mathewhe/aqua_rat huggingface dataset:
Question: Two trains one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 4 hours and 9 hours respectively. The ratio of their speeds is
(A) 3 : 2
(B) 4 : 3
(C) 4 : 7
(D) 8 : 5
(E) None
Rationale: Sol.
Let us name the trains as A and B. Then,
(A's speed) : (B's speed) = √b : √a
= √9 : √4
= 3 : 2.
Answer A
Answer: (A) 3 : 2
Question: father is aged three times more than his son ronit. after 8 years, he would be two and half times if ronit's age. after further 8 years , how many times would he be of ronit's age?
(A) 2 times
(B) 2.5 times
(C) 3 times
(D) 3.8 times
(E) 4 times
Rationale: ronit's present age be x years . then, father's present age= (x+3x)years= 4x years
therefore (4x + 8) = 5/2 (x + 8)
8x + 16 = 5x + 40
3x = 24 , x= 8, ratio = (4x + 16)/(x + 16)= 48/24=2,
correct answer (A)
Answer: (A) 2 times
Question: What is the perimeter, in meters, of a rectangular garden 16 meters wide that has the same area as a rectangular playground 16 meters long and 12 meters wide?
(A) 48
(B) 56
(C) 60
(D) 56
(E) 192
Rationale: Say Length of garden is L meters.
Then (L*16) = 16 * 12 [Given area is same. Area= L * B]
Therefore L works out to 12 meters.
Perimeter of Garden = 2* (12+16) = 56 meter.
Answer is D
Answer: (D) 56
Question: To deliver an order on time, a company has to make 25 parts a day. After making 25 parts per day for 3 days, the company started to produce 5 more parts per day, and by the last day of work 100 more parts than planned were produced. Find how many parts the company made and how many days this took.
(A) 600
(B) 500
(C) 575
(D) 655
(E) 675
Rationale: Let x be the number of days the company worked. Then 25x is the number of parts they planned to make. At the new production rate they made:
3⋅25+(x−3)⋅30=75+30(x−3)
Therefore: 25x=75+30(x−3)−100
25x=75+30x−90−100
190−75=30x−25
115=5x
x=23
So the company worked 23 days and they made 23⋅25+100=675 pieces.
So answer is E.
Answer: (E) 675
Question: In how many ways, a committee of 5 members can be selected from 6 men and 5 ladies, consisting of 3 men and 2 ladies?
(A) 451
(B) 124
(C) 531
(D) 145
(E) 200
Rationale: (3 men out 6) and (2 ladies out of 5) are to be chosen.
Required number of ways = (6c3x5c2)
= [6x5x4/3x2x1] x [5x4/2x1] = 200.
Ans: E
Answer: (E) 200
Question: For all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when m is even. What is [9]*[4] equivalent to?
(A) [108]
(B) [54]
(C) [36]
(D) [27]
(E) [18]
Rationale: [9]*[4] = 27*2 = 54 = (1/2)(108) =[108]
The answer is A.
Answer: (A) [108]
Question: A sum of money invested at C.I. amounts to Rs. 800 in 3 years to Rs. 890 in 4 years. The rate of interest per annum is?
(A) 2 1/2 %
(B) 4%
(C) 5%
(D) 6 2/3 %
(E) 11 1/4%
Rationale: S.I. on Rs. 800 for 1 year = (890 - 800) = Rs.90 Rate = (100 * 90)/(800 * 1) = 11 1/4%
ANSWER:E
Answer: (E) 11 1/4%
Question: X Y
+Y X
________
The sum of the two digit numbers above is a three digit number PQ1, where each letter X, Y, P, and Q represents a different non zero digit. Which of the following can be the value of X?
I)	7
II)	8
III)	9
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) all I , II and III
Rationale: it can be a combination of 9,2 or 8,3 or 7,4
I choose E as an answer.
Answer: (E) all I , II and III
Question: What is the probability that a leap year has 53 Sundays and 52 Mondays?
