mathewhe/aqua_rat huggingface dataset:
Question: There are 30 children in a classroom, each student will get 1 dozen pencils and 2 dozen erasers, there are 6 teachers. how many pencils will each teacher have to give out to each student?
(A) 6
(B) 4
(C) 3
(D) 2
(E) 5
Rationale: Each student is supposed to get 12 pencils and there are 6 teachers. 6 x 2 is 12. With each teacher giving out 2 pencils to each student, each student will then get 12 pencils like they are supposed to. The answer is D.
Answer: (D) 2
Question: In a certain pond, 50 fish were caught, tagged, and returned to the pond. A few days later, 50 fish were caught again, of which 2 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what is the approximate number of fish in the pond?
(A) 400
(B) 625
(C) 1,250
(D) 2,500
(E) 10,000
Rationale: total fish = x
percentage of second catch = (2/50)*100 = 4%
so, x * 4% = 50
x = 1250
ANSWER:C
Answer: (C) 1,250
Question: There are, in a certain league, 20 teams, and each team face another team for a total of 4 times. How many games are played in the season?
(A) 450
(B) 760
(C) 110
(D) 180
(E) 400
Rationale: By using the formula, t[n(n - 1) / 2], where t = no. of games between two teams and n = total no. of teams, we get: 760
Option B.
Answer: (B) 760
Question: The average price of 10 oranges is Rs. 12 while the average price of 8 of these oranges is Rs. 11.75. Of the remaining two oranges, if the price of one orange is 40% more than the price of the other, what is the price of each of these two oranges?
(A) Rs 5, Rs 7.50
(B) Rs 8, Rs 12
(C) Rs 10, Rs 16
(D) Rs 10.8, Rs 15.2
(E) None of these
Rationale: Explanation :
Total price of the two oranges = Rs. [(12 x 10) (11.75 x 8)]
= Rs. (120 - 94) = Rs. 26.
Let the price of one orange be Rs. x.
Then, the price of other orange = Rs. (x + 40% of x) = Rs. x + x2/5 = Rs. 7x/5
So, x + 7x/5 = 26
12x = 130
x = 10.8
The prices of the two oranges are Rs. 10.8 and Rs. 15.2
Answer : D
Answer: (D) Rs 10.8, Rs 15.2
Question: On a map, 2 inches represent 30 miles. How many miles approximately is the distance if you measured 38 centimeters assuming that 1-inch is 2.54 centimeters?
(A) 226
(B) 228
(C) 230
(D) 224
(E) 232
Rationale: 1 inch = 2.54 cm
2 inch = 2.54 * 2 cm
5.08 cm = 30 miles
38 cms = 30/5.08*38 = 224 miles
Answer : D
Answer: (D) 224
Question: A and B together have Rs. 1210. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does B have?
(A) Rs. 460
(B) Rs. 484
(C) Rs. 550
(D) Rs. 664
(E) Rs. 764
Rationale: Explanation:
4/15A=2/5B
A=(2/5X15/4)B
A/B=3/2
A:B=3:2
B's share = Rs.(1210X2/5)= Rs. 484.
ANSWER IS B
Answer: (B) Rs. 484
Question: A Sum at compound interest amounts to Rs.7500 in 2 years and to Rs.9000 in 3 years then rate per annum is
(A) 11%
(B) 12%
(C) 15%
(D) 20%
(E) 22%
Rationale: 1500/7500 *100=20%
ANSWER:D
Answer: (D) 20%
Question: Four circular cardboard pieces, each of radius 7cm are placed in such a way that each piece touches two other pieces. The area of the space encosed by the four pieces is
(A) 12
(B) 32
(C) 42
(D) 52
(E) 58
Rationale: required area = 14*14 - (4 * 1/4 * 22/7 * 7 *7) sq cm
= 196 - 154 = 42 sq cm. Answer: C
Answer: (C) 42
Question: If the price of an article went up by 15%, then by what percent should it be brought down to bring it back to its original price?
(A) 17.39%
(B) 2/8%
(C) 2/1%
(D) 1/3%
(E) 2/7%
Rationale: Let the price of the article be Rs. 100.
