mathewhe/aqua_rat huggingface dataset:
Question: 53 x 22 = 1276 then (4221)n=()10?
(A) 3896
(B) 3897
(C) 3898
(D) 3899
(E) None
Rationale: Sol:
As we don't know the base system here we take the base as n. So 53 in base n can be written as 5n+3, and 22 as 2n+2 and 1276 as n3+2n2+7n+6
⇒⇒ (5n + 3)(2n + 2) = n3+2n2+7n+6
⇒⇒ 10n2+16n+6=n3+2n2+7n+6
⇒⇒ n3−8n2−9n=0
⇒⇒ n(n2−8n−9)=0
⇒⇒ (n + 1)(n - 9) = 0
So n = 9
(4221)9=4×93+2×92+2×9+1
= 3716 + 162 + 18 + 1 = 3897
Answer B
Answer: (B) 3897
Question: Four friends, Thomas, Mike, Brian, and John, went on a fishing trip. If Mike caught 4 more than Brian did, John caught 12 less than Thomas did, and Thomas caught 4 more than Mike did, how many more fish did Brian catch than John did?
(A) 6
(B) 4
(C) 8
(D) 1
(E) 12
Rationale: In this word problem, the first key is to turn the story into equations:
Mike caught 4 more than Brian did: M = 4 + B
John caught 12 less than Thomas did: J = T - 12
Thomas caught 4 more than Mike did: T = 4 + M
Then, in classic GMAT style, the problem doesn't ask you to solve for a single variable, but instead to solve for the difference between B and J (how many more fish did Brian catch than John did?). This means that your goal is to get the equations in terms of B and J so that you can solve for the expression B - J.
Taking the first equation and solving for B, you have B = M - 4.
Taking the second equation and solving for J you have J = T - 12, and then with the third equation you can replace T with 4 + M so that both B and J are in terms of M: J = (4 + M) - 12.
So if B = M - 4 and J = M - 8, then:
B - J = (M - 4) - (M - 8)
B - J = M - 4 - M + 8 (remove the parentheses by distributing the multiplication)
B - J = 4, so the answer is B.
Answer: (B) 4
Question: A group of 3 integers is to be selected one after the other, and at random and without replacement, from list L above. What is the probability that the 3 integers selected are not 3 consecutive integers?
(A) 3/5
(B) 7/10
(C) 3/4
(D) 4/5
(E) 14/15
Rationale: Determining that there were 120 ways to select 3 numbers from that group was the perfect first step. Next, you just have to figure out which combinations of 3 involve three consecutive integers. Thankfully, it's not that hard - and you can list them out:
123
234
345
456
567
678
789
89&10
Thus there are 8 ways (out of 120) that ARE three consecutive integers and the other 112/120 are NOT three consecutive integers.
112/120 = 14/15
Final Answer:E
Answer: (E) 14/15
Question: Ram's age and Shyam's age are in the ratio 3 : 4. Seven years ago the ratio of their ages was 2: 3. Find the ratio of their ages five years hence?
(A) 33:21
(B) 44:44
(C) 33:45
(D) 26:33
(E) 44:66
Rationale: Let ages of Ramu and Shyamu be x and y respectively.
x/y = 3/4 => x = 3/4 y
Also (x - 7) / (y - 7) = 2/3
=> 3x - 21 = 2y - 14
3x = 2y + 7
But x = 3/4 y
3 * 3/4 y = 2y + 7
9y = 8y + 28 => y = 28 years
Ratio of their ages five years hence
= (21 + 5) / (28 + 5) = 26/33.
Answer:D
Answer: (D) 26:33
Question: Dick and Jane each saved $4,000 in 1989. In 1990 Dick saved 10 percent more than in 1989, and together he and Jane saved a total of $6,500. Approximately what percent less did Jane save in 1990 than in 1989?
