mathewhe/aqua_rat huggingface dataset:
Question: A committee of 7 is chosen from 8 men and 5 women so as to contain at least 2 men and 3 women. How many different committees could be formed?
(A) 308
(B) 700
(C) 1404
(D) 2620
(E) 3510
Rationale: The only cases possible are :
1. 2 men and 5 women : 8C2 * 5C5 = 28
2. 4 men and 3 women: 8C4*5C3 = 280
Rest of the cases will either have 1 or 0 men (not allowed) or will have 1 or 2 or 0 women (not allowed)
Total possible combinations = 28+280 = 308. Thus A is the correct answer.
Answer: (A) 308
Question: Two taps can separately fill a cistern 10 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 20 minutes. The waste pipe can empty the full cistern in?
(A) 2.8
(B) 8
(C) 6
(D) 9
(E) 5
Rationale: 1/10 + 1/15 - 1/x = 1/20
x = 20/7 = 2.8
Answer: A
Answer: (A) 2.8
Question: A survey of n people in the town of Eros found that 50% of them preferred Brand A. Another survey of 125 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 = 125
Total = 125 + 125 = 250
Answer (E)
Answer: (E) 250
Question: There were totally 100 men.85 are married.75 have T.V, 85 have radio,70 have A.C. How many men have T.V, radio, A.C and also married?
(A) 11
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: 100-(100-85)-(100-75)-(100-85)-(100-70)= 100-15-25-15-30=100-85=15
ANSWER:E
Answer: (E) 15
Question: If x is divisible by 9, 108, and 36, which of the following must be the least multiple of x?
(A) 108
(B) 36
(C) 9
(D) 324
(E) 120
Rationale: If x is divisible by 9, 108, and 36, then x must be a multiple of 9,4 and 3.
Hence,the least multiple of x will be 9*4*3=108.
ANSWER:A
Answer: (A) 108
Question: If q and b are positive numbers, and q^3 + b^3 = 75, then the greatest possible value of q is between:
(A) 0 and 3
(B) 3 and 5
(C) 4 and 5
(D) 5 and 7
(E) 6 and 9
Rationale: Yes the question is ambiguous, and the answer is certainly not C between 4 and 5 .
The question stated: q and b are positive numbers but not positive integers.
so fractions are allowed to be a part of calculation.
So if the answer is C then the value 4.5 = 9/2 must comply the equation.
(9/2)^3 + b^3 = 75
so, b^3 = -129/8 , which is not possible according to the question.
Moreover the question didn't mentioninclusive or not, so we can't assume that b is 4 .
hi asif,
question is correct IMO.
Sincemaximumvalues areuniqueso you cant take any value and make it satisfy with equation
question is asking that maximum value ofa(means that unique value ofa) is between...
its not saying all value of that range will satisfy.
Answer: (C) 4 and 5
Question: A farmer wishes to start a 100 square metres rectangular vegetable garden. Since he has only 30 m barbed wire, he fences three sides of the garden letting his house compound wall act as the fourth side fencing. The dimension of the garden is:
(A) 15 m × 6.67 m
(B) 20 m × 5 m
(C) 30 m × 3.33 m
(D) 40 m × 2.5 m
(E) None of these
Rationale: We have : 2b + l = 30 ⇒ l = 30 – 2b.
Area = 100 m2 ⇒ l × b = 100 ⇒ b(30 – 2b) = 100
⇒ b2 – 15b + 50 = 0 ⇒ (b – 10)(b – 5) = 0
⇒ b = 10 or b = 5.
When b = 10, l = 10 and when b = 5, l = 20.
Since the garden is rectangular,
so its dimension is 20 m × 5 m.
Answer B
Answer: (B) 20 m × 5 m
Question: Two trains starting at the same time from two stations 200 km apart and going in opposite directions cross each other at a distance of 110 km from one of the stations. What is the ratio of their speeds ?
(A) 11:9
(B) 11:20
(C) 9:20
(D) 11:8
(E) None of these
Rationale: Explanation :
In the same time, they cover 110 km and 90 km respectively.
=> Ratio of their speeds = 110 : 90 = 11 : 9
Answer : A
Answer: (A) 11:9
Question: Oil is poured in a cylindrical barrel at a rate of 5 cubic meters per hour, the level of oil in the tank rises at a rate of 1 meters per hour. Which of the following best approximates the radius of the tank in meters?
