mathewhe/aqua_rat huggingface dataset:
Question: In a card game, a combination of three aces beats all others. If Jose is the first to draw from a standard deck of 52 cards, what is the probability that he wins the game with the best possible combination?
(A) 1/5000
(B) 1/5520
(C) 1/5525
(D) 1/5545
(E) 1/5600
Rationale: he best possible combination is the case when he wins in his first two draws
There are 52 cards in a deck of cards with 4 aces in it.
Probability of first card to be ace = 4/52
Probability of Second card to be ace = 3/51
Probability of third card to be ace = 2/50
Probability of Best possible case = (4/52)*(3/51)*(2/50) = 1/5525
C
Answer: (C) 1/5525
Question: At a certain health club, 30 percent of the members use both the pool and sauna, but 50 percent of the members who use the pool do not use the sauna. What percent of the members of the health club use the pool?
(A) 33 1/3%
(B) 46 2/3%
(C) 50%
(D) 62 1/2%
(E) 75%
Rationale: P = pool S = sauna
given P+S = 30 then let only S be x and only P will be 100 - (30+x) = 70 -x
50% of (70-x) = x => 35 - 0.5x = x => x = 23 1/3% so only P = 70 -23 1/3 = 46 2/3%
Answer B
Answer: (B) 46 2/3%
Question: The number of bacteria in a petri dish increased by 50 percent every 2 hours. If there were 108 million bacteria in the dish at 1: 00 p.m., at what time were there 32 million bacteria in the dish?
(A) 7: 00 p.m.
(B) 8: 00 p.m.
(C) 6: 00 a.m.
(D) 8: 00 a.m.
(E) 10: 00 a.m.
Rationale: Given:
The number of bacteria in a petri dish increased by 50 percent every 2 hours
There were 108 million bacteria in the dish at 2: 00 p.m
Since the bacteria is increasing by 50% every 2 hours, this means that the number is multiplied by 1.5 every 2 hours.
Required: At what time were there 32 million bacteria in the dish?
Assume that there were n intervals of 2 hours between 32 million and 108 million.
32 * (1.5)^n = 108
(3/2)^n = 108/32 = 27/8 = (3/2)^3
Hence n = 3 intervals.
Each interval was of 2 hours. Therefore, the number of hours = 6
Subtracting 6 hours from 1 PM, we get 7 AM as the answer.
Option A
Answer: (A) 7: 00 p.m.
Question: Ram's salary is 25% more than Raja's. How much percent is Raja's salary less than Ram's?
(A) 10%
(B) 15%
(C) 20%
(D) 25%
(E) 50%
Rationale: Raja's salary less than Ram's by 25/(100+25) * 100% = 20%
Answer is C
Answer: (C) 20%
Question: A box contains 7 pairs of shoes (14 shoes in total). If two shoes are selected at random, what it is the probability that they are matching shoes?
(A) 1/190
(B) 1/20
(C) 1/19
(D) 1/13
(E) 1/9
Rationale: The problem with your solution is that we don't choose 1 shoe from 14, but rather choose the needed one AFTER we just took one and need the second to be the pair of it. So, the probability would simply be: 1/1*1/13(as after taking one at random there are 13 shoes left and only one is the pair of the first one)=1/13
Answer: D.
Answer: (D) 1/13
Question: In a certain game, you perform three tasks. You flip a coin, and success would be heads. You roll a single die, and success would be a two. You pick a card from a full playing-card deck, and success would be picking a spades card. If exactly one of these three tasks is successful, then you win the game. What is the probability of winning?
(A) 11/16
(B) 15/32
(C) 14/36
(D) 23/48
(E) 17/56
Rationale: The answer is D
Probability of just one enent will be happining
So, Probability heads=1/2
Probability number 2 =1/6
Probability picking a spades card =1/4
so, Probability win by getting tails= 1/2*5/6*3/4 = 15/48
Probability win by getting number 6 = 1/2*1/6*3/4 = 3/48
Probability win by picking a spades card =1/2*5/6*1/4=5/48
Probability wining= 15/48+3/48+5/48 =23/48
Answer: (D) 23/48
Question: In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr?
