mathewhe/aqua_rat huggingface dataset:
Question: Peter rolls two dice at the same time. What is the probability that the total sum of numbers on the dices is 3?
(A) a) 1/12
(B) b) 1/36
(C) c) 1/6
(D) d) 1/18
(E) e) 1/3
Rationale: We can have 6 different outcomes on a dice.
Total outcomes on two dices = 6*6
We need only the cases where sum of the outcomes is 3,
They can be {1, 2}, {2, 1}
A total of 2 outcomes
Probability = favorable outcomes/ total outcomes = 2/36 = 1/18.
Option D
Answer: (D) d) 1/18
Question: Let A = {x: x is a natural number and a factor of 18}
B= {x: x is a natural number and less than 6}
Find A ∪ B and A ∩ B
(A) A ∩ B = {1,2,3}
(B) A ∩ B = {2,5,4}
(C) A ∪ B = {5,7,9}
(D) A ∪ B = {1,2,3}
(E) A ∪ B = {2,5,4}
Rationale: A= {1,2,3,6,9,18}
B= {1,2,3,4,5} Therefore , correct answer : A ∩ B = {1,2,3} (A)
Answer: (A) A ∩ B = {1,2,3}
Question: How much greater is the combined area in square inches of the front and back of a rectangular sheet of paper measuring 11 inches by 9 inches than that of a rectangular sheet of paper measuring 4.5 inches by 11 inches?
(A) 50%
(B) 87%
(C) 100%
(D) 187%
(E) 200%
Rationale: Let's just look at the dimensions (no calculation needed).
With dimension 11 the same, the other dimension 9 is twice 4.5
Then the area will be double which means 100% greater.
The answer is C.
Answer: (C) 100%
Question: 756 can be expressed as a product of primes as
(A) 2 × 2 × 3 × 3 × 7 × 7
(B) 2 × 3 × 3 × 3 × 7 × 7
(C) 2 × 2 × 2 × 3 × 3 × 7
(D) 2 × 2 × 3 × 3 × 3 × 7
(E) None of these
Rationale: Explanation:
It is clear that 756 = 2 × 2 × 3 × 3 × 3 × 7
Answer: Option D
Answer: (D) 2 × 2 × 3 × 3 × 3 × 7
Question: The average age of 8 men increases by 2 years when two women are included in place of two men of ages 20 and 24 years. Find the average age of the women?
(A) 11
(B) 12
(C) 30
(D) 98
(E) 15
Rationale: 20 + 24 + 8 * 2 = 60/2 = 30
Answer: C
Answer: (C) 30
Question: Look at this series: 1000, 200, 40, ... What number should come next?
(A) 17
(B) 10
(C) 15
(D) 18
(E) 8
Rationale: E
8
This is a simple division series. Each number is divided by 5.
Answer: (E) 8
Question: A box contains 4 yellow balls and 5 black balls. One by one, every ball is selected at random without replacement. What is the probability that the fourth ball selected is black?
(A) 2/5
(B) 3/7
(C) 5/9
(D) 2/3
(E) 3/4
Rationale: Each ball has an equal chance (1/9) of being selected fourth.
The probability that a black ball is selected fourth is 5/9.
The answer is C.
Answer: (C) 5/9
Question: A team has to design a flag. The team two yellow strips of cloth and four green strips of cloth that they must use as is to make the flag. How many different flags can the team design with the materials at hand?
(A) 15
(B) 48
(C) 240
(D) 288
(E) 720
Rationale: The # of permutations of total 2+4=6 strips where 2 are identical yellow and 4 are identical green is 6!/(2!*4!)=15 (note that they must use all the materials at hand, also I guess that the strips must be either only vertical or only horizontal).
Answer: A.
