divelab/Sys2Bench huggingface dataset:
Question: If the annual increase in the population of a town is 10% and the present number of people is 11000, what will the population be in 2 years?
Options:
A)12100
B)15240
C)12456
D)11452
E)13310
Rationale: The required population is = 11000 (1 + 10/100)^2
= 11000 * 11/10 * 11/10
= 13310
Answer is E
Answer: E
Question: In the following series how many times the sum of two consecutive digits is even?
1 2 3 4 6 3 4 2 5 9 3 6 7 4 1 2 3 6 7 6 5 4 3
Options:
A)5
B)2
C)3
D)4
E)6
Rationale: 4+6
4+2
5+9
9+3
so 4 times
ANSWER:D
Answer: D
Question: (4x - 7)(4x + 7) + (2x - 9)(2x + 9) =
Options:
A)20x2 - 2x - 100
B)20x2 - 130
C)12x2 - 32
D)12x2 + 32
E)None
Rationale: Solution:
(4x - 7)(4x + 7) + (2x - 9)(2x + 9) =
[(4x)2 - 72] + [(2x)2 - 92] =
(16x2 - 49) + (4x2 - 81) =
16x2 - 49 + 4x2 - 81 =
20x2 - 130
Answer B
Answer: B
Question: Solve: 18800+470+20
Options:
A)2
B)5
C)4
D)0
E)1
Rationale: 18800+470+20=(18800/470)+20=40/20=2.
Answer is A.
Answer: A
Question: 45 men can complete a work in 18 days. Six days after they started working, 30 more men joined them. How many days will they now take to complete the remaining work?
Options:
A)6.6
B)10
C)15
D)7.2
E)8
Rationale: 45*18 men can complete the work in 1 day
1 man's 1 day work = 1/810
45 men 6 days work = 6*1/18 = 1/3
remaining work = 1-1/3 = 2/3
75 men's 1 day's work = 75/810 = 5/54
2/3 work is done by them in 54/5 * 2/3 = 7.2 days
Answer is D
Answer: D
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 16 hours and 81 hours respectively. The ratio of their speeds is?
Options:
A)4:9
B)9:4
C)4:5
D)4:1
E)4:2
Rationale: Let us name the trains A and B.
Then, (A's speed) : (B's speed)
= √b : √a = √81 : √16
= 9:4
Answer:B
Answer: B
Question: A bag contains 6 white and 4 black balls .2 balls are drawn at random. Find the probability that they are of same colour.
Options:
A)7/19
B)7/15
C)7/29
D)7/12
E)7/92
Rationale: Let S be the sample space
Then n(S) = no of ways of drawing 2 balls out of (6+4) = \inline {\color{Black}10C_{2}} = =45
Let E = event of getting both balls of same colour
Then,n(E) = no of ways (2 balls out of six) or (2 balls out of 4)
=\inline {\color{Black}6C_{2}+4C_{2}} = = 15+6 = 21
Therefore, P(E) = n(E)/n(S) = 21/45 = 7/15
Answer: B
Answer: B
Question: A train 100 m long crosses a platform 125 m long in 15 sec; find the speed of the train?
Options:
A)87 kmph
B)65 kmph
C)54 kmph
D)16 kmph
E)18 kmph
Rationale: D = 100 + 125 = 225
T = 15
S = 225/15 * 18/5 = 54 kmph
Answer:C
Answer: C
Question: Difference of two numbers is 1670. If 7.5% of the number is 12.5% of the other number , find the number ?
Options:
A)2660, 1000
B)3660, 2000
C)3000, 4160
D)2490, 4150
E)2505, 4175
Rationale: Let the numbers be x and y. Then, 7.5 % of x =12.5% of y
X = 125*y/75 = 5*y/3.
Now, x-y =1670
5*y/3 –y =1670
2*y/3= 1670
y =[ (1670*3)/2] =2505.
One number = 2505, Second number =5*y/3 =4175.
Answer E.
Answer: E
Question: Their are two boxes containing a total number of 60 balls, each box has an equal number of red and blue balls. What is the probability of getting a red ball from one box and a blue ball from the other
Options:
A)1/2
B)1/4
C)1/16
D)1/8
E)1
Rationale: The number of possible selections is 60.
