mathewhe/aqua_rat huggingface dataset:
Question: A magician holds one six-sided die in his left hand and two in his right. What is the probability the number on the dice in his left hand is greater than the sum of the dice in his right?
(A) 7/108
(B) 5/54
(C) 1/9
(D) 2/17
(E) 1/4
Rationale: The least sum of the numbers of the two dice in the right hand is 2. The maximum sum of the numbers on these two dice can be 5, for the left hand dice to be able to have a greater number.
Therefore the number on the dice in the left hand must be 3 or more.
Number of ways to get a sum of 2 with the two dice in the right hand= 1
Number of ways to get a sum of 3 with the two dice in the right hand= 2
Number of ways to get a sum of 4 with the two dice in the right hand= 3
Number of ways to get a sum of 5 with the two dice in the right hand= 4
Therefore required probability = P(two right dice have a sum of 2)*P(left dice has 3) + P(right dice have sum of 2 or 3)*P(left dice has 4) + P(two right dice have a sum of 2,3, or 4)*P(left dice has 5) + P(two right dice have a sum of 2,3,4,or 5)*P(left dice has 6)
= (1/36)*(1/6) + (3/36)*(1/6) + (6/36)*(1/6) + (10/36)*(1/6)
= (1/216) * (1+3+6+10)
= 20/216
= 5/54
Option B
Answer: (B) 5/54
Question: There are 6 ladies and 4 gents to dine at a round table. In how many ways can they seat themselves so that no two gents are seated together.
(A) 85400
(B) 36400
(C) 86400
(D) 14400
(E) 88600
Rationale: First arrange the ladies. This is a circular arrangment. 6 Gents can be arranged in 5! ways.
Now there are 6 spaces (space in between two ladies) and we have to seat 5 gents there.
First select 4 places out of 5 available places. can be done in 5C4ways. Then arrange 5 gents there in 5! ways.
Total: 5!*5C4*4! = 14400
D is the answer.
Answer: (D) 14400
Question: A man covered a certain distance at some speed. If he had moved
3 kmph faster, he would have taken 40 minutes less. If he had moved
2 kmph slower, he would have taken 40 minutes more. What is the distance in km?
(A) 40
(B) 30
(C) 35
(D) 60
(E) 55
Rationale: speed= 2v1v2/v1-v2=2*3*2/3-2=12 km/hr
dist=12*40/16(1+12/3)=40 km
ANSWER A
Answer: (A) 40
Question: The average score of a cricketer for twelve matches is 48 runs. If the average for first eight matches is 40, then average for last four matches is
(A) 33.25
(B) 89
(C) 64
(D) 68
(E) 90
Rationale: Explanation:
=(48×12)−(40×8)/4
=(576−320)/4=64
Answer: Option C
Answer: (C) 64
Question: Last year’s receipts from the sale of greeting cards during the week before Mother’s Day totaled $239 million, which represented 10 percent of total greeting card sales for the year. Total greeting card sales for the year totaled how many million dollars?
(A) 2,390
(B) 2,100
(C) 1,890
(D) 1,701
(E) 210
Rationale: 10% ---- 239 millions
for 100% => ( 239 * 100% )/10% = 2390.
Option A.
Answer: (A) 2,390
Question: If A^5 + B^5 = 2500, then the greatest possible value of A is between
(A) 0 and 3
(B) 3 and 6
(C) 6 and 9
(D) 9 and 12
(E) 12 and 15
Rationale: for the greatest possible value of A^5, we must minimize the value of B^5 i.e. lets say B^5 = 0
then we need to find a number A such that A^5 < 2500. 4^5 = 1024 and 5^5 = 3125 so we can say that the maximum possible value of A can be a little more than 4 hence answer = between 3 and 6
hence B
Answer: (B) 3 and 6
Question: Two trains of equal are running on parallel lines in the same direction at 52 km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is?
(A) 50 m
(B) 72 m
(C) 80 m
(D) 82 m
(E) 84 m
Rationale: Let the length of each train be x m.
