mathewhe/aqua_rat huggingface dataset:
Question: The perimeter of a rectangular yard is completely surrounded by a fence that measures 10 meters. What is the length of the yard if the area of the yard is 6 meters squared?
(A) 8
(B) 1
(C) 5
(D) 7
(E) 3
Rationale: Perimeter of rectangular yard = 2(l + b) = 10 --> l + b = 5
Area = l * b = 6
b = 5 - l
l(5 - l) = 6
5l - l^2 = 6
l^2 - 5l + 6 = 0
Upon simplifying we get l = 2 or 3. Only 3 is there in the answer choice.
Answer: E
Answer: (E) 3
Question: If n = 6^11 – 6, what is the units digit of n?
(A) 0
(B) 1
(C) 4
(D) 6
(E) 8
Rationale: Always divide the power (incase 11) by 4 and use the remainder as the new power. The question now becomes 6^3 - 6. Now 6^3 has last digit 6. , we subtract 6 from 6 = 0 is the answer. Option A
Answer: (A) 0
Question: A bag contains 6 red, 5 blue and 2 green balls. If 2 ballsare picked at random, what is the probability that both are red?
(A) 4/21
(B) 2/13
(C) 5/26
(D) 5/27
(E) 4/27
Rationale: P(Both are red),
=6C213C2=6C213C2
=5/26
C
Answer: (C) 5/26
Question: XXX can do piece of work in 30 days while YYY alone can do it in 40 days. In how many days can XXX and YYY working together do it?
(A) 17 1/7
(B) 15 1/7
(C) 20 1/7
(D) 22 1/7
(E) 13 1/7
Rationale: XXX one day worl = 1/30
YYY one day work = 1/40
(xxx + yyy) one day work = 1/30+1/40
==>7/20
No of days req for XXX and YYY to finish the work = 1/7/120 = 17 1/7 days
ANSWER A
Answer: (A) 17 1/7
Question: The average monthly salary of laborers and supervisors in a factory is Rs.1250 per month; where as the average monthly salary of 6 supervisors is Rs.2450. If the average monthly salary of the laborers is Rs.950 find the number of laborers?
(A) 87
(B) 42
(C) 78
(D) 76
(E) 26
Rationale: 5x 6x 2x
50 25 100
250x + 150x + 200x = 4200
600x = 4200
x = 7 => 6x =42
Answer: B
Answer: (B) 42
Question: Three distinct single-digit numbers. A,B,C are in GP. If abs(x) for real x is the absolute value of x(x if x is +ve or 0 and -x if x is -ve), then the number of different possible values of abs(A+B+C) is
(A) 5
(B) 6
(C) 3
(D) 4
(E) 7
Rationale: A,B,C may be
(1,2,4) & (4,2,1)
(1,3,9) & (9,3,1)
(2,4,8) & (8,4,2)
(4,6,9) & (9,6,4)
find abs(A+B+C) for these 8 GPs
7,13,15,19
So,we get 4 different values
ANSWER:D
Answer: (D) 4
Question: If a train, travelling at a speed of 90 kmph, crosses a pole in 6 sec, then the length of train is?
(A) 281 m
(B) 112 m
(C) 117 m
(D) 125 m
(E) 150 m
Rationale: E
E = 90 * 5/18 * 6 = 150 m
Answer: (E) 150 m
Question: we have 5 weights one of 2 kg one of 3 kg one of 5 kg one of 10 kg one of 50 kg by using only three weight how many weight u can weight
(A) 12
(B) 16
(C) 15
(D) 10
(E) 8
Rationale: select 3 weight out of 5, 5C3=10
ANSWER:D
Answer: (D) 10
Question: Find a sum for first 8 prime no's from number series?
(A) 77
(B) 79
(C) 89
(D) 34
(E) 36
Rationale: Required sum = (2+ 3+ 5+ 7+11+ 13+17+ 19) = 77
Note: 1 is not a prime number
Option A
Answer: (A) 77
Question: Rs.1500 is divided into two parts such that if one part is invested at 6% and the other at 5% the whole annual interest from both the sum is Rs.81. How much was lent at 5%?
