mathewhe/aqua_rat huggingface dataset:
Question: Each week, Harry is paid x dollars per hour for the first 30 hours and 2x dollars for each additional hour worked that week. Each week, James is paid x dollars per per hour for the first 40 hours and 2x dollars for each additional hour worked that week. Last week James worked a total of 41 hours If Harry and James were paid the same amount last week, how many hours did Harry work last week ?
(A) 35
(B) 36
(C) 37
(D) 38
(E) 39
Rationale: James worked for 41 hours hence he earned 40*x+1*2x=42x dollars;
We know that Harry also earned the same 42x dollars, out of which he earned 30x dollars for thefirst 30 hoursplus 12x additional dollars. Since for each additional hour he gets 2x dollars then he worked for 12x/2x=6 additional hours, so Harry worked for total of 30+6=36 hours.
Answer: B.
Answer: (B) 36
Question: A certain sum of money doubles itself in 10 years in how much many years will it trible itself at the same rate?
(A) 20
(B) 88
(C) 77
(D) 66
(E) 21
Rationale: 100 ---- 100 --- 10
100 --- 10
--------------------
300 ---- 20 years
Answer: A
Answer: (A) 20
Question: How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5 % per annum of simple interest ?
(A) 3.5 years
(B) 4 years
(C) 4.5 years
(D) 5 years
(E) None
Rationale: Solution
Time = (100x81/450x45)years = 4 years.
Answer B
Answer: (B) 4 years
Question: Three partners A,B and C shared the profit in a software business in the ratio 5:7:8. They had partnered for 14 months, 8 months and 7 months respectively. Find the ratio of their investments?
(A) 19:49:64
(B) 20:49:64
(C) 20:49:65
(D) 20:50:64
(E) None of these
Rationale: Explanation:
Let their investments be Rs. x for 14 months, Rs. y for 8 months and Rs. z for 7 months respectively
Then, 14x : 8y : 7z = 5 : 7 : 8
Now, 14x/8x = 5/7
=> y = (49/20)x
14x/7z = 5/8
=> z = (16/5)x
=>x:y:z = x:(49/20)x:(16/5)x
= 20:49:64
Option B
Answer: (B) 20:49:64
Question: A basketball team scored x points per game in its first n games of the season, and in all the following games it scored an average (arithmetic mean) of y points per game. What was the average number of points per game in its first n + 2 games?
(A) x + 3y/(n + 3)
(B) x + y/(n + 3)
(C) (x + 3y)/(n + 3)
(D) (nx + 3y)/(n + 2)
(E) (3x + ny)/(n + 3)
Rationale: Total points in first n games = nx
Total marks in next 3 games is 3y
So, Average marks in n + 2 games = (nx+3y)/(n+2)
Hence, correct answer will be (D)
Answer: (D) (nx + 3y)/(n + 2)
Question: Indu gave Bindu Rs.5000 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest?
(A) 8
(B) 2
(C) 9
(D) 5
(E) 1
Rationale: 5000
= D(100/4)2
D = 8
Answer: A
Answer: (A) 8
Question: The average weight of 25 boys sitting in a class had some value. A new boy added to them whose weight was 46 kg only. Due to his arrival, the average weight of all the boys decreased by 5 kg. Find the average weight of first 25 boys?
(A) 150
(B) 152
(C) 176
(D) 180
(E) 182
Rationale: 25x + 46 = 26(x – 5)
x = 176
C
Answer: (C) 176
Question: A baker filled with a measuring cup with 3/5 cup water. He poured 1/2 of the water into the batter, and then spilled 1/8 of the water on the floor. How much water will the baker needed to add what is left in the cup to have 50% more than what he started with?
(A) 1/8 cup
(B) 3/8 cup
(C) 1/4 cup
(D) 1/2 cup
(E) 29/40 cup
Rationale: E
3/5 is the original water in cup .half in batter.So left is 3/10 out which 1/8 is spilled out.So again left with 1/8.
so 50% more than what he started was = 3/5+1/2*(3/5)=9/10
Amount of water needed to add = 9/10 - 1/8=29/40
E
Answer: (E) 29/40 cup
Question: Find the number of bricks, each measuring 24 cm x 12 cm x 8 cm, required to construct a wall 24 m long, 8m high and 60 cm thick, if 10% of the wall is filled with mortar?
