mathewhe/aqua_rat huggingface dataset:
Question: The ages of three friends are prime numbers. The sum of the ages is less than 51. If the ages are in Arithmetic Progression (AP) and if at least one of the ages is greater than 10, what is the difference between the maximum possible median and minimum possible median of the ages of the three friends?
(A) 0
(B) 1
(C) 13
(D) 6
(E) 8
Rationale: Let the numbers are a-d, a , a+d
sum <51 => a-d+a+a+d < 51 => middle number a <17
prime numbers are 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47
a can be 3,5,7,11,13
if a is 3 -> a-d can be 2 only; a+d not possible thus reject this.
if a is 5, a-d can be 2 and 3; only a-d = 3 satisfies
=> three numbers can be 3,5,7 ->reject this , as it is given at least one is >10
if a = 7 ; a-d can be 3 and a+d can be 11
This satisfies all the conditions hence the median is 7=> min median.
if a = 11, the three element pair is 3,11,19 or 5,11,17
median = 11; we are not sure if its the max median possible
if a = 13, 7,13,19 pair is possible
median = 13; reject 11 as the max.
thus difference = 13-7 = 6
ANSWER:D
Answer: (D) 6
Question: A coin is tossed live times. What is the probability that there is at the least one tail?
(A) 31/32
(B) 1/16
(C) 1/2
(D) 1/32
(E) None of these
Rationale: Let P(T) be the probability of getting least one tail when the coin is tossed five times.
P(T)= There is not even a single tail.
i.e. all the outcomes are heads.
P(T)= 1/32 ; P(T) = 1 - 1/32 = 31/32
ANSWER:A
Answer: (A) 31/32
Question: How many 4 digit numbers are there, if it is known that the first digit is even, the second is odd, the third is prime, the fourth (units digit) is divisible by 3, and the digit 5 can be used only once?
(A) 20
(B) 150
(C) 225
(D) 300
(E) 304
Rationale: 4 options for the first digit: 2, 4, 6, 8;
5 options for the second digit: 1, 3, 5, 7, 9;
4 options for the third digit: 2, 3, 5, 7;
4 options for the fourth digit: 0, 3, 6, 9.
Four digit # possible without the restriction (about the digit 2): 4*5*4*4=320
Numbers with five 5-s, 5X5X 4*1*1*4=16.
Thus there are 320-16=304 such numbers.
Answer: E.
Answer: (E) 304
Question: Out of 9 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them?
(A) A)5/7
(B) B)5/21
(C) C)16/21
(D) D)5/6
(E) E)5/3
Rationale: P(at least one graduate) = 1 - P(no graduates)
= 1 - ⁶C₃/¹⁰C₃
= 1 - (6 * 5 * 4)/(7 * 9 * 8)
= 16/21
Answer:C
Answer: (C) C)16/21
Question: 4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 8 mat-weavers in 8 days?
(A) 25
(B) 19
(C) 39
(D) 61
(E) 16
Rationale: Let the required number of bottles be x.
More weavers, More mats (Direct Proportion)
More days, More mats (Direct Proportion)
Wavers	4	:	8 :: 4 : x
Days	4:8
4 * 4 * x = 8 * 8 * 4
x =	(8 * 8 * 4)/(4 x 4)
x = 16.
Answer is E.
Answer: (E) 16
Question: Ravi and Kumar are working on an assignment. Ravi takes 6 hours to type 32 pages on a computer, while Kumar takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?
(A) 7 hours 30 minutes
(B) 8 hours
(C) 8 hours 15 minutes
(D) 8 hours 25 minutes
(E) 7 hours 35 minutes
Rationale: Number of pages typed by Ravi in 1 hour =	32/6	=	16/3	.
Number of pages typed by Kumar in 1 hour =	40/5	= 8.
Number of pages typed by both in 1 hour =	(16/3+ 8)	=	40/3	.
Therefore Time taken by both to type 110 pages =	(	110 x	3/40	)	hours
= 8	1/4 hours (or) 8 hours 15 minutes.