(A) √35/22
(B) √10/3
(C) 4
(D) 5
(E) 10
Rationale: Here's my re-worked solution:
volume = 5 = pi (r^2)(1)
5 = 22/7 (1)(r^2)
35/22 = r^2
r = sqrt(35/22)
Ans: A
Answer: (A) √35/22
Question: A tank is filled in 10 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?
(A) 70 hours
(B) 30 hours
(C) 35 hours
(D) 50 hours
(E) 60 hours
Rationale: 1/A + 1/B + 1/C = 1/10 ( a, b and c 1 hour work)
given.. 1/B= 2/A and 1/C = 2/B = 4/A
hence 1/A + 2/A + 4/A = 1/10
on solving.... we get 1/A = 1/70 ( work done by A in 1 hour)
therefore time taken by A is 70 hours to finish the whole work
ANSWER:A
Answer: (A) 70 hours
Question: In a sports club with 30 members, 17 play badminton and 17 play tennis and 2 do not play either. How many members play both badminton and tennis?
(A) 4
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: Let x play both badminton and tennis so 17-x play only badminton and 19-x play only tennis. 2 play none and there are total 30 students. hence,
(17-x)+(17-x)+x+2=30
34-2x+x=30
34-x=30
x=4
So 4 members play both badminton and tennis.
A
Answer: (A) 4
Question: A train 146 m long is running at a speed of 98 kmph. How long does it take to pass a man who is running at 12 kmph in the same direction as the train?
(A) 6 sec
(B) 9 sec
(C) 12 sec
(D) 18 sec
(E) 15 sec
Rationale: Answer : A.
Speed of the train relative to man = (98 - 12) kmph
= (86* 5/18) m/sec = (215/9)m/sec
Time taken by the train to cross the man
= Time taken by It to cover 146 m at 219/9 m / sec = 146 *9/ 219 sec = 6sec
Answer: (A) 6 sec
Question: The length of a rectangular landscape is 4times its breadth. There is a playground in it whose area is 1200 square mtr & which is 1/3rd of the total landscape. What is the length of the landscape?
(A) 100
(B) 110
(C) 120
(D) 140
(E) 160
Rationale: Sol. x * 4x = 3 * 1200
x = 30
Length = 4 * 30 = 120
C
Answer: (C) 120
Question: A circular box kept around a circular place. If the difference between the circumference of the outer circle and the inner circle is 44m, find the width of the box?
(A) 6 m
(B) 9 m
(C) 10 m
(D) 7 m
(E) 11 m
Rationale: Let radius of the outer circle be R and radius of the inner circle be r.
Circumference of the outer circle =
Circumference of the inner circle =
But,
or, R - r =
Thus, width of the road = 7 m
D
Answer: (D) 7 m
Question: The soldiers of Ghost platoon want to call in some mortars on Taliban fighters shooting at them from a mud compound. The compound is 300m away at 5 deg (compass heading). Firebase Darvishan is 10 kilometers away at 290 deg from Ghost platoon. If the mortar shells are landing 100m directly east of the compound, how should Ghost platoon tell the gunnser at Firebase Darvishan to make corrections on their shots?
(A) Drop 100.1M Right .27 deg
(B) Drop 106.771M Right 3 deg
(C) Drom 91.501M, Left .34 deg
(D) Drop 99.918M Right .24deg
(E) Drop 85.345M Right 1.28 deg
Rationale: Drop 99.918M Right .24deg
Answer: (D) Drop 99.918M Right .24deg
Question: The sum of the first 40 positive even integers is 2,550. What is the sum of the odd integers from 101 to 200, inclusive?
(A)  6,500
(B)  7,500
(C)  10,500
(D)  15,000
(E)  19,600
Rationale: 101+103+.......199
If we remove 100 from each of these it will be sum of 1st 100 odd numbers.
so 101+103+.......199 = 40 * 100 + (1+3+5+7+......)
sum of 1st 100 natural numbers = (100 * 101) / 2 = 5050
Sum of 1st 40 positive even integers = 2550
sum of 1st 100 odd numbers = 5050 - 2550 = 2500
so 101+103+.......199 = 40 * 100 + (1+3+5+7+......) = 4000 + 2500 =6500
A is the answer.
Answer: (A)  6,500
Question: It was calculated that 50 men could complete a piece of work in 10 days. When work was scheduled to commence, it was found necessary to send 25 men to another project. How much longer will it take to complete the work?
(A) 20 days.
(B) 15 days.
(C) 22 days.
(D) 30 days.
(E) 18 days.