(A) 299
(B) 666
(C) 778
(D) 900
(E) 977
Rationale: (x*5*1)/100 + [(1500 - x)*6*1]/100 = 81
5x/100 + 90 – 6x/100 = 81
x/100 = 9
=> x = 900
Answer:D
Answer: (D) 900
Question: 5 + 5 + 5 + 2 × 5^2 + 2 × 5^3 + 2 × 5^4 + 2 × 5^5 + 2 × 5^6 + 2 × 5^7 =
(A) 5^9
(B) 5^7
(C) 5^10
(D) 5^8
(E) 5^11
Rationale: We have the sum of 9 terms. Now, if all terms were equal to the largest term 2*5^7 we would have: sum=9*(2*5^7)=18*5^7=~5^9, so the actual sum is less than 5^9 and more than 5^7 (option B) as the last term is already more than that. So the answer is clearly D.
Answer: D
Answer: (D) 5^8
Question: Kim has 3 pairs of shoes; each pair is a different color. If Kim randomly selects 2 shoes without replacement from the 6 shoes, what is the probability that she will select 2 shoes of the same color?
(A) 2/5
(B) 1/5
(C) 1/9
(D) 1/10
(E) 1/25
Rationale: Total pairs = 6C2 = 15; Same Color Pairs= 3C1*1C1=3; Prob = 1/5
Ans B
Answer: (B) 1/5
Question: A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour?
(A) 3.6
(B) 7.2
(C) 8.4
(D) 10
(E) None of these
Rationale: Speed=(600/5*60)m/sec=2 m/sec=(2*18/5)km/hr=7.2km/hr.
Correct Option: B
Answer: (B) 7.2
Question: 90 is divided into two parts in such a way that seventh part of first and ninth part of second are equal. Find the smallest part?
(A) 66
(B) 35
(C) 42
(D) 27
(E) 11
Rationale: x/7 = y/9 => x:y = 7:9
7/16 * 90 = 35
Answer: B
Answer: (B) 35
Question: Surface area of a sphere is 2464 cm2. If its radius is doubled, then the surface area of the new sphere will be
(A) 4920 cm2
(B) 4727 cm2
(C) 9856 cm2
(D) 19712 cm2
(E) None
Rationale: Sol.
Let the original radius be r.
Then, original surface area = 4Πr2 = 2464 cm2(given).
New radius = 2r.
∴ New surface area = 4Π (2r)2
= 4 x 4Πr2
= (4x2464) cm2
= 9856 cm2
Answer C
Answer: (C) 9856 cm2
Question: The ratio of the volumes of two cubes is 729 : 1331. What is the ratio of their total surface areas?
(A) 81 : 121
(B) 81 : 126
(C) 81 : 120
(D) 81 : 128
(E) 81 : 122
Rationale: Ratio of the sides = ³√729 : ³√1331 = 9 : 11
Ratio of surface areas = 92 : 112 = 81 : 121
Answer: A
Answer: (A) 81 : 121
Question: A person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 6km?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 8
Rationale: M = 4
S = 2
US = 4 - 2 = 2
D = 6
T = 6/2 = 3
Answer: A
Answer: (A) 3
Question: Anita, Indu and Geeta can do a piece of work in 18 days, 27 days and 36 days respectively. They start working together. After working for 4 days. Anita goes away and Indu leaves 7 days before the work is finished. Only Geeta remains at work from beginning to end. In how many days was the whole work done?
(A) 16
(B) 77
(C) 88
(D) 55
(E) 41
Rationale: 4/18 + (x -7)/27 + x/36 = 1
x = 16 days
Answer: A
Answer: (A) 16
Question: What will come in place of the x in the following Number series? 46080, 3840, 384, 48, x
(A) 8
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: 46080 /12 = 3840
3840 /10 = 384
384 /8 = 48
48 /6 = 8
A
Answer: (A) 8
Question: How many seconds will a 400 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) 20
(B) 30
(C) 40
(D) 24
(E) 60
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 = 400 * 3/50 = 24 sec.
Answer: Option D
Answer: (D) 24
Question: A man can row a boat at 20 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 60 km downstream?