Option C
Answer: (C) 8 hours 15 minutes
Question: If x is the sum of six consecutive integers, then x is divisible by which of the following: I. 6 II. 3 III. 7
(A) I only
(B) III only
(C) II,III only
(D) II only
(E) I,III only
Rationale: We're told that X is the SUM of 6 CONSECUTIVE INTEGERS. We're asked what X is divisible by....
Let's TEST VALUES....
IF we use the 6 consecutive integers: 6, 7,8,9,10 and 11, then the sum = 51.
51 is divisible by 3
51 is NOT divisible by 6
51 is NOT divisible by 7
There's only one answer that 'fits' with these facts. Answer : D
Answer: (D) II only
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) 10 kmph
(B) 21 kmph
(C) 8 kmph
(D) 12 kmph
(E) 14 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: Find the C.I. on a sum of Rs.1600 for 9 months at 20% per annum, interest being compounded quarterly?
(A) Rs.7288
(B) Rs.2542
(C) Rs.2522
(D) Rs.2625
(E) Rs.6271
Rationale: A = 1600(21/20)3
= 2522
Answer: C
Answer: (C) Rs.2522
Question: Johnson completes a piece of work in 10 days, Vincent completes the same work in 40 days. If both of them work together, then the number of days required to complete the work is
(A) 7 days
(B) 8 days
(C) 9 days
(D) 10 days
(E) 12 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.
That is, the required No. of days = 10 × 40/50 = 8 days.
B)
Answer: (B) 8 days
Question: A restaurant meal cost $35.50 and there was no tax. If the tip was more than 10 percent but less than 15 percent of the cost of the meal, then the total amount paid must have been between
(A) $40 and $42
(B) $39 and $41
(C) $38 and $40
(D) $37 and $39
(E) $36 and $37
Rationale: The total amount for the meal was between 35.5*1.1=39.05 and 35.5*1.15=~41. Only option which covers all possible values of the meal is B.
Answer: B.
Answer: (B) $39 and $41
Question: When 30 per cent of a number is added to another number the second number increases by its 20 per cent. What is the ratio between the first and the second number?
(A) 3 : 2
(B) 2 : 3
(C) 2 : 5
(D) Data inadequate
(E) None of these
Rationale: 30% of I + II = II × 120⁄100
or, 3⁄10I = 2⁄10II ⇒ I : II = 2 : 3.
Answer B
Answer: (B) 2 : 3
Question: what is the probability of getting sum of 10 on rolling three dices?
(A) 28/216
(B) 27/216
(C) 29/216
(D) 26/216
(E) 25/216
Rationale: The no of ways to roll three dies is 6^3=216
The possibles of getting sum as 10 is
631=3!=6
622=3!/2!=3
541=3!=6
523=3!=6
442=3!/2!=3
433=3!/2!=3
Total possibles for getting sum as 10 is 27
The probabilty is 27/216
ANSWER:B
Answer: (B) 27/216
Question: The last digit of the number obtained by multiplying the numbers 41 x 42 x 43 x 44 x 45 x 46 x 47 x 48 x 49 will be ?
(A) 0
(B) 1
(C) 4
(D) 5
(E) 7
Rationale: Solution
Last digit will be multiplication of 1x2x3x4x5x6x7x8x9.
It includes 5 & 2 so, 5x2=10, 0 will be the last digit.
Correct Option: A
Answer: (A) 0
Question: A club wants to mix 20 pounds of candy worth $8.00 per pound with candy worth $5.00 per pound to reduce the cost of the mixture to $6.00 per pound. How many pounds of the $5.00 per pound candy should be used?
(A) 20
(B) 30
(C) 40
(D) 50
(E) 60
Rationale: Let number of pounds of 5$ candy to be used be w
6 = (20*8 + 5*w)/(20 +w)
=>120 + 6w = 160 + 5w
=> w = 40
Answer C
Answer: (C) 40
Question: The remainder when K=1+3+3^2+3^3+..........+3^200 is divided 13.
(A) 12
(B) 7
(C) 0
(D) 5
(E) 3
Rationale: K=1+3+3^2+3^3+..................+3^200
Is a Geometric progression having common ratio as '3' and number of terms as '201'.