Let E be the event of getting an even number on one die and an odd number on the other. Since there exist an equal number of blue and red balls, probability of picking a blue or red ball is = 30/60 = 1/2
P(E) = 1 - 1/2
= 1/2.
Answer:A
Answer: A
Question: Find the simple interest on Rs.500 for 9 months at 6 paisa per month?
Options:
A)337
B)270
C)287
D)266
E)281
Rationale: I = (500*9*6)/100
= 270
Answer: B
Answer: B
Question: Peter invested an amount of Rs. 12,000 at the rate of 10% p.a simple interest and another amount at the rate of 20% p.a. simple interest. The total interest earned at the end of one year on the total amount invested became 14% p.a. Find the total amount invested?
Options:
A)20000
B)3888
C)2677
D)29812
E)2322
Rationale: Let the second amount be Rs. x. Then,
(12000 * 10 * 1)/100 + (x * 20 * 1)/100 = [(12000 + x) * 14 * 1] / 100
120000 + 20x = 16800 + 14x
x = 8000
Total investment = 12000 + 8000 = Rs. 20,000.
Answer: A
Answer: A
Question: Jim and Renee will play one game of Rock, Paper, Scissors. In this game, each will select and show a hand sign for one of the three items. Rock beats Scissors, Scissors beat Paper, and Paper beats Rock. Assuming that both Jim and Renee have an equal chance of choosing any one of the hand signs, what is the probability that Renee will win?
Options:
A)5/6
B)2/3
C)1/2
D)5/12
E)3/9
Rationale: There are 3*3=9 combinations (cases) possible. In 3 cases there will be a tie (rock-rock, scissors/scissors, paper/paper). Now, out of 6 cases left Jim and Renee have equal chances of winning, so in 3 cases Jim will win and in other 3 Renee will win. So the probability Renee winning the game is (favorable outcomes) / (total # of outcomes) = 3/9
Answer: E.
Answer: E
Question: A statue is being carved by a sculptor. The original piece of marble weighed 250 kg. In the first week 30 percent is cut away. In the second week 20 percent of the remainder is cut away. In the third week the statue is completed when 25 percent of the remainder is cut away. What is the weight of the final statue?
Options:
A)105 kg
B)103 kg
C)108 kg
D)125 kg
E)117 kg
Rationale: A
105 kg
250 × 0.7 × 0.8 × 0.75 = 105 kg.
Answer: A
Question: A chair is bought for Rs.600/- and sold at a loss of 30% find its selling price
Options:
A)s.420/-
B)s.550/-
C)s.560/-
D)s.590/-
E)s.580/-
Rationale: 100 % ------> 600 (100 * 6 = 600)
70 % ------> 540 (70 * 6 = 420)
Selling price = Rs.420/-
A)
Answer: A
Question: 30 people attend a party. 4 men are single and the rest are there with their wives. There are no children in the party. In all 22 women are present. Then the number of married men at the party is ?
Options:
A)5
B)6
C)4
D)8
E)9
Rationale: Total people = number of men + number of women
30 = 4 + number of married men + 22
number of married men = 30- 22-4 = 4 men
ANSWER: C
Answer: C
Question: The average age of a committee of 8 members is 40 years. A member aged 55 years
retired and his place was taken by another member aged 39 years . The average age of
present committee is;
Options:
A)39 years
B)38 years
C)36 years
D)35 years
E)34 years
Rationale: Exp. Total age of the committee = 40*8 = 320,
Total age when a member is retired
and a new one was joined = 320-55 +39, =304
Average age of present committee = 304/8 = 38.
Answer: B
Answer: B
Question: Three positive integers a, b, and c are such that their average is 22 and a ≤ b ≤ c. If the median is (a + 11), what is the least possible value of c?