(A) 30/17 hours
(B) 30/15 hours
(C) 36/13 hours
(D) 30/13 hours
(E) 80/13 hours
Rationale: Speed downstream
= 20 + 6 = 26 kmph.
Time required to cover 60 km downstream
= d/s = 60/26
= 30/13 hours.
Answer: D
Answer: (D) 30/13 hours
Question: Of the 28 participants in a certain competition, half are male, and half of the males are younger than 18 years of age. If half of the female competitors are also younger than 18 years of age, into how many distinct groups of 4 competitors could the participants be divided if each group must contain two males under 18 years of age and 2 females over 18 years of age?
(A) 341
(B) 441
(C) 641
(D) 941
(E) 201
Rationale: M under 18 - 7
F above 18 - 7
How many distinct groups can be formed now: 7c2 * 7c2 = 441
Answer : B
Answer: (B) 441
Question: Find the quadratic equations whose roots are the reciprocals of the roots of 2x2 + 5x + 3 = 0?
(A) 3x2 + 5x - 2 = 0
(B) 3x2 + 5x + 2 = 0
(C) 3x2 - 5x + 2 = 0
(D) 3x2 - 5x - 2 = 0
(E) None of these
Rationale: The quadratic equation whose roots are reciprocal of 2x2 + 5x + 3 = 0 can be obtained by replacing x by 1/x.
Hence, 2(1/x)2 + 5(1/x) + 3 = 0
=> 3x2 + 5x + 2 = 0
ANSWER:B
Answer: (B) 3x2 + 5x + 2 = 0
Question: A train covers a distance of 100km in 1 hour. If its speed is decreased by 20km/hr, the time taken by the car to cover the same distance will be?
(A) 1hr
(B) 1hr 15min
(C) 50min
(D) 1hr 30min
(E) 1hr 45min
Rationale: Speed = 100/1 = 100km/hr
New speed = 100-20 = 80 km/hr
Time taken = 100/80 = 1hr 15min
Answer is B
Answer: (B) 1hr 15min
Question: Ram completes a piece of work in 15 days, Raja completes the same work in 20 days. If both of them work together, then the number of days required to complete the work is?
(A) 6 days
(B) 8 days
(C) 10 days
(D) 8.57 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.
That is, the required No. of days = 15 × 20/35 = 8.57 days
Answer : D
Answer: (D) 8.57 days
Question: A cube of side one meter length is cut into small cubes of side 10 cm each. How many such small cubes can be obtained?
(A) 10
(B) 100
(C) 1000
(D) 10000
(E) 102
Rationale: Along one edge, the number of small cubes that can be cut
= 100/10 = 10
Along each edge 10 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut = 10 * 10 * 10 = 1000
Answer: Option C
Answer: (C) 1000
Question: Four 6 faced dice are thrown together. The probability that all the four show the same number on them is ?
(A) 1/248
(B) 1/216
(C) 1/144
(D) 1/200
(E) 1/242
Rationale: It all 4 numbers have to be same basically we want quadruplets. 1111, 2222, 3333, 4444, 5555 and 6666. Those are six in number. Further the four dice can fall in 6 * 6 * 6 * 6 = 1296 ways.
Hence the probability is 6/1296 = 1/216
Answer:B
Answer: (B) 1/216
Question: In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit
(A) 70
(B) 77
(C) 289
(D) 27
(E) 10
Rationale: Explanation:
Let C.P.= Rs. 100.
Then, Profit = Rs. 320,
S.P. = Rs. 420.
New C.P. = 125% of Rs. 100 = Rs. 125
New S.P. = Rs. 420.
Profit = Rs. (420 - 125) = Rs. 295
Required percentage = (295/420) * 100
= 70%(approx)
Answer: A) 70%
Answer: (A) 70
Question: A and B complete a work in 6 days. A alone can do it in 10 days. If both together can do the work in how many days?
(A) 8 days
(B) 12 days
(C) 15 days
(D) 16 days
(E) 3.75 days
Rationale: Explanation:
1/6 + 1/10 = 8/30 = 4/15
15/4 = 3.75 days
Answer E
Answer: (E) 3.75 days
Question: The area of square ABCD above is 20. The shaded region is the intersection of the square and a circular region centered at C. What is the area of the shaded region?