(A) 20%
(B) 70%
(C) 50%
(D) 30%
(E) 40%
Rationale: 1990
Dick saved = $ 4400
Jane saved = $ 2100 (jane saved $2800 less than she did the prior year)
Jane saved approximately $2800/4000$ (70%) less in 1990
Answer: B
Answer: (B) 70%
Question: 2/5 of the fish in an aquarium are red and 1/4 of the fish are brown. 3/4 of the red fish and 3/5 of the brown fish are male. If the rest of the fish in the aquarium are female, what is the probability that a fish randomly picked from the aquarium is male?
(A) 2/5
(B) 3/10
(C) 7/10
(D) 9/20
(E) 11/20
Rationale: 3/4*2/5 + 3/5*1/4 = 9/20
The answer is D.
Answer: (D) 9/20
Question: A young girl counted in the following way on the fingers of her left hand. She started collang the thumb 1, the index finger 2, the middle finger 3, the ring finger 4, the little finger 5, then reversed direction calling the ring finger 6, the the middle finger 7, the index finger 8, the thumb 9 then back to the index finger for 10, the middel finger for 11, and so on. She counted up to 1994. She ended on her
(A) thumb
(B) the index finger
(C) the middle finger
(D) the ring finger
(E) the little finger
Rationale: Notice the pattern. The thumb lands up at numbers 1,9,17,25,33,... so every 8th number
By this patter the thumb is also at number 1993 (multiple of 8 + 1)
Hence 1994 has to be the index finger
Answer is B
Answer: (B) the index finger
Question: How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 66 km/hr?
(A) 11
(B) 30
(C) 29
(D) 88
(E) 61
Rationale: Speed of train relative to man = 66 - 3 = 63 km/hr.
= 63 * 5/18 = 35/2 m/sec.
Time taken to pass the man = 500 * 2/35 = 28.57 sec.
approx. 29 sec
Answer: C
Answer: (C) 29
Question: Raffle tickets numbered consecutively from 101 through 350 are placed in a box. What is the probability that a ticket selected at random will have a number with a hundreds digit of 1 ?
(A) 2/5
(B) 2/7
(C) 33/83
(D) 99/250
(E) 98/250
Rationale: SOLUTION
The number of integers from 101 to 350, inclusive is 250, out of which 100 (from 200 to 299) will have a hundreds digit of 2. Thus the probability is 98/250
Answer: E
Answer: (E) 98/250
Question: A group of 8 students are seated in a linear arrangement. There are 2 girls who must sit together always. in how many arrangements can the students sit?
(A) A.1296
(B) B.1850
(C) C.2880
(D) D.3546
(E) E.10080
Rationale: Glue two girls together: {AB}
6 units {AB}, {C},{D}, {E}, {F}, {G}, {H} can be arranged in 7! ways. Each girls within their unit can be arranged in 2! ways.
Therefore the final answer is 7!*2!=
Answer: E.
Answer: (E) E.10080
Question: A starts a business with a capital of Rs. 85,000. B joins in the business with Rs.42500 after some time. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1?
(A) 8 months
(B) 9 months
(C) 1months
(D) 12months
(E) 23months
Rationale: Let B joins for x months. Then
A:B = 85000*12 : x* 42500 = 3 : 1
=> 850*12 : 425x= 3 : 1
=> 850*12/ 425x = 3/1 = 3
=> 850*4 /425x = 1
=> 2*4/x = 1
=> x = 8
Answer is A
Answer: (A) 8 months
Question: Of three numbers, the third is four times the second and the second is two times the first. If their average is 165, the smallest of the three numbers is:
(A) 18
(B) 19
(C) 45
(D) 21
(E) 22
Rationale: Explanation:
Let first number be x.
So,2nd no. = 2x & 3rd no.=8x.
So,x+2x+8x=165 × 3 = 495
11x = 495/11
x = 495/11
Hence,smallest Number x=45
Answer: C
Answer: (C) 45
Question: Using all the letters of the word "NOOKIASS", how many words can be formed, which begin with N and end with S?
(A) 550
(B) 160
(C) 720
(D) 620
(E) 820
Rationale: There are five letters in the given word.
Consider 8 blanks ....
The first blank and last blank must be filled with N and S all the remaining three blanks can be filled with the remaining 6 letters in 6! ways.
