
(E) 4/25
Rationale: Let S be the sample space and E be the event of selecting 1 girl and 2 boys.
Then, n(S)= Number ways of selecting 3 students out of 25
= 25C3 `
=(25 x 24 x 23)/(3 x 2 x 1)
= 2300.
n(E)= (10C1 x 15C2)
=10 x((15 x 14)/(2 x 1))
= 1050.
P(E) =	n(E)/n(S)=(1050/2300)=21/46.
Answer: (E) 4/25
Question: The current of a stream runs at the rate of 5 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) A)7.63
(B) B)2.6
(C) C)8.83
(D) D)6.69
(E) E)3
Rationale: S = 5
M = x
DS = x + 5
US = x - 5
6/(x + 5) + 6/(x - 5) = 2
x = 8.83
Answer:C
Answer: (C) C)8.83
Question: Which of the following numbers should not be included in the set?
331, 482, 551, 263, 384, 242, 111
(A) 263
(B) 384
(C) 242
(D) 111
(E) None of these
Rationale: Solution
In each number except 384,the product of first and third digits is the middle one. Answer B
Answer: (B) 384