Options:
A)21
B)23
C)25
D)27
E)29
Rationale: Solution:
We know that the average value is 22 therefore (a+b+c)/3 = 22
so a+b+c = 66
and b = a + 11
therefore a + (a + 11) + c = 66
The least value of c is when c = b
so take c = a + 11
hence, a + (a + 11) + (a + 11) = 66
i.e., a = 44/3 a non integer therefore c is not equal to b
so take c = b+1 therefore c = a+12
a + (a + 11) + (a + 12) = 66
i.e., a= 43/3 again a non integer therefore c is not equal to b+1
next take c= b+2 therefore c = a+13
a + (a + 11) + (a + 13) = 66
i.e., a=42/3 = 14
hence, a = 14, b = 25, and c = 27
Answer: D
Answer: D
Question: John was thrice as old as Tom 6 years ago. John will be 15/13 times as old as Tom in 6 years. How old is Tom today?
Options:
A)5
B)7
C)9
D)11
E)13
Rationale: J-6 = 3(T-6), so J = 3T-12
J+6 = 15/13 * (T+6)
13J + 78 = 15T + 90
13(3T-12) + 78 = 15T + 90
24T = 168
T = 7
The answer is B.
Answer: B
Question: A computer is programmed to multiply consecutive even integers 2*4*6*8*…*n until the product is divisible by 2211, What is the value of n?
Options:
A)22
B)134
C)62
D)122
E)672
Rationale: Factorise 2211.. 3*11*67..
So n has to be a multiple of largest prime number,61..
So n=2*61=134..
ans :B
Answer: B
Question: The calendar for the year 2007 will be the same for the year
Options:
A)2017
B)2018
C)2014
D)2016
E)2015
Rationale: Explanation:
For a year to have the same calendar with 2007 ,the total odd days from 2007 should be 0.
Year:	2007	2008	2009	2010	2011	2012	2013	2014	2015	2016	2017
Odd Days: 1 2 1 1 1 2 1 1 1 2 1
Take the year 2014 given in the choice.
Total odd days in the period 2007-2013 = 5 normal years + 2 leap year
= 5 x 1 + 2 x 2 = 9 odd days
= 2 odd day (As we can reduce multiples of 7 from odd days which will not change anything)
Take the year 2016 given in the choice.
Number of odd days in the period 2007-2015 = 7 normal years + 2 leap year
= 7 x 1 + 2 x 2 = 11 odd days
= 4 odd days
(Even if the odd days were 0, calendar of 2007 will not be same as the calendar of 2016 because 2007 is not a leap year whereas 2016 is a leap year. In fact, you can straight away ignore this choice due to this fact without even bothering to check the odd days)
Take the year 2017 given in the choice.
Number of odd days in the period 2007-2016 = 7 normal years + 3 leap year
= 7 x 1 + 3 x 2 = 13 odd days
= 6 odd days
Take the year 2018 given in the choice.
Number of odd days in the period 2007-2017 = 8 normal years + 3 leap year
= 8 x 1 + 3 x 2 = 14 odd days
= 0 odd day (As we can reduce multiples of 7 from odd days which will not change anything)
Also, both 2007 and 2018 are not leap years.
Since total odd days in the period 2007-2017 = 0 and both 2007 and 2018 are of same type, 2018 will have the same calendar as that of 2007
Answer: Option B
Answer: B
Question: For an upcoming charity event, a male vocalist has agreed to sing 4 out of 6 “old songs” and 2 out of 5 “new songs.” How many ways can the singer make his selection?
Options:
A)25
B)50
C)150
D)480
E)600
Rationale: Number of ways the vocalist can sing "old songs" = C64=15
Number of ways the vocalist can sing "new songs" = C52=10
Therefore total number of ways the singer can make the selection = (Number of ways the vocalist can sing "old songs")*(Number of ways the vocalist can sing "new songs")= 15*10=150
Answer: C
Answer: C
Question: An gun can take a maximum of four shots at an enemy plane moving away from it. The probability of hitting the plane at the 1st, 2nd, third and 4th shots are 1.4, 1.3, 1.2 & 1.1 respectively. What is the probability that the plane is hit when all the four shots are fired?