The number of words = 6! = 720.
Answer: C
Answer: (C) 720
Question: A 75m long train is running at 54 km/hr. In how much time will it cross an electric pole?
(A) 5
(B) 10
(C) 15
(D) 20
(E) 25
Rationale: Speed of the train = ( 54 * 5 / 18) m/sec = 15 m / sec. Length of the train = (Speed x Time)
Time = (Length of the train / Speed)
=(75/ 15) = 5sec
Answer: A
Answer: (A) 5
Question: At what time between 9’o clock and 10’o clock will the hands of a clock point in the opposite directions?
(A) 16 4⁄11 minutes past 9
(B) 16 4⁄11 minutes past 8
(C) 55 5⁄61 minutes past 7
(D) 55 5⁄61 minutes past 8
(E) None of these
Rationale: At 9’o clock, the Minute Hand is ahead of Hour Hand by 45 minutes. The hands will be opposite to each other when there is a space of 30 minutes between them.
This will happen when the Minute Hand gains 15 minutes space over Hour Hand.
Time taken by Minutes Hand to gain 15 minutes
= 15 × (1 + 1⁄11) = 15 + 15⁄11 = 15 + 14⁄11 + 16 4⁄11 minutes.
Hence the Hands are opposite to each other at 16 4⁄11 minutes past 9.
Answer A
Answer: (A) 16 4⁄11 minutes past 9
Question: Lina works 10 days a month at d dollars per day for m months out of the year. Which of the following represents her monthly pay?
(A) m/(10d)
(B) 5md/6
(C) 10d
(D) 10d/m
(E) 10md
Rationale: Total income of Lina in a year = d*10*m dollars. Now Monthly income = Total/12 = d*10*m / 12 = 5md/6 Answer is B
Answer: (B) 5md/6
Question: If 9x^2-16y^2=3x+4y,then what will give the answer?
(A) 3x-4y=0
(B) 3x-4y=2
(C) 3x-4y=1
(D) 3x+4y=0
(E) 3x+4y=1
Rationale: 9x^2-16y^2=3x+4y
(3x+4y)(3x-4y)=3x+4y
3x-4y=(3x+4y)/(3x+4y)
3x-4y=1
Answer is option C
Answer: (C) 3x-4y=1
Question: During one month at a particular restaurant, 1/5 of the burgers sold were veggie burgers and 1/4 of the rest of the burgers sold were double-meat. If x of the burgers sold were double-meat, how many were veggie burgers?
(A) x/8
(B) x
(C) 2x/3
(D) 3x/4
(E) 4x/5
Rationale: Let y be the number of total burgers.
veggie = y/5 , non veggie = 4y/5
1/4 of the rest of the burgers sold were double-meat
=> 4y/5 * 1/4 = double meat = x
=> y/5 = x= veggie
Hence B
Answer: (B) x
Question: A train 280 m long, running with a speed of 63 km/hr will pass a tree in?
(A) 15 sec
(B) 16 sec
(C) 18 sec
(D) 20 sec
(E) 22 sec
Rationale: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 280 * 2/35 = 16 sec
ANSWER:B
Answer: (B) 16 sec
Question: Tough and Tricky questions: Work/Rate Problems.
A group of 4 junior lawyers require 3 hours to complete a legal research assignment. How many hours would it take a group of three legal assistants to complete the same research assignment assuming that a legal assistant works at two-thirds the rate of a junior lawyer?
Source: Chili Hot GMAT
(A) 13
(B) 10
(C) 9
(D) 6
(E) 5
Rationale: # of people times the # of hours:
4*3 = 12 --> 3 lawyers do 12worksin 3 hours.
3*6/3 = 6 --> 3 assistants do 6 worksin 2 hours
So, since the amount of work the assistants do is half the work the lawyers do, the time will be double, soANS D
Answer: (D) 6
Question: A bowl contains 3 parts of which are milk and 5 parts water. How much of the mixture must be drawn off and replaced with milk sothat the mixture may be half milk and half water?