(A) 35000
(B) 45000
(C) 55000
(D) 65000
(E) None of these
Rationale: Explanation:
Volume of the wall = (2400 x 800 x 60) cm3
Volume of bricks = 90% of the volume of the wall
= [(90/100) x 2400 x 800 x 60] cm3
Volume of 1 brick = (24 x 12 x 8) cm3
Number of bricks = [(90/100) x (2400 x 800 x 60) ]/ (24 x 12 x 8) = 45000
Answer: B
Answer: (B) 45000
Question: Excluding stoppages, the speed of a bus is 84 kmph and including stoppages, it is 70 kmph. For how many minutes does the bus stop per hour?
(A) 12 min
(B) 10 min
(C) 15 min
(D) 14 min
(E) 13 min
Rationale: Due to stoppages, it covers 14 km less.
Time taken to cover 14 km = (14/84 x 60) min = 10 min
Answer : B
Answer: (B) 10 min
Question: When x is multiplied by 3, the result is 18 more than the result of subtracting x from 70. What is the value of x?
(A) -4
(B) -2
(C) 11
(D) 13
(E) 22
Rationale: The equation that can be formed is:
3x-18=70-x
or, 4x=88
or, x=22.
E answer.
Answer: (E) 22
Question: An express traveled at an average speed of 80 km/hr, stopping for 3 min after every 45 kn. How long did it take to reach its destination 480 km from the starting point?
(A) 5 hrs 21 min
(B) 4 hrs 21 min
(C) 6 hrs 41 min
(D) 6 hrs 27 min
(E) 4 hrs 34 min
Rationale: D
6 hrs 27 min
Time taken to cover 480 km = 480/80 = 6 hrs.
Number of stoppages = 480/45 - 1 = 9
Total time of stoppages = 3 * 9 = 27 min
Hence, total time taken = 6 hrs 27 min.
Answer: (D) 6 hrs 27 min
Question: What would be the compound interest on Rs.7700/- at 15 ¼% per year for 2 years compounded annually
(A) 2527.57
(B) 2257.57
(C) 2572.57
(D) 2752.57
(E) 2725.57
Rationale: Principal = Rs. 7700/-
time = 2 years
rate = 15 ¼%
Amount = P(1+R/100)n
= 7700 × (1 + 61/(4 × 100)2)
= 7700 × [(1 + 61/400)2]
= 7700 × [(461/400)2)]
= 7700 × 461/400 × 461/400
= 7700 × 1.1525 × 1.1525
= 7700 × 1.32825625
= 10227.573125
C.I = 10227.573125 - 7700 = 2527.57/-
Answer is A.
Answer: (A) 2527.57
Question: Two letters from the word BARKHINT are selected at random. What is the probability that at least one of the selected letters is a consonant?
(A) 30/28
(B) 40/28
(C) 25/28
(D) 27/28
(E) 32/28
Rationale: There are 6 consonants and 2 vowels in BARKHINT .
probability that at least one of the selected letters is a consonant = 1 - (Probability of both vowels)
Probability of both vowels = 2C2/8C2 = 1/28
So,Answer is 1 - 1/28 = 27/28
Answer : D
Answer: (D) 27/28
Question: James purchased n items from a catalog for $12 each. Postage and handling charges consisted of $5 for the first item and $2 for each additional item. Which of the following gives the total dollar amount for Kim’s purchase, including postage and handling, in terms of n ?
(A) 13n + 3
(B) 13n + 4
(C) 13n + 2
(D) 13n + 6
(E) 13n + 5
Rationale: its A
n items for $12 each
total price $12n
postage and handling of $5 for 1st item and $2 for the rest
total postage and handling = $ [5+ (n-2)]
= $ n+3
total cost
12n+n+3 = 13n+3
Answer: (A) 13n + 3
Question: A bag contains 26 purple jellybeans, 15 green jellybeans, and 9 yellow jellybeans; these jellybeans are the only items in the bag. If a person picks a jellybean at random out of the bag, what is the probability that the jellybean will be green?