Options:
A)0.53435
B)0.69766
C)1.34354
D)1.45465
E)1.46566
Rationale: Required probability:
=(0.4×0.7×0.8×0.9)+(0.6×0.3×0.8×0.9)+(0.6×0.7×0.2×0.9)+(0.6×0.7×0.8×0.1)+(0.4×0.3×0.8×0.9)+(0.4×0.7×0.2×0.9)+(0.4×0.7×0.8×0.1)+(0.6×0.3×0.2×0.9)+(0.6×0.3×0.8×0.1)+(0.6×0.7×0.2×0.1)+(0.4×0.3×0.2×0.9)+(0.6×0.3×0.2×0.1)+(0.4×0.3×0.8×0.1)+(0.4×0.7×0.2×0.1)+(0.4×0.3×0.2×0.1)=(0.4×0.7×0.8×0.9)+(0.6×0.3×0.8×0.9)+(0.6×0.7×0.2×0.9)+(0.6×0.7×0.8×0.1)+(0.4×0.3×0.8×0.9)+(0.4×0.7×0.2×0.9)+(0.4×0.7×0.8×0.1)+(0.6×0.3×0.2×0.9)+(0.6×0.3×0.8×0.1)+(0.6×0.7×0.2×0.1)+(0.4×0.3×0.2×0.9)+(0.6×0.3×0.2×0.1)+(0.4×0.3×0.8×0.1)+(0.4×0.7×0.2×0.1)+(0.4×0.3×0.2×0.1)
=0.2016+0.1296+0.756+0.336+0.864+0.504+0.224+0.324+0.144+0.0084+0.0216+0.0036+0.0096+0.0056+0.002=0.2016+0.1296+0.756+0.336+0.864+0.504+0.224+0.324+0.144+0.0084+0.0216+0.0036+0.0096+0.0056+0.002
=0.6976=0.6976
Edit: Thank you Vaibhav for providing an alternative method.
Alternate Method:
probability that the plane is hit when all the four shots are fired,
P=1−probability of not hitting the targetP=1−probability of not hitting the target
=1−(0.6×0.7×0.8×0.9)=1−(0.6×0.7×0.8×0.9)
=1−0.3024=1−0.3024
=0.6976
B
Answer: B
Question: Find smallest number that you can write using all the vowels(A,E,O,I,U) exactly once?
Options:
A)5000
B)6000
C)1000
D)4000
E)3000
Rationale: A
fIvE thOUsAnd(5000)
Answer: A
Question: A circular path of 13 m radius has marginal walk 2 m wide all round it. Find the cost of leveling the walk at 25p per m2?
Options:
A)Rs.43
B)Rs.23
C)Rs.44
D)Rs.20
E)Rs.41
Rationale: π (152 - 132) = 176
176 * 1/4 = Rs.44
Answer: C
Answer: C
Question: There is food for 760 men for 22 days. How many more men should join after two days so that the same food may last for 4 days more?
Options:
A)3022
B)3040
C)3099
D)3088
E)3066
Rationale: 760 ---- 22
760 ---- 20
x ----- 4
x*4 = 760*20
x = 3800
760
-------
3040
Answer: B
Answer: B
Question: A person crosses a 1000 m long street in 5 minutes. What is his speed in km per hour?
Options:
A)5.2 km/hr.
B)8.2 km/hr.
C)12.0 km/hr.
D)3.2 km/hr.
E)4.2 km/hr.
Rationale: C
12.0 km/hr.
Speed=(1000/5 * 60) m/sec
= 3.33 m/sec.
Converting m/sec to km/hr
=(3.33*18/5) km/hr
= 12.0 km/hr.
Answer: C
Question: Which of the following is closest to the difference between sum Z of all proper fractions (fractions less than 1) in the form 1/x , where x is a positive digit, and the product of all proper fractions in the form y/(y+1), where y is a positive digit?
Options:
A)2.82
B)2.72
C)1.82
D)1.72
E)0.82
Rationale: Sum Z of all proper fractions (fractions less than 1) in the form 1/x, where x is a positive digit:
1/1 + 1/2 + 1/3 +.....+ 1/9
This is a harmonic progression. Harmonic progression is inverse of arithmetic progression.
Approximate sum of a harmonic progression with even number of terms = number of terms * (average of middle 2 terms)
Approximate sum of a harmonic progression with odd number of terms = number of terms * (middle term)
The actual sum will be slightly more than the approximation.
Here we have 9 terms (odd).