Since Sum to n terms in GP = a(r^n-1)/(r-1)
where a=First term and r =common ration
Hence,
1*(3^201 -1 )/(3-1)
Rem of (3^201-1)/2 divided by 13
3^201 -1 /26
WKT, 3^3 = 27 = 26+1
{(26+1)^67 - 1}/26
{1-1}/26
=>0.C
Answer: (C) 0
Question: In a room filled with 5 people, 3 people have exactly 2 siblings in the room and 2 people have exactly 1 sibling in the room. If two individuals are selected from the room at random, what is the probability that those two individuals are NOT siblings?
(A) 2/3
(B) 2/5
(C) 3/5
(D) 3/10
(E) 7/10
Rationale: The 5 people consist of one set of 2 siblings and one set of 3 siblings.
The number of ways to choose 2 people is 5C2 = 10.
The number of ways to choose 2 from the first group of siblings is 2C2 = 1.
The number of ways to choose 2 from the second group of siblings is 3C2 = 3.
The number of ways to choose 2 people who are siblings is 3+1 = 4.
The number of ways to choose 2 people who are not siblings is 10-4=6.
P(the two people are not siblings) = 6/10 = 3/5
The answer is C.
Answer: (C) 3/5
Question: How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length?
(A) 82.1 sec
(B) 12.1 sec
(C) 16.1 sec
(D) 13.1 sec
(E) 12.15sec
Rationale: Speed = 72 * 5/18 = 20 m/sec
Total distance covered = 110 + 132 = 242 m.
Required time = 242/20 = 12.1 sec.
Answer:B
Answer: (B) 12.1 sec
Question: A 180 meter long train crosses a man standing on the platform in 9 sec. What is the speed of the train?
(A) 72
(B) 108
(C) 1266
(D) 188
(E) 211
Rationale: S = 180/9 * 18/5 = 72 kmph
Answer: A
Answer: (A) 72
Question: If the annual interest on a principal is 8%, how many years before the amount is double?
(A) 11.3
(B) 12
(C) 12.5
(D) 10.2
(E) 11.2
Rationale: P = (P*8*R)/100
R = 12.5
Answer: C
Answer: (C) 12.5
Question: The first doughnut is priced at $1 and then if you purchase additional doughnuts as dozens then the price is $6/dozen. What is the total number of doughnuts purchased if you paid $24?
(A) 44
(B) 46
(C) 48
(D) 50
(E) 52
Rationale: $24 = 4 * $6
The number of doughnuts is 4*12 = 48
The answer is C.
Answer: (C) 48
Question: The toll T, in dollars, for a truck using a certain bridge is given by the formula T = 1.50 + 0.50( x − 2), where x is the number of axles on the truck. What is the toll for an 18-wheel truck that has 2 wheels on its front axle and 2 wheels on each of its other axles?
(A)  $ 2.50
(B)  $ 3.00
(C)  $ 3.50
(D)  $ 4.00
(E)  $ 5.00
Rationale: Number of wheels in truck = 18
Number of wheels on its front axle =2
number of wheels remaining = 16
number of axles remaining axles = 16/2 = 8
Total number of axles = 9
T = 1.50 + 0.50( 9 − 2)
= 1.50 + .5*7
= 1.5 +1.5 = 5 $
Answer E
Answer: (E)  $ 5.00
Question: How many different sets of positive square integers D, each greater than 1, add up to 75?
(A)  1
(B)  4
(C)  7
(D)  11
(E)  13
Rationale: E = 13 is the correct answer.
Answer: (E)  13
Question: A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current?
(A) 1.7
(B) 1.5
(C) 1.3
(D) 1.2
(E) 1.9
Rationale: 72 --- 9 DS = 8
? ---- 1
45 ---- 9 US = 5
? ---- 1 S = ?
S = (8 - 5)/2 = 1.5
Answer: B
Answer: (B) 1.5
Question: A envelop weight 8.2 gm,if 800 of these envelop are sent with an advertisement mail. How much wieght?