Rationale: One day work = 1 / 10
One man’s one day work = 1 / ( 10 * 50)
Now:
No. Of workers = 25
One day work = 25 * 1 / ( 10 * 50)
The total no. of days required to complete the work = (50 * 10) / 25 = 20
Answer:A
Answer: (A) 20 days.
Question: A retail appliance store priced a video recorder at 20 percent above the wholesale cost of $200. If a store employee applied the 25 percent employee discount to the retail price to buy the recorder, how much did the employee pay for the recorder?
(A)  $198
(B)  $216
(C)  $220
(D)  $180
(E)  $240
Rationale: Wholesale cost of video recorder = 200 $
Video recorder was priced at 20 percent above 200 = 240 $
% discount given by store employee = 25
Emlpoyee paid = .75 * 240 = 180 $
Answer D
Answer: (D)  $180
Question: A room 5m 55cm long and 3m 74 cm broad is to be paved with square tiles. Find the least number of square tiles required to cover the floor
(A) 176
(B) 170
(C) 160
(D) 179
(E) 174
Rationale: Let x and y be the sides of the rectangle. Then, Correct area = xy.
Area of the room = (544 x 374) cm2.
Size of largest square tile = H.C.F. of 544 cm and 374 cm = 34 cm.
Area of 1 tile = (34 x 34) cm2.
Number of tiles required =(544*374)/(34*34)=176
ANSWER A 176
Answer: (A) 176
Question: Suppose that 25% of all the wise people are nice and half of all the nice
people are wise. Suppose further that 25% of all the people are neither
wise nor nice. What percent of all the people are both wise and nice?
(A) 10%
(B) 15%
(C) 20%
(D) 25%
(E) 30%
Rationale: Let k be the number of all the people who are both nice and wise. Then, the
number of wise people is 4k and the number of nice people is 2k. The number of people
who are either wise or nice or both is 4k + 2k − k = 5k. If the number of all people is
x, then x − 0.25x = 5k, so x = 20k/3.
correct answer B
Answer: (B) 15%
Question: A firm has 4 senior partners and 4 junior partners. How many different groups of 3 partners can be formed in which at least one member of the group is a senior partner. (2 groups are considered different if at least one group member is different)
(A) 40
(B) 44
(C) 48
(D) 52
(E) 56
Rationale: The total number of ways to form a group of 3 is 8C3 = 56
The number of groups without a senior partner is 4C3 = 4
The number of groups which include a senior partner is 56-4 = 52
The answer is D.
Answer: (D) 52
Question: The average of 15 result is 55. Average of the first 7 of them is 57 and that of the last 7 is 61. Find the 8th result?
(A) 760
(B) 720
(C) 700
(D) 786
(E) 797
Rationale: Sum of all the 13 results = 15 * 55 = 825
Sum of the first 7 of them = 7 * 57 = 399
Sum of the last 7 of them = 7 * 61 = 427
So, the 8th number = 825 + 399 - 427= 797.
E
Answer: (E) 797
Question: If you wanted to plant a certain number of flowers, but knew that 1 in 5 would not grow, how many flowers would you need to plant if you want a total of 20?
(A) 20
(B) 30
(C) 28
(D) 25
(E) 32
Rationale: 20 / (5-1) = 5
5 * 5 = 25
25 - (5-1) = 20
The correct answer is D
Answer: (D) 25
Question: The average of 10 numbers is calculated as 15. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is?
(A) 10
(B) 13
(C) 16
(D) 18
(E) 22
Rationale: Explanation:
10 * 15 + 36 – 26 = 160/10 = 16
C)
Answer: (C) 16
Question: [1+(1/5)]^n=2?
What is the value of n?
(A) 1.999
(B) 2.999
(C) 3.88
(D) 4.88
(E) 5.88
Rationale: 1+1/5 = 6/5 = 1.2
1.2*1.2 = 1.44 *1.2 = 1.728 *1.2 = 2.0736
so if N is integer, N=4. if not, N = 3.8
(1.2)^3.8 = 1.999
ANSWER:C
Answer: (C) 3.88
Question: If x, y, and s are positive numbers such that 10*x/(x+y)+ 20*y/(x+y)=s and if x is less than y, which of the following could be the value of s?
(A) 10
(B) 12
(C) 15
(D) 18
(E) 30
Rationale: Answer choice C: s= 15
(10x + 20y)/(x+y) = 15
10x + 20y = 15x + 15y
5y = 5x
y = x
Doesn't work because the problem states that x<y.