(A) 2/5
(B) 3/5
(C) 1/5
(D) 1/7
(E) 2/7
Rationale: Suppose the vessel initially contains 8 litres of liquid.
Let x litres of this liquid be replaced with water.
Quantity of water in new mixture = 3 -	3x	+ x litres
8
Quantity of syrup in new mixture = 5 -	5x litres
8
3 -	3x	+ x = 5 -	5x
8	8
5x + 24 = 40 - 5x
10x = 16
x =	8	.
5
So, part of the mixture replaced = 8	x	1 =	1/5
5	8	5
C
Answer: (C) 1/5
Question: Mr. Smith calculated the average of 10three digit numbers. But due to a mistake he reversed the digits of a number and thus his average increased by 59.4. The difference between the unit digit and hundreds digit of that number is :
(A) a) 6
(B) b) 3
(C) c) 2
(D) d) 1
(E) e) 0
Rationale: Since the average increased by 59.4 and there were a total of 10 numbers, it means the incorrect number was 594 greater than the correct number.
Say, the correct number was abc (where a, b and c are the digits of the 3 digit number)
Then the incorrect number was cba.
100c + 10b + a - (100a + 10b + c) = 594
99c - 99a = 99(c - a) = 594
594 = 99*6 = 99(c - a)
So c - a = 6
Answer (A)
Answer: (A) a) 6
Question: A crate of apples contains 1 bruised apple for every 30 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 15 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) 840
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 15 are not fit to sell
or,
0.75x=15
x=1500/75=20
thus total number of bruised apples =20
total number of apples =30*20=600
Answer: D
Answer: (D) 600
Question: Find the SI on Rs 8000 for 4 yrs at 10% per annum rate of interest?
(A) Rs 3000
(B) Rs 3500
(C) Rs 4000
(D) Rs 4400
(E) Rs 4800
Rationale: Simple Interest =
PTR
100
= 8000 X 5 X
10
100
= Rs 4000
C
Answer: (C) Rs 4000
Question: In the xy-coordinate plane, the graph of y = -x^2 + 9 intersects line L at (p,5) and (t,-8). What is the least possible value of the slope of line L?
(A) -6.5
(B) 2
(C) -2
(D) -6
(E) -10
Rationale: We need to find out the value of p and L to get to the slope.
Line L and Graph y intersect at point (p,5). hence, x= p and Y=5 should sactisfy the graph. soliving
5 = -p2 +9
p2 = 4
p = + or - 2
simillarly point (t,-8) should satisfy the equation. hence x=t and Y=-8.
-7 = -t2+9
t = +or - 4
considering p = -2 and t =4, the least slope is (-8-5)/(4-2) = -6.5
IMO option A is correct answer.
Answer: (A) -6.5
Question: A began a business with Rs.85,000. He wasjoined afterwards by B with Rs.42,500. For how muchperiod does B join, if the profits at the end of the yr are dividedin the ratio of 3:1?
(A) 5 months
(B) 8 months
(C) 9 months
(D) 11 months
(E) 21 months
Rationale: Suppose B joined for x months. Then,
Then, 85000 x 12	=	3
42500 x x	1
x = 85000 x 12 = 8.
42500 x 3
So, B joined for 8 months.
B
Answer: (B) 8 months
Question: A batsman makes a score of 56 runs in the 17th inning and thus increases his averages by 3. What is his average after 17th inning?
(A) 25
(B) 8
(C) 27
(D) 29
(E) 39
Rationale: Let the average after 17 innings = x
Total runs scored in 17 innings = 17x
Average after 16 innings = (x-3)
Total runs scored in 16 innings = 16(x-3)
Total runs scored in 16 innings + 56 = Total runs scored in 17 innings
=> 16(x-3) + 56 = 17x
=> 16x - 48 + 56 = 17x
=> x = 8
Answer is B.
Answer: (B) 8
Question: At present, the ratio between the ages of Arun and Deepak is 4:3. After 6 years, Arun's age will be 26 years. What is the age of Deepak at present?
