mathewhe/aqua_rat huggingface dataset:
Question: An unbiased cubic die is thrown.What is the probability of getting a multiple of 2?
(A) 1/6
(B) 3/4
(C) 2/6
(D) 1/2
(E) 1
Rationale: S={1,2,3,4,5,6}
P(E)=n(E)/n(S)
n(s)=Total numbers in a die=6
Let E be the event of getting the multiple of 2
then ,E={2,4,6}
P(multiple of 2) = 3/6=1/2
ans D
Answer: (D) 1/2
Question: 125 liters of a mixture of milk and water contains in the ratio 3:2. How much water should now be added so that the ratio of milk and water becomes 3:4?
(A) 3:9
(B) 3:1
(C) 3:7
(D) 3:4
(E) 3:6
Rationale: Milk = 3/5 * 125 = 75 liters
Water = 50 liters
75 : (50+P) = 3:4
150 + 3P = 400 => P = 50
50 liters of water are to be added for the ratio become 3:4.
Answer: D
Answer: (D) 3:4
Question: A fruit vendor purchased 20 dozens of bananas at Rs. 15 per dozen. But one-fourth of the bananas were rotten and had to be thrown away. He sold two-third of the remaining bananas at Rs. 22.50 per dozen. At what price per dozen should he sell the remaining bananas to make neither a profit nor a loss?
(A) 77
(B) 15
(C) 66
(D) 44
(E) 21
Rationale: CP of 20 dozen of bananas = 15 * 20 = Rs. 300
Number of bananas which are rotten = 1/4 * 20 = 5 dozen.
SP of two-third of remaining bananas = (2/3 * 15) * 22.5 = Rs. 225
SP of remaining 5 dozens of bananas to make no profit and no loss =(300 - 225) = Rs. 75.
SP of 1 dozen bananas = 75/5 = Rs. 15.
Answer:B
Answer: (B) 15
Question: A telephone number contains 10 digit, including a 3-digit area code. Bob remembers the area code and the next 5 digits of the number. He also remembers that the remaining digits are not 0, 1, 2, 5, or 7. If Bob tries to find the number by guessing the remaining digits at random, the probability that he will be able to find the correct number in at most 2 attempts is closest to which of the following ?
(A) 1/625
(B) 2/625
(C) 4/625
(D) 25/625
(E) 50/625
Rationale: Probability of choosing right numbers in two places = 1/5 * 1/5 = 1/25
Probability of not choosing right numbers in two places = 1-1/25 = 24/25
--
At most two attempts: 1) Wrong-1st Attempt, Right - 2nd, 2) Right - 1st Attempt
1) = 24/25 * 1/25 = 24/625
2) = 1/25
Add 1 and 2, 24/625 + 1/25 = 49/625 ~ 50/625
Answer E
Answer: (E) 50/625
Question: What is the greatest prime factor of 8^12 - 2^30?
(A) 2
(B) 3
(C) 5
(D) 7
(E) 11
Rationale: 8^12 - 2^30?
8 = 2^3
8^12 = 2^36
2^36 - 2^30 = 2^30 (2^6 - 1) = 2^30 (64 - 1) = 2^30 (63) = 2^30 (7*3*3)
hence 2,3,7 are the prime factors of 8^12 - 2^30. here, 7 is the greatest prime factor.
Option D is correct.
Answer: (D) 7
Question: In the biology lab of "Jefferson" High School there are 0.036*10^5 germs, equally divided among 36000*10^(-3) Petri dishes. How many germs live happily in a single dish?