(A) 15%
(B) 20%
(C) 25%
(D) 30%
(E) 35%
Rationale: Probability of green beans = 15 / (26 + 15 + 9) = 3/10 = 30%
Answer is D
Answer: (D) 30%
Question: If x is a positive integer, then the least value of x for which x! is divisible by 100 is?
Can someone please explain intuitively what the question is asking?
(A) 5
(B) 9
(C) 10
(D) 15
(E) 30
Rationale: In order x! to be divisible by 1,00, it should have at least 2 trailing zeros. A trailing 0 in factorial of a number is produced by 2 and 5 in it: 2*5 = 10. So, we need 10 to be in x! at least in power of 2.
5! = 120 has 1 trailing zeros.
10! will have 2 trailing zeros.
Answer: C.
Answer: (C) 10
Question: A can run a kilometer race in 4 1/2 min while B can run same race in 5 min. How many meters start can A give B in a kilometer race, so that the race mat end in a dead heat?
(A) 200 m
(B) 876 m
(C) 868 m
(D) 100 m
(E) 862 m
Rationale: A can give B (5 min - 4 1/2 min) = 30 sec start.
The distance covered by B in 5 min = 1000 m.
Distance covered in 30 sec = (1000 * 30)/300 = 100 m.
A can give B 100m start.
Answer:D
Answer: (D) 100 m
Question: If 2/3rd of the contents of a container evaporated on the 1st day. And 1/4th of the remaining evaporated on the second day. What part of the contents of the container is left at the end of the second day?
(A) 1/4
(B) 1/12
(C) 1/18
(D) 1/6
(E) 1/2
Rationale: After first day, 1/3 of the contents remain.
After second day,
(1/3) - (1/4(2/3)) = (1/3) - (1/6) = 1/6 of the contents remain
ANSWER:D
Answer: (D) 1/6
Question: A sum fetched a total simple interest of 4052.25 at the rate of 9 %.p.a. in 5 years. What is the sum?
(A) 9005
(B) 8925
(C) 2345
(D) 6474
(E) 8723
Rationale: Principal = (100 x 4052.25)/(9 x 5)
= 405225/45
= 9005.
ANSWER A
Answer: (A) 9005
Question: Every day a certain bank calculates its average daily deposit for that calendar month up to and including that day. If on a randomly chosen day in June the sum of all deposits up to and including that day is a prime integer greater than 100, what is the probability that the average daily deposit up to and including that day contains fewer than 5 decimal places?
(A)
(B)
(C)
(D)
(E)
(A) 1/10
(B) 2/15
(C) 4/15
(D) 3/10
(E) 11/30
Rationale: average=p/d has less than 5 decimal places? Where p=prime>100 and d is the chosen day.
If the chosen day, d, is NOT of a type 2^n5^m (where n and m are nonnegative integers) then average=p/d will not be a terminating decimal and thus will have more than 5 decimal places.
How many such days are there of a type 2n5m: 1, 2, 4, 5, 8, 10, 16, 20, 25 (1=2^0∗5^0, 2=2^2, 4=2^2, 5, 8=2^3, 10=2∗5, 16=2^4, 20=22∗5, 2^5=52), total of 9 such days (1st of June, 4th of June, ...).
Now, does p divided by any of these d′s have fewer than 5 decimal places? Yes, as p/d∗10,000=integer for any such d (10,000 is divisible by all these numbers: 1, 2, 4, 5, 8, 10, 16, 20, 25).
So, there are 9 such days out of 30 in June: P=9/30=3/10 .
Answer: D.
Answer: (D) 3/10
Question: (3 x 10^4) + (2 x 10^3) + (4 x 10^2) =
(A) 302400
(B) 32400
(C) 30240
(D) 3240
(E) 324
Rationale: When you multiply a number by 10 you just add a zero
=> 3 x 10^4 => add 4 zeros => 3 x 10^4 = 30000
=>2 x 10^3 = 2000
=> 4 x 10^2 = 400
=>3 x 10^4 + 2 x 10^3 + 4 x 10^2 = 30000 + 2000 + 400 = 32400
=> answer is B ( 32400)
Answer: (B) 32400
Question: The ratio of the cost price and the selling price is 4:5. The profit percent is:
(A) 22%
(B) 31%
(C) 25%
(D) 30%
(E) 29%
Rationale: C
25%
Let C.P. = $ 4x. Then, S.P. = $ 5x
Gain = (5x - 4x) = $ x
Gain % = (x * 100)/ 4x = 25%.