(A) 15
(B) 12
(C) 13
(D) 18
(E) 19
Rationale: Let the present ages of Arun and Deepak be 4x and 3x years respectively.
Then, 4x + 6 = 26 => x = 5
Deepak's age = 3x = 15 years.
ANSWER A
Answer: (A) 15
Question: If x is real, find the maximum value of the expression -2x^2 + 9x + 11.
(A) 12.125
(B) 15.125
(C) 18.125
(D) 21.125
(E) 24.125
Rationale: This is an equation of a downward facing parabola.
The maximum value is the top point of the parabola.
-2x^2+9x+11 = (-2x+11)(x+1)
The roots are 11/2 and -1.
The maximum value must be when x is halfway between these two points.
x = 2.25
The maximum value is -2(2.25)^2+9(2.25)+11 = 21.125
The answer is D.
Answer: (D) 21.125
Question: A pump can fill a tank with water in 4 hours. Because of a leak, it took 7 hours to fill the tank. The leak can drain all the water in ?
(A) 15hr 10min
(B) 16hr 20min
(C) 9hr 20min
(D) 15hr
(E) 14hr 25min
Rationale: Work done by the leak in 1 hour = 1/4 - 1/7 = 3/28
Leak will empty the tank in 28/3 hrs = 9hr 20min
Answer is C
Answer: (C) 9hr 20min
Question: A box contains five bulbs out of which 3 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good.
(A) 39/10
(B) 29/10
(C) 19/10
(D) 9/10
(E) 125/128
Rationale: Required probability
= 1 - 1/10
= 9/10
Answer: D
Answer: (D) 9/10
Question: A certain company consists of 7 managers and 8 non-managers. How many different teams of 3 employees can be formed in which at least one member of the team is a manager and at least one member of the team is not a manager? (Two groups are considered different if at least one group member is different)
(A) 84
(B) 108
(C) 135
(D) 270
(E) 364
Rationale: Total # of teams of 3 possible is 15C3=455
# of teams with only managers or only non-managers is: 7C3+8C3=35+56=91;
# of teams of 3 with at least one manager or at least one non-manager is: 455-91=364.
ANSWER:E
Answer: (E) 364
Question: The L.C.M. of 2 numbers is 30. The numbers are in the ratio 2:3. Find their sum?
(A) 36
(B) 25
(C) 48
(D) 32
(E) 56
Rationale: Let the numbers be 2x and 3x
L.C.M. = 6x
6x = 30
x = 5
The numbers are = 10 and 15
Required sum = 10+15 = 25
Answer is B
Answer: (B) 25
Question: If an average hard drive had a capacity of 0.4 TB in 2000, and average hard drive capacities double every 5 years, what will be the average hard drive capacity in 2050?
(A) 256
(B) 512
(C) 4096
(D) 1024
(E) 1536
Rationale: 0.4*2^10=0.4*1024=409.6
The answer is C.
Answer: (C) 4096
Question: A new tower has just been built at the Verbico military hospital; the number of beds available for patients at the hospital is now 4 times the number available before the new tower was built. Currently, 1/3 of the hospital's original beds, as well as 1/5 of the beds in the new tower, are occupied. For the purposes of renovating the hospital's original wing, all of the patients in the hospital's original beds must be transferred to beds in the new tower. If patients are neither admitted nor discharged during the transfer, what fraction of the beds in the new tower will be unoccupied once the transfer is complete?
(A) 11/30
(B) 29/60
(C) 17/30
(D) 31/45
(E) 11/15
Rationale: I think D - 31/45 is the correct answer.
Here goes:
Lets assume originally the number of beds = x
After the new tower, the total combined no of beds = 4x
So old = x, New = 3x
Now 1/3 of x are occupied and 1/5 of 3x are occupied which simplifies to (3/5)x
We are shifting 1/3 of x to the new ward so there will now be:
1/3 of x plus 3/5 of x occupied in the new ward. Add them up to get 14/15 of x
There are 3x beds in New Tower so ratio is:
(14/15)x / 3x = 14/45 of x
Subtract that from 45/45 of x and you get the number of un-occupied beds to total capacity of New Tower =31/45
D
Answer: (D) 31/45
Question: A man walked diagonally across a square lot. Approximately, what was the percent saved by not walking along the edges?