Then, distance covered = 2x m.
Relative speed = 52 - 36 = 16 km/hr.
= 16 * 5/18 = 40/9 m/sec.
2x/36 = 40/9 => x = 80.
ANSWER:C
Answer: (C) 80 m
Question: At Deluxe paint store, Fuchsia paint is made by mixing 5 parts of red paint with 3 parts of blue paint. Mauve paint is made by mixing 3 parts of red paint with 5 parts blue paint. How many liters of blue paint must be added to 40 liters of Fuchsia to change it to Mauve paint?
(A) 9
(B) 12
(C) 15
(D) 16
(E) 26.6
Rationale: in 40 liters, Red = 5/8 * 40 = 25 and Blue = 15
so, 25/(15+x) = 3/5
or, x = 26.6 (Answer E)
Answer: (E) 26.6
Question: If 6 (A's capital) = 8 (B's capital) = 10 (C's capital). Then the ratio of their capitals is:
(A) 3:4:5
(B) 12:15:20
(C) 20:15:12
(D) 6:8:10
(E) 8:4:12
Rationale: Explanation:
6A = 8B = 10 C
A:B:C = 1/6:1/8:1/10
= 20:15:12
ANSWER IS C
Answer: (C) 20:15:12
Question: Find the probability that a leap year selected at random will not have 53 Sundays
(A) 6/7
(B) 5/7
(C) 4/7
(D) 3/7
(E) 2/7
Rationale: There are 366 days in a leap year: 52 weeks and 2 more days. So, 52 Sundays and 2 days.
These 2 days can be: {Mon, Tue}, {Tue, Wed}, {Wed, Thu}, {Thu, Fri}, {Fri, Sat}, {Sat,Sun} and {Sun, Mon} (7 cases). In order to have 53 Sundays we should have either {Sat,Sun} or {Sun, Mon} case.
The probability of that is 2/7.
So, probability of not having 53 sundays is 1 - 2/7 = 5/7
Answer: B.
Answer: (B) 5/7
Question: Seven children â€” A, B, C, D, E, F, and G â€” are going to sit in seven chairs in a row. Children A & B must sit next to each other, and child C must be somewhere to the right of A & B. How many possible configurations are there for the children?
(A) 600
(B) 720
(C) 1440
(D) 4320
(E) 4800
Rationale: This problem is a notch harder than anything you are likely to see on the GMAT. If you can master the principles in this problem, you certainly will be able to handle almost any problem the GMAT could concoct.
First, consider the restriction of A & B. As with problem #1 above, there are 12 possibilities for A & B, counting both position and order.
Now, put the other five in any order â€” thatâ€™s 120 possibilities, for a total number of configurations of 1440. That number does not take into account the restriction with C.
Think about those 1440 configurations. In exactly half of them, C will be to the right of A & B, and exactly half, C will be to the left of A & B. Therefore, in (1/2)*1440 = 720 configurations, C will be to the right of A & B. Answer = B
Answer: (B) 720
Question: On an order of 4 dozen boxes of a consumer product, a retailer receives an extra dozen free. This is equivalent to allowing him a discount of:
(A) 10%
(B) 20%
(C) 30%
(D) 40%
(E) 50%
Rationale: Clearly, the retailer gets 1 dozen out of 5 dozens free.
Equivalent discount = 1/5 * 100 = 20%.
Answer B) 20%
Answer: (B) 20%
Question: Pipe A runs 60 liters of water per minute into a pool that has a total volume of 3,600 liters. Pipe B fills a third of the pool in 12 hours.
Working together how long will it take both pipes to fill the pool?
(A) 2 hours and 36 minutes
(B) 36/37 hours
(C) 9 hours and 12 minutes
(D) 15 hours
(E) 1 hour and 48 minutes.
Rationale: Pipe A has a rate of 60 liters per minute which equals a rate of 3600 liters per hour.
Pipe B has a rate of 100 liters per hour.