Answer: (C) 25%
Question: The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 6 years ago was 20 years. The present age of the husband is:
(A) 20 years
(B) 30 years
(C) 60 years
(D) 38 years
(E) 35 years
Rationale: D
38 years
Sum of the present ages of husband, wife and child = (27 x 3 + 3 x 3) years = 90 years.
Sum of the present ages of wife and child = (20 x 2 + 6 x 2) years = 52 years.
Husband's present age = (90 - 52) years = 38 years.
Answer: (D) 38 years
Question: A and B together finish a wor in 20 days.They worked together for 15 days and then B left. Afer another 10 days,A finished the remaining work. In how many days A alone can finish the job?
(A) 30
(B) 40
(C) 50
(D) 60
(E) 70
Rationale: Explanation:
(A+B)'s 15 days work = (1/20 × 15) = ¾
Remaining work = (1 - ¾) = ¼
Now, ¼ work is done by A in 10 days.
Whole work will bedone by A in (10 × 4 = 40) days.
Answer: B
Answer: (B) 40
Question: If n and k are integers whose product is 400, which of the following statements must be true?
(A) n + k > 0
(B) n is not equal to k.
(C) Either n or k is a multiple of 10.
(D) If n is even, then k is odd.
(E) If n is odd, then k is even.
Rationale: For the product of two integers to be even at least one integer must be even.
A. n+k>0 --> not necessarily true: nk=(−20)∗(−20)=400
B. n does not equal k --> not necessarily true: nk=20∗20=400
C. Either n or k is a multiple of 10 --> not necessarily true: nk=16∗25=400
D. If n is even, then k is odd --> not necessarily true, nn can be even and kk be even too --> nk=20∗20=400
E. If n is odd, then k is even --> this must be true, if one of the factors is odd (nn) the second one (kk) must be even for their product to be even.
Answer: E.
Answer: (E) If n is odd, then k is even.
Question: In a camp,there is a meal for 140 men or 200 children.If 150 children have taken the meal,how many men will be catered to with the remaining meal ?
(A) 35
(B) 30
(C) 40
(D) 50
(E) 60
Rationale: Solution
There is a meal for 200 children. 150 children have taken the meal.
Remaining meal is to be catered to 50 children.
Now, 200 children = 140 men
50 children =( 140/200x50)men= 35 men. Answer A
Answer: (A) 35
Question: The average of 65 numbers is 40. If two numbers, 40 and 60 are discarded, then the average of the remaining numbers is nearly
(A) 28.32
(B) 39
(C) 38.78
(D) 39.68
(E) 30
Rationale: Explanation :
Total sum of 63 numbers = (65 * 40) - (40+60) = 2600 - 100 = 2500
Average = 2457/63 = 39.68
Answer : D
Answer: (D) 39.68
Question: If you roll one fair six-sided die, what is the probability that the number is odd or greater than 3?
(A) 1/2
(B) 2/3
(C) 3/4
(D) 4/5
(E) 5/6
Rationale: The numbers which satisfy the conditions are 1, 3, 4, 5, and 6.
The probability is 5/6
The answer is E.
Answer: (E) 5/6
Question: If a man buys 10 lollipops for $80 and sold them for $5 dollars determine his loss.
(A) 50
(B) 60
(C) 70
(D) 80
(E) 30
Rationale: Cost of 10 lollipops = $80
Sold each lollipop for $5
So he sold 10 lollipops for $(10 × 5) = $50
Loss = $(80 – 50) = $30
answer :E
Therefore, loss = $ 30.
Answer: (E) 30
Question: Tough and Tricky questions: Statistics.
Set X consists of prime numbers {3, 11, 7, K, 17, 19}. If integer W represents the product of all elements in set X and if 11W is an even number, what is the range of set X?
