mathewhe/aqua_rat huggingface dataset:
Question: Last summer, Roger worked x days at 2 hours/day at a job, and he was paid at a rate of r dollars per hour. For the whole summer, he earned $1000. This summer, he will work at another job that offers the same pay rate, r dollars per hour. This summer he will work H days at 5 hours/day, so that he will earn $4000 for the entire summer. In terms of x, which of the following equals H?
(A) x
(B) 2x/3
(C) 2x
(D) 4x/3
(E) 8x/5
Rationale: Last Summer story
Total hours: 2x
rate: $r per hour
2rx = 1000; rx = 500
This Summer story
Total hours: 5H
rate: $r per hour
Total payment = 5rH = 4000
5rH = 8 *500 = 8rx
5H=8x
H= 8x/5
Answer is E
Answer: (E) 8x/5
Question: Two trains of equal lengths take 8 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?
(A) 22
(B) 12
(C) 77
(D) 10
(E) 21
Rationale: Speed of the first train = 120/8 = 15 m/sec.
Speed of the second train = 120/15 = 8 m/sec.
Relative speed = 15 + 8 = 23 m/sec.
Required time = (120 + 120)/23 = 10 sec.
Answer: D
Answer: (D) 10
Question: Complete the series
13, 9, 5, 1, -3, -7, -11, -15, ...
(A) -4
(B) 0
(C) 3
(D) -2
(E) -19
Rationale: In the above series clearly we know we can get the next term by subtract 4 from the previous term so the answer is Option E) -19
Answer: (E) -19
Question: The operation T is defined by x T y=1/x+1/y for all nonzero numbers x and y. If z is a number greater than 1, which of the following must be true.
I. x T (-z)=0
II. z T z/z-1=z
III. 2/z T 2/z=1
(A) a.) I
(B) b.) I and II only
(C) c) I and III only
(D) d) II and III only
(E) e) None of these
Rationale: Statement I is not TRUE
Statement II is not TRUE
Statement III is not TRUE
Answer : E
Answer: (E) e) None of these
Question: A courtyard is 25 meter long and 18 meter board is to be paved with bricks of dimensions 20 cm by 10 cm. The total number of bricks required is?
(A) 22877
(B) 27778
(C) 20000
(D) 22500
(E) 17799
Rationale: Number of bricks =Courtyard area/1 brick area
=(2500×1800/20×10)=22500
Answer: D
Answer: (D) 22500
Question: Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?
(A) 8 min
(B) 5 min
(C) 10 min
(D) 14 min
(E) 15 min
Rationale: Due to stoppages, it covers 9 km less.
Time taken to cover 9 km = (9/54 x 60) min = 10 min.
Answer : C.
Answer: (C) 10 min
Question: A grocer has a sale of Rs. 5420, Rs. 5660, Rs. 6200, Rs. 6350 and Rs. 6500 for 5 consecutive months. Find the sale he should have in the sixth month, so that he gets an average sale of Rs. 6000?
(A) Rs. 5870
(B) Rs. 5991
(C) Rs. 6020
(D) Rs. 6850
(E) None of these
Rationale: Explanation:
Total sale for 5 months = Rs. (5420 + 5660 + 6200 + 6350 + 6500) = Rs. 30,130
Therefore, required sale = Rs. [(6000 * 6) – 30,130] = Rs. (36000 – 30,130) = Rs. 5870
ANSWER A
Answer: (A) Rs. 5870
Question: 4,18,100,294,___
(A) 1000
(B) 1100
(C) 1210
(D) 1452
(E) 1552
Rationale: 2^3-2^2=4 ;
3^3-3^2=18;
5^3-5^2=100;
7^3-7^2=294;
so, 11^3-11^2= 1210
ANSWER:C
Answer: (C) 1210
Question: The sum of the numbers is 220. If the first number be twice the second and third number be one-third of the first, then the second number is:
(A) 48
(B) 54
(C) 72
(D) 60
(E) 27
Rationale: Let the second number be x. Then, first number = 2x and third number = 2x/3.