We need y to be larger, so let's try answer choice D: s=18
10x + 20y = 18x + 18y
2y = 8x
y/x = 8/2
Success! x<y.
The correct answer is D.
Answer: (D) 18
Question: The sum of the first five terms of a G.P is 363. If the common ratio is 1/3 find the first term.
(A) 323
(B) 243
(C) 232
(D) 332
(E) 432
Rationale: Sum of the first n terms of a G.P = a (1 -rn )/1 - r ,
a [ 1 - (1/3) 5 ]/ (1 - 1/3) = 363
a = 363 [ 1-1/3 ] /1- (1/3) 5 = ( 363* 2/3) / ( 1- 1/242 ) = 242/ ( 242/243 )
a = 243
ANSWER:B
Answer: (B) 243
Question: It takes 3 workers a total of 15 hours to build a giant machine with each worker working at the same rate. If 5 workers start to build the machine at 11:00 AM, and one extra worker per hour is added beginning at 1:00 PM, at what time will the machine be complete?
(A) 4:30
(B) 4:45
(C) 5:00
(D) 5:15
(E) 5:30
Rationale: 3 workers build 1/15 of a machine in one hour.
1 worker builds 1/45 of a machine in one hour.
In the first 2 hours, 5 workers build 5*(1/45)*2=10/45 of a machine.
From 1:00 to 2:00, 6 workers build another 6/45. The total is 16/45.
From 2:00 to 3:00, 7 workers build another 7/45. The total is 23/45.
From 3:00 to 4:00, 8 workers build another 8/45. The total is 31/45.
From 4:00 to 5:00, 9 workers build another 9/45. The total is 40/45.
To build another 5/45, 10 workers need (5/10)*60 minutes which is 30 minutes.
The machine is complete at 5:30.
The answer is E.
Answer: (E) 5:30
Question: If an object travels 200 feet in 4 seconds, what is the object's approximate speed in miles per hour? (Note: 1 mile = 5280 feet)
(A) 36
(B) 34
(C) 356
(D) 12
(E) 45
Rationale: 1 mile = 5280 feet
=> 1 feet = 1/5280 miles
If the object travels 200 feet in 4 sec
then it travels 200/4 * 60 * 60 feet in 1 hour (1 hr = 60 min * 60 sec)
= 3600 * 50 feet in 1 hour
= 180000 feet in 1 hr
= 180000/5280 miles in 1 hour
= 18000/528 miles/hr ~ 34 miles/hr
Answer - B
Answer: (B) 34
Question: In a certain country 1/7 of 8 = 5. Assuming the same proportion, what would be the value of 1/5 of 40 ?
(A) 54
(B) 25
(C) 45
(D) 35
(E) 52
Rationale: D
35
Answer: (D) 35
Question: A scuba diver descends at a rate of 80 feet per minute. a diver dive from a ship to search for a lost ship at the depth of 4000feet below the sea level..how long will he take to reach the ship?
(A) 70 minutes
(B) 72 minutes
(C) 50 minutes
(D) 66 minutes
(E) 67 minutes
Rationale: Time taken to reach = 4000/80= 50 minutes
ANSWER:C
Answer: (C) 50 minutes
Question: A boy rides his bicycle 10 km at an average speed of 12 km/hr and again travels 12 km at an average speed of 10 km/hr. His average speed for the entire trip is approximately?
(A) 10.8 km/hr
(B) 12.8 km/hr
(C) 11.8 km/hr
(D) 16.8 km/hr
(E) 17.8 km/hr
Rationale: A
10.8 km/hr
Total distance traveled = 10 + 12 = 22 km /hr.
Total time taken = 10/12 + 12/10 = 61/30 hrs.
Average speed = 22 * 30/61 = 10.8 km/hr.
Answer: (A) 10.8 km/hr
Question: If one root of the equation 2x^2 + 3x – k = 0 is 5, what is the value of k?
(A) 65
(B) 79
(C) 68
(D) 87
(E) 90
Rationale: We just enter this root into the equation in order to recieve an equation to find the answer!
2*5^2+3*5-k=0
k=50+15=65
The answer is A
Answer: (A) 65
Question: For 600 km journey it will take 8hrs, if 120 km is done by bus and the rest by car. It takes 20 minutes more, if 200 km is done by busand the rest by car. The ratio of the speed of the train to that of the cars is?
(A) 1 : 3
(B) 3 : 4
(C) 1 : 6
(D) 2 : 7
(E) 3 : 8
Rationale: Let the speed of the train be x km/hr and that of the car be y km/hr.