(A) 2.5 sec
(B) 2.7 sec
(C) 3.5 sec
(D) 2.9 sec
(E) 9.5 sec
Rationale: Speed = 144 * 5/18 = 40 m/sec
Time taken = 100/40
= 2.5 sec.
Answer: A
Answer: (A) 2.5 sec
Question: A survey of n people in the town of Eros found that 50% of them preferred Brand A. Another survey of 100 people in the town of Angie found that 60% preferred Brand A. In total, 55% of all the people surveyed together preferred Brand A. What is the total number of people surveyed?
(A) 50
(B) 100
(C) 150
(D) 200
(E) 250
Rationale: It is simply a weighted average question. Since the given average of 50% and 60% is 55% (right in the middle), it means the number of people surveyed in Eros (n) is same as the number of people surveyed in Angie.
So n = 100
Total = 100 + 100 = 200
Answer (D)
Answer: (D) 200
Question: A person was asked to state his age in years. His reply was, "Take my age three years hence, multiply it by 3 and then subtract three times my age three years ago and you will know how old I am." What was the age of the person?
(A) 18
(B) 99
(C) 77
(D) 55
(E) 44
Rationale: Let the present age of the person be x years.
Then, 3(x + 3) - 3(x - 3) = x
3x + 9 - 3x + 9 = x => x = 18
Answer: A
Answer: (A) 18
Question: If A,B,C,D,E,F,G,H,I,J are in an decreasing Arithmetic Progression as such. Then Which of the following operations will result in only median being modified not the mean.
A) A is removed
B) A and J are removed
C) B and I are removed
D) A,B,C,H,I,J are removed
E) A and E are removed
(A) 1) A and B
(B) 2) A and E
(C) 3) A,C,E
(D) 4) None of them
(E) 5) All of them
Rationale: There are 10 equidistant numbers on the number line.
Mean and median will be the average of middle two numbers.
If you remove two numbers which is equidistant from either extreme (e.g. B and I), the total deviation on either side of the mean stays the same so mean stays the same. Also, the median is still the average of middle two numbers. But there is no change possible where median will change and mean will not change.
Answer: D
Answer: (D) 4) None of them
Question: A tank is filled in SIXTEEN hours by three pipes A, B and C. Pipe A is twice as fast as pipe B, and B is twice as fast as C. How much time will pipe B alone take to fill the tank?
(A) 56 hours
(B) 28 hours
(C) 55 hours
(D) 66 hours
(E) 47 hours
Rationale: 1/A + 1/B + 1/C = 1/16 (Given)
Also given that A = 2B and B = 2C
=> 1/2B + 1/B + 2/B = 1/16
=> (1 + 2 + 4)/2B = 1/16
=> 2B/7 = 16
=> B = 56 hours.
Answer: A
Answer: (A) 56 hours
Question: The sum of three consecutive multiples of 3 is 72. What is the largest number?
(A) 21
(B) 24
(C) 27
(D) 36
(E) 42
Rationale: Let the numbers be 3x, 3x + 3, 3x + 6
Then, 3x + 3x + 3 + 3x + 6 = 72 ===> 9x = 63 ==> x = 7.
so the largest number is 3x + 6 = 27.
hence the correct answer is option C) 27.
Answer: (C) 27
Question: If you select two cards from a pile of cards numbered 1 to 10, what is the probability that the sum of the numbers is more than 17?
(A) 1/5
(B) 1/10
(C) 2/15
(D) 1/45
(E) 2/45
Rationale: The number of ways to choose two cards is 10C2=45.
There are 2 ways, {9,10} and {8,10}, to get a sum more than 17.
P(sum more than 17)=2/45
The answer is E.
Answer: (E) 2/45
Question: Sum of 36 odd numbers is?