100 + 3600 (A+B) = Together they have a rate of 3700 liters per hour.
3600 (The pool) / 3700 = 36/37 hours
Answer -B
Answer: (B) 36/37 hours
Question: At what rate percent per annum will the simple interest on a sum of money be 6/5 of the amount in 10 years?
(A) 4%
(B) 7%
(C) 9%
(D) 3%
(E) 12%
Rationale: Let sum = x. Then, S.I. = 6x/5, Time
= 10 years.
Rate = (100 * 6x) / (x * 5 * 10)
= 12%
Answer:E
Answer: (E) 12%
Question: Angela, Bernie, and Colleen can complete a job, all working together, in 3 hours. Angela and Bernie, working together at their respective rates, can complete the same job in 5 hours. How long would it take Colleen, working alone, to complete the entire job?
(A) 7.5 hours
(B) 10 hours
(C) 12 hours
(D) 16 hours
(E) 20 hours
Rationale: A+B+C complete the job in 3 hours.
A+B complete the job in 5 hours.
A+B and C complete the job in 3 hours -->1/(A+B) + 1/C = 1/3-->1/5+1/C=1/3 ----> C=7.5 hours. ANS A
Answer: (A) 7.5 hours
Question: HCF and LCM two numbers are 16 and 396 respectively. If one of the numbers is 36, then the other number is?
(A) 36
(B) 66
(C) 132
(D) 176
(E) 364
Rationale: 16 * 396 = 36 * x
x = 176
ANSWER:D
Answer: (D) 176
Question: A man has Rs. 312 in the denominations of one-rupee notes, five-rupee notes and twenty-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
(A) 36
(B) 24
(C) 28
(D) 32
(E) 38
Rationale: Explanation :
Let the number of notes of each denomination be x
Then, x + 5x + 20x = 312
=> 26x = 312
=> x = 312/26 = 12
the total number of notes that he has = 3x = 3 × 12 = 36
Answer : A
Answer: (A) 36
Question: If shares of two persons in profits are Rs.400 and Rs.500 then ratio of their capitals is
(A) 3:4
(B) 4:5
(C) 4:3
(D) 1:3
(E) 1:2
Rationale: profit=time*capital
so 400:500=4:5
ANSWER:B
Answer: (B) 4:5
Question: Brian is analyzing the performance of certain stocks. He finds that for the first fifteen days of a 30 day period, the daily closing price per share of Phoenix Pharma Inc. conformed to the function f(x)=0.4x+2f(x)=0.4x+2 , where x represents the day in the period. He found that for the last 15 days in the same period, the stock followed the function f(x)=(−1/7)x+9f(x)=(−1/7)x+9, where x represents the day in the period. Approximately what is the median closing price per share of Phoenix Pharma Inc. for the entire 30 day period?
(A) 4.7
(B) 5.55
(C) 6.71
(D) 8
(E) 11.1
Rationale: First 15 days: F1, x= 1 to 15 and f(x)= 2.4 to 8
Last 15 days: F2, x= 16 to 30 and f(x) = ~4.7 to ~6.7 (30th to 16th)
Median is average of 15th and 16th value when all of the above values are arranged in order
Do not try to calculate all the values. Go for the choices.
11.1 - outside the range of values
8- last value
6.71 - last value for the F2, so already we have 15 values less than 6.71. Additionally F1 has some values less.
4.7 - First value for the F2, so already we have 15 values greater than 4.7. Additionally F1 has some values greater.
Hence 5.55 must be the answer.
ANSWER:B
Answer: (B) 5.55
Question: Set J consists of 10 consecutive even numbers. If the smallest term in the set is -4, what is the range of the positive integers in set J?
(A) 8
(B) 12
(C) 14
(D) 16
(E) 18
Rationale: Since there are only 10 integers, another approach is the just list all 10.