Answer: (A) 15
Question: Due to construction, the speed limit along an 5-mile section of highway is reduced from 60 miles per hour to 40 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
(A) A) 3.12
(B) B) 2.5
(C) C) 10
(D) D) 15
(E) E) 24
Rationale: Old time in minutes to cross 5 miles stretch = 5*60/60 = 5*1/1 = 5
New time in minutes to cross 5 miles stretch = 5*60/40 = 5*3/2 = 7.5
Time difference = 2.5
Ans:B
Answer: (B) B) 2.5
Question: Two trains 140 m and 170 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
(A) 10.9 sec
(B) 11.16 sec
(C) 53.8 sec
(D) 10.8 sec
(E) 10.4 sec
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 140 + 170 = 310 m.
Required time = 310 * 9/250 = 11.16 sec.
Answer: B:
Answer: (B) 11.16 sec
Question: If the perimeter of a rectangular garden is 600 m, its length when its breadth is 150 m is?
(A) 150 m
(B) 899 m
(C) 200 m
(D) 166 m
(E) 187 m
Rationale: 2(l + 150) = 600 => l
= 150 m
Answer: A
Answer: (A) 150 m
Question: What is the least number that should be added to 1053, so the sum of the number is divisible by 23?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: (1053 / 23) gives a remainder 18 so we need to add 5.
The answer is E.
Answer: (E) 5
Question: Find a sum for 1st 5 prime number's?
(A) 25
(B) 28
(C) 30
(D) 34
(E) 36
Rationale: Required sum = (2 + 3 + 5 + 7 + 11) = 28
Note: 1 is not a prime number
Option B
Answer: (B) 28
Question: In a ranch, the total number of black horses is 18% more than the number of male black horses. The total number of female horses is 16 times the number of black female horses. What percentage of male horses are black if the total number of male horses is double the number of female horses?
(A) 17.4
(B) 18.6
(C) 19.2
(D) 22.9
(E) 50.6
Rationale: Since we are dealing in percentage let us pick 100 as the number of black male horses.
That means that the total number of black horse is= 110 (18% more),
therefore the number of black female horse is 18.
The total number of female horses is 16x the number of black female horses= 16*18=288 female horses.
Male horse total population is twice the population of the female horses= 288*2=576
Therefore percentage of male horses that are brown= 100/576*100=17.4
Correct option is A
Answer: (A) 17.4
Question: In a shop, the cost of 4 shirts, 4 pairs of trousers and 2 hats is $560. The cost of 9 shirts, 9 pairs of trousers and 6 hats is $1,290. What is the total cost of 1 shirt, 1 pair of trousers and 1 hat?
(A) 110$
(B) 120$
(C) 130$
(D) 140$
(E) 150$
Rationale: et x be the price of one shirt, y be the price of one pair of trousers and z be the price of one hat.
4x + 4y + 2z = 560 :
9x + 9y + 6z = 1,290
3x + 3y + 2z = 430 : divide all terms of equation C by 3
x + y = 130 : subtract equation D from equation B
3(x + y) + 2z = 430 : equation D with factored terms.
3*130 + 2z = 430
z = 20 : solve for z
x + y + z = 130 + 20 = $150
Answer: (E) 150$
Question: 49 x 49 x 49 x 49 = 7?
(A) 4
(B) 7
(C) 8
(D) 16
(E) 20
Rationale: Solution
49 * 49 * 49 * 49 = (72 * 72 * 72 * 72) = 7(2 + 2 + 2 + 2) = 78
so, the correct answer is 8
Answer C
Answer: (C) 8
Question: A bag consists of 60 marbles, of which 5 are blue, 9 are red, and the remainder are white. If Lisa is to select a marble from the bag at random, what is the probability that the marble will be red or white?
(A) 11/12
(B) 2/4
(C) 1/4
(D) 1/8
(E) 1/16
Rationale: bag consists of 60 marbles, of which 5 are blue, 9 are red
remainder are white. So, white = 60 - 5 - 9 = 46.
probability that the marble will be red or white = probability that the marble will be red + probability that the marble will be white
probability that the marble will be red or white = 9/60+46/60 = 55/60 = 11/12
Hence, answer will be A.