(A) 1/9
(B) 1/8
(C) 1/3
(D) 1/7
(E) 1/2
Rationale: A leap year has 52 weeks and two days
Total number of cases = 7
Number of favourable cases = 1
i.e., {Saturday, Sunday}
Required Probability = 1/7
Answer:D
Answer: (D) 1/7
Question: Machine Z can produce x units in 3/4 of the time it takes machine N to produce x units. Machine N can produce x units in 2/3 the time it takes machine O to produce x units. If all three machines are working simultaneously, what fraction of the total output is produced by machine N?
(A)  1/2
(B)  1/3
(C)  4/13
(D)  8/29
(E)  6/33
Rationale: Let the following be true:
Z makes x in time t
Then the following follows:
N makes x in 4t/3
O makes x in 3/2(4t/3) = 2t
M:N:O = 1:4/3:2=3:4:6
So N=4/(3+4+6)=4/13=C
Answer: (C)  4/13
Question: If cement, gravel and sand are to be mixed in 7:10:13 and 7 tons of cement is available how many tons of mixture can be produced assuming that sufficient gravel and sand is readily available.
(A) 35 7/8
(B) 30
(C) 34 2/7
(D) 34 5/7
(E) 34 6/7
Rationale: Cement:Gravel:Sand = 7:10:13 --> total of 7+10+13 = 30 parts.
If we use 7 tons of cement, then we'll get 7/7*30 = 30 tons of mixture.
Answer: B.
Answer: (B) 30
Question: If the cost price is 90% of the selling price, then what is the profit percent?
(A) 5%
(B) 11%
(C) 13%
(D) 21%
(E) 19%
Rationale: Let S.P. = $100
C.P. = $90
Profit = $10
Profit% = 10/90 * 100 = 25/6 = 11% approximately
Answer is B
Answer: (B) 11%
Question: If w and y are positive integer and w/y is an even integer, which of the following can be an odd integer?
(A) x
(B) xy
(C) x−y
(D) x+2y
(E) w/3
Rationale: C w-Y
Let says w =12 Y=3 iT BECOMES w-Y =9 This is odd True
w = 12 Y = 6 THEN w-Y = 2, Which is even hence this is False.
so both Yes and NO situations are exists for this Option. C can't be the correct answer same logic goes for E. I believe this question is incomplete b'coz of Irrelevant Options.
Answer: (E) w/3
Question: Which of the following is equal to 3.14 x 10^6) ?
(A) 3.14
(B) 3140000
(C) 31400
(D) 314
(E) 314000
Rationale: = 3.14 x 10^6
= 3.14 x 1000000
= 3140000.
Answer is B.
Answer: (B) 3140000
Question: 9 men and 12 boys finish a job in 12 days, 12 men and 12 boys finish it in 10 days. 10 men and 10 boys shall finish it in how many days?
(A) 19 days
(B) 18 days
(C) 12 days
(D) 27 days
(E) 26 days
Rationale: 9M + 12B ----- 12 days
12M + 12B ------- 10 days
10M + 10B -------?
108M + 144B = 120M +120B
24B = 12M => 1M = 2B
18B + 12B = 30B ---- 12 days
20B + 10B = 30B -----? => 12 days
Answer: C
Answer: (C) 12 days
Question: A box contains 10 tablets of medicine A and 17 tablets of medicine B. What is the least number of tablets that should be taken from the box to ensure that at least two tablets of each kind are among the extracted.
(A) 12
(B) 15
(C) 17
(D) 19
(E) 21
Rationale: The worst case scenario will be if we remove all 17 tablets of medicine B first. The next 2 tablets we remove have to be of medicine A, so to guarantee that at least two tablets of each kind will be taken we should remove minimum of 17+2=19 tablets.
Answer:D.
Answer: (D) 19
Question: Which is better investment 11% stock at 143 or 9 Â¾% stock at 117
(A) 11 % stock at 143
(B) 9 3/4 stock at 117
(C) both
(D) cannot be compared
(E) none of these
Rationale: Let the investment in each (143*117)
Income in first case = (11/143*143*117)=1287
Income in second case=((39/117*4)*143*117)=1394.25
Clearly, 9 Â¾% stock at 117
ANSWER B
Answer: (B) 9 3/4 stock at 117
Question: 96% of the population of a village is 23040. The total population of the village is?