We get: -4, -2,0,2, 4, 6, 8, 10, 12, 14
Range of POSITIVE INTEGERS =14-2= 12
Answer: B
Answer: (B) 12
Question: Someone on a skateboard is traveling 15 miles per hour. How many feet does she travel in 30 seconds? (1 mile = 5280 feet)
(A) 600 ft
(B) 660 ft
(C) 670 ft
(D) 680 ft
(E) 700 ft
Rationale: per second => 15*5280 ft/60*60 =22 ft
30 seconds => 22 * 30 = 660 ft
Answer : B
Answer: (B) 660 ft
Question: A ratio between two numbers is 3 : 4 and their L.C.M. is 84. The first number is
(A) 60
(B) 45
(C) 21
(D) 15
(E) None
Rationale: Sol.
Let the required numbers be 3x and 4x. Then, their L.C.M. is 12x.
∴ 12x = 84⇔ x = 7. Hence, the first number is 21.
Answer C
Answer: (C) 21
Question: The number x of cars sold each week varies with the price y in dollars according to the equation x = 800,000 – 50y. What would be the total weekly revenue T, in dollars, from the sale of cars priced at $ 15,000?
(A) 50,000
(B) 750,000
(C) 850,000
(D) 7,500,000
(E) T=750,000,000
Rationale: number of cars sold = x=800000-50y
y=15000
x=800000-750000=50000
revenue from 50000 cars=15000*50000=750000000 E
Answer: (E) T=750,000,000
Question: On Saturday morning, Malachi will begin a camping vacation and he will return home at the end of the first day on which it rains. If on the first three days of the vacation the probability of rain on each day is 0.2, what is the probability that Malachi will return home at the end of the day on the following Monday?
(A) 0.008
(B) 0.128
(C) 0.488
(D) 0.512
(E) 0.64
Rationale: Probability of rain on Saturday OR Probability of rain on Sunday (given that it didn't rain on Saturday) OR Probability of rain on Monday (given that it didn't rain on Sunday)
= 0.2 + (0.8 x 0.2) + (0.8 x 0.8 x 0.2)
= 0.2 + 0.16 + (0.128 <- The actual answer!)
=0.488
ANSWER:C
Answer: (C) 0.488
Question: What will come in place of the x in the following Number series? 6, 12, 21, x , 48
(A) 33
(B) 45
(C) 75
(D) 56
(E) 85
Rationale: (A)
The pattern is + 6, + 9, + 12, +15 ………..
So the missing term is = 21 + 12 = 33
Answer: (A) 33
Question: A person sells 36 oranges per rupee and suffers a loss of 4%. Find how many oranges per rupee to be sold to have again of 8%?
(A) 30
(B) 31
(C) 32
(D) 33
(E) None of these
Rationale: 1⁄36 : (100 - 4) :: x : (100 + 8)
⇒ x = 108/96×36=132
He sells 32 oranges per rupee.
Answer C
Answer: (C) 32
Question: A can do a job in 20 days and B can do it in 30 days. A and B working together will finish twice the amount of work in days?
(A) 22 1/6
(B) 24
(C) 22 1/0
(D) 22 1/9
(E) 22 1/1
Rationale: 1/20 + 1/30 = 5/60 = 1/12
12 = 12 *2 = 24 days
Answer: B
Answer: (B) 24
Question: A walks at 10 kmph and 7 hours after his start, B cycles after him at 20 kmph. How far from the start does B catch up with A?
(A) 100km
(B) 140km
(C) 50km
(D) 120km
(E) 200km
Rationale: Suppose after x km from the start B catches up with A. Then, the difference in the time taken by A to cover x km and that taken by B to cover x km is 7 hours.
x/10 - x/20 = 7
x = 140 km
Answer is B
Answer: (B) 140km
Question: A car travells the first 1/2 of certain distance with a speed of 10km/hr the next 1/4 distance witha a speed of 20 km/hr, and the last 1/4 distance with a speed of 60 km/hr. the average speed of the carfor the whole journey is?