15% of 100 = 15
New price = 100 + 15 = Rs. 115
Required percentage = (115 - 100)/115 * 100
= 20/115 * 100 = 17.39 %.
Answer:A
Answer: (A) 17.39%
Question: What percent of 17 is 17 percent of 1?
(A)  0.001
(B)  0.01
(C)  0.1
(D)  14
(E)  1
Rationale: 17 % of 1 = (17/100) * 1 = 17/100
To determine what percentage of 17 this is :
[17][/100*17] *100 = 1%
Ans : E
Answer: (E)  1
Question: Find k if 24 / k = 4.
(A) 6
(B) 7
(C) 8
(D) 4
(E) 3
Rationale: Since 24 /k = 4 and 24/ 6 = 4, then
k = 6 correct answer A
Answer: (A) 6
Question: Average of first five multiples of 3 is
(A) 9
(B) 11
(C) 13
(D) 15
(E) 16
Rationale: Explanation:
Average=3(1+2+3+4+5)5=455=
Answer: Option A
Answer: (A) 9
Question: Find a sum for 1st 4 prime number's?
(A) 25
(B) 17
(C) 30
(D) 34
(E) 36
Rationale: Required sum = (2 + 3 + 5 + 7 ) = 17
Note: 1 is not a prime number
Option B
Answer: (B) 17
Question: The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 60 metres?
(A) 18
(B) 17
(C) 17
(D) 12
(E) 13
Rationale: Speed of the boat downstream = 15 + 3 = 18 kmph
= 18 * 5/18 = 5 m/s
Hence time taken to cover 60 m = 60/5 = 12 seconds.
Answer: D
Answer: (D) 12
Question: The population of a city increases by 7% per year but due to migration it decrease by 1% per years. What will be the percentage increase in population in 3 years?
(A) 9%
(B) 9.10%
(C) 27%
(D) 12%
(E) None of these
Rationale: Actual increase in population=6%
Let, earlier population=100 then the population after 3 years
=100(1+6/100)^3=119.1016
∴Required percentage=9.1016%
ANSWER:B
Answer: (B) 9.10%
Question: A baker makes chocolate cookies and peanut cookies. His recipes allow him to make chocolate cookie in batches of 5 and peanut cookies in batches of 6. If he makes exactly 94 cookies, what is the minimum number of chocolate chip cookies he makes?
(A) 7
(B) 14
(C) 21
(D) 28
(E) 40
Rationale: 5C+6P=94
We need to maximize P to minimize C so that the eq is also satisfied
Try substitution for CP to solve so that eqn is satisfied
The least value of C for which equation gets satisfied is 5
i.e. 5*8+6*9=40+54=94
Hence E is the answer
Answer: (E) 40
Question: A bag contains 9 wool scarves, exactly one of which is red and exactly one of which is green. If Deborah reaches in and draws three scarves, simultaneously and at random, what is the probability that she selects the red scarf but not the green scarf?
(A) 1/4
(B) 2/9
(C) 3/11
(D) 4/19
(E) 5/26
Rationale: Total possible ways to choose three scarves is 9C3 = 84
We need to choose the red scarf and two of 7 other scarves (not the green scarf).
The number of successful possibilities is 7C2 = 21
P(red scarf but not green scarf) = 21/84 = 1/4
The answer is A.
Answer: (A) 1/4
Question: A car takes 6 hours to cover a distance of 540 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
(A) 50 Kmph
(B) 45 Kmph
(C) 54 Kmph
(D) 56 Kmph
(E) 60 Kmph
Rationale: Time = 6
Distence = 540
3/2 of 6 hours = 6 * 3/2 = 9 Hours
Required speed = 540/9 = 60 Kmph
E
Answer: (E) 60 Kmph
Question: 4 Women & 6 men have to be seated in a row given that no two women can sit together. How many different arrangements are there.
(A) 6! x 7P4
(B) 6! x 9P4
(C) 6! x 5P4
(D) 6! x 3P4
(E) 6! x 2P4
Rationale: Let us first sit all the 6 men in 6 positions in 6! ways. Now there are 7 gaps between them in which 4 women can sit in 7P47P4 ways.