(A)  14
(B)  16
(C)  17
(D)  20
(E)  26
Rationale: Since 11W = Even therefore W has to beEVENsince 11 is a odd integer (Even * Odd = Even)
Similarly, W is the product of all integers in set X But all integers in Set X are odd except the unknown K and since X contains only prime numbers, K has to equal to 2... ( 2 is the only even prime number and the product of all prime numbers in set X has to be Even, Even * Odd = Even)
Since you know value of K you can calculate the range = Largest integer in the set minus Smallest integer in the set = 19-2 =17
Answer is C
Answer: (C)  17
Question: If D is the least common multiple of 90,196, and 300, which of the following is NOT a factor of D?
(A) 600
(B) 700
(C) 900
(D) 2,100
(E) 4,900
Rationale: IF D is the least common multiple of 90,196 and 300, which of the following is NOT a factor of D?
A- 600
B- 700
C- 900
D- 2100
E- 4900
90 = 2 * 3 * 3 * 5
196 = 2 * 2 * 7 * 7
300 = 2 * 2 * 3 * 5 * 5
LCM = 2 * 2 * 3 * 3 * 5 * 5 * 7 * 7
(TWO 2, TWO 3, TWO 5, TWO 7)
600 = 2 * 2 * 2 * 3 * 5 * 5
700 = 2 * 2 * 5 * 5 * 7
900 = 2 * 2 * 3 * 3 * 5 * 5
2100 = 2 * 2 * 3 * 5 * 5 * 7
4900 = 2 * 2 * 5 * 5 * 7 * 7=A
Answer: (A) 600
Question: A train 330 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
(A) 18 sec
(B) 15 sec
(C) 4 sec
(D) 16 sec
(E) 12 sec
Rationale: Speed of train relative to man
= (60 + 6) km/hr
= 66 km/hr
[66 * 5/18] m/sec
= [55/3] m/sec.
Time taken to pass the man
= [330 * 3/55] sec
= 18 sec
Answer:A
Answer: (A) 18 sec
Question: The cost of 20 kgs. of sugar is Rs.400. What is the cost of 12.5 kgs. of sugar?
(A) Rs.200
(B) Rs.150
(C) Rs.250
(D) Rs.125
(E) Rs.225
Rationale: Explanation:
The cost of .153 kgs. of sugar = 400x 12.5/20 = Rs.250
Answer: Option C
Answer: (C) Rs.250
Question: If a(a - 4) = 5 and b(b -4) = 5, where a ≠ b, then a + b =
(A) −48
(B) −4
(C) 4
(D) 9
(E) 48
Rationale: i.e. if a = -1 then b =5
or if a = 5 then b = -1
But in each case a+b = -1+5 = 4
Answer: option C
Answer: (C) 4
Question: A disease has infected an ant colony that consists ofworkersandsoldiers: 30% of the soldiers and 14% of theworkerswere infected. If that colony is inhabited by 7000 ants, out of which 1660 are infected, how manyworkersinhabit the colony?
(A) 1500
(B) 2500
(C) 2750
(D) 3000
(E) 3250
Rationale: From two question we get wo equations:
(1) 0,3s + 0,14w = 1660
(2) s + w = 7000
From (2) we get w=7000-s
In (1) 0,3s + 980-0,14s= 1660
0,16s=680
68000:16= 4250 =s
In (2) 4250 + w = 7000
w= 2750 C
Answer: (C) 2750
Question: What is the unit digit in 7^105
(A) 7
(B) 0
(C) 2
(D) 3
(E) 5
Rationale: Explanation:
Unit digit in 7^105 = Unit digit in [ (7^4)26 x 7 ]
But, unit digit in (7^4)26 = 1
Unit digit in 7105 = (1 x 7) = 7
A
Answer: (A) 7
Question: How many factors does 34^2 have?
(A) 2
(B) 8
(C) 20
(D) 25
(E) 26
Rationale: 36^2 = 6*6*6*6 = 2^4*3^4
Total factors = (4+1)*(4+1) = 5*4 = 20
Answer C.
Answer: (C) 20
Question: In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?
(A) 456
(B) 124
(C) 145
(D) 116
(E) 209
Rationale: We may have (1 boy and 3 girls) or (2 boys and 2 girls) or (3 boys and 1 girl) or (4 boys).