(A) 12km/hr
(B) 15km/hr
(C) 89km/hr
(D) 52km/hr
(E) 79km/hr
Rationale: Let the whole distance travelled be x km
and the average speed of the car for he whole journey be y km/hr
then (x/2)/10+(x/4)/20+(x/4)/60=x/y
x/20+x/80+x/240=x/y
1/15y=1
y=15km/hr
Answer(B)
Answer: (B) 15km/hr
Question: Two carpenters, working in the same pace, can build 2 desks in two hours and a half. How many desks can 4 carpenters build in 3 hours?
(A) 2.4.
(B) 3.6.
(C) 4.8.
(D) 5.5.
(E) 6.4
Rationale: W = 2 desks
T = 2.5 hrs
Rate of 2 carpenters = 2×R
Rate = work done/ time
2xR = 2/2.5
R = 1/2.5 = 2/5 (this is the rate of each carpenter)
Work done by 4 carpenters in 3 hrs = 4 × rate of each carpenter x time = 4× 2/5 × 3 =4.8 desks
C is the correct answer.
Answer: (C) 4.8.
Question: A bag contains a certain number of 50 paise coins, 20 paise coins and 10 paise coins inthe ratio 3:4:5. If the total value of all the coins in the bag is Rs.630, find the number of 50 paise coins ?
(A) 498
(B) 488
(C) 428
(D) 528
(E) 675
Rationale: 50*3k + 20*4k + 10*5k = 63000
280k = 63000 => k =225
50p coins = 3k = 3*225 = 675
ANSWER:E
Answer: (E) 675
Question: The average of four results is 222 and that of the first three is 219. The fourth result is?
(A) 231
(B) 201
(C) 85
(D) 192
(E) 215
Rationale: 4 * 222 â€“ 3 * 219 = 231
Answer: A
Answer: (A) 231
Question: A train passes a man standing on a platform in 8 seconds and also crosses the platform which is 267 metres long in 20 seconds. The length of the train (in metres) is:
(A) 178
(B) 176
(C) 175
(D) 96
(E) None of these
Rationale: Explanation:
Let the length of train be L m.
Acc. to question
(267+L)/20 = L/8
2136+8L=20L
L= 2136/12 = 178 m
Answer A
Answer: (A) 178
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?
(A) 76 km/hr
(B) 50 km/hr
(C) 17 km/hr
(D) 18 km/hr
(E) 14 km/hr
Rationale: Speed of the train relative to man
= (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr
= 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed
= (x - 5) km/hr. x - 5
= 45 ==> x = 50 km/hr.
Answer: B
Answer: (B) 50 km/hr
Question: In a cinema hall for the matinee show which started at 2.30 pm and ended at 5.30 pm the vehicle parking lot had only three wheelers (auto rickshaws) and four wheelers. Today the wheels of the vehicles parked was counted and found to be 240. What could be the number of three wheelers parked therein ?
(A) 10
(B) 48 wheelers
(C) 37
(D) 97
(E) 12
Rationale: 3X + 4y = 240
by substitute through options 48 is correct
Answer: B
Answer: (B) 48 wheelers
Question: To fill an art exhibit, the students in an art course are assigned to create one piece of artwork each in the following distribution: 1/3 are sculptures, 1/8 are oil paintings, 1/2 are watercolors, and the remaining 10 pieces are mosaics. How many students are in the art class?
(A) 80
(B) 120
(C) 240
(D) 320
(E) 400
Rationale: Let the total number of students in the art class = s
Distribution of artwork is as
1/3 are sculptures
1/8 are oil paintings
1/2 are watercolors, and the remaining 10 pieces are mosaics
(1/3)s +(1/8)s +(1/2)s + 10 = s
Since remaining 10 pieces are mosaics , (1/24)s = 10
s = 240
Answer C
Answer: (C) 240
Question: A garrison of 400 men had a provision for 31 days. After 26 days 275 persons re-enforcement leave the garrison. Find the number of days for which the remaining ration will be sufficient?
(A) 16 days
(B) 45 days
(C) 10 days
(D) 17 days
(E) 18 days
Rationale: 400 --- 31
400 --- 5
125 --- ?