(A) 6.56kg
(B) 6.8kg
(C) 6.7kg
(D) 6.9kg
(E) 7.8kg
Rationale: 800*8.2
6560.0gm
6.56kg
ANSWER:A
Answer: (A) 6.56kg
Question: A table is bought for Rs.400/- and sold at Rs.550/- find gain or loss percentage
(A) l10%oss
(B) 30%gain
(C) 37.5%gain
(D) 10%loss
(E) 25% loss
Rationale: Formula = (Selling price ~ Cost price)/Cost price * 100
= (550 - 400)/400 = 37.5% gain
C
Answer: (C) 37.5%gain
Question: A can finish a work in 18 days and B can do the same work in 15 days. B worked for 10 days and left the job. In how many days, A alone can finish the remaining work?
(A) 7
(B) 6
(C) 5
(D) 4
(E) 3
Rationale: B's 10 day's work = (10*1/15) = 2/3.
Remaining work =	(1- (2/3))=1/3
Now, 1/18 work is done by A in 1 day.
A= 18* 1/3 = 6 DAYS
ANSWER:B
Answer: (B) 6
Question: The breadth of a rectangular hall is two-thirds of its length. If the area of the hall is 2400 sq metres, what is the length in metres?
(A) 120
(B) 80
(C) 60
(D) 40
(E) None of these
Rationale: Let the length of the rectangular hall be ‘x’ m, then the breadth of the rectangular hall = 2x⁄3 m.
Area of hall = 2x⁄3 × x = 2x2⁄3
or, 2x2⁄3 = 2400 or x = 60 m
Answer C
Answer: (C) 60
Question: A man can row 4 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?
(A) 5.98
(B) 3.98
(C) 3.54
(D) 3.87
(E) 3.82
Rationale: M = 4
S = 1.2
DS = 4.8
US = 2.8
x/4.8 + x/2.8 = 1
x = 1.77
D = 1.77* 2 = 3.54
Answer:C
Answer: (C) 3.54
Question: The standard model numbers of cell phones in a company are 1 letter followed by 6 digits. How many different model numbers are possible if letters and digits can be repeated?
(A) 26 × 26 × 10 × 4
(B) 26 x 100 000
(C) 26 x 10
(D) 26 × 25 × 24 × 10 × 9 × 8 × 7
(E) 26 x 1 000 000
Rationale: OFFICIAL SOLUTION:
(E) The formula for permutations of events is the product of the number of ways each event can occur. There are 26 letters and 10 digits. So there are 26 options for a letter, and 10 × 10 × 10 × 10 × 10 × 10 for the six digits. The number of different license plates is 26 × 10 × 10 × 10 × 10 × 10 × 10 = 26 × 1 000 000.
The correct answer is choice (E).
Answer: (E) 26 x 1 000 000
Question: A,B,C can complete a piece of work in 25,5,10 days. Working together, they complete the same work in how many days?
(A) 2
(B) 4/5
(C) 50/17
(D) 10
(E) 24/7
Rationale: A+B+C 1day work = 1/25 + 1/5 + 1/10 = 17/50
A,B,C together will complete the job in 50/17 days
Answer is C
Answer: (C) 50/17
Question: If 70 percent of 600 is 40 percent of x, then x=?
(A) 105
(B) 168
(C) 342
(D) 660
(E) 1050
Rationale: Given: 0.7*600=0.4x --> 420=4/10*x --> x=1,050.
Answer: E.
Answer: (E) 1050
Question: Average of money that group of 4 friends pay for rent each month is $800.After one persons rent is increased by 20% the new mean is $860.What was original rent of friend whose rent is increased?
(A) 800
(B) 900
(C) 1000
(D) 1100
(E) 1200
Rationale: 0.2X = 4(860-800)
0.2X = 240
X = 1200
Answer E
Answer: (E) 1200
Question: In 100 m race, A covers the distance in 36 seconds and B in 45 seconds. In this race A beats B by:
(A) 20 m
(B) 25 m
(C) 22.5 m
(D) 9 m
(E) 12 m
Rationale: Distance covered by B in 9 sec. =	100/45 x 9	m = 20 m.
A beats B by 20 metres.
Answer: Option A
Answer: (A) 20 m
Question: A fort of 4000 soldiers has provisions for 100 days. After 20 days some of them left and the food was now enough for the same period of 100 days as before. How many of them left?