So total ways are 6! x 7P4
Answer:A
Answer: (A) 6! x 7P4
Question: n the youth summer village there are 150 people, 75 of them are not working, 50 of them have families and 100 of them like to sing in the shower. What is the largest possible number of people in the village, which are working, that don't have families and that are singing in the shower?
(A) 25.
(B) 50.
(C) 75
(D) 100
(E) 150
Rationale: total =150
not working =75
having family=50
like to sing in shower = 100
working=150-75=75
not having family = 150-50=100
like to sing in shower = 100
largest possible number is the lowest possible among the above
ANSWER:C
Answer: (C) 75
Question: A metallic sheet is of rectangular shape with dimensions 46 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m3) is:
(A) 4830
(B) 5120
(C) 6420
(D) 4800
(E) 8960
Rationale: l = (46 - 16)m = 30 m,
b = (36 -16)m = 20 m,
h = 8 m.
Volume of the box = (30 x 20 x 8) m3 = 4800 m3.
Answer: Option D
Answer: (D) 4800
Question: A and B started a partnership business investing some amount in the ratio of 3 : 5. C joined then after six months with an amount equal to that of B. In what proportion should the profit at the end of one year be distributed among A, B and C?
(A) 3 : 5 : 2
(B) 3 : 5 : 5
(C) 6 : 10 : 5
(D) 6 : 11 : 2
(E) Data inadequate
Rationale: Let the initial investments of A and B be 3x and 5x.
A : B : C = (3x x 12) : (5x x 12) : (5x x 6) = 36 : 60 : 30 = 6 : 10 : 5.
Answer:C
Answer: (C) 6 : 10 : 5
Question: Truck X is 13 miles ahead of Truck Y, which is traveling the same direction along the same route as Truck X. If Truck X is traveling at an average speed of 47 miles per hour and Truck Y is traveling at an average speed of 53 miles per hour, how long will it take Truck Y to overtake and drive 5 miles ahead of Truck X?
(A) 2 hours
(B) 2 hours 20 minutes
(C) 2 hours 30 minutes
(D) 2 hours 45 minutes
(E) 3 hours
Rationale: Relative speed = 53-47 = 6 miles per hour
Dist required = 13+5 = 18 miles
Time taken to overtake = 18/6 = 3 hours.
E is the answer.
Answer: (E) 3 hours
Question: The G.C.D. of 1.08, 0.36 and 0.6 is?
(A) 0.03
(B) 0.9
(C) 0.18
(D) 0.12
(E) none of these
Rationale: Given numbers are 1.08,0.36 and 0.60.
H.C.F of 108, 36 and 60 is 12
H.C.F of given numbers=0.12.
Correct Options:D
Answer: (D) 0.12
Question: Statement : A man must be wise to be a good wrangler. Good wranglers are talkative and boring.
Conclusions :
I. All the wise persons are boring.
II. All the wise persons are wranglers.
(A) Only conclusion I follows
(B) Only conclusion II follows
(C) Either I or II follows
(D) Neither I nor II follows
(E) Both I and II follow
Rationale: Explanation:
Neither I nor II follows.
D)
Answer: (D) Neither I nor II follows
Question: Q-1) Of the 84 parents who attended a meeting at a
school, 35 volunteered to supervise children during
the school picnic and 22 volunteered both to supervise
children during the picnic and to bring refreshments to
the picnic. If the number of parents who volunteered
to bring refreshments was 1.5 times the number of
parents who neither volunteered to supervise children
during the picnic nor volunteered to bring
refreshments, how many of the parents volunteered to
bring refreshments?
(A) 25
(B) 36
(C) 38
(D) 42
(E) 45
Rationale: i used the following formula: total = group1 + group2 + neither - both
using the information from the question stem, we have:
84 total people
35 who supervise (group1)
x who neither supervise nor bring refreshments
1.5x people who bring refreshments (group2)
22 who supervise AND bring refreshments (both)
therefore...