(A) 26799
(B) 24000
(C) 26682
(D) 29973
(E) 12312
Rationale: X * (96/100) = 23040
X = 240 * 100
X = 24000
Answer: B
Answer: (B) 24000
Question: Simplify:935421 x 625
(A) 594983125
(B) 584932715
(C) 584938125
(D) 584638125
(E) 584641258
Rationale: 935421 x 625 = 935421 x 54 = 935421 x (10/2)^ 4
935421 x 10^4/2^4=9354210000/16
= 584638125
Answer is D
Answer: (D) 584638125
Question: 1. Internet: $80, with no sales tax, plus $10 shipping fee
2. Store X: $90, a 10% discount, plus 10% tax on discounted price
3. Store Y: $90, no tax
4. Store Z: $90, a 10% sales tax, and $10 rebate after tax
Isaac can purchase a certain item in four different ways, as shown in the table. What is the lowest price for which he can purchase this item?
(A) 88.1
(B) 89.0
(C) 89.1
(D) 89.50
(E) 90.0
Rationale: 1. Internet: $80, with no sales tax, plus $10 shipping fee --> 80+10=90;
2. Store X: $90, a 10% discount, plus 10% tax on discounted price --> 90*0.9*1.1=89.1
3. Store Y: $90, no tax --> 90;
4. Store Z: $90, a 10% sales tax, and $10 rebate after tax --> 90*1.1-10=89.
So the lowest price is $89.
Answer: B.
Answer: (B) 89.0
Question: 3 men and 8 women complete a task in same time as 6 men and 2 women do. How much fraction of work will be finished in same time if 2 men and 3 women will do that task.
(A) 1/2
(B) 1/10
(C) 1/18
(D) 1/16
(E) 1/11
Rationale: 3 m + 8 w = 6 m + 2 w
3 m = 6 w
1 m = 2 w
Therefore 3 m + 8 w = 14 w
2 m + 3 w =7 w
Answer is 7/14 =1/2
Answer: A
Answer: (A) 1/2
Question: There are 10 cans in the refrigerator. 5 of them are red and 5 of them are blue. In how many ways we can remove 8 cans so that at least one red and at least one blue cans to remain the refrigerator.
(A) 410
(B) 490
(C) 493
(D) 455
(E) 445
Rationale: Answer: A.
Answer: (A) 410
Question: If W is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of W?
(A) 10
(B) 12
(C) 14
(D) 16
(E) 18
Rationale: W = 30!
8
W = 30 x 29 x 28 x 27 x 26 x 25 x 24 x 24 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 09 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
Out of these 30 , 27 , 24 , 21 , 18, 15 , 12 , 09 , 06 , 3 are factors of 3
3 x 10 , 3 x 3 x 3 , 3 x 8 , 3 x 3 x 2, 3 x 5 , 3 x 4 , 3 x 3 x 3 , 3 x 2 , 3
So we have a total of 14 three's ...
Therefore the maximum value of K can be 14 (C)
Answer: (C) 14
Question: At what rate percent per annum will a sum of money double in 6 years.
(A) 12.5%
(B) 13.5%
(C) 11.5%
(D) 14.5%
(E) 16.6%
Rationale: Let principal = P, Then, S.I.=P and Time=8 years
Rate = [(100 x P)/ (P x 6)]% = 16.6% per annum. Answer: E
Answer: (E) 16.6%
Question: What decimal fraction is 70 ml of a litre ?
(A) .7
(B) .07
(C) .05
(D) 0.07
(E) None of these
Rationale: Answer
Required fraction = 70/1000
= 7/100
= .07
Correct Option: B
Answer: (B) .07
Question: There are 8 baskets numbered from 1 to 8 and filled with apples. 10 children are asked to pick apples one by one from each basket such that the number of apples picked by each child from each basket is equal to the number marked on the basket. If there were 1000 apples in total and the baskets were filled in such a way that none of the basket became empty in the process, how many apples were left in the end?
(A) 640
(B) 680
(C) 720
(D) 760
(E) 800
Rationale: Each child takes a total of 1+2+3+4+5+6+7+8 = 8*9/2 = 36 apples.