(A) 1294
(B) 1295
(C) 1296
(D) 1297
(E) 1298
Rationale: sum of 1st n odd no.s = 1+3+5+7+... = n^2
so, Sum of 1st 36 odd numbers = 36^2 = 1296
ANSWER:C
Answer: (C) 1296
Question: Ram covers a part of the journey at 20 kmph and the balance at 70 kmph taking total of 8 hours to cover the distance of 400 km. How many hours has been driving at 20 kmph?
(A) 3.2 hr
(B) 3.4 hr
(C) 3.6 hr
(D) 3.8 hr
(E) 4.2 hr
Rationale: let see d/t =v then x/20 + (400-x)/70 =8
x= 64 kmh
t = 64/20 = 3.2 hr
ANSWER:A
Answer: (A) 3.2 hr
Question: A train passes a station platform in 31 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
(A) 228
(B) 240
(C) 165
(D) 166
(E) 1811
Rationale: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 20 = 300 m.
Let the length of the platform be x m . Then,
(x + 300)/31 = 15 => x = 165 m.
Answer: C
Answer: (C) 165
Question: A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 16 cm. What is the length of the wire?
(A) 7 cm
(B) 6 cm
(C) 4 cm
(D) 3 cm
(E) 9 cm
Rationale: Volume of the wire (in Cylindrical shape) is equal to the volume of the sphere.
π(16)2 * h = (4/3)π (12)3 => h
= 9 cm
Answer: E
Answer: (E) 9 cm
Question: Company M produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month, 2/3 were basic and the rest were deluxe. If it takes 1.5 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?
(A) 7/15
(B) 14/31
(C) 3/7
(D) 17/35
(E) 1/2
Rationale: The easiest way for me is to plug in numbers.
Let the number of basic stereos produced be 40, and number of delux stereos produced be 20. Total of 60 stereos.
If it takes an hour to produce a basic stereo then it will take 1.5 hours to produce a deluxe stereo.
40 basic stereos = 40 hours.
20 delux stereos = 30 hours.
Total hours = 70.
Then the fraction would be 30/70 = 3/7 Therefore answer
C.
Answer: (C) 3/7
Question: In a six-sided polygon WQRSTV ∠W measures 48° less than the average (arithmetic mean) of the remaining five angles. What does ∠W equal to, in degrees?
(A)  72
(B)  80
(C)  88
(D)  96
(E)  104
Rationale: The sum of interior angle in a polygon is (n-2)*180
so for a six sided figure, (6-2)*180 = 720
let the A.M of the other 5 angles be 'm'
--> m*5 + W = 720, we know ∠W=m-48
--> m*5 + m - 48 = 720, solving we get m=128
hence ∠W= 128-48 = 80
Ans B.
Answer: (B)  80
Question: Calculate the value of r: 6r^2-17r+6 = 254
(A) 8
(B) 10
(C) 5
(D) 9
(E) 3
Rationale: Using the elimination method substitute options for x and find the correct option.
Answer: A
Answer: (A) 8
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
(A) 2888
(B) 288
(C) 178
(D) 150
(E) 2821
Rationale: Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train = (Speed x Time) = (50/3 * 9) m = 150 m.Answer: D
Answer: (D) 150
Question: A person crosses a 600600 metre long street in 55 minutes. What is his speed in km per hour?
(A) 8.2
(B) 4.2
(C) 6.1
(D) 7.2
(E) 9.1
Rationale: Explanation:
Solution 1Distance =600=600 metre =0.6=0.6 km
Time =5=5 minutes =112=112 hour
Speed=distancetime=0.6(112)Speed=distancetime=0.6(112) =7.2 km/hr
Answer is D
Answer: (D) 7.2
Question: If M/N = 6/5,then 3M+2N = ?
If p/q = 5/4 , then 2p+q= ?