84 = 35 + 1.5x + x - 22
solving, we get x = 28
since we want the value of those who bring refreshments AND supervise:
1.5(28) = 42
answer is D
Answer: (D) 42
Question: A bag contains 3 red, 4 blue and 4 green balls. If 2 ballsare picked at random, what is the probability that both are red?
(A) 2/15
(B) 2/21
(C) 3/55
(D) 3/29
(E) 4/27
Rationale: P(Both are red),
=3C211C2=3C211C2
=3/55
C
Answer: (C) 3/55
Question: If a quality control check is made inspecting a sample of 2 light bulbs from a box of 11 lighbulbs, how many different samples can be chosen?
(A) 6
(B) 24
(C) 55
(D) 66
(E) 72
Rationale: Try using the formula for combinations:
n!/r!(n-r)!
11!/2!(11-2)!
11!/2!*9!
11*10/2*1
=55
C
Answer: (C) 55
Question: Find the odd man out. 15, 25, 30, 53, 90, 110, 130
(A) 15
(B) 25
(C) 53
(D) 90
(E) 115
Rationale: Explanation :
All except 53 are multiples of 5
Answer : Option C
Answer: (C) 53
Question: Wane covered a distance of 340 miles between city A and city B taking a total of 5 hours. If part of the distance was covered at 60 miles per hour speed and the balance at 80 miles per hour speed, how many hours did she travel at 60 miles per hour?
(A) 1 hour 45 minutes
(B) 2 hours
(C) 2 hours 30 minutes
(D) 3 hours
(E) None of these
Rationale: Wane covered a distance of 340 miles between city A and city B taking a total of 5 hours.time taken at 60:time taken at 80::(greater speed-average speed):(average speed-lower speed)
average speed is 340/5=68
That gives the answer 3:2=D
Answer: (D) 3 hours
Question: Can anyhow help me with an easy solution for this
3, 4, 100, 5, 4, 144, 7, 3, ?
(A) 144
(B) 265
(C) 276
(D) 225
(E) 169
Rationale: 3, 4, 100, 5, 4, 144, 7, 3, ?
3+4=7 and 7+3=10 and 10^2=100
5+4=9 and 9+3=12 and 12^2=144
7+3=10 and 10+3=13 and 13^2=169
ANSWER:E
Answer: (E) 169
Question: For the past n days, the average (arithmetic mean) daily production at a company was 50 units. If today's production of 110 units raises the average to 55 units per day, what is the value of n?
(A) 9
(B) 11
(C) 13
(D) 15
(E) 17
Rationale: The daily production was raised by 5 units for n days, which has a weighting of 5n.
5n = 110-55 = 55
n = 11
The answer is B.
Answer: (B) 11
Question: How many positive integers less than 350 are there such that they are multiples of 17 or multiples of 18?
(A) 36
(B) 37
(C) 38
(D) 39
(E) 40
Rationale: 350/17 = 20 (plus remainder) so there are 20 multiples of 17
350/18 = 19 (plus remainder) so there are 19 multiples of 18
We need to subtract 1 because 17*18 is a multiple of both so it was counted twice.
The total is 20+19-1 = 38
The answer is C.
Answer: (C) 38
Question: A certain clock marks every hour by striking a number of times equal to the hour,and the time required for a stroke is exactly equal to the time interval between strokes. At 6:00 the time lapse between the beginning of the first stroke and the end of the last stroke is 44 seconds. at 12:00 ,how many seconds elapse between the beginning of the first stroke and the end of the last stroke?
(A) A.72
(B) B.50
(C) C.92
(D) D.46
(E) E.44
Rationale: At 6:00 it'll chime 6 times. If we assume that the time taken to chime is x, then time between chimes is also x. So you have 6 chimes, which is 6x and 5 time intervals between chimes. This means that 11x = 44 seconds. Thus x = 4 seconds.
By a similar logic, at 12:00, there are 12 chimes and 11 intervals so the total time is (12+11)x = 23x = 92 seconds.
Answer C
Answer: (C) C.92
Question: For every positive integer n, the nth term of sequence is given by an= 1/n - 1/(n+1). What is the sum of the first 200 terms?