(A) 100
(B) 200
(C) 300
(D) 400
(E) 500
Rationale: 0.037*10^5 can be written as 3600
74000*10^(-3) can be written as 36
Required= 3600/36= 100
ANSWER:A
Answer: (A) 100
Question: A man purchases a cow for Rs.3000 and sold it on the same day allowing the buyer a credit of 2 years. If the buyer will pay Rs.3600 after 2 year at a rate of simple interest 50/7 % per annum, then the man has a gain of
(A) Rs 171.43
(B) Rs 172.43
(C) Rs 173.43
(D) Rs 174.43
(E) Rs 175.43
Rationale: value of Rs3000 after 2 years at 50/7 % S.I will be = 3000 + (3000*2*50/7)/100 = 3000 + 428.57
= 3428.57
therefore C.P of article after 2 years will be Rs 3428.57
but the buyer pays Rs 3600
therefore gain = 3600-3428.57 = Rs 171.43
ANSWER:A
Answer: (A) Rs 171.43
Question: Number of ways in which the letters of word GARDEN can be arranged with vowels in alphabetical order, is
(A) 360
(B) 240
(C) 120
(D) 480
(E) None of these
Rationale: Solution
Order of vowels of fixed
∴ required number of ways are 6!/2!. Answer A
Answer: (A) 360
Question: Find out the wrong number in the following series:
5, 15, 30, 80, 180, 540, 1080
(A) 5
(B) 15
(C) 80
(D) 180
(E) 540
Rationale: 5*3=15 15*2=30
lykwise 30*3=90 90*2=180
180*3=540 540*2=1080
so 80 is wrong no because we r continously multipying by 3 and 2
ANSWER:C
Answer: (C) 80
Question: Two pipes A and B together can fill a cistern in 4 hours. Had they been opened separately, then B would have taken 6 hours more than A to fill cistern. How much time will be taken by A to fill the cistern separately?
(A) 2
(B) 6
(C) 4
(D) 9
(E) 8
Rationale: Let the cistern be filled by pipe A alone in x hours.
Then, pipe B will fill it in (x + 6) hours.
1/x + 1/(x + 6) = 1/4
x2 - 2x - 24 = 0
(x - 6)(x + 4) = 0 => x = 6.
Answer: B
Answer: (B) 6
Question: What is the area of a square field whose diagonal of length 20 m?
(A) 338
(B) 377
(C) 200
(D) 887
(E) 1771
Rationale: d2/2 = (20 * 20)/2 = 200
Answer:C
Answer: (C) 200
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are picked at random, what is the probability that they are all blue?
(A) 1/455
(B) 1/451
(C) 1/457
(D) 1/459
(E) 1/452
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
Probability that all the three marbles picked at random are blue = 3C3/15C3
= (1 * 3 * 2 * 1)/(15 * 14 * 13)
= 1/455
Answer: A
Answer: (A) 1/455
Question: Nine people are on an elevator that stops at exactly 9 floors. What is the probability that exactly one person will push the button for each floor?
(A) 9!/9^9
(B) 9^9/9!
(C) 9/9!
(D) 9/9^9
(E) 1/9^9
Rationale: Each person out of 9 has 9 options, hence total # of outcomes is 9^9;
Favorable outcomes will be 9!, which is # of ways to assign 9 different buttons to 9 people
So basically # of arrangements of 9 distinct objects: 9!.
P=favorable/total=9!/9^9
Answer: A.
Answer: (A) 9!/9^9
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 288 m
(B) 667 m
(C) 240 m
(D) 176 m
(E) 197 m
Rationale: Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 36 = 15
x + 300 = 540
x = 240 m.
Answer: C
Answer: (C) 240 m
Question: A sum was put a simple interest at a certain rate for 4 years. Had it been put at 3% higher rate, it would have fetched Rs. 120 more. The sum is:
(A) s.750
(B) s.1000
(C) s.1250
(D) s.1500
(E) s.1750
Rationale: Explanation :
Let the sub be Rs.x and the initial rate be R%.Then
x Ã— (R+3) Ã— 4/100âˆ’xÃ—RÃ—4/100=120
â‡’x Ã— 3Ã—4/100=120
â‡’x Ã— 4 /100=40
â‡’4x=4000
â‡’x=1000
Answer : Option B
Answer: (B) s.1000
Question: Vijay bought 160 shirts at the rate of Rs. 265 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 20%?