(A) 18−9/4∗π
(B) 18−10/2∗π
(C) 9+9/4∗π
(D) 9+9/2∗π
(E) 9/2−9/4∗π
Rationale: =Square - Quarter circle
=20- pi*20/4
=20- pi*10/2
ANSWER:B
Answer: (B) 18−10/2∗π
Question: In the equation p = 36.12q, q and p are integers. If p/q leaves a remainder of r, which of the following must divide into r?
(A) 2
(B) 3
(C) 4
(D) 6
(E) 12
Rationale: 1) It says it is a equation, so p=36.12q should be 36.12 * q..
2) It says q is an integer, again it means 36.12 * q..
Otherwise q would be just a digit and it would be mentioned..
Although not clearly mentioned that 36.12q is actually 36.12 * q, BUT entire info points towards that..
and that is why I have taken p/q = 36.12
Answer: (B) 3
Question: Working alone, A can complete a certain kind of job in 6 hours. A and D, working together at their respective rates, can complete one of these jobs in 4 hours. In how many hours can D, working alone, complete one of these jobs?
(A)  8
(B)  10
(C)  12
(D)  14
(E)  16
Rationale: Let total time taken by D to complete the job = D
total time taken by A to complete the job = 6
Work done by A in an hour
1/A = 1/6
Working together A and D can complete the job in 4 hours
1/A + 1/D = 1/4
=>1/D = 1/4 - 1/A
= 1/4 - 1/6
= 1/12
=> D = 12 hours
Answer C
Answer: (C)  12
Question: Some part of a 50% solution of acid was replaced with an equal amount of 30% solution of acid. If, as a result, 40% solution of acid was obtained, what part of the original solution was replaced?
(A) 1/5
(B) 1/4
(C) 1/2
(D) 3/4
(E) 4/5
Rationale: Original Acid : Total ratio = 50:100 . let us say you replaced x part of this. So you are left with (1-x) of the original. So volume of acid left is (1-x)50.
in the new solution.. you added x of 30% solution. i.e 30x acid
(1-x)50 + 30x is the volume of acid. The total volume is still 100. And this concentration is 40%
[(1-x)50 + 30x] / 100 = 40/100
solve to get x=1/2
ANSWER:C
Answer: (C) 1/2
Question: If y ¤ z = y^(2z) for all positive integers, then (3 ¤ 4) ¤ 2 =
(A) 3^8
(B) 3^12
(C) 3^16
(D) 3^24
(E) 3^32
Rationale: y ¤ z = y^(2z)
3 ¤ 4 = 3^(8)
(3 ¤ 4) ¤ 2 = (3^8) ¤ 2 = (3^8)^4 = 3^32
Correct Option: E
Answer: (E) 3^32
Question: The set S consists of 5 numbers: {1,2,3,4,5}. If all possible subsets including the null set are created and one subset is chosen at random, what is the probability that the subset has 4 as its largest number?
(A) 1/2
(B) 1/4
(C) 1/8
(D) 1/16
(E) 5/32
Rationale: The set S has 2^5 = 32 subsets.
The number 5 is in half of these subsets.
Of the remaining 16 subsets, 4 is an element in 8 of them.
Thus 4 is the largest number in 8 subsets of S.
The probability that 4 is the largest number is 8/32 = 1/4.
The answer is B.
Answer: (B) 1/4
Question: A fruit seller had some apples. He sells 80% and still has 500 apples. Originally, he had ?
(A) 1588 apples
(B) 2500apples
(C) 500 apples
(D) 2000 apples
(E) None
Rationale: Answer
âˆµ 20% of N = 500
âˆ´ N = (500 x 100)/20 = 2500
Correct Option:B
Answer: (B) 2500apples
Question: In what proportion must rice at Rs 3.10 per kg be mixed with rice at Rs 3.60 per kg, so that the mixture be worth Rs 3.25 a kg?