(A) 40/41
(B) 50/51
(C) 100/101
(D) 200/201
(E) 400/401
Rationale: a1 = 1 - 1/2
a2 = 1/2 - 1/3
a3 = 1/3 - 1/4
etc...
a200 = 1/200 - 1/201
The sum of these terms is 1-1/201 = 200/201
The answer is D.
Answer: (D) 200/201
Question: ((-1.9)(0.6) – (2.6)(1.2))/5.0 = ?
(A) -0.852
(B) 1.0
(C) 1.07
(D) 1.71
(E) 2.71
Rationale: Dove straight into calculation but quickly realized that the sum of two negatives is a negative so there is only one option.
-0.852
Answer A
Answer: (A) -0.852
Question: A person can row at 10 kmph in still water. If the velocity of the current is 2 kmph and it takes him 5 hour to row to a place and come back, how far is the place?
(A) 24km
(B) 30km
(C) 48km
(D) 12km
(E) 15km
Rationale: Speed of down stream = 10+2 = 12kmph
speed of upstream = 10-2 = 8kmph
Let the required distance be xkm
x/12 + x/8 = 5
2x+3x = 120
x = 24 km
Answer is A
Answer: (A) 24km
Question: A train crosses a platform of 150 m in 10 sec, same train crosses another platform of length 250 m in 15 sec. then find the length of the train?
(A) 150m
(B) 180m
(C) 159m
(D) 250m
(E) 50 m
Rationale: Length of the train be ‘X’
X + 150/10= X + 250/15
3X + 450 = 2X + 500
X = 50m
Answer:E
Answer: (E) 50 m
Question: 6^(x-4)=6
What is the value of x ?
(A) 5
(B) 2
(C) -6
(D) 6
(E) 4
Rationale: x-4=1
x=5; Answer:A
Answer: (A) 5
Question: In "Clash Royal" App Game, Warrior "The Bomber" is a very good defensive options. It can be purchased from the card shop.
The cost of the bomber is quite interesting.
The Cost of 1st bomber is: 2
The Cost of 2nd bomber is: 4
The Cost of 3rd bomber is: 6
The Cost of 4th bomber is: 8
The Cost of 5th bomber is: 10
i.e to buy 5 bombers you need 2+4+6+8+10 = 30 coins.
How many bombers can you buy using 1000 coins ? ?
(A) 61
(B) 62
(C) 63
(D) 64
(E) 65
Rationale: Solution
62
The Cost of 1st bomber is: 2 i.e Total coins spend: 2
The Cost of 2nd bomber is: 4 i.e Total coins spend: 6
The Cost of 3rd bomber is: 6 i.e Total coins spend: 12
The Cost of 4th bomber is: 8 i.e Total coins spend: 20
The Cost of 5th bomber is: 10 i.e Total coins spend: 30
The Cost of 6th bomber is: 12 i.e Total coins spend: 42
The Cost of 7th bomber is: 14 i.e Total coins spend: 56
The Cost of 8th bomber is: 16 i.e Total coins spend: 72
The Cost of 9th bomber is: 18 i.e Total coins spend: 90
The Cost of 10th bomber is: 20 i.e Total coins spend: 110
The Cost of 11th bomber is: 22 i.e Total coins spend: 132
The Cost of 12th bomber is: 24 i.e Total coins spend: 156
The Cost of 13th bomber is: 26 i.e Total coins spend: 182
The Cost of 14th bomber is: 28 i.e Total coins spend: 210
The Cost of 15th bomber is: 30 i.e Total coins spend: 240
The Cost of 16th bomber is: 32 i.e Total coins spend: 272
The Cost of 17th bomber is: 34 i.e Total coins spend: 306
The Cost of 18th bomber is: 36 i.e Total coins spend: 342
The Cost of 19th bomber is: 38 i.e Total coins spend: 380
The Cost of 20th bomber is: 40 i.e Total coins spend: 420
The Cost of 21st bomber is: 42 i.e Total coins spend: 462
The Cost of 22nd bomber is: 44 i.e Total coins spend: 506
The Cost of 23rd bomber is: 46 i.e Total coins spend: 552
The Cost of 24th bomber is: 48 i.e Total coins spend: 600
The Cost of 25th bomber is: 50 i.e Total coins spend: 650
The Cost of 26th bomber is: 52 i.e Total coins spend: 702
The Cost of 27th bomber is: 54 i.e Total coins spend: 756
The Cost of 28th bomber is: 56 i.e Total coins spend: 812
The Cost of 29th bomber is: 58 i.e Total coins spend: 870
The Cost of 30th bomber is: 60 i.e Total coins spend: 930
The Cost of 31st bomber is: 62 i.e Total coins spend: 992
Answer B
Answer: (B) 62
Question: In a single throw of a die, what is probability of getting a number greater than 4?