(A) Rs. 258
(B) Rs. 333
(C) Rs. 277.5
(D) Rs. 285
(E) None of these
Rationale: Total CP per shirt = 265 + 1400/160 + 1.75 + 320/160 = Rs. 277.5
SP = CP[(100 + profit%)/100]
= 277.5 * [(100 + 20)/100] = Rs. 333.
ANSWER:B
Answer: (B) Rs. 333
Question: If x, 5, 6, 7 are there and the range and median of them are the same, what is the value of x?
(A) 0
(B) 1
(C) 6
(D) 3
(E) 4
Rationale: Try taking the values of x as you suggested and then see if the median and the range are equal.
Once you do that, you will get the answer yourself.
Tried substituting values starting with 5, 6, 7 ...
only x = 6 satisfies the condition.
C
Answer: (C) 6
Question: The triplicate ratio of 1:4 is?
(A) 1:7
(B) 1:8
(C) 1:3
(D) 1:64
(E) 1:2
Rationale: 1^3: 4^3 = 1:64
Answer: D
Answer: (D) 1:64
Question: If y exceeds x by 25%, then x is less than y by?
(A) 29%
(B) 80%
(C) 87%
(D) 20%
(E) 28%
Rationale: X=100	y=125
125--------25
100--------? => 20%
Answer: C
Answer: (C) 87%
Question: One week a certain truck rental lot had a total of 20 trucks, all of which were on the lot Monday morning. If 50 percent of the trucks that were rented out during the week were returned to the lot on or before Saturday morning of that week, and if there were at least 12 trucks on the lot that Saturday morning, what is the greatest number of different trucks that could have been rented out during the week?
(A) 18
(B) 16
(C) 12
(D) 8
(E) 4
Rationale: A) 18 trucks rented means 2 were left and 9 were returned - 11 trucks - no good
B) 16 trucks rented means 4 were left and 8 were returned - 12 trucks - good
Answer is (B)
Answer: (B) 16
Question: From the given equation find the value of B: BÂ² + 1B - 56
(A) 3
(B) 5
(C) 8
(D) 12
(E) 4
Rationale: (B âˆ’ 7)(B + 8)
B = 7 or 8
Answer is C
Answer: (C) 8
Question: What is 12.5 % of 4/12 of 600?
(A) 25
(B) 24
(C) 30
(D) 27
(E) 28
Rationale: 12.5 % = 12.5 / 100 = 1/8 of 4/12 = 1/8 * 4/12 = 1 / 24 of 600 = 1/24 * 600 = 25
Ans -A
Answer: (A) 25
Question: If Raj was one-third as old as Rahim 5 years back and Raj is 17 years old now, How old is Rahim now?
(A) 40
(B) 41
(C) 36
(D) 48
(E) 54
Rationale: Explanation:
Raj’s age today = 17 decades,
Hence, 5 decades back, he must be 12 years old.
Rahim must be 36 years old, Because (3×12).
5 years back Rahim must be 41 years old today. Because (36+5). Answer: B
Answer: (B) 41
Question: If x/|y| = -1 which of the following must be true?
(A) x^1 = y^1
(B) x^3 = y^3
(C) x^4 = y^4
(D) x^5 = y^5
(E) x^2 = y^2
Rationale: x/|y| = -1
|y| = -x, this implies that x is 0 or negative.
Square: y^2 = x^2.
Answer: D.
Alternatively you can try number plugging: try x = -2 and y = 2 or -2. You'll see that only E is always true.
Answer E
Answer: (E) x^2 = y^2
Question: The cost of 2 benchs and 3 tables is Rs.1300. The cost of 3 benchs and 2 tables is Rs.1200. The cost of each table is more than that of each bench by?
(A) 900
(B) 200
(C) 100
(D) 400
(E) 600
Rationale: C
100
2C + 3T = 1300 --- (1)
3C + 3T = 1200 --- (2)
Subtracting 2nd from 1st, we get
-C + T = 100 => T - C = 100
Answer: (C) 100
Question: For any number Z, Z* is defined as the greatest positive even integer less than or equal to y. What is the value of 6.45 – 6.45*?