(A) 20%
(B) 30%
(C) 35%
(D) 40%
(E) 50%
Rationale: Let the side of the square(ABCD) be x metres.
Then, AB + BC = 2x metres.
AC = 2x = (1.41x) m.
Saving on 2x metres = (0.59x) m.
Saving % = 0.59x x 100 % = 30% (approx.)
2x
B)
Answer: (B) 30%
Question: Find the number which is nearest to 3105 and is exactly divisible by 21.
(A) 3104
(B) 3106
(C) 3108
(D) 3109
(E) 3103
Rationale: On dividing 3105 by 21, we get 18 as remainder.
Number to be added to 3105 = (21 - 18) - 3.
Hence, required number = 3105 + 3 = 3108.
ANSWER C 3108
Answer: (C) 3108
Question: The Royal Hawaiian Hotel decorates its Rainbow Christmas Tree with non-flashing white lights and a series of colored flashing lights - red, blue, green, orange, and yellow. The red lights turn red every 20 seconds, the blue lights turn blue every 30 seconds, the green lights turn green every 45 seconds, the orange lights turn orange every 60 seconds, and yellow lights turn yellow every 1 minute and 20 seconds. The manager plugs the tree in for the first time on December 1st precisely at midnight and all lights begin their cycle at exactly the same time. If the five colored lights flash simultaneously at midnight, what is the next time E all five colored lights will all flash together at the exact same time?
(A) 0:03 AM
(B) 0:04 AM
(C) 0:06 AM
(D) 0:12 AM
(E) 0:24 AM
Rationale: Time taken by each light to on
Red = 20 secs
Blue = 30 secs
Green = 45 secs
Orange = 60 secs
Yellow = 80 secs
We need to take LCM to find the time all five colored lights will flash together.
LCM = 720 secs
=12 mins
=0.12 AM
Ans = D
Answer: (D) 0:12 AM
Question: If 7% of the sale price of a watch is equivalent to 8% of its cost price and 9% of its sale price exceeds 10% of its cost price by Re 1, then what is the cost price of the watch?
(A) Rs 400
(B) Rs 350
(C) Rs 300
(D) Rs 280
(E) Rs 380
Rationale: Let C.P. = X and S.P. = Y
=> 7 % of Y = 8% of X and 9% of Y =10% of X + 1
=> 7Y = 8X and 9Y = 10X + 100
=> 9 x (8X / 7) = 10 X + 100
=> X = Rs. 350
ANSWER:B
Answer: (B) Rs 350
Question: Ratio between two numbers is 3: 4 and their sum is 420. Find the smaller number?
(A) 150
(B) 125
(C) 140
(D) 180
(E) 200
Rationale: 3x+4x = 420
x=60== 3x=180
ANSWER D
Answer: (D) 180
Question: A 2member committee comprising of one male & one female member is to be constitute out of 5 males and 3females. Among st the females. Ms.A refuses to be a member of the committee in which Mr.B is taken as the member. In how many different ways can the committee be constituted ?
(A) 10
(B) 14
(C) 16
(D) 18
(E) 21
Rationale: 5C1 * 3C1 -1
= 15-1
= 14
B
Answer: (B) 14
Question: The speed of a boat in still water in 42 km/hr and the rate of current is 8 km/hr. The distance travelled downstream in 44 minutes is:
(A) 86.6 km
(B) 46.6 km
(C) 36.6 km
(D) 35.6 km
(E) 26.6 km
Rationale: Speed downstream = (42 + 8) = 50 kmph
Time = 44 minutes =44/60 hour = 11/15 hour
Distance travelled = Time × speed =11/15×50 = 36.6 km
ANSWER:C
Answer: (C) 36.6 km
Question: In a graduating class of 232 students, 144 took geometry and 119 took biology. What is the difference between the greatest possible number P and the smallest possible number of students that could have taken both geometry and biology?