2x + x + 2x/3 = 220
11x/3 = 220
x = 60
ANSWER:D
Answer: (D) 60
Question: A and B started a business investing Rs. 80,000 and Rs 20,000 respectively. In what ratio the profit earned after 2 years be divided between A and B respectively?
(A) 4:1
(B) 3:2
(C) 18:20
(D) 18:4
(E) 17:4
Rationale: A: B = 80000 : 20000
= 8 : 2
= 4 : 1
ANSWER:A
Answer: (A) 4:1
Question: 60 percent of movie theatres in Town X have 3 screens or less. 20% of those theatres sell an average of more than $300 worth of popcorn per showing. 56 percent of all the movie theatres in Town X sell $300 or less of popcorn per showing. What percent of all the stores on the street have 4 or more screens and sell an average of more than $300 worth of popcorn per day?
(A) 12
(B) 18
(C) 32
(D) 40
(E) 44
Rationale: let's take numbers here.
Assume that the total number of movie theaters in the town = 100
Then number of movie theaters with 3 screens or less = 60
=> Number of movie theaters with 4 screens or more = 40
Movie theaters with 3 screens or less selling popcorn at more than $300 = 20% of 60 = 12
Number of movie theaters selling popcorn at $300 or less = 56
=> Number of movie theaters selling popcorn at more than $300 = 100-56 = 44
Of these 44 theaters, 12 are those with 3 screens or less
Therefore 32 (44-12) must be those with four screens or more
C is the answer
Answer: (C) 32
Question: When n is divided by 24, the remainder is 4. What is the remainder when 4n is divided by 8?
(A) 3
(B) 4
(C) 5
(D) 0
(E) 7
Rationale: Let n=4 (leaves a remainder of 4 when divided by 24)
4n = 4(4) =16, which leaves a remainder of 0 when divided by 8.
Answer D
Answer: (D) 0
Question: 14, 28, 20, 40, 32, 64, ...?
(A) 10
(B) 25
(C) 56
(D) 21
(E) 36
Rationale: First, multiply by 2 and then subtract 8.
14
14*2=28
28-8=20
20*2=40
40-8=32
32*2=64
64-8=56
ANSWER:C
Answer: (C) 56
Question: A number 15B is divisible by 6. Which of these will be true about the positive integer B?
(A) B will be even
(B) B will be Odd
(C) B will be divisible by 6
(D) Both a & b
(E) A, B and C
Rationale: 15B is divisible by 6
=> 3*5*B is divisible by 3*2
=> 5*B is divisible by 2
=> B has to be even.
Ans A
Answer: (A) B will be even
Question: A man can swim in still water at 4.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
(A) 1.09
(B) 1.6
(C) 1.2
(D) 1.5
(E) 1.1
Rationale: M = 4.5
S = x
DS = 4.5 + x
US = 4.5 + x
4.5 + x = (4.5 - x)2
4.5 + x = 9 -2x
3x = 4.5
x = 1.5
Answer: D
Answer: (D) 1.5
Question: If 4 Men or 6 Women take 4 days to complete some work, how many days will 8 Men and 4 Women working together take to complete the work?
Can anyone explain please?
(A) 1. 3/2 days
(B) 2. 4/9 Days
(C) 3. 9/4 days
(D) 4.5/2 days
(E) 5.3 days
Rationale: 4 men or 6 women takes 4 days to complete the work
So 4M = 6W
W = 2/3M
1 man in 1 day does 1 unit of work
so 4 M in 4 M = 16 units of work
now 8 M and 4 W = 8 M + 4(2/3)M
= 8M + 8M/3
= 36M
Since both set do the same work
36M in n Days = 16 units of work
n = 16/36 = 4/9 days.
B
Answer: (B) 2. 4/9 Days
Question: Find the compound interest on Rs.16,000 at 20% per annum for 9 months, compounded quartely.
(A) Rs.2522
(B) Rs.2512
(C) Rs.2572
(D) Rs.2592
(E) None
Rationale: Solution
Principal	= Rs.16,000;
Time=9 months	= 3 quarters;
Amount
=Rs.[16000x(1+5/100)³]
=[16000x21/20x21/20x21/20]
= Rs.18522.