(A) 0.45
(B) 0.5
(C) 6.45
(D) 0.25
(E) 6.0
Rationale: Since Z* is defined as the greatest positive even integer less than or equal to Z, then 6.45* =6 (the greatest positive even integer less than or equal to 6.45 is 6).
Hence, 6.45 – 6.45* = 6.45 - 6 = 0.45
Answer: A.
Answer: (A) 0.45
Question: If the cost price is 75% of selling price then what is the profit percentage.
(A) 30.33
(B) 31.33
(C) 32.33
(D) 33.33
(E) 34.33
Rationale: selling price=Rs100 : then cost price=Rs 75:profit =Rs 25.
Profit={(25/75)*100}%=33.33%
Answer is D.
Answer: (D) 33.33
Question: In the graph below, no axes or origin is shown. If point B's coordinates are (12,3), which of the following coordinates would most likely be A's?
(A) (17, -2)
(B) (10, 6)
(C) (6, 8)
(D) (-10, 3)
(E) (-2, -17)
Rationale: wherever be the axis as per question y coordinate of point A will be greater than 3 and X coordinate will be lower than 10.
A rules..
Answer: (A) (17, -2)
Question: Find the value of x. (47% of 1442 - 36% of 1412) + 61 = x?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: B) 2
Answer: (B) 2
Question: There are 30 players in a chess group, and each player plays each of the others once. Given that each game is played by two players, how many total games will be played?
(A) 10
(B) 30
(C) 435
(D) 60
(E) 90
Rationale: 30 players are there.
two players play one game with one another.
so 30C2=30*29/2
=435
SO OPTION C is correct
Answer: (C) 435
Question: In a certain random experiment, exactly one of the outcomes A, B, and V will occur. In each random experiment, the probability that outcome A will occur is 1/3 , and the probability that outcome B will occur is 1/3. What is the probability that when the random experiment is conducted 6 independent times, each of outcomes A, B, and V will occur twice?
(A) 5/243
(B) 1/12
(C) 10/81
(D) 1/6
(E) 16/81
Rationale: Number of ways in which a group of 2A,2B,2V can be formed in any order = 6!/(2!*2!*2!) [ formula for total of 6 items with 2 each of similar kind)
Total number of ways in which the die can be thrown independently = _ _ _ _ _ _ ; there are 6 places .First can be filled in 3 different ways A/B/V; Second in 3 diff ways again and so on.
So total number of ways = 3X3X3X3X3X3 = 3^6
There fore probability = 6!/(2!x2!x2!) by 3^6 = 90/3^6 = 10/81 Answer C
Answer: (C) 10/81
Question: Prove that if a and b are different integers, then there exist infinitely many positive integers n such that a+n and b+n are relatively prime.
(A) (a+n, b+n) = 50
(B) 4
(C) 3
(D) 2
(E) (a+n, b+n) = 1
Rationale: Let a ,and b be two different integers. Assume for instance a < b, and let n = (b-a)k+ I-a. For k sufficiently large, n will be positive integer. We have a+n = (b-a)k+l, b+n = (b-a) (k+l)+l, hence a+n and b+n will be positive integers. If we had d|a+n and d|b+n, we would have d|a-b, and, in view of d|a+n, also d|1, which implies that d = 1. Thus, (a+n, b+n) = 1.
So Answer is E (a+n, b+n) = 1
Answer: (E) (a+n, b+n) = 1
Question: While calculating the edge of a square, a worker makes an error of 2% in excess. What % error does he make in calculating area? (%)
(A) 4.09
(B) 4.0
(C) 4.04
(D) 4.02
(E) 4.01
Rationale: Explanation:
Given Error = 2% while measuring the side of a square.