(A) 650
(B) 700
(C) 750
(D) 800
(E) 850
Rationale: 2000 ---- 50
4000 ---- 80
x ----- 100
x*100 = 4000*80
x=3200
4000
-------
800
Answer: D
Answer: (D) 800
Question: Girl and Boy together can complete a piece of work in 35 days while Girl alone can complete the same work in 60 days. Boy alone will be able to complete the same working in:
(A) 72
(B) 75
(C) 84
(D) 88
(E) 90
Rationale: Subtraction of fraction
ab−cd=ad−cbbd
Girl
and Boy finish one work with company = 35
days
(Girl+Boy)′
s one day’s work = 135
Girl alone finish the same work = 60
days
Girl′
s one day’s work = 160
B′
s one day’s work = (A+B)′s one day’s work - A′
s one day’s work
135−160=184
Hence B alone can complete the work in 84 days
Answer: (B) 75
Question: A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same time during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is:
(A) 15 hours
(B) 20 hours
(C) 25hours
(D) 28 hours
(E) 18 hours
Rationale: Let the first pipe alone can fill the tank in x hours
Then the second pipe can fill the tank in (x-5) hours
and the third pipe can fill the tank in (x-5)-4 = (x-9) hours
part filled by first pipe and second pipe together in 1 hr = part filled by third pipe in 1 hr
(1/x)+1/(x−5)=1/(x−9)
(x−5)(x−9)+x(x−9)=x(x−5)
x^2−14x+45+x^2−9x=x^2−5x
−14x+45+x^2−9x=−5x
x^2−18x+45=0
(x−15)(x−3)=0
x=15 or 3
We can not take the value of x = 3 because, (x-9) becomes negative which is not possible
because the third pipe can fill the tank in (x-9) hours
Hence, x = 15
Answer is A
Answer: (A) 15 hours
Question: You collect baseball cards. Suppose you start out with 15. Since her father makes baseball cards, Cindy decides to quadruple your baseball cards. Since you're nice, you give Mike 10 baseball cards. Tiffany gives you another 12 baseball cards. Pearl gives you another 23 baseball cards. How many baseball cards do you have at the end?
(A) 55
(B) 65
(C) 75
(D) 95
(E) 85
Rationale: Solution
Start with 15 baseball cards.
Cindy quadruples the number of baseball cards you have: 15 × 4 = 60 baseball cards.
Mike takes 10 baseball cards from you: 60 - 10 = 50 baseball cards.
Tiffany gives you 12 baseball cards: 50 + 12 = 62 baseball cards.
Pearl gives you 23 baseball cards: 62 + 23 = 85 baseball cards.
So you have 85 at the end.
Correct answer : E
Answer: (E) 85
Question: It costs a man 75 dollars to buy the things that he needs to make hotdogs. The city allows him to sell his hotdog somewhere near the city hall. However, the city hall charges him 1 dollar for each hotdog sold
Calculate the break even point if the price he charges for 1 hotdog is $1.50
(A) 140
(B) 150
(C) 160
(D) 170
(E) 180
Rationale: Let x be the number of hotdogs sold
Let C be the cost of buying and selling x hotdogs
Let R be the revenue made for selling x hotdogs
R = selling price of 1 hotdog × number of hotdogs sold
R = 1.50x
C = fixed cost + variable cost
variable cost = fee charged for 1 hotdog × number of hotdogs sold
variable cost = 1x
C = 75 + 1x
R = C
1.50x = 75 + 1x
1.50x - 1x = 75 + 1x - 1x
0.5x = 75
x = 150 since 0.5 × 150 = 75
The break even point is to sell 150 hotdogs.
Answer B
Answer: (B) 150
Question: In what time will a railway train 60 m long moving at the rate of 36 kmph pass a telegraph post on its way?
(A) 3
(B) 5
(C) 4
(D) 6
(E) 7
Rationale: T = 60/36 * 18/5 = 6 sec
Answer:D
Answer: (D) 6
Question: A contractor is engaged for 30days on the condition that he receives Rs.25 for each day he works &is fined Rs.7.50 for each day is absent. He gets Rs.490 in all. For how many days was he absent?