Answer: (A) 11/12
Question: Harriet planned to complete a certain task on Wednesday, January 1, but because of illness the completion date was postponed 43 days. On which day of the week in February was the task completed?
(A) Monday
(B) Tuesday
(C) Wednesday
(D) Thursday
(E) Friday
Rationale: This type of story problem is essentially just about a repeating pattern and a 'remainder.'
We're told that Harriet planned to complete a certain task on WEDNESDAY, January 1, but because of illness the completion date was postponed 43 DAYS. We're asked on what day of the week the task was actually completed on.
Since the task was supposed to be completed on a Wednesday....
A 1 day postponement would be Thursday
A 2 day postponement would be Friday
A 3 day postponement would be Saturday
A 4 day postponement would be Sunday
A 5 day postponement would be Monday
A 6 day postponement would be Tuesday
A 7 day postponement would be Wednesday
A 8 day postponement would be Thursday
Etc.
So this question is ultimately asking how many 'groups of 7' are there, and how many 'leftover days' are there, when you postpone 43 days.
43/7 = 6 remainder 1
This means that there are 6 full weeks AND 1 extra day after a Wednesday....Thus, the task was completed on a Thursday.
D
Answer: (D) Thursday
Question: A cube of side 8 meter length is cut into small cubes of side 16 cm each. How many such small cubes can be obtained?
(A) 10780
(B) 127600
(C) 125000
(D) 152000
(E) 10000
Rationale: Along one edge, the number of small cubes that can be cut
= 800/16 = 50
Along each edge 50 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut
=50 * 50 * 50 = 125000
Answer:C
Answer: (C) 125000
Question: Set X consists of the integers from 0 to 12, inclusive, while set Y consists of the integers from 6 to 10, inclusive. How many distinct integers do belong to the both sets at the same time?
(A) 4
(B) 10
(C) 5
(D) 9
(E) 8
Rationale: X= {0,1,2,3,4, 5,6, 7, 8, 9, 10, 11, 12}
Y = {6, 7, 8, 9, 10}
Common elements = {6, 7, 8, 9, 10} = 5 elements
Answer: Option C.
Answer: (C) 5
Question: Maxwell leaves his home and walks toward Brad's house at the same time that Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 110 kilometers, Maxwell's walking speed is 4 km/h, and Brad's running speed is 7 km/h, what is the distance traveled by Brad?
(A)  16
(B)  18
(C)  20
(D)  70
(E)  30
Rationale: Time taken = Total Distance / Relative Speed
Total Distance = 110 kms
Relative Speed (Opposite side) (As they are moving towards each other speed would be added ) = 7+ 4 = 11 kms/hr
Time taken = 110 / 11 = 10 hrs
Distance traveled by Brad = Brad's speed * time taken = 7 * 10 = 70 kms... Answer - D
Answer: (D)  70
Question: A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12500 after a year?
(A) 3630
(B) 3637
(C) 3630
(D) 3750
(E) 3635
Rationale: 6300:4200:10500
3:2:5
3/10 * 12500 = 3750
Answer: D
Answer: (D) 3750
Question: Mudit's age 30 years hence will be thrice his age four years ago. Find Mudit's present age?
(A) 12
(B) 19
(C) 27
(D) 21
(E) 15
Rationale: Explanation:
Let Mudit's present age be 'm' years.
m + 30 = 3(m - 4)
=> 2m = 42 => m = 21 years.
Answer:D
Answer: (D) 21
Question: Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 24,500. What was Simran's share in the profit ?
(A) 10,529
(B) 10,512
(C) 10,110
(D) 10,500
(E) 10,511
Rationale: The ratio of their investments:
50000x36 : 80000x30 = 3 : 4
Simran's share of profit = (24500x3/7) = Rs.10,500.