If the correct value of the side of square is 100, the measured value:
=> 100 + 2% *100
= 100+2=102
The area of square with edge 100 = side*side
=> 100*100
=> 10000
The area of square with side 102 = 102*102= 10404
Error in area calculation = 10404-1000 = 404
% error= (404/10000)*100
= 4.04%
ANSWER: C
Answer: (C) 4.04
Question: 3, 22, 7, 45, 15, ?, 31 Complete the series
(A) 91
(B) 92
(C) 93
(D) 94
(E) 95
Rationale: 3+4*1=7
7+4*2=15
15+4*4=16
Similarly
22+23*1=45
45+23*2=91
ANSWER:A
Answer: (A) 91
Question: Find the value of y from (12)^2 x 6^4 ÷ 432 = y?
(A) 2134
(B) 2234
(C) 2540
(D) 2560
(E) 432
Rationale: 432
E
Answer: (E) 432
Question: A train 120 m long running at 60 kmph crosses a platform in 20 sec. What is the length of the platform?
(A) 213
(B) 298
(C) 350
(D) 726
(E) 267
Rationale: D = 60 * 5/18 = 20
= 333 â€“ 120
= 213
Answer: A
Answer: (A) 213
Question: The average salary of a person for the months of January, February, March and April is Rs.8000 and that for the months February, March, April and May is Rs.8500. If his salary for the month of May is Rs.6500, find his salary for the month of January?
(A) 2177
(B) 2876
(C) 4500
(D) 2981
(E) 2711
Rationale: Sum of the salaries of the person for the months of January, February, March and April = 4 * 8000 = 32000 ----(1)
Sum of the salaries of the person for the months of February, March, April and May = 4 * 8500 = 34000 ----(2)
(2)-(1) i.e. May - Jan = 2000
Salary of May is Rs.6500
Salary of January = Rs.4500.Answer: C
Answer: (C) 4500
Question: A car gets 40 kilometers per gallon of gasoline. How many gallons of gasoline would the car need to travel 150 kilometers?
(A) 3.5 gallons
(B) 2.7 gallons
(C) 5.75 gallons
(D) 3.75 gallons
(E) 7.50 gallons
Rationale: Each 40 kilometers, 1 gallon is needed. We need to know how many 40 kilometers are there in 150 kilometers?
150 Ã· 40 = 3.75 Ã— 1 gallon = 3.75 gallons
correct answer is D) 3.75 gallons
Answer: (D) 3.75 gallons
Question: The schedule of G first year students was inspected. It was found that M were taking a Mathematics course, L were taking a Language course and B were taking both a Mathematics course and a Language course. Which of the following expression gives the percentage of the students whose schedule was inspected who were taking neither a mathematics course nor a language course?
(A) 100 x G/B+L+M)
(B) 100 x (B+L+M)/G
(C) 100 x (G-L-M)/G
(D) 100 x (G-B-L-M)/G
(E) 100 x (G+B-L-M)/G
Rationale: Explanatory Answer
M students are taking a math course.
L students are taking a language course.
B students are taking both a math and a language course.
Number of students taking at least one of the two courses = M U L
M U L = M + L - B
Hence, number of students taking neither of the two courses = G - (M + L - B) = G + B - M - L
Expressed as a percent of the total number of students, we get 100 x (G+B-L-M)/G
Answer E
Answer: (E) 100 x (G+B-L-M)/G
Question: Each day a man meets his wife at the train station after work, and then she drives him home. She always arrives exactly on time to pick him up. One day he catches an earlier train and arrives at the station an hour early. He immediately begins walking home along the same route the wife drives. Eventually his wife sees him on her way to the station and drives him the rest of the way home. When they arrive home the man notices that they arrived 12 minutes earlier than usual. How much time did the man spend walking?
(A) 45 minutes
(B) 50 minutes
(C) 40 minutes
(D) 54 minutes
(E) 35 minutes
Rationale: As they arrived 12 minutes earlier than usual, they saved 12 minutes on round trip from home to station (home-station-home) --> 6 minutes in each direction (home-station) --> wife meets husband 6 minutes earlier the usual meeting time --> husband arrived an hour earlier the usual meeting time, so he must have spent waking the rest of the time before their meeting, which is hour-6 minutes=54 minutes.