Required number
of ways	= (6C1 x 4C3) + (6C2 x 4C2) + (6C3 x 4C1) + (6C4)
= (6C1 x 4C1) + (6C2 x 4C2) + (6C3 x 4C1) + (6C2)
= (24 + 90 + 80 + 15)
= 209.
Ans: E
Answer: (E) 209
Question: The factorial expression 10!/2! is not divisible by which of the following integers?
(A) 3
(B) 5
(C) 6
(D) 7
(E) None of these
Rationale: 10!/2! => 10 x 9 x 8 x7 x 6 x 5 x 4x3
(A) 3 Can divide 12 or 9
(B) 5 Can divide 10
(C) 6 Can divide 12
(D) 7 can divide 7,21,28
Hence answer will be (E)
Answer: (E) None of these
Question: If f(f(n)) + f(n) = 2n+3, f(0) = 1 then f(2013) = ?
(A) 2014
(B) 2088
(C) 270
(D) 1881
(E) 1781
Rationale: f (f(0)) + f(0) = 2(0) + 3 ⇒⇒ f(1) = 3-1 = 2, f(1) = 2
f(f(1)) + f(1) = 2(1) + 3 ⇒⇒ f(2) = 5-2 = 3, f(2) = 3
f(f(2)) + f(2) = 2(2) + 3 ⇒⇒ f(3) = 7-3 = 4, f(3) = 4
..............
f(2013) = 2014
Ans: A
Answer: (A) 2014
Question: An equity analyst needs to select 4 stocks for the upcoming year and rank these securities in terms of their investment potential. If the analyst has narrowed down the list of potential stocks to 5, in how many ways can she choose and rank her top 4 picks?
(A) 210
(B) 350
(C) 110
(D) 120
(E) 840
Rationale: Number of ways of ch0osing 4 stocks = 5C4
Number of ways of ranking the chosen stocks = 4!
Hence total ways of chosing and ranking = 5C4 * 4! = 120
Correct Option: D
Answer: (D) 120
Question: The first half of a 600-mile trip was travelled in x hours and the second half in y hours. Which of the following is equal	to the average speed, in miles per hour, for the entire trip?
(A) 300/(x + y)
(B) 600/(x + y)
(C) 150/x + 150/y
(D) 300/x + 300/y
(E) 600/x + 600/y
Rationale: Time taken to cover first half i.e 300 miles of a 600 mile trip = x
time taken to cover the second half i.e 300 miles of a 600 mile trip = y
Total time taken = x+y
Average speed for the entire trip =total distance /total time
=600/(x+y)
Answer B
Answer: (B) 600/(x + y)
Question: Chris age after 20 years will be 5 times his age 5 years back. what is the present age of Chris?
(A) A)20
(B) B)25
(C) C)15
(D) D)22
(E) E)5
Rationale: Chris present age= x
after 20 years = x+20
5 years back = x-5
x+20= 5(x-5)
x=5
Answer is E
Answer: (E) E)5
Question: A sum of money becomes triple itself in 5 years at simple interest. How many years will it become seven times at the same rate?
(A) 12 Â½ years
(B) 62 Â½ years
(C) 18 Â½ years
(D) 72 Â½ years
(E) 14 Â½ years
Rationale: 100 ---- 200 ---- 5
200 ---- 5
100 ---- 2 1/2
------------------
700 ---- 14 Â½ years
Answer:E
Answer: (E) 14 Â½ years
Question: A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 12 minutes. How long will it take to go 5 km in stationary water?
(A) 40 minutes
(B) 1 hour
(C) 1 hour 25 min
(D) 1 hour 30 min
(E) 1 hour 10 min
Rationale: speed (upstream) =2/1 = 2 kmhr
speed (downstream)=1/(12/60)= 5 kmhr
speed in still water = 1/2 (2+5) = 3.5 kmhr
time taken in stationary = 5/3.5 = 1 hrs 25 min
ANSWER:C
Answer: (C) 1 hour 25 min
Question: Three students appear at an examination of Mathematics. The probability of their success are 1/3, 1/4, 1/5 respectively. Find the probability of success of at least two.