Sum = 9 * 1/5
= 9/5
Product of all proper fractions in the form y/(y+1), where y is a positive digit:
1/2 * 2/3 * 3/4 *.....*9/10
We will be left with 1/10.
Required = 9/5 - 1/10
= 1.8 - 0.1
= 1.7
Closest is 1.72
Answer (D).
Answer: D
Question: 926 + 9.026 + 0.926 + 9.0026 = ?
Options:
A)944.9546
B)944.1246
C)944.4246
D)944.9446
E)None of these
Rationale: Explanation :
926 + 9.026 + 0.926 + 9.0026 = 944.9546. Answer : Option A
Answer: A
Question: If @ is a binary operation defined as the difference between an integer n and the product of n and 5, then what is the largest positive integer n such that the outcome of the binary operation of n is less than 12?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: @(n) = 5n - n
We need to find the largest positive integer such that 5n - n < 12.
Then 4n < 12 and n < 3.
The largest possible integer is n = 2.
The answer is B.
Answer: B
Question: Pat, kate and mark charged a total of 189 hours to a certain project . If pat charged twice as much time to the project as kate and 1/3 as much times as mark, how many more hours did mark charge to the project than kate.
Options:
A)18
B)36
C)72
D)90
E)105
Rationale: Let Kate charge for x hours,
then Pat charged for 2x and Mat - for 6x.
So, 2x+6x+x = 189 -total hours charged for,
x= 21.
Mat charged 6x-x or 5x for more hours than kate, or for 105 hours .
E is correct
Answer: E
Question: The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit?
Options:
A)2000
B)2787
C)2927
D)1627
E)1811
Rationale: Explanation:
Let C.P. be Rs. x.
Then, (1920 - x)/x * 100 = (x - 1280)/x * 100
1920 - x = x - 1280
2x = 3200 => x = 1600
Required S.P. = 125 % of Rs. 1600 = 125/100 * 1600 = Rs. 2000.
Answer:A
Answer: A
Question: In how many ways can the letters of the word APPEARED be arranged?
Options:
A)1206
B)1348
C)2520
D)3000
E)5040
Rationale: APPEARED has 8 words, but A, P and E are repeated two times. Thus ways = 8! / 2!2!2! = 5040 ways
E
Answer: E
Question: If KING is coded as 17 and MASS is coded as 29 Then COP is coded as
Options:
A)21
B)20
C)19
D)13
E)None
Rationale: KING = 11+9+14+7=41 i.e (4*4)+(1*1)=17
MASS = 13+1+19+19=52 i.e (5*5)+(2*2)=29
CON= 3+14+15=32 i.e(3*3)+(2*2)=13
ANSWER:D
Answer: D
Question: A train running at the speed of 60 km/hr crosses a pole in 9 sec. What is the length of the train?
Options:
A)287
B)699
C)677
D)168
E)150
Rationale: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 9 = 150 m
Answer: E
Answer: E
Question: A certain fraction has the same ratio to 1/36, as 4/5 does to 2/9. What is this certain fraction?
Options:
A)1/5
B)1/10
C)1/15
D)1/20
E)1/25
Rationale: x / (1/36) = (4/5) / (2/9)
x = 4*9*1 / 36*5*2 = 1/10
The answer is B.
Answer: B
Question: 3, 15, x, 51, 53,159,161 value of x ?
Options:
A)17
B)34
C)54
D)64
E)112
Rationale: 3*5=15
15+2=17
17*3=51
51+2=53
ANSWER:A
Answer: A
Question: A chemical lab is scheduled to go through two air ventilation systems, a basic system and a more advanced system that takes forty minutes and 2 hours respectively to fully ventilate the room. If both ventilation systems were to operate at the same time with their respective constant rates, how many hours would it take to fully ventilate the chemical lab?
Options:
A)1/2
B)1/3
C)2/5
D)5/4
E)3/2
Rationale: The rate of the basic system is 1 room/ (2/3 of an hour) = 3/2 rooms per hour
The rate of the advanced system is 1/2 of a room per hour
The combined rate is 2 rooms per hour.
The time to ventilate one room is 1/2 of an hour.
The answer is A.