(A) 8
(B) 10
(C) 15
(D) 17
(E) 19
Rationale: 30 * 25 = 750
490
-----------
260
25 + 7.50 = 32.5
260/32.5 = 8
A
Answer: (A) 8
Question: {-10, -6, -5, -4, -2.5, -1, 0, 2.5, 4, 6, 7, 10}
A number is to be selected at random from the set above. What is the probability that the number selected will be a solution of the equation (x-5)(x+8)(2x-5) = 0?
(A) 1/12
(B) 1/6
(C) 1/4
(D) 1/3
(E) 1/2
Rationale: Roots of the equation (x-5)(x+10)(2x-5)=0 are x=5,x=-8 and x=5/2=2.5. So, one solutions present in our set of 12 distinct numbers, therefore P=1/12
Answer: A.
Answer: (A) 1/12
Question: The average score of a cricketer for seven matches is 56 runs. If the average for first four matches is 46, then average for last three matches is
(A) 33.25
(B) 32.25
(C) 65
(D) 67
(E) 69
Rationale: Explanation:
=(56×7)−(46×4)/3
=(392−184)/3=69
Answer: Option E
Answer: (E) 69
Question: Find the arithmetic mean L of all roots of the following equation- see an attachment.
(A) 2
(B) 1
(C) 0.5
(D) -1/3
(E) 0.3
Rationale: arithmetic mean L your answer C and E are same, can you correct one of them please. thanks.C
Answer: (C) 0.5
Question: If in a game of 80, P can give 16 points to Q and R can give 20 points to P, then in a game of 150, how many points can R give to Q?
(A) 48
(B) 60
(C) 54
(D) 90
(E) 100
Rationale: Explanation:
When P scores 80, Q scores 64.
When R scores 80, P scores 60
Hence, when R scores 150, Q scores (60 * 64 * 150) / (80 * 80) = 90
Therefore, in a game of 150, R can give 60 points to Q.
ANSWER B
Answer: (B) 60
Question: Find: S.l. on Rs 3000 at 18% per annum for the period from 4th
(A) 118
(B) 105
(C) 108
(D) 110
(E) 111
Rationale: Explanation:
(24 + 31 + 18) days = 73 days = 1/5 year .
P = Rs 3000 and R = 18 % p.a.
S.I=(3000 *18 * 1/5)/100
ANSWER IS C
Answer: (C) 108
Question: In how much time will interest on Rs. 2300 at 4 1/2 percent p/a be Rs.310.50
(A) 5years
(B) 2years
(C) 4years
(D) 3 years
(E) 2 1/2 years
Rationale: 310 = (2300*T*9/2)/100
T = (310.50x100x2)/(300x9)= 3 years.
Answer: D
Answer: (D) 3 years
Question: What will be the fraction of 8%
(A) 1/20
(B) 1/50
(C) 1/75
(D) 2/25
(E) None of these
Rationale: Explanation:
8*1/100 = 2/25.
Option D
Answer: (D) 2/25
Question: Two boys picked up 30 mangoes .In how many ways can they divide them if all mangoes be identical?
(A) A)4^30
(B) B)2^30
(C) C)1^30
(D) D)3^30
(E) E)6^30
Rationale: Each Mango can be given to any one of the two people or in other words..30 mango can be divided into 2 ways...so all 30 can be divided in 2^30 ways
ANS:B
Answer: (B) B)2^30
Question: Compound interest earned on a sum for the second and the third years are Rs.12500 and Rs.14000 respectively. Find the rate of interest?
(A) 18% p.a.
(B) 22% p.a.
(C) 20% p.a.
(D) 12% p.a.
(E) None of these.
Rationale: Rs.14000 - 12500 = Rs.1500 is the interest on Rs.12500 for one year.
Rate of interest = (1500/12500) * 100 = 12% p.a
ANSWER:D
Answer: (D) 12% p.a.
Question: A bag contains six white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color?
(A) 15/8
(B) 8/15
(C) 5/6
(D) 5/3
(E) 5/1
Rationale: Two balls can be picked from ten balls in 10Câ‚‚ ways.