Answer: D
Answer: (D) 54 minutes
Question: There are 5 different letters and 5 letter boxes of same size shape and colors. How many method are possible to post the letters?
(A) 50
(B) 51
(C) 52
(D) 53
(E) 54
Rationale: 50000 ->1
41000 ->5
31100 ->10
32000 ->10
21110 ->10
22100 ->15
11111 ->1
1+5+10+10+10+30+1=52
ANSWER:C
Answer: (C) 52
Question: A bag contains a certain number of 50 paise coins, 20 paise coins and 10 paise coins inthe ratio 2:3:4.
(A) 50p coins = 400 20p coins = 600 10p coins = 800
(B) 50p coins = 480 20p coins = 600 10p coins = 800
(C) 50p coins = 400 20p coins = 600 10p coins = 780
(D) 50p coins = 400 20p coins = 608 10p coins = 800
(E) 50p coins = 400 20p coins = 600 10p coins = 820
Rationale: 50*2k + 20*3k + 10*4k = 40000
200k = 40000 => k = 200
50p coins = 2k = 2*200 = 400
20p coins = 3k = 3*200 = 600
10p coins = 4k = 4*200 = 800
Answer:A
Answer: (A) 50p coins = 400 20p coins = 600 10p coins = 800
Question: The difference of two numbers is 1360. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ?
(A) 240
(B) 270
(C) 295
(D) 360
(E) 269
Rationale: Let the smaller number be x. Then larger number = (x + 1360).
x + 1360 = 6x + 15
5x = 1345
x = 269
Smaller number = 270.
ANSWER E
Answer: (E) 269
Question: The rate of a certain chemical reaction is directly proportional to the concentration of chemical B present and inversely proportional to the concentration of chemical A present. If the concentration of chemical B present is increased by 50 percent, which of the following is closest to the percent change in the the concentration of chemical B required to keep the reaction rate unchanged.
(A) 100 % decrease
(B) 30% decrease
(C) 40% decrease
(D) 50% increase
(E) 60% increase
Rationale: Let's say here is the formula of how A and B affects the reaction speed:
rate = B/A
After the concentration A is increased by 50%, the percentage of A
become 1.5A, to keep 'rate' the same, need to have 1.5B.
Which means B increased by 50%
Answer : D
Answer: (D) 50% increase
Question: Ace Transport has acquired two trucks to carry different types of cargo. One costs $70,000; the other costs $52,000. The company expects that the first will last 165,000 miles, after which it can be sold for salvage for about $4,000. The other will fetch the same salvage price, but will last 200,000 miles. The two trucks convoy together, so they always show the same mileage readings. If the value of each truck declines at different constant rates for every mile driven, at what mileage reading will the residual values of the two trucks be equal?
(A) 87,500 miles
(B) 100,000 miles
(C) 107,750 miles
(D) 112,500 miles
(E) The residual values will never be equal.
Rationale: Truck 1 : 70,000 = m1 * 165,000 + 4,000 , where m1 is the depreciation $ per mile
Solve for m1 = 0.4
So the depreciation line for Truck 1 is y = 0.4 x + 4,000 , where y is in dollars and x is in mileage.
Similarly for Truck 2 : 52,000 = m2 * 200,000 + 4,000
and this gives m2 = 0.24
and similar line for Truck 2 is y = 0.24 x + 4,000.
The question is where values are same, and in terms of the equation, it's where the two depreciation lines meet.
so solve for x, 0.4 x + 4,000 = 72,000
0.24x + 4,000 = 52,000
gives x = 112,500,
ANSWER:D
Answer: (D) 112,500 miles
Question: An association of mathematics teachers has 1,260 members. Only 560 of these members cast votes in the election for president of the association. What percent of the total membership voted for the winning candidate if the winning candidate received 60 percent of the votes cast?