If PQRST is a parallelogram what it the ratio of triangle PQS & parallelogram PQRST
(A) 18/5
(B) 28/5
(C) 27/5
(D) 26/5
(E) 38/5
Rationale: 3M+2N (divide by N)
3M/N+2
3*(6/5)+2
28/5 ANSWER:B
Answer: (B) 28/5
Question: At a certain company, each employee has a salary grade s that is at least 1 and at most 5. Each employee receives an hourly wage p, in dollars, determined by the formula p = 9.50 + 0.25(s – 2). An employee with a salary grade of 5 receives how many more dollars per hour than an employee with a salary grade of 1?
(A) $0.50
(B) $1.00
(C) $1.25
(D) $1.50
(E) $1.75
Rationale: OA is definitely wrong. The answer should be E.
Answer: (E) $1.75
Question: If a and b are positive integers and (3^a)^b = 3^3, what is the value of 3^a*3^b?
(A) 3
(B) 9
(C) 81
(D) 27
(E) 243
Rationale: 3^ab =3^3 therefore ab=3 either a=1or3 or b=3 or 1
therefore 3^a* 3^b = 3^(a+b)= 3^4 =81
C
Answer: (C) 81
Question: What is the probability that a leap year has 53 Sundays and 52 Mondays?
(A) 1/9
(B) 1/7
(C) 1/2
(D) 1/1
(E) 1/5
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:B
Answer: (B) 1/7
Question: A man can row upstream at 55 kmph and downstream at 65 kmph, and then find the speed of the man in still water?
(A) 27
(B) 70
(C) 60
(D) 80
(E) 24
Rationale: US = 55
DS = 65
M = (55 + 65)/2
= 60
Answer:C
Answer: (C) 60
Question: In a room with 10 people, 6 people have exactly 1 friend in the room and 5 people have exactly 2 friends in the room (Assuming that friendship is a mutual relationship, i.e. if Jane is Paul's friend, Paul is Jane's friend). If two individuals are selected from the room at random, what is the probability that those two individuals are NOT friends?
(A) 5/21
(B) 3/7
(C) 4/5
(D) 5/7
(E) 16/21
Rationale: (6/10)(7/9) + (5/10)(6/9) if you choose one of the 6 with one other friend, then you have a 7/9 chance of not picking their friend 2nd. If you choose one of the 5 with 2 friends, you have a 6/9 chance of not picking one of their friends second. Add them up.
42/90 + 30/90
72/90 = 4/5
C. 4/5
Answer: (C) 4/5
Question: If an integer x is to be selected at random from 1 to 100, inclusive, what is probability x(x+1) will be divisible by 2?
(A) 3
(B) 1
(C) 2
(D) 4
(E) 5
Rationale: because x(x+1) is always an even product of even*odd or odd*even factors,
there is a probability of 1 that that it will be divisible by 2,
1*1=1
Answer : B
Answer: (B) 1
Question: The parameter of a square is equal to the perimeter of a rectangle of length 18 cm and breadth 14 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)
(A) 77.14 cm
(B) 25.14 cm
(C) 84.92 cm
(D) 94.94 cm
(E) 23.57 cm
Rationale: Let the side of the square be a cm.
Parameter of the rectangle = 2(18 + 14) = 64 cm Parameter of the square = 64 cm
i.e. 4a = 64
A = 16
Diameter of the semicircle = 16 cm
Circimference of the semicircle
= 1/2(∏)(16)
= 1/2(22/7)(16) = 352/14 = 25.14 cm to two decimal places
ANSWER:B
Answer: (B) 25.14 cm
Question: A boatman can row 96 km downstream in 8 hr. If the speed of the current is 4 km/hr, then find in what time will be able to cover 8 km upstream?
(A) 6 hr
(B) 2 hr
(C) 4 hr
(D) 1 hr
(E) None of these
Rationale: Explanation :
Speed downstream = 96⁄8 = 12 kmph
Speed of current = 4 km/hr
Speed of the boatman in still water = 12-4 = 8 kmph
Speed upstream = 8-4 = 4 kmph
Time taken to cover 8 km upstream = 8⁄4 = 2 hours. Answer : Option B
Answer: (B) 2 hr
Question: Two tests had the same maximum mark. The pass percentages in the first and the second test were 40% and 45% respectively. A candidate scored 216 marks in the second test and failed by 75 marks in that test. Find the pass mark in the first test?