400*5 = 125*x => x =16 days.
Answer: A
Answer: (A) 16 days
Question: Simplify: 0.4*0.5+0.3*0.2
(A) 0.52
(B) 0.26
(C) 0.48
(D) 0.64
(E) 0.46
Rationale: Given exp. = 0.4*0.5+(0.3*0.2) = 0.2+0.06 = 0.26
Answer is B.
Answer: (B) 0.26
Question: The population of a village is 12000. It increases annually at the rate of 24% p.a. What will be its population after 2 years?
(A) 14567
(B) 18451
(C) 18789
(D) 18786
(E) 14400
Rationale: Formula :
( After =100 denominator
Ago = 100 numerator)
12000 × 124/100 × 124/100 = 18451
B
Answer: (B) 18451
Question: For each month of a given year except December, a worker earned the same monthly salary and donated one-tenth of that salary to charity. In December, the worker earned N times his usual monthly salary and donated one-fifth of his earnings to charity. If the worker's charitable contributions totaled one-sixth of his earnings for the entire year, what is the value of N?
(A) 8/5
(B) 22
(C) 3
(D) 11/3
(E) 4
Rationale: Let monthly salary for each of the 11 months except December was x, then
11x*1/10 + Nx*1/5 = 1/6(11x + Nx);
11/10 + N/5 = 1/6(11 + N)
11+2N/10 = 11+N/6 =>66+12N = 110+10N =>2N=44
N = 22
Answer: B
Answer: (B) 22
Question: A man gets a simple interest of Rs.300 on a certain principal at the rate of 5% p.a in two years. Find the compound interest the man will get on twice the principal in two years at the same rate?
(A) s.256
(B) s.315
(C) s.415
(D) s.514
(E) s.615
Rationale: Let the principal be Rs.P
S.I at 5% p.a in 2 years on Rs.P = Rs.300
(P)(2)(5)/100 = 300
P = 3000
C.I on Rs.2P i.e., Rs.6000 at 5% p.a in two years
=6000{ [1 + 5/100]^2 - 1}
= 6000(41/400)
= Rs.615
Answer:E
Answer: (E) s.615
Question: A woman gains 20% by selling an article for a certain price. If the sells it at double the price, the percentage of profit will be:
(A) 60%
(B) 34%
(C) 140%
(D) 100%
(E) 55%
Rationale: C
C.P. = Rs. x.
Then, S.P. = Rs. (12% of x) = Rs. 6x/5
New S.P. = 2 * 6x/5 = Rs. 12x/5
Profit = 12x/5 - x = Rs. 7x/5
Profit = 7x/5 * 1/x * 100 = 140%.
Answer: (C) 140%
Question: Jupiter travels around the sun at a speed of approximately 8.1 miles per second. The approximate speed is how many miles per hour?
(A) 20,180
(B) 23,120
(C) 26,140
(D) 29,160
(E) 32,240
Rationale: 8.1 * 3600 = 29,160
The answer is D.
Answer: (D) 29,160
Question: If 12 men can reap 120 acres of land in 36 days, how many acres of land can 24 men reap in 62 days?
(A) 266.5
(B) 413.3
(C) 425.8
(D) 189.3
(E) 249.6
Rationale: 12 men 120 acres 36 days
24 men ? 62 days
120 * 24/12 * 62/36
120 * 2 *31/18
240* 1.72 = 413.3
Answer:B
Answer: (B) 413.3
Question: In the question A^B means A raised to the power of B. What is the value of A such that
X^2-11x+A and X^2 -14X +2A will have a common factor?