Answer: A
Question: A charity solicited P persons over the phone who agreed to an average pledge of Rs.R each. Q of these people who had pledged an average of Rs. S each never sent in the pledged amount. Which of the following expressions represents the percentage of pledged money that the charity received?
Options:
A)100*(PR/QS)
B)100*(QS/PR)
C)100 (PR - QS)
D)100(1-QS/PR)
E)100(PR-QS/PR)
Rationale: Explanatory Answer
Total amount solicited from P persons, each of whom agreed to pledge Rs.R = Rs.P*R
Of these Q did not send the pledged amount. Average value of amount not sent = Rs.S.
Hence, the total amount pledged but not received = Rs.Q*S
The charity therefore, received Rs.(PR - QS)
Expressing the amount received as a percentage of amount pledge, we get ((PR-QS)/PR)*100
Or, the expression can be rewritten as 100(1-QS/PR)
Answer D
Answer: D
Question: A man swims downstream 24km and upstream 16km taking 4 hours each time, what is the speed of the man in still water?
Options:
A)8
B)5
C)24
D)12
E)36
Rationale: 24 --- 4 DS = 6
? ---- 1
16 ---- 4 US = 4
? ---- 1 M = ?
M = (6+ 4)/2 = 5
Answer: B
Answer: B
Question: A confused bank teller transposed the rupees and paise when he cashed a cheque for Shailaja, giving her rupees instead of paise and paise instead of rupees. After buying a toffee for 50 paise, Shailaja noticed that she was left with exactly three times as much as the amount on the cheque. Which of the following is a valid statement about the cheque amount?
Options:
A)Over Rupees 13 but less than Rupees 14
B)Over Rupees 7 but less than Rupees 8
C)Over Rupees 22 but less than Rupees 23
D)Over Rupees 18 but less than Rupees 9
E)Over Rupees 4 but less than Rupees 5
Rationale: Explanation :
original :- 100 p + r.
mistaken :- 100r + p.
=> 100p + r -50 = 300r + 3p.
=> 97p = 299r + 50.
=> p = (299r + 50)/97.
Since 97 is prime, the numerator has to be a mult of 97.
now, 299 leaves a remainder of 8 when divided by 97.
now, checking the options:
1. 299 * 13 + 50 / 97 ---> 8*13 + 50/97 --> not divisible.
2. 8*7 + 50 / 97 --> not divisible.
3. 8*22 + 50/97 --> not divisible.
4. 8*18 + 50/97 --> divisible.
Answer : D
Answer: D
Question: If the radius of a cylinder is doubled and so height is made 3 times, what is the new volume of the cylinder divided by the old one?
Options:
A)8.
B)12.
C)6.
D)4.
E)10.
Rationale: let v and v' be the original and the changed volume
now
v=pir^2h
v'=pi(2r)^2(3h)
v'=12v
B) 12
Answer: B
Question: Sum of the squares of 3 no.'s is 222 and the sum of their products taken two at a time is 131. Find the sum?
Options:
A)22
B)24
C)26
D)28
E)30
Rationale: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 222 + 2* 131
a + b + c = √484 = 22
A
Answer: A
Question: If the cost price of 18 pens is equal to the selling price of 15 pens, the gain percent is:
Options:
A)9%
B)20%
C)50%
D)80%
E)34%
Rationale: Solution :
Let cost price of the price be Rs.1
15 pens C.P. = 15
18 pens S.P. = 18
Gain = 3/15*100 = 20 %
Answer :B
Answer: B
Question: If A,B,C are three integers and AB+C is even ; which of the following must be true? A)C is Odd B)B is Odd C)AB is even
Options:
A)None of the above
B)I only
C)II only
D)III only
E)III,II only
Rationale: If AB is Odd then C will not even. O+E = O
If AB is even then C will not be odd.
If B is even AB is even always. But If C is Odd E+O = O
If B is Odd AB is even or odd depends on A
None of the above are true.
Answer : A
Answer: A
Question: Two pipes A and B can separately fill a tank in 2 minutes and 15 minutes respectively. Both the pipes are opened together but 4 minutes after the start the pipe A is turned off. How much time will it take to fill the tank?