Then, 120 + 480 = 8 1 + 4 = 1 ....(i)
x y x y 15
And, 200 + 400 = 25 1 + 2 = 1 ....(ii)
x y 3 x y 24
Solving (i) and (ii), we get: x = 60 and y = 80.
Ratio of speeds = 60 : 80 = 3 : 4
B
Answer: (B) 3 : 4
Question: Three walls have wallpaper covering a combined area of 300 square meters. By overlapping the wallpaper to cover a wall with an area of 180 square meters, the area that is covered by exactly two layers of wallpaper is 34 square meters. What is the area that is covered with three layers of wallpaper?
(A) 43 Square Meters
(B) 36 Square Meters
(C) 42 Square Meters
(D) 83.3 Square Meters
(E) 120 Square Meters
Rationale: 300 - 180 = 120 sq m of the wallpaper overlaps (in either two layers or three layers)
If 36 sq m has two layers, 120 - 34 = 86 sq m of the wallpaper overlaps in three layers. 86 sq m makes two extra layers hence the area over which it makes two extra layers is 43 sq m.
Answer (A).
Answer: (A) 43 Square Meters
Question: One hour after Sid started walking the 60 miles from X to Y, James started walking from X to Y as well. Sid walks 3 miles per hour and James walks 1 mile per hour faster than Sid . How far from X will James be when he catches up to Sid ?
(A) 8 miles
(B) 9 miles
(C) 12 miles
(D) 11 miles
(E) 13 miles
Rationale: First, determine how far Sid has walked in the one hour. he has walked three miles which means he is three miles ahead of James when he sets off. James walks at four miles/hour which means that every hour, james will get one mile closer to Sid . If he gets one mile closer every hour, it will take him three hours to catch up to him which means he travels 3hours * 4 miles/hour = 12 miles and he travels 4 hours * 3 miles/hour = 12 miles. He will be 12 miles from X when he catches up to her.
A slightly different way to solve...
We don't know how long they will walk before they catch up to one another but we do know that A walks for one hour more than J. J = T and A = T+1. We are looking for the distance at which they meet up which means the distance will be the same. D=r*t so,
r*t (james) = r*t (Sid )
r*(t) = r*(t+1)
4t = 3t+3
t=3
d=r*t
d=4*3
d=12
C) 12 miles
Answer: (C) 12 miles
Question: The price of 2 sarees and 4 shirts is $1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay ?
(A) 3800
(B) 3300
(C) 2400
(D) 4200
(E) 1400
Rationale: C
$2400
Let the price of a saree and a shirt be $x and $y respectively.
Then, 2x + 4y = 1600 .... (i)
and x + 6y = 1600 .... (ii)
Divide equation (i) by 2, we get the below equation.
=> x + 2y = 800. --- (iii)
Now subtract (iii) from (ii)
x + 6y = 1600 (-)
x + 2y = 800
----------------
4y = 800
----------------
Therefore, y = 200.
Now apply value of y in (iii)
=> x + 2 x 200 = 800
=> x + 400 = 800
Therefore x = 400
Solving (i) and (ii) we get x = 400, y = 200.
Cost of 12 shirts = $(12 x 200) = $2400.
Answer: (C) 2400
Question: If doubling a number and adding 20 to the result gives the same answer as multiplying the number by 8 and taking away 4 from the product, the number is
(A) 2
(B) 3
(C) 4
(D) 6
(E) 7
Rationale: Solution
Let the number be x.	= Then, 2x+20 = 8x–4
= 6x = 24
‹=›x = 4.
Answer C
Answer: (C) 4
Question: The diameter of the wheel of a car is 120m. How many revolution/min must the wheel makein order to keep a speed of 60 km/hour approximately?
(A) 210
(B) 245
(C) 230
(D) 254
(E) 265
Rationale: Distance to be covered in 1 min. = (60 X 1000)/(60) m = 1000 m.
Circumference of the wheel = (2 x (22/7) x 0.60) m = 3.77 m.
Number of revolutions per min. =(1000/3.77) = 265
E
Answer: (E) 265
Question: Indu gave Bindu Rs.6500 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest?
(A) 12.8
(B) 20
(C) 10.4
(D) 11.6
(E) 15
Rationale: 6500 = D(100/4)2
D = 10.4
Answer: C
Answer: (C) 10.4
Question: Anand and Deepak started a business investing Rs. 27,500 and Rs. 35,000 respectively. Out of a total profit of Rs. 13,800, Deepak's share is?