Answer: D
Answer: (D) 10,500
Question: The probability that a man will be alive for 10more yrs is 1/4 & the probability that his wife will alive for 10 more yrs is 1/3. The probability that none of them will be alive for 10 more yrs, is
(A) 1/2
(B) 1
(C) 3/2
(D) 3/5
(E) 1/3
Rationale: Sol. Required probability = Pg.) x P(B) = (1— D x(1 —I) =: x 1=1/2
Ans.(A)
Answer: (A) 1/2
Question: If a number x is in octal form and having zero as unit place then if we change that number x in decimal form then what is the probability that number x having zero as unit place?
(A) 11/64
(B) 11/69
(C) 11/66
(D) 11/64
(E) 11/61
Rationale: example (8)10=(10)8(8)10=(10)8, (16)10=(20)8(16)10=(20)8, (24)10=(30)8(24)10=(30)8, (32)10=(40)8(32)10=(40)8, (40)10=(50)8(40)10=(50)8, . . .
So out of five numbers end with zero in octal form, only one (50)8=(40)10(50)8=(40)10 has zero in decimal format. So the required probability is 1/5
My initial thinking:
Let the number be "ab0" in octal form. Remember here a, b < 8. So total possibilities are 64.
If we convert the given number into decimal format, then (ab0)8 = 64a + 8b.
We will find for how many values of 64a + 8b ends in zero.
64a + 8b = 60a + (4a + 8b)
For (0,0), (1, 2), (1, 7), (2, 4), (3, 1), (3, 6), (4, 3), (5, 5), (6, 2), (6, 7), (7, 4), (0, 0) the above expression gives unit digit 0.
So required probability = 11/64
(Imp: Still I am not comfortable with the solution I have written as it is not specified whether the given number is 3 digit or not. Just learn how I tried to solve it. )
Answer:A
Answer: (A) 11/64
Question: If the average (arithmetic mean) of the four numbers K + 1, 2K + 3, 3K – 5 and 5K + 1 is 63, what is the value of K?
(A)  11
(B)  15 3/4
(C)  22
(D)  23
(E)  22 10/11
Rationale: K +1 + 2K +3 + 3K - 5 + 5K +1 = 11K
(11K )/4 = 63
11K = 63 * 4= 252
K = 252 / 11 = 22 10/11
Answer E.
Answer: (E)  22 10/11
Question: A small company employs 5 men and 3 women. If a team of 4 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 2 women?
(A)  1/14
(B)  1/7
(C)  2/7
(D) 1/2
(E)  3/7
Rationale: Total ways to choose 4 employees from 8 employees = 8C4
Two women = 3C2
Two Men = 5C2
P = (5C2 * 3C2)/8C2 = 3/7 hence E.
Answer: (E)  3/7
Question: A wheel rotates 10 times every minute and moves 30 cm during each rotation. How many metres does
the wheel move in one hour?
(A) 6 metre
(B) 18 metre
(C) 180 metre
(D) 1800 metre
(E) 2200 metre
Rationale: Expl : Number of times wheel moves in 1 hour = 10 * 60 = 600
:. Distance moves = (600 *30) cm = 18000 cm
In metres = 180 metre
Answer: C
Answer: (C) 180 metre
Question: A is a working partner and B is a sleeping partner in the business. A puts in Rs.15000 and B Rs.25000, A receives 10% of the profit for managing the business the rest being divided in proportion of their capitals. Out of a total profit of Rs.9600, money received by A is?
(A) 2726
(B) 1827
(C) 1199
(D) 4200
(E) 1781
Rationale: Explanation:
15:25 => 3:5
9600*10/100 = 960
9600 - 960 = 8640
8640*3/8 = 3240 + 960
= 4200
Answer:D
Answer: (D) 4200
Question: 15 litres of mixture contains 20% alcohol and the rest water. If 2litres of water be mixed with it, the percentage of alcohol in the new mixture would be?