The total number of apples taken by 10 children is 10*36 = 360
The number of apples left in the end is 1000 - 360 = 640 apples.
The answer is A.
Answer: (A) 640
Question: If two numbers x, a perfect square and y, a perfect cube are added results a two digit number, whose digits if reversed, difference is 9, Find x and y ?
(A) x=4,y=8
(B) x=4,y=9
(C) x=4,y=7
(D) x=4,y=9
(E) x=5,y=8
Rationale: 4+8=12
when reversed 21
21-12=9
x=4,y=8
ANSWER:A
Answer: (A) x=4,y=8
Question: The food in a camp lasts for 40 men for 35 days. If ten more men join, how many days will the food last?
(A) 34days
(B) 32days
(C) 30days
(D) 28days
(E) 26days
Rationale: one man can consume the same food in 40*35 = 1400 days.
10 more men join, the total number of men = 50
The number of days the food will last = 1400/50 = 28 days.
Answer: D
Answer: (D) 28days
Question: The total of the ages of Amar, Akbar and Anthony is 80 years. What was the total of their ages three years ago ?
(A) 71 years
(B) 72 years
(C) 73 years
(D) 74 years
(E) 75 years
Rationale: Answer : A.
Required sum = (80 - 3 x 3) years = (80 - 9) years = 71 years.
Answer: (A) 71 years
Question: If (x+4)^2/(x+10)=8, then the difference between the two possible values of x is:
(A) 2
(B) 6
(C) 12
(D) 16
(E) 24
Rationale: (x+4)^2/(x+10)=8
(x+4)^2=8(x+10)
x^2+8x+16=8x+80
x^2-64=0
(x-8)(x+8)=0
x=8 or x=-8
The answer is D.
Answer: (D) 16
Question: If m and n are nonzero integers and 390m = 150n, then mn must be divisible by
(A) 10
(B) 45
(C) 50
(D) 65
(E) 75
Rationale: 390m = 150n;
m/n = 5/13.
m is a multiple of 5 and n is a multiple of 13, therefore mn must be a multiple of 5*13 = 65.
Answer: D.
Answer: (D) 65
Question: A is the average (arithmetic mean) of the first 7 positive multiples of 6 and B is the median of the first 3 positive multiples of positive integer n. If the value of A^2 – B^2 is zero, what is the value of n?
(A) 8
(B) 10
(C) 12
(D) 16
(E) 24
Rationale: If A^2 - B^2 = 0, then let's assume that A = B.
A must equal the 4th positive multiple of 4, thus A = 24, which also equals B.
B is the second positive multiple of n, thus n = 24/2 = 12.
The answer is C.
Answer: (C) 12
Question: Two pipes P and Q can fill a cistern in 10 and 25 minutes respectively. Both are opened together, but at the end of 5 minutes the first is turned off. How much longer will the cistern take to fill?
(A) 12 1/7
(B) 12 1/4
(C) 12 1/3
(D) 12 1/2
(E) 12 1/5
Rationale: 5/10+ x/25 = 1
x= 12 1/2 Answer: D
Answer: (D) 12 1/2
Question: 4 litres of water is mixed in certain amount of pure milk whose cost is Rs. 3 per litre. If the dishonest milkman earns a profit of 20% by selling the mixture at initial price then what is the quantity of pure milk obtained by the customer?
(A) 24
(B) 20
(C) 18
(D) 25
(E) None of these
Rationale: cost given = Rs 3/ltr.
i.e cost earned through water mixture= 4*3 = 12 rs
therefore earned 20%, that is on water .. therefore total earned = 12*100/20 = 60 rs.
hence 60/3 = 20 ltr overall mixture!
ANSWER:B
Answer: (B) 20
Question: When two coins are tossed,Find the probability of getting all tails?
(A) 1/3
(B) 3/4
(C) 1/8
(D) 3/8
(E) 1/4
Rationale: When two coins are tossed,
S = {HH, HT, TH, TT} where H = Head and T = Tail
Let E = event of getting all tails
Then E = {TT}
so, P(E) = n(E)/n(S) =1/4
Answer: (E) 1/4
Question: Ravi purchased 20 dozens of toys at the rate of Rs. 340 per dozen. He sold each one of them at the rate of Rs. 33. What was his percentage profit?