(A) 7728
(B) 2888
(C) 8400
(D) 2882
(E) 2781
Rationale: Ratio of their shares = 27500 : 35000 = 11:14
Deepak's share = 13800 * 14/25 = Rs. 7728.
Answer: A
Answer: (A) 7728
Question: A math teacher has 27 cards, each of which is in the shape of a geometric figure. Half of the cards are rectangles, and a third of the cards are rhombuses. If 8 cards are squares, what is the maximum possible number of cards that re circles.
(A) 9
(B) 10
(C) 11
(D) 12
(E) 13
Rationale: a square is a special kind of rhombus (sides are perpendicular)
a square is a special kind of rectangles (sides with same length)
Among the 27 cards with have:
15 rectangles
10 rhombus
8 squares
Among the 15 rectangles, there could be 8 special ones (with sides of same length) that are squares. That lets at least 7 rectangles that are not square.
Among the 10 rectangles, there could be 8 special ones (with sides perpendicular) that are squares. That lets at least 2 rhombus that are not square.
We have 8 squares.
So the minimum different cards that represent a square, a rhombus or a rectangle is 2 + 7 + 8 = 17
Which means that the maximum number of circles that you could have is 27 - 17 = 10
Answer (B)
Answer: (B) 10
Question: Dexter was born between October 6th and 10th (6th and 10th excluding). His year of birth is also known. What is the probability of Dexter being born on a Saturday?
(A) 0 or 1/3
(B) 1/7 or 3/7
(C) 1/3 or 1/7
(D) 1/3 or 1/4
(E) cannot be determined.
Rationale: Explanation :
Since the year of birth is known, the birthday being on Saturday can have a zero probability.
Also since between 6th and 10th, there are three days i.e. 7th,8th and 9th.
Therefore, probability of birthday falling on Saturday can be 1/3.
Answer : A
Answer: (A) 0 or 1/3
Question: 3 houses are available in a locality.3 persons apply for the houses.Each apply for one house without consulting others.the probablity that all 3 apply for the same house is:
(A) 2/9
(B) 1/9
(C) 8/9
(D) 7/9
(E) 1/4
Rationale: let there be three house a,b,c then there would be 27 ways in which 3 person x,y,z select house
there will be 1 case when x,y,z will buy house a
another when they buy house b
and another when they buy house c
so the prob that they buy same house is 3*1/27=1/9
ANSWER:B
Answer: (B) 1/9
Question: A dishonest dealer professes to sell goods at the cost price but uses a false weight and gains 25%. Find his false weight age?
(A) 177
(B) 199
(C) 800
(D) 171
(E) 128
Rationale: 25 = E/(1000 - E) * 100
1000 - E = 4E
1000 = 5E => E = 200
1000 - 200 = 800
Answer: C
Answer: (C) 800
Question: From a group of boys and girls, 15 girls leave. They are then left 2 boys for each girl. After this, 72 boys leave. There are then 5 girls for each boy. Find the number of girls in the beginning
(A) 20
(B) 10
(C) 30
(D) 55
(E) 40
Rationale: Assume the number of boys at present = x
Then, the number of girls at present = 5x
Before the boys left, the number of boys were (x+72) and number of girls were 5x
Hence, 2(5x) = x + 72
=> 10x = x + 72
=> x = 8
Number of girls in the beginning = (5x + 15) = (5×8 + 15) = 55
Answer is D.
Answer: (D) 55
Question: When positive integer N is divided by positive integer J, the remainder is 27. If N/J = 204.09, what is value of J?
(A) 300
(B) 320
(C) 360
(D) 410
(E) 420
Rationale: When a number is divided by another number, we can represent it as : Dividend = Quotient * Divisor + Remainder
So, Dividend/Divisor = Quotient + Remainder/Divisor
Given that N/J = 204.09
Here 204 is the quotient.
Given that Remainder = 27
So, 204.09= 204 + 27/J
So, J = 300
Answer: A
Answer: (A) 300
Question: The length of a train and that of a platform are equal. If with a speed of 180 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?
(A) 1500
(B) 266
(C) 299
(D) 750
(E) 261
Rationale: Speed = [180 * 5/18] m/sec = 50 m/sec; Time = 1 min. = 60 sec.
Let the length of the train and that of the platform be x meters.
Then, 2x/60 = 50 => x = 50 * 60 / 2 = 1500
Answer: A
Answer: (A) 1500