(A) 16.67%
(B) 23%
(C) 18.3%
(D) 17.64%
(E) 21.23%
Rationale: Alcohol in the 15litres of mix. = 20% of 15litres = (20*15/100) = 3litres
water in it = 15-3 = 12litres
new quantity of mix. = 15+2 = 17 litres
Quantity of alcohol in it = 3litres
Percentage of alcohol in new mix. = 3*100/17 = 17.64%
Answer is D
Answer: (D) 17.64%
Question: A committee is composed of w women and m men. If 3 women and 2 men are added to the committee, and if one person is selected at random from the enlarged committee, then the probability that a woman is selected can be represented by
(A) w/m
(B) w/(w+m)
(C) (w+3)/(m+2)
(D) (w+3)/(w+m+3)
(E) (w+3)/(w+m+5)
Rationale: The total number of members on the enlarged committee is (w+3)+(m+2)=w+m+5;
The total number of women on the enlarged committee is w+3.
Thus, the probability that a woman is selected is P=favorable/total=(w+3)/(w+m+5).
Answer: E.
Answer: (E) (w+3)/(w+m+5)
Question: The output of a factory was increased by 10% to keep up with rising demand. To handle the holiday rush, this new output was increased by 30%. By approximately what percent would the output now have to be decreased in order to restore the original output?
(A) 20%
(B) 24%
(C) 30%
(D) 32%
(E) 79%
Rationale: The original output increases by 10% and then 30%.
Total % change = a + b + ab/100
Total % change = 10 + 30 + 10*30/100 = 43%
Now, you want to change it to 0, so,
0 = 43 + x + 43x/100
x = -43(100)/143 = 30% approximately
Answer is C
Answer: (C) 30%
Question: What is the product of all the possible values of x if x^2(x + 2) + 7x(x + 2) + 6(x + 2) = 0?
(A) –29
(B) –12
(C) 12
(D) 29
(E) 168
Rationale: x^2(x + 2) + 7x(x + 2) + 6(x + 2) = 0
=> (x+2)(x^2 + 7x + 6) = 0
=>(x+2)(x+1)(x+6)=0
=> x= -1 or -2 or -6
product =-12
answer option -12
ANSWER:B
Answer: (B) –12
Question: A jogger running at 9 kmph alongside a railway track in 240 meters ahead of the engine of a 120 metres long train running at 45 kmph in the same direction . in how much time will the train pass the jogger ?
(A) 18 seconds
(B) 26 seconds
(C) 36 seconds
(D) 16 seconds
(E) 46 seconds
Rationale: Total Distance(d) = 240+120 = 360 meter
Relative speed (s) = 45 - 9 = 36 Kmph = 36*5/18 = 10mps
d = s* t
360 = 10*t
t = 36 seconds
ANSWER:C
Answer: (C) 36 seconds
Question: The side of a square is increased by 15% then how much % does its area increases?
(A) 52.65
(B) 56.25
(C) 50.75
(D) 32.25
(E) 52.75
Rationale: a = 100 a2 = 10000
a = 115 a2 = 13225
----------------
10000 --------- 3225
100 -------? => 32.25 %
ANSWER: D
Answer: (D) 32.25
Question: A crate of apples contains 1 bruised apple for every 25 apples in the crate. Three out of every 4 bruised apples are considered not fit to sell, and every apple that is not fit to sell is bruised. If there are 12 apples not fit to sell in the crate, how many apples are there in the crate?
(A) 270
(B) 360
(C) 480
(D) 600
(E) 400
Rationale: as given 3 out of every 4 bruised apple is not fit to sell
or, 75% of the bruised apples are not fit to sell.
as per the question 12 are not fit to sell
or,
0.75x=12
x=1200/75=16
thus total number of bruised apples =16
total number of apples =25*16=400
Answer: E
Answer: (E) 400
Question: set s contains the following numbers 10, 14, 19, 27, 36, 49, 67, 70,94. It was found that Mark had inadvertently interchanged the digits of one of the numbers. Steve, in charge of statistics, rectified this error, and as a result mean and median were changed and the shift in mean was of 5.
Whats the number that was incorrectly noted?
(A) 36
(B) 49
(C) 94
(D) 27
(E) 41
Rationale: Firstly the NEW median will be 27 or 49...
secondly the change in SUM will be 9*5 = 45, so the difference in number and in reversed order will be 45...
and the reversed NUMBER and actual number should be on either side of the MEDIAN 36..
lets see the choices on these points..