Options:
A)10
B)9
C)12
D)11
E)15
Rationale: 4/12 + x/15 = 1
x = 10
ANSWER A
Answer: A
Question: A man can do a job in 10 days. His father takes 20 days and his son finishes it in 25 days. How long will they take to complete the job if they all work together?
Options:
A)6.3
B)6.9
C)5.3
D)6.1
E)6.2
Rationale: 1 day work of the three persons = (1/10 + 1/20 + 1/25) = 19/100
So, all three together will complete the work in 100/19 = 5.3 days.
Answer:C
Answer: C
Question: 9 men and 12 boys finish a job in 12 days, 12 men and 12 boys finish it in 10 days. 10 men and 10 boys shall finish it in how many days?
Options:
A)12
B)10
C)8
D)5
E)6
Rationale: 9M + 12B ----- 12 days
12M + 12B ------- 10 days
10M + 10B -------?
108M + 144B = 120M +120B
24B = 12M => 1M = 2B
18B + 12B = 30B ---- 12 days
20B + 10B = 30B -----? => 12 days
ANSWER A
Answer: A
Question: The average (arithmetic mean) of 20, 40, and 60 is 6 more than the average of 10, 70, and what number?
Options:
A)15
B)25
C)35
D)22
E)55
Rationale: a1 = 120/3 = 40
a2 = a1 -6 = 34
sum of second list = 34*3 = 102
therefore the number = 102 -80 = 22
ANSWER:D
Answer: D
Question: According to a survey, at least 70% of people like apples, at least 70% like bananas and at least 80% like cherries. What is the minimum percentage of people who like all three?
Options:
A)15%
B)20%
C)25%
D)0%
E)35%
Rationale: It seems that something is wrong with your answer options.
1) minimum applesbananas:
[XXXXXXXXXXXXXX------] - apples
[-----XXXXXXXXXXXXXXX] - bananas
mimimum ab = 70 - (100-70) = 40%
2) minimum (applesbananas)cherries:
[XXXXXXXXX-----------] - applesbananas
[----XXXXXXXXXXXXXXXX] - cherries
mimimum ab = 40 - (100-80) =20%
B
Answer: B
Question: A father said his son , " I was as old as you are at present at the time of your birth. " If the father age is 44 now, the son age 5 years back was
Options:
A)14
B)17
C)11
D)19
E)99
Rationale: Let the son's present age be x years .Then, (44 - x) = x x= 22.
Son's age 5 years back = (22 - 5) = 17 years
Answer: B
Answer: B
Question: After decreasing 24% in the price of an article costs Rs.912. Find the actual cost of an article?
Options:
A)1881
B)1211
C)1200
D)1882
E)1222
Rationale: CP* (76/100) = 912
CP= 12 * 100 => CP
= 1200
Answer: C
Answer: C
Question: A bag contains 4 white balls, 3 black balls, and 2 red balls. One by one, three balls are drawn out without replacement. What is the probability that the third ball is red?
Options:
A)2/9
B)1/4
C)3/8
D)5/16
E)2/5
Rationale: The probability for each ball to be drawn third is equal.
Then the probability a red ball is drawn third is 2/9.
The answer is A.
Answer: A
Question: 164 candies are distributed to children with the same number. What can’t be the range including the number of children?
Options:
A)1~10
B)10~20
C)20~30
D)40~50
E)80~90
Rationale: -> In 164=1*164=2*82=4*41=6*24, you can come up with 4 cases. One is distributing 77 candies to 2 children each. Another is distributing 2 candies to 77 children each. Also, you can distribute 22 candies to 7 children. The other is distributing 7 candies to 22 children. Amongst these cases, what is not included is D. 10~20. Therefore, the answer is B.
Answer: B
Question: Before being simplified, the instructions for computing income tax in Country R were to add 2 percent of one's annual income to the average (arithmetic mean) of 100 units of Country R's currency and 1 percent of one's annual income. Which of the following represents the simplified formula for computing the income tax, in Country R's currency, for a person in that country whose annual income is S?
Options:
A)50+A/200
B)50+3S/100
C)50+S/40
D)100+S/50
E)100+3S/100
Rationale: 50+S/40=C
Answer: C