C.I	= Rs.(18522 - 16000)
= Rs.2522.
Answer A
Answer: (A) Rs.2522
Question: A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is?
(A) 1
(B) 8
(C) 9
(D) 7
(E) 5
Rationale: DS = 6
US = 4
S = ?
S = (6 - 4)/2 = 1 kmph
Answer: A
Answer: (A) 1
Question: Of the 600 residents of Clermontville, 35% watch the television show Island Survival, 40% watch Lovelost Lawyers and 50% watch Medical Emergency. If all residents watch at least one of these three shows and 18% watch exactly 2 of these shows, then how many Clermontville residents X watch all of the shows?
(A)  150
(B)  108
(C)  42
(D)  21
(E)  -21
Rationale: OA is D.
100= A+B+C-AB-AC-BC+ABC, which is the same as the following formula
100= A+B+C+(-AB-AC-BC+ABC+ABC+ABC)-2ABC.
The term between parantheses value 18% so the equation to resolve is
100=35+40+50-18-2ABC
therefore the value of ABC is 3.5% of 600, X is 21. D is the correct answer
Answer: (D)  21
Question: A man said to his son, "I was two-third of your present age when you were born". If the present age of the man is 48 years, find the present age of the son?
(A) 25.7 years
(B) 28 years
(C) 29.3 years
(D) 28.8 years
(E) 30 years
Rationale: Explanation:
Present age of the son be P, he was born P years ago.
The age of the man was: (48 - P).
His age when the son was born should be equal to 2/3 of P.
(48 - P) = 2/3 P
5P = 144 => P = 28.8
ANSWER IS D
Answer: (D) 28.8 years
Question: At a meeting of the 6 Joint Chiefs of Staff, the Chief of Naval Operations does not want to sit next to the Chief of the National Guard Bureau. How many ways can the 6 Chiefs of Staff be seated around a circular table?
(A) 120
(B) 480
(C) 4040
(D) 2520
(E) 5040
Rationale: Bunuel, I'm also a little confused with the number of arrangements of n distinct objects in a circle. Why is it given by (n-1)!. In theveritasanswer they say:answer E (4040), should be the number of ways to arrange all 6 without the seating restriction given. Is this incorrect?C
Answer: (C) 4040
Question: X and Y are two towns. Ganesh covers the distance from X to Y at an average speed of 43 Km/hr. However, he covers the distance from Y to X at an average speed of 35 Km/hr. His average speed during the whole journey in km/hr. is :
(A) 34
(B) 43
(C) 40
(D) 38.6
(E) 29
Rationale: Solution: Average speed = 2XY / X+Y
= 2*43*35 / 43+35
= 38.6
Answer : D
Answer: (D) 38.6
Question: A department store receives a shipment of 1,000 shirts, for which it pays Rs. 9,000. The store sells the shirts at a price 80 percent above cost for one month, after which it reduces the price of the shirts to 20 percent above cost. The store sells 75 percent of the shirts during the first month and 50 percent of the remaining shirts afterwards. How much gross income did sales of the shirts generate?
(A) 10500
(B) 11500
(C) 12500
(D) 13500
(E) 14500
Rationale: actual price of one shirt=9 rupees
price of one shirt for first month=16.2 rupees
total number of shirts sold that month=750
total income from 1st month=Rs.12150
price of one shirt after 1st month=10.8rupees
total number of shirts sold this time=125
total income after 1st month=1350 rupees
so GROSS INCOME=12150+1350=Rs.13500
ANSWER:D
Answer: (D) 13500
Question: A box contains 8 pairs of shoes (16 shoes in total). If two shoes are selected at random, what it is the probability that they are matching shoes?
(A) 1/190
(B) 1/20
(C) 1/19
(D) 1/10
(E) 1/15
Rationale: The problem with your solution is that we don't choose 1 shoe from 16, but rather choose the needed one AFTER we just took one and need the second to be the pair of it. So, the probability would simply be: 1/1*1/15(as after taking one at random there are 15 shoes left and only one is the pair of the first one)=1/15
Answer: E.