(A) 16.4%
(B) 1.2%
(C) 5.6%
(D) 34.1%
(E) 12.2%
Rationale: A
C.P. of 1 toy = 340/12 = Rs. 28.3
S.P of 1 toy = Rs. 33
Profit = 4.6/31.25 * 100 = 16.4%
Answer is A
Answer: (A) 16.4%
Question: Let x, y and z be distinct integers, x and y are odd and positive, and z is even and
positive. Which one of the following statements cannot be true?
(A) (x – z)^2 * y is even
(B) (x – z)*y^2 is odd
(C) (x – z)*y is odd
(D) (x – y)^2 * z is even
(E) none
Rationale: Explanation :
Let x = 5, y= 3, z = 2 (according to the given condition)
(x – z)2 * y :- ( 5 - 2)2 * 3 = 27
(x – z) * y2 :- (5 - 2) * 32 = 27
(x – z) * y :- (5 - 2) * 3 = 9.
(x – y)2 * z :- (5 - 3)2 * 2 = 8.
Answer : A
Answer: (A) (x – z)^2 * y is even
Question: Boy sells a book for Rs. 450 he gets a loss of 10%, find CP of the book?
(A) Rs.300
(B) Rs.400
(C) Rs.500
(D) Rs.550
(E) Rs.600
Rationale: Find cost price
Let C.P. of book = x and S.P. = Rs. 450
S.P. of book = C.P. – (10% of C.P.)
S.P. = x – (0.10x)
450 = 0.9 x
x i.e cost price = Rs.500
C
Answer: (C) Rs.500
Question: The radius of a cylindrical vessel is 7cm and height is 3cm. Find the whole surface of the cylinder?
(A) 520 sq cm
(B) 840 sq cm
(C) 440 sq cm
(D) 120 sq cm
(E) 5 sq cm
Rationale: Explanation:
r = 7 h = 3
2πr(h + r) = 2 * 22/7 * 7(10) = 440 sq cm
Answer: C
Answer: (C) 440 sq cm
Question: What will $2000 amount to in three years if it is invested at 20% per year compound interest, with the interest being compounded annually?
(A) $3124
(B) $3260
(C) $3328
(D) $3456
(E) $3680
Rationale: After one year: 1.2 * $2000
After two years: (1.2)^2 * $2000
After three years: (1.2)^3 * $2000 = $3456
The answer is D.
Answer: (D) $3456
Question: Solve the equation for x : 6x - 27 + 3x = 4 + 9 - x?
(A) 4
(B) 5
(C) 3
(D) 9
(E) 6
Rationale: 9 x + x = 13 + 27
10 x = 40 => x = 4
Answer:A
Answer: (A) 4
Question: Pipes A and B can fill a tank in 5 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in:
(A) 3 9/17 hours
(B) 1 13 /17 hours
(C) 2 8/11 hours
(D) 4 1/ 2 hours
(E) 5 1/ 2 hours
Rationale: Explanation:
Pipes A and B can fill the tank in 5 and 6 hours respectively. Therefore,
part filled by pipe A in 1 hour =1/5
part filled by pipe B in 1 hour = 1/6
Pipe C can empty the tank in 12 hours. Therefore,
part emptied by pipe C in 1 hour =1/12
Net part filled by Pipes A,B,C together in 1 hour
=1/5+1/6-1/12=17/60
i.e., the tank can be filled in 60/17=3 9/17 hours.
Answer: Option A
Answer: (A) 3 9/17 hours
Question: In a certain store, the profit is 320% of the cost. If the cost increases by 40% but the selling price
remains constant, approximately what percentage of the selling price is the profit
(A) 67%
(B) 80%
(C) 90%
(D) 100%
(E) None of above
Rationale: Explanation:
Let C.P.= Rs. 100.
Then, Profit = Rs. 320,
S.P. = Rs. 420.
New C.P. = 140% of Rs. 100 = Rs. 140
New S.P. = Rs. 420.