(A) 75%
(B) 26.67%
(C) 42%
(D) 34%
(E) 25%
Rationale: Total Number of members = 1260
Number of members that cast votes = 560
Since , winning candidate received 60 percent of the votes cast
Number of votes for winning candidate = (60/100)*560 = 336
Percent of total membership that voted for winning candidate = (336/1260)*100 = 26.67%
Answer B
Answer: (B) 26.67%
Question: Out of 450 students of a school, 325 play football, 175 play cricket and 50 neither play football nor cricket. How many students play both football and cricket ?
(A) 75
(B) 100
(C) 125
(D) 150
(E) None of these
Rationale: Explanation:
Students who play cricket, n(A) = 325
Students who play football, n(B) = 175
Total students who play either or both games,
=n(A∪B)=450−50=400Required Number,n(A∩B)=n(A)+n(B)−n(A∪B)=325+175−400=100
Option B
Answer: (B) 100
Question: ?% of 360 = 129.6
(A) 277
(B) 36
(C) 64
(D) 72
(E) None of these
Rationale: ?% of 360 = 129.6
or, ? = 129.6×100/360=36
Answer B
Answer: (B) 36
Question: Factory X's bulbs work for over 5000 hours in 79% of cases, whereas factory Y's bulbs work for over 5000 hours in 85% of cases. It is known that factory X supplies 80% of the total bulbs available. What is the chance that a purchased bulb will work for longer than 5000 hours?
(A) 80.2%
(B) 88%
(C) 87.4%
(D) 85%
(E) 83.9%
Rationale: For X, 80% of 79% will work.
For Y, 20% of 85% will work. *20% is the rest of the bulb supply in the market.
So, the probability that a purchased bulb will work is:
0.80(0.79) = .632
0.20(0.85) = 0.17
The combined probability then is 63.2 + 17 = 80.2%
ANS A
Answer: (A) 80.2%
Question: The average monthly income of P and Q is Rs. 5050. The average monthly income of Q and R is Rs. 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of P is:
(A) 4050
(B) 3500
(C) 4000
(D) 4500
(E) 5000
Rationale: Let P, Q and R represent their respective monthly incomes. Then, we have:
P + Q = (5050 x 2) = 10100 .... (i)
Q + R = (6250 x 2) = 12500 .... (ii)
P + R = (5200 x 2) = 10400 .... (iii)
Adding (i), (ii) and (iii), we get: 2(P + Q + R) = 33000 or P + Q + R = 16500 .... (iv)
Subtracting (ii) from (iv), we get P = 4000.
P's monthly income = Rs. 4000.
Answer: C
Answer: (C) 4000
Question: If the sum of 5 consecutive integers is x, which of the following must be true?
I. x is an even number
II. x is an odd number
III. x is a multiple of 6
(A)  I only
(B)  II only
(C)  None
(D)  I and III
(E)  II and III
Rationale: I. If you start off with an even number, the sum (x) is even, and if you start off with an odd number the sum (x) is odd. Therefore this is not always true.
II. Same as above. This need not be always true.
III. Say, the first number is p. Then the sum of the five numbers = p + (p+1) + (p+2)...... + (p+4)
= 5p + 10 = 5 (p+2) => divisible by 5.
Therefore C is the answer.
Answer: (C)  None
Question: On 8th Feb, 2005 it was Tuesday. What was the day of the week on 8th Feb, 2004?
(A) Tuesday
(B) Monday
(C) Sunday
(D) Friday
(E) Wednesday
Rationale: 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 : C
Answer: (C) Sunday
Question: The points A(0, 0), B(0, 4a - 5) and C(2a + 1, 2a + 5) form a triangle. If angle ABC = 90, what is the area of triangle ABC?
(A) 80
(B) 82.5
(C) 78.5
(D) 75.5
(E) 74
Rationale: 1/2bh=1/2(2a+1)(2a+5)
Now 4a-5=2a+5
2a=10 ,a=5
Therefore,
A(0,0); B(0,15); C(10,15)
1/2*11*15=82.5
Answer: B
Answer: (B) 82.5