A. 36... reverse = 63 but 63−36≠4563−36≠45.... eliminate
B. 49... reverse = 94, and 94-49 = 45, BUT both 49 and 94 lie on the SAME side of 36, so no effect on MEDIAN... ELIMINATE
C. 94... SAME as B.. eliminate
D. 27.... reverse = 72.. 72-27 = 45.. yes and 27 is lesser than 36 and 72 is >36 so median will shift to 49... CORRECT
E. 41.... reverse 14, but 41−14≠4541−14≠45.. eliminate
ANSWER:D
Answer: (D) 27
Question: Let C be defined as the sum of all prime numbers between 0 and 28. What is C/3
(A) 155
(B) 100/3
(C) 61
(D) 47
(E) 43
Rationale: Prime numbers between 0 and 30 - 2 , 3 , 5 , 7, 11 , 13 , 17 , 19 , 23
Sum,C = 100
C/3 = 11/3
Answer B
Answer: (B) 100/3
Question: A salesman's income consists of a commission and a base salary of $350 per week. Over the past 5 weeks, his weekly income totals have been $406, $413, $420, $436 and $495. What must his average (arithmetic mean) commission be per week over the next two weeks so that his average weekly income is $500 over the 7-week period?
(A) $315
(B) $245
(C) $365
(D) $715
(E) $730
Rationale: Total weekly income over 5 weeks=$406+$413+$420+$436+$495=$2170
For avg weekly income to be $500 over 7 weeks, we need total weekly income over 7 weeks=$3500
Now, $3500-$2170=$1330
From this, we subtract base salary for 2 weeks i.e $350*2=$700
Therefore, commission=$1330-$700=$730 for 2 weeks
Avg weekly commission=$315
Answer A
Answer: (A) $315
Question: Tanks P and B are each in the shape of a right circular cylinder. The interior of tank P has a height of 10 meters and a circumference of 8 meters, and the interior of tank B has a height of 8 meters and a circumference of 10 meters. The capacity of tank P is what percent of the capacity of tank B?
(A) 75%
(B) 80%
(C) 100%
(D) 120%
(E) 125%
Rationale: B.
For P, r=8/2pi. Its capacity = (4pi)^2 * 10= 160pi
For B, r=10/pi. Its capacity = (5pi)^2 *8 = 200pi
P/B = 160pi/200pi = 0.8
Answer: (B) 80%
Question: In how many different ways can the letters of the word 'HEALTH' be arranged?
(A) 10 ways
(B) 20 ways
(C) 30 ways
(D) 60 ways
(E) 360 ways
Rationale: Totally there are 6 letters on the word HEALTH. it contains 2H,1E,1A,1L,1T.
The no of ways is 6!/2!=360 ways.
ANSWER:E
Answer: (E) 360 ways
Question: The sector of a circle has radius of 21 cm and central angle 135o. Find its perimeter?
(A) 91.5 cm
(B) 91.8 cm
(C) 99.5 cm
(D) 91.6 cm
(E) 91.3 cm
Rationale: Perimeter of the sector
= length of the arc + 2(radius)
= (135/360 * 2 * 22/7 * 21) + 2(21)
= 49.5 + 42
= 91.5 cm
Answer: A
Answer: (A) 91.5 cm
Question: Chris wants to pay back his debt to the bank. He has already paid back 60% of the initial debt. His family offered to help by paying 33% of the initial debt, so now he only needs an additional $105 in order to pay off the debt. What was the initial amount of the debt Chris owed to the bank?
(A) $1,500
(B) $2,000
(C) $2,500
(D) $3,000
(E) None
Rationale: Answer
Chris already has both 60% and 33% of the debt:
=60%+ 33% = 93%
The remaining amount that he will need to pay is equal to:
=100%-93%=7%
We know that this additional amount is $105; this allows us to find the initial total amount of his debt:
7%=$105
$105/7=$105/0.07= $1,500
answer is A.