Profit = Rs. (420 - 140) = Rs. 280
Required percentage = (280/420) * 100
= 66.67%(approx) =67%
Answer: A
Answer: (A) 67%
Question: A family consists of grandparents, parents and three grand children. The average age of the grandparents is 67 years, that of the parents is 37 years and that of the grandchildren is 6 years. What is the average age of the family?
(A) 28 4â„7 years
(B) 31 5â„7 years
(C) 32 2â„7 years
(D) 27 1â„2 years
(E) None of these
Rationale: Required average = (67Ã—2+37Ã—2+6Ã—3/2+2+3)
=226/7
= 32 2â„7 years
Answer C
Answer: (C) 32 2â„7 years
Question: A starts a business with a capital of Rs. 85,000. B joins in the business with Rs.42500 after some time. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1?
(A) 5 months
(B) 6 months
(C) 7 months
(D) 8 months
(E) 9 months
Rationale: Explanation:
Let B joined for x months. Then
85000×12:42500 × x = 3:1
⇒850×12:425x=3:1
⇒850×12×1=3×425x
Answer: Option D
⇒850×4=425x
⇒x=8
Answer: (D) 8 months
Question: A train 240 m in length crosses a telegraph post in 16 seconds. The speed of the train is?
(A) 77 kmph
(B) 55 kmph
(C) 54 kmph
(D) 58 kmph
(E) 76 kmph
Rationale: S = 240/16 * 18/5
= 54 kmph
Answer: C
Answer: (C) 54 kmph
Question: A & B throws a pair of dice and winner is one who gets a sum of 9 first.if A starts throwing first
Then what is the ratio of A winning over B?
(A) 8/9
(B) 9/8
(C) 7/8
(D) 6/9
(E) 5/9
Rationale: probability of a person throwing first and winning is given by 1/(2-p)
1/(2-(1/9))=9/17 prob of a
prob of b is 8/17
prob (a/b) 9/8
ANSWER:B
Answer: (B) 9/8
Question: A boy wants to go abroad by boat and return by flight. He has a choice of 8 different boat to go and 6 flight to return. In how many ways, can the boy perform his journey?
(A) 20
(B) 48
(C) 46
(D) 50
(E) 70
Rationale: Ans.(B)
Sol. Number of choices to go by ship = 8 Number of choices to return by airline = 6 From, fundamental principle, total number of ways of performing the journey = 8 x 6 = 48 ways
Answer: (B) 48
Question: A man is standing on a railway bridge which is 180 m long. He finds that a train crosses the bridge in 20 seconds but himself in 8 seconds. Find the length of the train and its speed.
(A) 10 m/sec
(B) 15 m/sec
(C) 18 m/sec
(D) 19 m/sec
(E) 25 m/sec
Rationale: If length of train is l and speed of train is s, then
l/s = 8
(l+180)/s = 20
(l+180)/l = 20/8 =5/2
2l+360 =5*l
3*l= 360
l=120 mtrs
s= l/8 = 120/8 = 15 m/sec
ANSWER:B
Answer: (B) 15 m/sec
Question: How many ways are there to arrange the letters in the word accessibility ?
(A) 1
(B) 1260
(C) 3780
(D) 7560
(E) 778377600
Rationale: 13 total words, 2C, 2S, 2I
= 13! / 2! 2! 2! = 778377600 Answer E
Answer: (E) 778377600
Question: Sam and Nik start from A and B respectively at the same time and travel towards each other at constant speeds along the same route. Sam meets Nik at point C on the road which is 600m away from starting point A and 400m away from point B. The speed of Sam is 50 m/m(meter/minute). How much time did Sam take to cover the distance between A and B?
(A) 10 minutes
(B) 15 minutes
(C) 20 minutes
(D) 22 minutes
(E) 17 minutes
Rationale: total distance from A to B-
A - C = 600m, B - C = 400m;
therefore A-B = 1000m;
Vs=50 m/m;
therefore,
t = 1000/50 = 20 minutes.
option C
Answer: (C) 20 minutes
Question: A cycle is bought for Rs.900 and sold for Rs.1080, find the gain percent?