(A) 3/5
(B) 3/2
(C) 5/3
(D) 5/7
(E) 7/3
Rationale: C.P of 1 kg of cheaper rice = Rs 3.10
C.P of 1 kg of expensive rice = Rs 3.60
the mixture be worth for 1 kg = Rs 3.25
By the alligation rule : Quantity of cheaper rice / Quantity of expensive rice
= (3.6 - 3.25)/(3.25 - 3.10)
= (0.35)/(0.15)
= 7/3
E
Answer: (E) 7/3
Question: Two trains, each 100 meters long, moving in opposite directions, completely pass each other in 10 seconds. If one train is moving twice as fast the other, then what is the speed of the faster train (in km/hr)?
(A) 48 km/hr
(B) 56 km/hr
(C) 64 km/hr
(D) 72 km/hr
(E) 80 km/hr
Rationale: Let the speed of the slower train be x m/s
Then, the speed of the faster train is 2x m/s
The relative speed is 3x m/s
(100 + 100)/10 = 3x
x = 20/3
So, the speed of the faster train is 40/3 = 40/3 * 18/5 = 48 km/hr
The answer is A.
Answer: (A) 48 km/hr
Question: A train covers a distance in 50 min, if it runs at a speed of 48kmph on an average. The speed at which the train must run to reduce the time of journey to 20min will be.
(A) 60 km/h
(B) 55 km/h
(C) 40 km/h
(D) 120 km/h
(E) 65 km/h
Rationale: Time=50/60 hr=5/6hr
Speed=48mph
distance=S*T=48*5/6=40km
time=20/60hr=1/3hr
New speed = 40* 3/1 kmph= 120kmph
Answer : D
Answer: (D) 120 km/h
Question: The present ratio between the ages of Paul and Ben is 5:2. In 4 years time Paul will be 28. What is the present age of Ben?
(A) 13
(B) 12
(C) 11
(D) 15
(E) 10
Rationale: Let the present ages of Paul and Ben be 5x years and 2x years respectively
4x+4 = 28
4x = 24
x = 6
Ben's age = 2x = 12 years
Answer is B
Answer: (B) 12
Question: Jennie’s take-home pay last year was the same each month, and she saved the same fraction of her take-home pay each month. The total amount of money that she had saved at the end of the year was 3 times the amount of that portion of her monthly take-home pay that she did NOT save. If all the money that she saved last year was from her take-home pay, what fraction of her take-home pay did she save each month?
(A) 1/7
(B) 1/5
(C) 1/4
(D) 1/3
(E) 1/2
Rationale: Suppose the portion of her salary that she saved is X
and the remaining portion is Y
X+Y= total take home salary
given, 12X = 3Y
or 4X = Y
Total take-home salary= X+ 4X= 5X
hence, she saved 1/5-th portion of her take home salary
B
Answer: (B) 1/5
Question: Look at this series: V, VIII, XI, XIV, __, XX, ... What number should fill the blank?
(A) IX
(B) XXIII
(C) XVII
(D) XV
(E) X
Rationale: C
XVII
This is a simple addition series; each number is 3 more than the previous number.
Answer: (C) XVII
Question: A man engaged a servant on the condition that he would pay him Rs.900 and a uniform after one year service. He served only for 9 months and received uniform and Rs.650, find the price of the uniform?
(A) Rs.80
(B) Rs.85
(C) Rs.90
(D) Rs.100
(E) Rs.120
Rationale: 9/12 = 3/4 * 900 = 675
650
-------------
25
1/4 -------- 25
1 --------- ? => Rs.100
ANSWER:D
Answer: (D) Rs.100
Question: Count each 7 which is not immediately preceded by 5 but is immediately followed by either 2 or 3. How many such 7's are there?
5 7 2 6 5 7 3 8 7 3 2 5 7 2 7 3 4 8 2 6 7 8
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: 8 7 3
2 7 3
count 2
ANSWER:A
Answer: (A) 2
Question: Each factor of 230 is inscribed on its own plastic ball, and all of the balls are placed in a jar. If a ball is randomly selected from the jar, what is the probability that the ball is inscribed with a multiple of 42?