(A) 768
(B) 243
(C) 246
(D) 288
(E) 224
Rationale: Let the maximum mark in each test be M.
The candidate failed by 75 marks in the second test.
pass mark in the second test = 249 + 75 = 324
45/100 M = 324
Pass mark in the first test = 40/100 M = 40/45 * 324 = 288.
Answer:D
Answer: (D) 288
Question: Three pieces of timber 36 m, 42 m and 54 m long have to be divided into planks of the same length, What is the greatest possible length of each plank ?
(A) 7 m
(B) 1 m
(C) 2 m
(D) 6 m
(E) None of these
Rationale: Answer
Greatest possible length of each plank = H.C.F of 36, 42, 54 = 6 m
Correct Option: D
Answer: (D) 6 m
Question: A polygon has 54 diagonals. How many sides does it have?
Self made
(A)  12
(B)  13
(C)  14
(D)  15
(E)  16
Rationale: The best way to solve this problem is to use the formula: An n sided polygon can have n*(n - 3)/2 diagonals
n*(n - 3)/2 = 54
n*(n - 3) = 108
Substitute n from the answer choices. n = 12
Answer: A
Answer: (A)  12
Question: A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 30%?
(A) 650
(B) 882
(C) 772
(D) 652
(E) 271
Rationale: Cost price = Rs.500
profit = 30% of 500 = Rs.150
Selling price = Cost price + Profit
= 500 + 150 = 650
Answer:A
Answer: (A) 650
Question: Nitin’s salary is reduced by 10% and then reduced salary is increased by 10%. Find ,how many percentage his present salary is less as compared to his previous salary?
(A) 6%
(B) 8%
(C) 1%
(D) 2%
(E) 9%
Rationale: 10*10
-------- = 1%
100
Answer: C
Answer: (C) 1%
Question: Jill, who lives in City C, plans to visit 5 different cities, M, L, S,N,and O. She plans to visit each city exactly once and return to City C after the 5 visits. She can visit the cities in any order. In how many different orders can she visit the 5 cities?
(A)  3
(B)  120
(C)  8
(D)  9
(E)  12
Rationale: 5! = 120 =B
Answer: (B)  120
Question: A pair of articles was bought for $900 at a discount of 10%. What must be the marked price of each of the article?
(A) $300
(B) $500
(C) $350
(D) $400
(E) $600
Rationale: S.P. of each of the article = 900/2 = $450
Let M.P = $x
90% of x = 450
x = 450*100/90 =$500
Answer is B
Answer: (B) $500
Question: Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is
(A) 17/29
(B) 17/25
(C) 17/21
(D) 17/20
(E) 17/23
Rationale: n(S) = 20
n(Even no) = 10 = n(E)
n(Prime no) = 8 = n(P)
P(EᴜP) = 10/20 + 8/20 - 1/20 = 17/20
Answer:D
Answer: (D) 17/20
Question: Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. If the faster train passes the slower train in 36 seconds,what is the length of each train?
(A) 88
(B) 70
(C) 62
(D) 50
(E) 54
Rationale: Explanation:
Assume the length of each train = x
Total distance covered for overtaking the slower train = x+x = 2x
Relative speed = 46-36 = 10km/hr = (10×10)/36 = 100/36 m/s
Time = 36 seconds
2x/ (100/36) = 36
=> (2x × 36 )/100 = 36
=> x = 50 meter
Answer: Option D
Answer: (D) 50
Question: What is the 4 digit number in which the 1st digit is 1/3 of the second, the 3rd is the sum of the 1st and 2nd, and the last is three times the second?