(A) 27%
(B) 20%
(C) 25%
(D) 40%
(E) 28%
Rationale: 900 ---- 180
100 ---- ? => 20%
Answer: B
Answer: (B) 20%
Question: The present average age of a family of five members is 26 years. If the present age of the youngest member in the family is ten years, then what was the average age of the family at the time of the birth of the youngest member ? (Assume no death occurred in the family since the birth of the youngest)?
(A) 28 years
(B) 11 years
(C) 20 years
(D) 17 years
(E) 16 years
Rationale: Present total age of the members = 26(5) = 130 years.
Present age of the youngest member = 10 years
Present total age of the remaining four members = 130 -10 = 120 years
Their average age at the time of the birth of the youngest member
= [120 - (4 * 10)] / 4
= 30 - 10
= 20 years.
Answer: C
Answer: (C) 20 years
Question: In a school the number of girls is 15 more that that of the boys. now if 19% of the girls were newly joined and 25% of the boys were newly joined the number of girls is 9 more than that of the boys how many girls and boys were there?
(A) 156
(B) 157
(C) 158
(D) 159
(E) 160
Rationale: In a school the number of girls is 15 more that that of the boys.
Means G = 15 + B ------ 1
now if 19% of the girls were newly joined and 25% of the boys were newly joined
Total Girls are 1.19G
Total Boys are 1.25B
girls is 9 more than that of the boys.
1.19G = 9 + 1.25B ------ 1
Solving 1 and 2
B= 147
G= 147 + 9 = 156
ANSWER:A
Answer: (A) 156
Question: Rose made a part payment of $300 toward buying a brand new car, which represents 5% of the total cost of the car, how much remains to be paid?
(A) $5700
(B) $5500
(C) $5800
(D) $5200
(E) $5880
Rationale: Explanation:
Let's start with what the total price of the car would be. If 5% is equal to $300 then 100% equals $x. We just have to multiply $300 by 20 to get total amount=$6000. Out of this amount we then need to deduct the amount already paid which was $300 so we have $6000-$300=$5700
Answer: Option A
Answer: (A) $5700
Question: A certain list of 100 data has an average (arithmetic mean) of 7 and a standard deviation of d, where d is positive. Which of the following pairs of data, when added to the list, must result in a list of 104 data with standard deviation less than d?
(A) -7 and 0
(B) 0 and 0
(C) 0 and 7
(D) 0 and 14
(E) 7 and 7
Rationale: Standard deviation shows how much variation there is from the mean. A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.
So when we add numbers, which are far from the mean we are stretching the set making SD bigger and when we add numbers which are close to the mean we are shrinking the set making SD smaller.
According to the above adding two numbers which are closest to the mean will shrink the set most, thus decreasing SD by the greatest amount.
Closest to the mean are 7 and 7 (actually these numbers equal to the mean) thus adding them will definitely shrink the set, thus decreasing SD.
Answer: E.
Answer: (E) 7 and 7
Question: If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is?
(A) 1/8
(B) 1/2
(C) 7/9
(D) 1/6
(E) 1/1
Rationale: The number of exhaustive outcomes is 36.
Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then = 18/36 = 1/2
P(E) = 1 - 1/2
= 1/2.
Answer:B
Answer: (B) 1/2
Question: Pipe A can fill a tank in 16 hrs and pipe B can fill it in 24 hrs. If both the pipes are opened in the empty tank. In how many hours will it be fill 5/4th of that tank?
(A) 10
(B) 12
(C) 14
(D) 16
(E) 18
Rationale: Part filled A in 1 hr= (1/16)
Part filled B in 1 hr= (1/24)
Part filled by (A+B) together in 1 hr=(1/16)+(1/24)=5/48
So, The tank will be full in 48/5 hrs
Time taken to fill Exact quarter tank = (48/5) * (5/4) = 12 hrs
Answer : B
Answer: (B) 12
Question: The area of the Rest room is 40 m2 that of a longer wall 10 m2 and of the shorter wall 1 m2, find the edge of the new cube?
(A) 40 m3
(B) 10 m2
(C) 80 m3
(D) 20 m3
(E) 50 m3
Rationale: lb = 40 ; lh = 10 ; fh = 1
(lbh)2 = 40 * 10 * 1 => lbh = 20 m3
ANSWER:D
Answer: (D) 20 m3