(A) 2/3
(B) 3/5
(C) 4/7
(D) 8/9
(E) 1/3
Rationale: E= {5,6}
n(E)=2
P(S)=n(E)/n(S)
=2/6
=1/3
Ans: E
Answer: (E) 1/3
Question: The area of a triangle will be when a = 3m, b = 5m, c = 10m, a, b, c being lengths of respective sides?
(A) 3
(B) 6
(C) 4
(D) 9
(E) 1
Rationale: S = (3 + 5 + 10)/2= 9 Answer:D
Answer: (D) 9
Question: Ben's income is 60% less than Rex's income, and Sam's income is 25% less than Ben's income. If Rex gave 60% of his income to Sam and 40% of his income to Ben, Ben's new income would be what fraction of Sam's new income?
(A) 8/9
(B) 11/12
(C) 8/13
(D) 11/13
(E) 12/13
Rationale: We can take some easy numbers and make calculations simpler.
Let R ( Rex's income) = 100
Q (Ben's income) = 40%R = 40
S (Sam's income) = 75% Q = (3/4)*40 = 30
Now, if Rex gives 40% to Ben --> Q = 40 + 40 = 80
60% given to Sam --> S = 30+60 = 90
The ratio is : Q/S = 80/90 = 8/9= A
Answer: (A) 8/9
Question: The average of 38 numbers is 45. If two numbers namely 32 and 45 are discarded, The average of
remaining numbers is?
(A) 35.5
(B) 47.5
(C) 39.5
(D) 45.3
(E) 44.3
Rationale: Total of 50 numbers = 38 * 45 = 1710
Average of 38 numbers = 1710-(32+45) / 36
= 1633 / 36 = 45.3
Answer is D
Answer: (D) 45.3
Question: A certain galaxy is known to comprise approximately 2 x 10^11 stars. Of every 50 million of these stars, one is larger in mass than our sun. Approximately how many stars in this galaxy are larger than the sun?
(A) 800
(B) 1,250
(C) 8,000
(D) 4,000
(E) 80,000
Rationale: Total no. of stars on galaxy = 2 * 10^11
Of every 50 million stars, 1 is larger than sun.
1 million = 10^6 therofore, 50 million = 50 * 10^6
total no. of stars larger than sun = 2 * 10^11 / 50 * 10^6
=20 * 10^3 /5
= 4000
therefore answer is D
Answer: (D) 4,000
Question: Out of 15 consecutive numbers, 2 are chosen at random. The probability that they are both odds or both primes is
(A) 27
(B) 29
(C) 12
(D) 11
(E) Cannot be determined
Rationale: Explanation:
There is no definite formula for finding prime numbers among 15 consecutive numbers. Hence the probability cannot be determined.
Answer:E
Answer: (E) Cannot be determined
Question: The average of first nine prime numbers which are odd is?
(A) 12.55
(B) 13.55
(C) 14.55
(D) 11.55
(E) 12.95
Rationale: Sum of first 10 prime no. which are odd = 113
Average = 113/9 = 12.55
ANSWER:A
Answer: (A) 12.55
Question: A total of 535 players participated in a single tennis knock out tournament. What is the total number of matches played in the tournament? (Knockout means if a player loses, he is out of the tournament). No match ends in a tie.
(A) 511
(B) 512
(C) 534
(D) 255
(E) 1023
Rationale: There are 535 players, only 1 person wins, 534 players lose. in order to lose, you must have lost a game.