(A) 1243
(B) 1345
(C) 1349
(D) 1467
(E) 1500
Rationale: First digit is 1/3 second digit => The numbers can be 1 & 3, 2& 6, 3 & 9.
First + second = third => we can eliminate 3 & 9 since 3 + 9 = 12.
Last is 3 times the second => we can eliminate option 2 & 6 since 3 * 6 = 18.
Hence the number is 1349
C
Answer: (C) 1349
Question: A man sells two articles for Rs.3640 each and he gains 25% on the first and loses 25% on the next. Find his total gain or loss?
(A) 9%loss
(B) 2%loss
(C) 6%loss
(D) 8%loss
(E) 1%loss
Rationale: Explanation:
(25*25)/100
= 6%loss
Answer:C
Answer: (C) 6%loss
Question: A merchant marks his goods up by 40% and then offers a discount of 20% on the marked price. What % profit does the merchant make after the discount?
(A) 21%
(B) 25%
(C) 69%
(D) 31%
(E) 12%
Rationale: Let the price be 100.
The price becomes 140 after a 40% markup.
Now a discount of 20% on 140.
Profit=112-100
12%
answer E
Answer: (E) 12%
Question: An athlete runs 200 metres race in 40 seconds. What is his speed?
(A) 23
(B) 38
(C) 18
(D) 30
(E) 28
Rationale: Speed=Distance/Time = 200/40 = 5 m/s = 5 * 18/5 = 3618 km/hr
Answer :C
Answer: (C) 18
Question: The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?
(A) 10 cm
(B) 16 cm
(C) 18 cm
(D) 20 cm
(E) 22 cm
Rationale: 2(l + b)	=	5
b	1
2l + 2b = 5b
3b = 2l
b =	2	l
3
Then, Area = 216 cm2
l x b = 216
l x	2	l	= 216
3
l2 = 324
l = 18 cm.
C)
Answer: (C) 18 cm
Question: How many seconds will a 500 meter 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) 300
(B) 400
(C) 500
(D) 600
(E) 700
Rationale: Let length of tunnel is x meter
Distance = 800+x meter
Time = 1 minute = 60 seconds
Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s
Distance = Speed*Time
800+x = (65/3) * 60
800+x = 20 * 65 = 1300
x = 1300 - 800 = 500 meters
Answer: Option C
Answer: (C) 500
Question: Two pipes can fill a tank in 18 minutes and 15 minutes. An outlet pipe can empty the tank in 45 minutes. If all the pipes are opened when the tank is empty, then how many minutes will it take to fill the tank?
(A) 22
(B) 77
(C) 18
(D) 10
(E) 81
Rationale: Part of the filled by all the three pipes in one minute
= 1/18 + 1/15 - 1/45 = (5 + 6 - 2)/90 = 9/90 = 1/10
So, the tank becomes full in 10 minutes.
Answer:D
Answer: (D) 10
Question: Eric, Nick and Archi make contributions to the Society Of Nature Protection in the ratio of 5:3:2.5. If altogether they contribute 5145 Nis, how much more money does Nick contribute than Archi?
(A) 128 Nis
(B) 212 Nis
(C) 234 Nis
(D) 245 Nis
(E) 288 Nis
Rationale: Normalising the fraction from 5:3:2.5 to 10:6:5 (Eric: Nick:Archi)
Given Nick contributes one unit more than Archi and one unit of 5145/(10+6+5) = 245
Answer is D: 245 Nis
Answer: (D) 245 Nis
Question: Two trains of equal are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is?
(A) 40
(B) 50
(C) 60
(D) 70
(E) 80
Rationale: Let the length of each train be x m.
Then, distance covered = 2x m.
Relative speed = 46 - 36 = 10 km/hr.
= 10 * 5/18 = 25/9 m/sec.
2x/36 = 25/9 => x = 50.
Answer: Option A
Answer: (A) 40
Question: At a certain diner, Joe ordered 3 doughnuts and a cup of coffee and was charged $ 2.25. Stella ordered 2 doughnuts and a cup of coffee and was charged $ 1.35. What is the price of 2 doughnuts?