Answer: (E) 1/15
Question: A team of five basketball players has an average height of 280 cm. two players whose average height is 190 cm, left the team and two new others whose average height is 204 cm, joined. Calculate the new average height of the players(in cm) is?
(A) 317.6 cm
(B) 417.6 cm
(C) 214.6 cm
(D) 217.6 cm
(E) 117.6 cm
Rationale: Total height = 280 * 5 = 1400 cm.
Total height of those who left = 190 * 2 = 380
Total height of those who joined = 204 * 2 = 408
New average
= [1400 - 720 + 408 ] / 5 = 1088/5 cm.
= 217.6 cm
Answer:D
Answer: (D) 217.6 cm
Question: Local kennel has cats and dogs in the ratio of 6:12. If there are 24 fewer cats than dogs, how many dogs are in the kennel?
(A) 50
(B) 48
(C) 52
(D) 54
(E) 56
Rationale: Lets work with the data given to us. We know that there ratio of cats to dogs is 6:12 or
cats 6
dogs 12
we can write number of cats as 6x and number of dogs as 12x and we know that 12x-6x= 24(therefore 6x = 24 => x=4)
Then # of dogs = 12x4= 48
Answer is B
Answer: (B) 48
Question: Of the 800 employees of Company X, 70 percent have been with the company for at least ten years. If y of theselong-termmembers were to retire and no other employee changes were to occur, what value of y would reduce the percent oflong-termemployees in the company to 50 percent ?
(A) 200
(B) 320
(C) 112
(D) 80
(E) 56
Rationale: Original (Long-Term is 70%)
Total = 800
Long-Term = .7(800) = 560
New (Long-Term is 50%)
New Total = 800 - y
New Long-Term = 560 - y
560 - y = .5 (800 - y)
y = 320
Answer: B
Answer: (B) 320
Question: Find a sum for first 9 prime number'ss?
(A) 125
(B) 128
(C) 130
(D) 100
(E) 120
Rationale: Required sum = (2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 ) = 100
Note: 1 is not a prime number
Option D
Answer: (D) 100
Question: By selling a 50meters cloth one gain the selling price of 20meters. Find the gain percent?
(A) 50%
(B) 100%
(C) 75%
(D) 25%
(E) 90%
Rationale: Let the cost of 1meter cloth be x
Gain = 50x-20x = 30x
gain % = 30x/30x*100 = 100%
Answer is B
Answer: (B) 100%
Question: Patrick purchased 70 pencils and sold them at a loss equal to the selling price of 20 pencils. The cost of 70 pencils is how many times the selling price of 70 pencils?
(A)  0.75
(B)  0.8
(C)  1
(D)  1.28
(E)  1.35
Rationale: Say the cost price of 70 pencils was $70 ($1 per pencil) and the selling price of 1 pencil was p.
Selling at a loss: 70 - 70p = 20p --> p = 7/9.
(cost price)/(selling price) = 1/(7/9) = 9/7 = 1.28.
Answer: D.
Answer: (D)  1.28
Question: The measure of the side of a square is multiplied by 6. If x represents the perimeter of the original square, what is the value of the new perimeter?
(A) 3x
(B) 4x
(C) 6x
(D) 12x
(E) 27x
Rationale: Original perimeter = x
Hence original side = x/4
New side = 6x/4
New perimeter = 4*6x/4 = 6x
Correct Option: C
Answer: (C) 6x
Question: In a river flowing at 2 km/hr, a boat travels 64 km upstream and then returns downstream to the starting point. If its speed in still water be 6 km/hr, find the total journey time.
(A) 10 hours
(B) 12 hours
(C) 14 hours
(D) 24 hours
(E) None of these
Rationale: Explanation :
speed of the boat = 6 km/hr
Speed downstream = (6+2) = 8 km/hr
Speed upstream = (6-2) = 4 km/hr
Distance travelled downstream = Distance travelled upstream = 64 km
Total time taken = Time taken downstream + Time taken upstream
= (64/8) + (64/4) = = 24 hr. Answer : Option D
Answer: (D) 24 hours
Question: This topic is locked. If you want to discuss this question please re-post it in the respective forum.