534 games.
Ans- C
Answer: (C) 534
Question: Three grades of milk are 2 percent, 3 percent and 5 percent fat by volume. If x gallons of the 2 percent grade, y gallons of the 3 percent grade, and z gallons of the 5 percent grade are mixed to give x+y+z gallons of a 4 percent grade, what is x in terms of y and z?
(A) y + 3z
(B) (y +z) / 4
(C) 2y + 3z
(D) z/2
(E) 3y + 4.5z
Rationale: Based on the given information, the following equation could be dervied: 2% * x + 4% * y + 5% * z = 4% * (x+y+z) Then use algebra to figure out -2%*x = 0%*y - 1%*z. Thus, 2x = z.
D
Answer: (D) z/2
Question: If x-y=8, which of the following must be true?
I. Both x and y are positive
II. If x is negative, y must be negative
III.If x is positive, y must be positive
(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III
Rationale: The best way to approach such questions is to plug in values for x and y
Given: x-y=8
I. Both x and y are positive:
Let x=10 and y=2
x-y=8
But,
Let x=6 and y=-2
x-y=8
Therefore, NOT TRUE
III. If x is positive, y must be positive
Let x=10 and y=2
x-y=8
But,
Let x = 6 and y=-2
x-y=8
Therefore, NOT TRUE
II. If x is negative, y must be negative
If x is negative, for the expression x-y=8 to be true, y must be a -ve number. Otherwise, the sum of two negative numbers will yield another negative number!
Therefore, TRUE
Ans: 'B'
Answer: (B) II only
Question: In a school 10% of the boys are same in number as 1/3th of the girls. what is the ratio of boys to the girls in the school?
(A) 5:2
(B) 2:3
(C) 10:3
(D) 3:7
(E) 2:5
Rationale: 10% of B = 1/3 G
10B/100 = G/3
B = 10G/3
B/G = 10/3
B:G = 10:3
Answer is C
Answer: (C) 10:3
Question: The speed of a train is 90 kmph. What is the distance covered by it in 10 minutes?
(A) 11 kmph
(B) 10 kmph
(C) 18 kmph
(D) 15 kmph
(E) 16 kmph
Rationale: D
15 kmph
90 * 10/60 = 15 kmph
Answer: (D) 15 kmph
Question: Working together, 7 identical pumps can empty a pool in 6 hours. How many hours will it take 2 pumps to empty the same pool?
(A) 25
(B) 24
(C) 22
(D) 23
(E) 21
Rationale: The answer is E
7 pumps take 6 hours. 1 Pump will take 6*7 hours . Hence 2 pumps will take (6*7)/2 = 21 hours
Answer: (E) 21
Question: How many positive integers W less than 10,000 are such that the product of their digits is 210?
(A) 24
(B) 30
(C) 48
(D) 54
(E) 72
Rationale: 210 is the answer when 2, 3, 5 and 7 are multiplied. 210 can also be arrive using 5,6 and 7 and 1, 5, 6 and 7.
So sum of arrangements of 2357, 567 and 1567. This translates to 4! +3! + 4!, this equals to 24 + 6 + 24 = 54, D is the answer.
Answer: (D) 54
Question: A bag contains 2 red, 3 green, and 3 white balls. Three balls are picked up one by one without replacement. What is the probability that there will be at least one red ball?
(A) 5/7
(B) 9/14
(C) 13/21
(D) 17/28
(E) 23/35
Rationale: P(no red balls) = 6/8*5/7*4/6 = 5/14
P(at least one red ball) = 1 - 5/14 = 9/14
The answer is B.
Answer: (B) 9/14
Question: Two trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a man in the slower train in 37 seconds. Find the length of the faster train?
(A) 270
(B) 370
(C) 266
(D) 299
(E) 126
Rationale: Relative speed = (72 - 36) * 5/18 = 2 * 5 = 10 mps.
Distance covered in 37 sec = 37 * 10 = 370 m.
The length of the faster train = 370 m.
Answer: B
Answer: (B) 370