Answer: (A) $1,500
Question: The length of a rectangular garden is 2 feet longer than 3 times its width. If the perimeter of the garden is 100 feet, find the length of the garden.
(A) 42
(B) 38
(C) 28
(D) 57
(E) 49
Rationale: Let L and W be the length and width of the garden. The statement "the length of a rectangular garden is 2 feet longer than 3 times its width" may be formulated by
L = 2 + 3 W
The formula for the perimeter is given by
P = 2 L + 2 W
Substitute P and L in the above equation by 100 and 2 + 3 W respectively to obtain
100 = 2(2 + 3 W) + 2 W
Solve for W and L
W = 12 and L = 2 + 3 W = 38.
Check that the perimeter of the rectangular garden is 100
P = 2 L + 2 W = 76 + 24 = 100
correct answer B
Answer: (B) 38
Question: Worker A takes 8 hours to do a job. Worker B takes 10 hours to do a job. How long should it take both A and B, working together to do same job.
(A) 4/9
(B) 2 4/9
(C) 3 4/9
(D) 4 4/9
(E) None of these
Rationale: Explanation:
In this type of questions, first we need to calculate 1 hours work, then their collective work as,
A's 1 hour work is 1/8
B's 1 hour work is 1/10
(A+B)'s 1 hour work = 1/8 + 1/10
= 9/40
So both will finish the work in 40/9 hours
=
4 4/9
Option D
Answer: (D) 4 4/9
Question: A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 47, the how old is B?
(A) 7
(B) 9
(C) 18
(D) 11
(E) 10
Rationale: Explanation:
Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years.
(2x + 2) + 2x + x = 47
⇒ 5x = 45
⇒ x = 9.
Hence, B's age = 2x = 18 years.
Answer: C
Answer: (C) 18
Question: Train T leaves New York at 7:00 am traveling to Boston at 80mph. Train B leaves Boston at 7:45 am traveling to New York at 70 mph on a parallel track. If the distance between New York and Boston is 210 miles, at what time will the two trains pass each other?
(A) 8:15 am
(B) 8:45 am
(C) 9:00 am
(D) 9:30 am
(E) Cannot be determined from the information given
Rationale: train T will cover 60 kms in 45 min at 7:45, the time when train B starts...
distance left to cover is 210-60=150..
combined speed=80+70=150..
so the trains meet in 1 hour i.e. 7:45 + 1 hr=8:45
B
Answer: (B) 8:45 am
Question: How many seconds will a train 150 meters long take to cross a bridge 200 meters long if the speed of the train is 54 kmph?
(A) 17 sec
(B) 21 sec
(C) 23.3 sec
(D) 27.5 sec
(E) 29 sec
Rationale: D = 150 + 200 = 350
S = 54 * 5/18 = 15 mps
T = 350/15 = 23.3 sec
C) 23.3 sec
Answer: (C) 23.3 sec
Question: Amit and Ravi invested capitals in the ratio 5:4. At the end of 8 months Amit withdrew and they got equal profits. Find for how long Ravi invested his money?
(A) 11 months
(B) 6 months
(C) 10 months
(D) 12 months
(E) None
Rationale: 8:5=4:x
That is 8*5=4*x
2*5=x
X=10 months
ANSWER:C
Answer: (C) 10 months
Question: Mike took a taxi to the airport and paid $2.50 to start plus $0.25 per mile. Annie took a different route to the airport and paid $2.50 plus $5.00 in bridge toll fees plus $0.25 per mile. If each was charged exactly the same amount, and Annie's ride was 26 miles, how many miles was Mike's ride?
(A) 20
(B) 30
(C) 36
(D) 46
(E) 54
Rationale: The cost of Annie's ride was 2.5+5+(0.25*26) = $14
Let x be the distance of Mike's ride.
The cost of Mike's ride is 2.5+(0.25*x) = 14
0.25*x = 11.5
x = 46 miles
The answer is D.
Answer: (D) 46