(A) 1/6
(B) 2/5
(C) 3/4
(D) 3/5
(E) 4/5
Rationale: The probability of success of at least two students will involve the following possibilities.
The first two students are successful, the last two students are successful, the first and third students are successful and all the three students are successful.
Therefore, the required probability = 1/3 x 1/4 x 4/5 + 1/4 x 1/5 x 2/3 + 1/3 x 1/5 x 3/4 + 1/3 x 1/4 x 1/5 = 10/60 = 1/6
ANSWER:A
Answer: (A) 1/6
Question: In how many ways can a group of 7 men and 5 women be made out of a total of 10 men and 7 women?
(A) 2200
(B) 2520
(C) 2689
(D) 2540
(E) 2680
Rationale: We need to select 7 men from 10 men and 5 women from 7 women. Number of ways to do this= 10C7 × 7C5=2520B)
Answer: (B) 2520
Question: A certain barrel, which is a right circular cylinder, is filled to capacity with 40 gallons of oil. The first barrel is poured into a second barrel, also a right circular cylinder, which is empty. The second barrel is twice as tall as the first barrel and has twice the diameter of the first barrel. If all of the oil in the first barrel is poured into the second barrel, how much empty capacity, in gallons, is left in the second barrel?
(A) There is no empty capacity
(B) 100 gallons
(C) 280 gallons
(D) 700 gallons
(E) 800 gallons
Rationale: Radius of first cylinder=r, diameter=2r, height=h
Radius of second cylinder=2r, diameter=2d and height=2h
Volume of first cylinder=pie (r^2)*h=40
Volume of second cylinder=pie(2r^2)2h
Put the value of pie (r^2)*h=40 in the second cylinder,volume= pie (r^2)*4*2=40*8=320 gallons
Empty capacity=280 gallons
Answer C
Answer: (C) 280 gallons
Question: A can give B 100 meters start and C 300 meters start in a kilometer race. How much start can B give C in a kilometer race?
(A) 110.22 meters
(B) 111.22 meters
(C) 222.22 meters
(D) 333.22 meters
(E) None of these
Rationale: Explanation:
A runs 1000 meters while B runs 900 meters and C runs 700 meters.
Therefore, B runs 900 meters while C runs 700 meters.
So, the number of meters that C runs when B runs 1000 meters = (1000 x 700)/900 = 777.77 meters
Thus, B can give C (1000 - 777.77) = 222.22 meters start
Answer: C
Answer: (C) 222.22 meters
Question: A man can reach certain place in 50hours. If he reduces his speed by 1/10th, he goes 500km less in time. Find his speed?
(A) 120km/hr
(B) 130km/hr
(C) 140km/hr
(D) 150km/hr
(E) 100km/hr
Rationale: Let the speed be x km/hr
50x-50* 9/10 *x = 500
50x - 45x = 500
5x = 500
x = 100km/hr
Answer is E
Answer: (E) 100km/hr
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 9 hours and 25 hours respectively. The ratio of their speeds is?
(A) 4:5
(B) 5:3
(C) 4:4
(D) 4:8
(E) 4:1
Rationale: Let us name the trains A and B.
Then, (A's speed) : (B's speed)
= √b : √a = √25 : √9
= 5:3
Answer: B
Answer: (B) 5:3
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that exactly three bulbs are good?
(A) 20/68
(B) 20/63
(C) 20/62
(D) 20/61
(E) 20/67
Rationale: Required probability = (⁵C₃ . ⁴C₁)/⁹C₄ = (10 * 4)/126
= 20/63
Answer:B
Answer: (B) 20/63
Question: The cost of the paint is rs.40.00 per kg. if 1kg of paint covers 20sq.ft, how much will it cost to paint outside of a cube having 10 feet each side
(A) Rs.1200
(B) Rs.672
(C) Rs.546
(D) Rs.876
(E) None of these
Rationale: Explanation:
surface area of a cube= 6 x 10^2 = 600s q.ft
quantity of paint required=(600/20)=30 kg
cost of painting= 40 x 30 = Rs.1200
Answer: A
Answer: (A) Rs.1200