(A) 144
(B) 119
(C) 113
(D) 88
(E) 31
Rationale: OFFICIAL SOLUTION:
First of all, notice that since 144 took geometry and 119 took biology, then the number of students who took both geometry and biology cannot be greater than 119.
{Total} = {geometry} + {biology} - {both} + {neither};
232 = 144 + 119 - {both} + {neither};
{both} = 31 + {neither}.
{both} is minimized when {neither} is 0. In this case {both} = 31.
The greatest possible number of students P that could have taken both geometry and biology, is 119.
Thus, the answer is 119 - 31 = 88.
Answer: D.
Answer: (D) 88
Question: If R and S are non-zero integers, and R/S > 1, then which of the following must be true?
(A) R > S
(B) 2R > S
(C) R^2< S^2
(D) R^3 < S^3
(E) RS > S
Rationale: E
Answer: (E) RS > S
Question: A completes a work in 20 days B in 60 days C in 45 days. All three persons working together on a project got a profit of Rs.26000 what is the profit of B?
(A) 4878
(B) 4675
(C) 4817
(D) 4818
(E) 4875
Rationale: We know that profits must be shared as the ratio of their efficiencies. But efficiencies are inversely proportional to the days. So efficiencies of A : B : C = 1/20 : 1/60 : 1/45 = 9 : 3 : 4
So B share in the total profit = 316×26000316×26000 = Rs.4875
Answer:E
Answer: (E) 4875
Question: The fourth proportional to 28, 14 and 18 is?
(A) 2
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: (14*18)/28 = 9
Answer: E
Answer: (E) 9
Question: Anand and Deepak started a business investing Rs. 40,000 and Rs. 35,000 respectively. Out of a total profit of Rs. 13,800, Deepak's share is?
(A) 2777
(B) 2888
(C) 6440
(D) 2882
(E) 2781
Rationale: Ratio of their shares =40000 : 35000 = 8:7
Deepak's share = 13800 * 7/15 = Rs. 6440.
Answer: C
Answer: (C) 6440
Question: Oranges are bought at 7 for Rs.2. At what rate per hundred must they be sold to gain 33%?
(A) 27
(B) 38
(C) 39
(D) 44
(E) 55
Rationale: 7 oranges bought for rs 2
1 orange cost =2/7
therefore for 100 oranges =100*(2/7)
gain =33%
200/7+(33/100)*200/7=rate per hundred he want to sell
ans :38
ANSWER:B
Answer: (B) 38
Question: A metal company's old machine makes bolts at a constant rate of 100 bolts per hour. The company's new machine makes bolts at a constant rate of 150 bolts per hour. If both machines start at the same time and continue making bolts simultaneously, how many minutes will it take the two machines to make a total of 350 bolts?
(A)  84
(B)  72
(C)  120
(D)  144
(E)  180
Rationale: Old Machine
100 bolts in 60 mins
so,
5/3 bolts in 1 min
New Machine
150 bolts in 60 mins
so,
5/2 bolts in 1 min
together,
5/3 + 5/2 =
25/6 bolts in 1 min
so, for 350 bolts
350 * 6 / 25 = 84 mins
Ans A
Answer: (A)  84
Question: The events A and B are independent, the probability that event A occurs is greater than 0, and the probability that event A occurs is twice the probability that event B occurs. The probability that at least one of events A and B occurs is 18 times the probability that both events A and B occur. What is the probability that event A occurs?
(A) 12/112
(B) 6/81
(C) 11/61
(D) 12/33
(E) 3/19
Rationale: Let us say probability of A occuring is a.
Let us say probability of B occuring is b.
a = 2b
Probability (either A or B or both) = 8 times Probability (A and B)
a*(1-b) + b*(1-a) + ab = 18*ab
Substituting a=2b in the second equation:
2b*(1-b) + b*(1-2b) + 2b*b = 18*2b*b
3b-2b^2 = 36b^2
3b = 38b^2
b = 3/38
So, a = 2b = 6/38=3/19
THE CORRECT ANSWER IS E.
Answer: (E) 3/19