If y ≠ 3 and 3q/y is a prime integer greater than 2, which of the following must be true?
I. q = y
II. y = 1
III. q and y are prime integers.
(A)  None
(B)  I only
(C)  II only
(D)  III only
(E)  I and III
Rationale: 3q/y and if q=y then ans is 3 and 3 is prime number, which is greater than 2. so ans must be B. Please post OA.
Answer: (A)  None
Question: In the xy-plane, the point (-2, -1) is the center of a circle. The point (1, -1) lies inside the circle and the point (-2, 4) lies outside the circle. If the radius r of the circle is an integer, then r =
(A) 6
(B) 5
(C) 4
(D) 3
(E) 2
Rationale: An easy way to solve this question will be just to mark the points on the coordinate plane.
You'll see that the distance between the center (-2, -1) and the point inside the circle (1, -1) is 3 units
(both points are on y=-1 line so the distance will simply be 1-(-2)=3)
So the radius must be more than 3 units.
The distance between the center (-2,-1) and the point outside the circle (-2,4) is 5 units
(both points are on x=-2 line so the distance will simply be 4-(-1)=5)
So the radius must be less than 5 units, which implies 3 < r < 5, thus as r is an integer then r=4.
Answer: C.
Answer: (C) 4
Question: Pablo plays 3 rounds of a game, in which his chances of winning each round are 1/3 ,1/6 , and 1/n, respectively. If n ≠ 0, what is the probability that Pablo wins the first two rounds, but loses the third?
(A) 1/18n
(B) (n-1)/18n
(C) 1/2n
(D) (n+2)/2n
(E) (3n-2)/2n
Rationale: 1/3 * 1/6 * (1-1/n)
= 1/18 * (n-1)/n
= (n-1)/18n
Answer - B
Answer: (B) (n-1)/18n
Question: Arun and Varun started business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, Akhil joined them with Rs. 20,000. What will be Varun's share in the total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business ?
(A) 7500
(B) 7502
(C) 7512
(D) 2988
(E) 7112
Rationale: Arun : Varun : Akhil = (20000 x 24) : (15000 x 24) : (20000 x 18) = 4:3:3
B's share = 25000 x 3/10 = Rs. 7500
Answer: A
Answer: (A) 7500
Question: he ratio between the sale price and the cost price of an article is 3:1. What is the ratio between the profit and the cost price of that article?
(A) 2:1
(B) 2:9
(C) 2:4
(D) 2:1
(E) 2:5
Rationale: Let C.P. = Rs. x and S.P. = Rs. 3x.
Then, Gain = Rs. 2x
Required ratio = 2x : x = 2:1.
Answer:A
Answer: (A) 2:1
Question: Boy sells a book for Rs. 630 he gets a loss of 10 %, To gain 10%, what should be the SP?
(A) 430
(B) 450
(C) 550
(D) 770
(E) 660
Rationale: Cost price = 630/90 x 100 = 700
To gain 10% = 700 x 10/100 = 70
SP = CP + gain = 700 + 70 = 770
Answer :D
Answer: (D) 770
Question: What is the difference between the place values of two 1's in the numeral 135.21
(A) 99.999
(B) 100.2
(C) 134
(D) 99.99
(E) 99.9
Rationale: Required difference = 100-0.01 = 99.99
Answer is D
Answer: (D) 99.99
Question: A company, Chauncy Co., has an annual travel budget of $57,000. The accounting department estimates that transportation expenses will increase 5 percent in the coming year, and nontransportation travel expenses will increase by 15 percent in the coming year. Last year, Chauncy Co. spent $19,500 on transportation-related expenses, and $35,000 on nontransportation travel expenses. If the annual travel budget does not increase this year, and if the accounting department’s estimates are correct, how far over the annual travel budget will expenses be this year?
(A) $3,725
(B) $500
(C) $4,225
(D) $5,725
(E) $60,725
Rationale: annual travel budget of $57,000
Let, Transportation expenses = T = 19500
and Non-Transportation expenses = N=35000
i.e. Increased Transportation expenses = 1.05T = 20475
and Increased Non-Transportation expenses = 1.15N = 40250
Total Expense = 20475+40250 = 60725
Expense over Budget = Budget - expense = 57000-60725 = 3725
Answer: Option A
Answer: (A) $3,725
Question: At what time between 2 and 3 o'clock will the hands of a clock be together?