(A) 1/16
(B) 5/42
(C) 1/8
(D) 3/16
(E) 1/4
Rationale: 210=2*3*5*7, so the # of factors 210 has is (1+1)(1+1)(1+1)(1+1)=16 (see below);
42=2*3*7, so out of 16 factors only two are multiples of 42: 42 and 210, itself;
So, the probability is 2/16=3/16.
Answer: D
Answer: (D) 3/16
Question: What is the average (arithmetic mean) of all the multiples of ten from 10 to 150 inclusive?
(A) 80
(B) 95
(C) 100
(D) 105
(E) 110
Rationale: The multiples of ten from 10 to 150 inclusive would be an evenly spaced set with 15 terms - 10, 20, 30,.......150
So average = (First term + Last Term)/2 = (10 + 150)/2 = 160/2 = 80
Hence, the correct answer is A.
Answer: (A) 80
Question: Micheal and Adam can do together a piece of work in 20 days. After they have worked together for 11 days Micheal stops and Adam completes the remaining work in 10 days. In how many days Micheal complete the work separately.
(A) 80 days
(B) 100 days
(C) 120 days
(D) 110 days
(E) 200 days
Rationale: Rate of both = 1/20
Together they do = 1/20*11 = 11/20
Left work = 1 - 11/20 = 9/20
Adam completes 9/20 work in 10 day
so he took 10*20/9 = 200/9 days to complete the left work alone.
Thus the rate of adam is 9/200
Rate of Micheal = 1/20 - 9/200 = 1/200
Thus micheal takes 200 days to complete the whole work.
ans. E.
Answer: (E) 200 days
Question: If a(a - 6) = 27 and b(b - 6) = 27, where a ≠ b, then a + b =?
(A) −48
(B) −2
(C) 6
(D) 48
(E) 46
Rationale: i.e. if a =-3 then b = 9
or if a = 9 then b =-3
But in each case a+b = -3+9 = 6
Answer: option E
Answer: (E) 46
Question: A rectangular field is to be fenced on three sides leaving a side of 34 feet uncovered.If the area of the field is 680 sq.ft, how many feet of fencing will be required?
(A) 74ft
(B) 88ft
(C) 22ft
(D) 11ft
(E) 66ft
Rationale: Given that length and area, so we can find the breadth.
Length x Breadth = Area
34 x Breadth = 680
Breadth = 20 feet
Area to be fenced = 2B + L = 2 (20) + 34 = 88 feet
Answer: A) 74ft
Answer: (A) 74ft
Question: In the arithmetic sequence t1, t2, t3, ..., tn, t1=23 and tn= tn-1 - 3 for each n > 1. What is the value of n when tn = 5?
(A) -1
(B) 7
(C) 10
(D) 14
(E) 20
Rationale: We know that t1 = 23
So, using the given formula we have:
t1=(t1-1) -3 =23
t0 - 3 = 23
t0= 26
The same way we find that t2= 20
It seems that the sequence goes like this:
t0 = 26
t1 = 23
t2 = 20
t3 = 17
t4 = 14
t5 = 11
t6 = 8
t7 = 5
So, ourANS is B.
Answer: (B) 7
Question: A grocery shop has a sale of Rs. 6235, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?
(A) 4857
(B) 4184
(C) 4012
(D) 5191
(E) 5291
Rationale: Let the sale in the sixth month =x
Then
(6235+6927+6855+7230+6562+x)/6 =6500
=>6235+6927+6855+7230+6562+x =6×6500
=> 33809+x=39000
=> x=39000−33809
=5191
ANSWER:D
Answer: (D) 5191
Question: The ratio of numbers is 3:4 and their H.C.F is 3. Their L.C.M is:
(A) 12
(B) 16
(C) 36
(D) 48
(E) 98
Rationale: Let the numbers be 3x and 4x.
Then their H.C.F = x. So, x = 3.
So, the numbers are 9 and 12.
L.C.M of 9 and 12 = 36.
ANSWER:C
Answer: (C) 36
Question: In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?
(A) 6.25
(B) 7
(C) 7.25
(D) 7.5
(E) 8
Rationale: So we calculate the runs in the first 10 overs
first 10 overs they got 32 runs
remaining 40 overs they got 250
250 / 40 =6.25
answer A
Answer: (A) 6.25
Question: In the next Cricket World Cup T-20, Team T has decided to score 200 runs only through 4s and 6s. In how many ways can the Team T score these 200 runs?