(A) $ 0.55
(B) $ 1.00
(C) $ 1.10
(D) $ 1.30
(E) $ 1.80
Rationale: 3D + C = 2.25......(1)
2D + C = 1.35........(2)
(1) - (2) --> D = 0.9 --> 2D = 1.8
Answer: E
Answer: (E) $ 1.80
Question: Jane makes toy bears. When she works with an assistant, she makes 80 percent more bears per week and works 10 percent fewer hours each week. Having an assistant increases Jane’s output of toy bears per hour by what percent T?
(A) 20%
(B) 80%
(C) 100%
(D) 180%
(E) 200%
Rationale: C.
Let's assume just Jane 40 bears per 40/hrs a week, so that is 1 bear/hr. With an assistant she makes 72 bears per 36 hours a week or 2 bears/hr ([40 bears * 1.8] / [40 hrs * .90]).
T=[(2 - 1)/1] * 100% = 100%.C
Answer: (C) 100%
Question: O(x) represents the least odd integer greater than x, whereas o(x) represents the greatest odd integer less than x. Likewise, E(x) represents the least even integer greater than x, whereas e(x) represents the greatest even integer less than x. According to these definitions, the value of O(5.3) + E(–6.7) + o(–7.3) + e(6.6) is:
(A) -4
(B) -2
(C) 0
(D) 2
(E) 4
Rationale: O(5.3) + E(–6.7) + o(–7.3) + e(6.6) = 7 + (-6) + (-9) + 6 = -2
The answer is B.
Answer: (B) -2
Question: A and B started business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in the total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?
(A) 7500
(B) 4366
(C) 2877
(D) 2768
(E) 26871
Rationale: A:B:C = (20000 * 24) : (15000 * 24) : (20000 * 18) = 4:3:3
B's share = 25000 * 3/10
= Rs. 7500.
Answer: A
Answer: (A) 7500
Question: The area of a square field is 28808 sq m. How long will a lady take to cross the field diagonally at the rate of 7.2 km/hr?
(A) 2.5 min
(B) 3 min
(C) 2 min
(D) 4 min
(E) 4.5 min
Rationale: Area of a square field = 28808 sq m
Let the side of square = a
a^2 = 28808
=> a = 169.73
Diagonal = (2)^(1/2) * a
= 1.414 * 169.73
=240
Speed of lady = 7.2 km / hour
= 7200 m / hour
= 120 m / min
Time taken by lady to cross the field diagonally = 240/120 = 2 min
Answer C
Answer: (C) 2 min
Question: A rectangular table seats 7 people on each of two sides, with every person directly facing another person across the table. If 14 people choose their seats at random, what is probability that person P directly faces person Q?
(A) 1/10
(B) 1/11
(C) 1/12
(D) 1/13
(E) 1/14
Rationale: Person P will be seated somewhere at the table.
Each of the other 13 people has an equal chance of sitting opposite person P.
The probability that person Q sits across is 1/13.
The answer is D.
Answer: (D) 1/13
Question: A man & his wife appear in an interview for 2vacancies in the same post. The probability of husband's selection is 1/7 & the probability of wife's selection is 1/5. What is the probability that only 1 of them is selected ?
(A) 1/3
(B) 2/3
(C) 2/7
(D) 3/11
(E) 4/5
Rationale: Let A = Event that the husband is selected and
B = Event that the wife is selected.
Then, P (A) = 1/7
and P(B) = 1/5
∴P(A¯) = (1 - 17/5) = 6/7
and
= (1 - 1/5) = 4/5
Required probability = P [(A and not B) or (B and not A)]
= P[(A and B¯) or (B and A¯)]
= P(A and B¯) + P(B and A¯)
= P(A).P(B¯) + P(B).P(A¯)
= (1/7* 4/5) + (1/5* 6/7)
= 10/35
= 2/7
C
Answer: (C) 2/7