We select one white ball and one red ball from five white balls and four red balls. This can be done âµ ways.
The required probability = (6 * 4) = 24/45 = 8/15
Answer: B
Answer: (B) 8/15
Question: Joe needs to paint all the airplane hangars at the airport, so he buys 360 gallons of paint to do the job. During the first week, he uses 1/4 of all the paint. During the second week, he uses 1/7 of the remaining paint. How many gallons of paint has Joe used?
(A) 18
(B) 128
(C) 175
(D) 216
(E) 250
Rationale: Total paint initially = 360 gallons
Paint used in the first week = (1/4)*360 = 90 gallons.
Remaning paint = 270 gallons
Paint used in the second week = (1/7)*270 = 38 gallons
Total paint used = 128 gallons.
Option B
Answer: (B) 128
Question: Let d > c > b > q. If c is twice as far from q as it is from d, and b is twice as far from c as it is from q, then (d - b)/(d - q) = ?
(A) 2/9
(B) 1/3
(C) 2/3
(D) 7/9
(E) 3/2
Rationale: Draw a number line and label with x and y. You would have:
Before calculating recognize it would be more effcient to express x or y in terms of the other. here 2x = 3y so x =3/2 y.
Now you can calculate d -b and d -a
d - b= x +2y = 7/2 y
d - q = x + 2x = 3x = 9/2y
Dividing both you get: 7/9
Answer D
Answer: (D) 7/9
Question: The ratio of two numbers is 2/3, and if a 1 is subtracted from the numerator and a 1 is added to the remainder the ratio becomes 1/2, then the numbers are.
(A) 6 and 9
(B) 6 and 10
(C) 6 and 8
(D) 6 and 7
(E) 6 and 11
Rationale: a:b=2:3 b=3/2a
a-1/b+1=1/2
solving this we get a=6 and b=9
ANSWER:A
Answer: (A) 6 and 9
Question: A jar full of whiskey contains 40% alcohol. A part of
this whiskey is replaced by another containing 19% alcohol
and now the percentage of alcohol was found to be 26%.
The quantity of whiskey replaced is?
(A) 2/3
(B) 1/3
(C) 1/4
(D) 1/2
(E) 1/5
Rationale: Strength of first jar 40% Strength of 2nd jar 19%
Mean Strength 26%
7 14
So,ratio of 1st and 2nd quantities =7:14 =1:2
Therefore required quantity replaced =2/3.
ANSWER A
Answer: (A) 2/3
Question: Which 2 digit number has its digits reversed when you double it and take 1?
(A) 33
(B) 34
(C) 35
(D) 36
(E) 37
Rationale: reverse it and you get 73 which is 2*37-1.
ANSWER:E
Answer: (E) 37
Question: The ratio of the ages of Mini and Minakshi is 4 : 3. The sum of their ages is 21 years. The ratio of their ages after 8 years will be
(A) 2 : 3
(B) 20 : 17
(C) 5 : 4
(D) 3 : 5
(E) 6 : 11
Rationale: Let Mini’s age = 4x and Minakshi’s age = 3x
Then 4x + 3x = 21
x = 3
Mini’s age = 12 years
And Minakshi’s age = 9 years
Ratio of their ages after 8 years = (12 + 8) : (9 + 8) = 20 : 17
ANSWER:B
Answer: (B) 20 : 17
Question: A goods train runs at the speed of 72 km/hr and crosses a 290 m long platform in 26 sec. What is the length of the goods train?
(A) 278
(B) 166
(C) 151
(D) 230
(E) 109
Rationale: Speed = 72 * 5/18 = 20 m/sec.
Time = 26 sec.
Let the length of the train be x meters.
Then, (x + 290)/26 = 20
x = 230 m.
Answer:D
Answer: (D) 230
Question: Find the difference between C.I and S.I on a sum of money Rs. 2000 for 2 years. at 4% p.a
(A) Rs.2.20
(B) Rs.3.20
(C) Rs.4.20
(D) Rs.5.20
(E) Rs.3.25
Rationale: P9r/100)^2 =2000(4/100)^2 =Rs.3.20 Answer : B
Answer: (B) Rs.3.20