(A) 13
(B) 15
(C) 16
(D) 17
(E) 18
Rationale: Team T can score a maximum of 50 fours and a minimum of 2 fours with an interval or spacing of 3 units to accommodate the 6's.
So the number of fours scored forms an AP 2, 5, 8, ... 50 with a common difference of 3.
Number of ways of scoring 200 only through 4's and 6's = (50 - 2)/3 + 1 = 17
Answer: D
Alternate solution: 4x + 6y = 200 --> 2x + 3y = 100
x = (100 - 3y)/2 --> 100 - 3y should be even. This is possible when 3y is even.
There are 17 even multiples of 3 between 0 and 100.
Answer: D
Answer: (D) 17
Question: On 8th Feb, 2005 it was Tuesday. What was the day of the week on 8th Feb, 2004?
(A) Saturday
(B) Tuesday
(C) Friday
(D) Sunday
(E) monday
Rationale: Explanation:
The year 2004 is a leap year. It has 2 odd days.
The day on 8th Feb, 2004 is 2 days before the day on 8th Feb, 2005.
Hence, this day is Sunday
Answer: D
Answer: (D) Sunday
Question: The average of four consecutive odd numbers is 24. Find the largest number
(A) 25
(B) 27
(C) 29
(D) 31
(E) 32
Rationale: Explanation:
Let the numbers are x, x+2, x+4, x+6, then
=>x+(x+2)+(x+4)+(x+6) / 4=24
=>4x+12) / 4=24
=>x+3=24=>x=21
So largest number is 21 + 6 = 27
Option B
Answer: (B) 27
Question: What is difference between biggest and smallest fraction among 1/3, 3/4, 4/5 and 5/6
(A) 2/5
(B) 1/2
(C) 1/6
(D) 1/7
(E) None of these
Rationale: Explanation:
1/3 = .33, 3/4 = .75, 4/5 = .8 and 5/6 = .833
So biggest is 5/6 and smallest is 1/3
Their difference is 5/6 - 1/3 = 3/6 = 1/2
Option B
Answer: (B) 1/2
Question: X does a work in 15 days. Y does the same work in 45 days. In how many days they together will do the same work?
(A) 10
(B) 12
(C) 20
(D) 11.25
(E) 15
Rationale: X's 1day's work= 1/15
Y's 1 day's work=1/45
(X+Y)'s 1day's work= (1/15+1/45)=1/11.25
both together will finish the work in 11.25 days.
correct option is D
Answer: (D) 11.25
Question: Two men A and B start from place X walking at 4 ½ kmph and 5 ¾ kmph respectively. How many km apart they are at the end of 5 ½ hours if they are walking in the same direction?
(A) 7 km
(B) 6 km
(C) 6 7/8 km
(D) 9 km
(E) 5 km
Rationale: RS = 5 ¾ - 4 ½ = 1 ¼
T = 3 ½ h.
D = 5/4 * 11/2 = 55/8
= 6 7/8 km
Answer:C
Answer: (C) 6 7/8 km
Question: Population is 22000. Population increases by 10% every year, then the population after 3 years is?
(A) 26630
(B) 29282
(C) 36620
(D) 26620
(E) 26820
Rationale: population after 1st year = 22000*10/100 = 2200 ===> 22000+2200 = 24000
population after 2nd year = 24000*10/100 = 2400 ===> 24000+2400 = 26620
population after 3rd year = 26620*10/100 = 2662 ===> 26620+2662 = 29282
ANSWER:B
Answer: (B) 29282
Question: The average age of three boys is 30 years and their ages are in the proportion 3 : 6 : 12. The age of the youngest boy is:
(A) 21 years
(B) 18 years
(C) 15 years
(D) 8.5 years
(E) None of these
Rationale: Total age of 3 boys = (30 Ã— 3) years = 90 years. Ratio of their ages = 3 : 6 : 12.
Age of the youngest = (60 Ã— 3â„21) years = 8.5 years.
Answer D
Answer: (D) 8.5 years