(A) -1/2
(B) 24
(C) -3
(D) 20
(E) 15
Rationale: due to quadratic equation..... the factor will be like (x-a)(x-b)
lets assume (x-k) is the common factor the
x=k is the root of both the eqn
X^2-11X+A=0 , & X^2-14X+2A=0
satisfying these two equations we get
k^2-11k+A=0 ..................................(1)
k^2-14k+2A=0 ..................................(2)
on solving we will get
k=A/3
substituting this in eq 1 we get A=0 and A= 24
so A=24
ANSWER:B
Answer: (B) 24
Question: Bob bikes to school every day at a steady rate of e miles per hour. On a particular day, Bob had a flat tire exactly halfway to school. He immediately started walking to school at a steady pace of y miles per hour. He arrived at school exactly t hours after leaving his home. How many miles is it from the school to Bob's home?
(A) (x + y) / t
(B) 2(e + t) / ey
(C) 2eyt / (e + y)
(D) 2(e + y + t) / ey
(E) x(y + t) + y(x + t)
Rationale: If we choose for d (distance): 10 miles, for e 10 and for y 5.
t would be 90 minutes or 1,5 hours.
If I try this for answer choice C it fits.
Answer: (C) 2eyt / (e + y)
Question: Dany bought a total of 28 game cards some of which cost $0.25 each and some of which cost $0.15 each. If Dany spent $4.2 to buy these cards, how many cards of each type did he buy?
(A) 4
(B) 10
(C) 7
(D) 28
(E) 12
Rationale: Let X be the number of cards that cost $0.25 each and Y the number of cards that cost $0.15 each. The total number of cards is 28. Hence
X + Y = 28
If X is the number of cards at $0.25, then the X cards cost
0.25 X
If Y is the number of cards at $0.15, then the Y cards cost
0.15 Y
The total cost of the X cards and the the Y cards is known to be $4.2 and also given by
0.25 X + 0.15 Y = 4.2
We now need to solve the system of equations
X + Y = 28
0.25 X + 0.15 Y = 4.2
The first equation gives Y = 28 - X. Substitute y by 28 - x in the second equation and solve
0.25 X + 0.15 (28 - X) = 4.2
X(0.25 - 0.15) + 4.2= 4.2
0.1 X = 0
X = 0 and Y = 28 - 0 = 28
correct answer D
Answer: (D) 28
Question: One fourth of a solution that was 10% sugar by weight was replaced by a second solution resulting in a solution that was 20 percent sugar by weight. The second solution was what percent sugar by weight?
(A) 65%
(B) 50%
(C) 22%
(D) 18%
(E) 8.5%
Rationale: Say the second solution (which was 1/4 th of total) was x% sugar, then 3/4*0.1+1/4*x=1*0.20 --> x=0.5. Alternately you can consider total solution to be 100 liters and in this case you'll have: 75*0.1+25*x=100*0.20 --> x=0.5.
Answer: B.
Answer: (B) 50%
Question: Three pipes A, B and C can fill a tank in 7 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 8 hours. How many hours will take C alone to fill the tank?
(A) 35/8
(B) 38/7
(C) 43/6
(D) 49/4
(E) 56/3
Rationale: The rate of A+B+C is 1/7 of the tank per hour.
After 2 hours, the tank is 2/7 full.
The rate of A+B is 5/7 * 1/8 = 5/56 of a tank per hour.
The rate of C is 1/7 - 5/56 = 3/56
C can fill the tank in 56/3 hours.
The answer is E.
Answer: (E) 56/3
Question: If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same sum at the rate and for the same time?
(A) Rs. 51.25
(B) Rs. 52
(C) Rs. 54.25
(D) Rs. 60
(E) Rs. 70
Rationale: Sum = (50 * 100) / (2 * 5) = Rs. 500
Amount = [500 * (1 + 5/100)2] = Rs. 551.25
C.I. = (551.25 - 500) = Rs. 51.25.
ANSWER:A
Answer: (A) Rs. 51.25
Question: What number comes next in this Number series.
5 3 4 4 6 9 7 ?
*Hint: check calende
(A) 8
(B) 3
(C) 6
(D) 1
(E) 7
Rationale: E
8 (the number of letters in the month November)
April : 5 letters
May : 3 letters
June : 4 letters
July : 4 letters
August: 6 letters
September : 9 letters
October : 7 letters
Answer: (A) 8