(A) (10 + 10/11) min past 8
(B) (10 + 10/11) min past 2
(C) (10 + 10/11) min past 3
(D) (10 + 10/11) min past 1
(E) (10 + 10/11) min past 4
Rationale: At 2 o'clock, the hour hand is at 2 and the minute hand is at 12, i.e. they are 10 min spaces apart.
To be together, the minute hand must gain 10 minutes over the hour hand.
Now, 55 minutes are gained by it in 60 min.
10 minutes will be gained in min. = min.
The hands will coincide at min. past 2.
Answer: B
Answer: (B) (10 + 10/11) min past 2
Question: A man misses a bus by 40 minutes if he travels at 30 kmph. If he travels at 40 kmph, then also he misses the bus by 10 minutes. What is the minimum speed required to catch the bus on time?
(A) 11
(B) 45
(C) 77
(D) 44
(E) 17
Rationale: Let the distance to be travelled to catch the bus be x km
x/30 - x/40 = 30/60 => (4x - 3x)/120 = 1/2 => x = 60 km
By traavelling 30 kmph time taken = 60/30 = 2 hours
By taking 2 hours, he is late by 40 min. So, he has to cover 60 km in at most speed = 60/(4/3) = 45 kmph.
Answer: B
Answer: (B) 45
Question: From 4 officers and 8 jawans in how many can 6 be chosen to include exactly one officer?
(A) 150
(B) 164
(C) 259
(D) 311
(E) 224
Rationale: Required number of ways = 4C1 * 8C5 = 224
Answer is E
Answer: (E) 224
Question: A taxi company costs $2.75 for the first quarter-mile and 12.5 cents for each additional quarter mile. What is the maximum distance you can travel with $6.50?
(A) 4 miles
(B) 5 3/4 miles
(C) 6 1/2 miles
(D) 7 3/4 miles
(E) 8 1/4 miles
Rationale: Use reverse calculation-
Total Cost = Fixed Cost ( For 1/4 miles ) + Variable cost ( Distance Travelled )
Or, 6.50 = 2.75 + 0.125 * d
Or, 3.75 = d/8
Or, d = 30 quarter miles
So, Total Distance = ( 30 + 1 ) Quarter miles
So, Distance = 31/4 => 73/4 miles
Hence answer will be (D)
Answer: (D) 7 3/4 miles
Question: A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 660 m long?
(A) 22
(B) 90
(C) 277
(D) 278
(E) 291
Rationale: Speed = 240/24 = 10 m/sec.
Required time = (240 + 660)/10 = 90 sec.
Answer: B
Answer: (B) 90
Question: Rajesh solved 80 per cent of the questions in an examination correctly. If out of 41 questions solved by Rajesh 37 questions are correct and of the remaining questions out of 8 questions 5 questions have been solved by Rajesh correctly then find the total number of questions asked in the examination.
(A) 75
(B) 65
(C) 60
(D) Cannot be determined
(E) None of these
Rationale: Suppose there are 8x questions a part from the 41 questions.
Then, 37+5x/41+8x=80%=45
⇒ 185 + 25x = 164 + 32x ⇒ 7x= 21 ⇒ x = 3
∴ Total no.of questions = 41 + 8x = 65
Answer B
Answer: (B) 65
Question: On rainy mornings, Mo drinks exactly N cups of hot chocolate (assume that N is an integer). On mornings that are not rainy, Mo drinks exactly 5 cups of tea. Last week Mo drank a total of 22 cups of tea and hot chocolate together. If during that week Mo drank 8 more tea cups than hot chocolate cups, then how many rainy days were there last week?
(A) 2
(B) 4
(C) 3
(D) 5
(E) 6
Rationale: T= the number of cups of tea
C= the number of cups of hot chocolate
T+C = 22 T-C=8 -> T= 15. C=7.
Mo drinks 5 cups of tea a day then number of days that are not rainy = 15/5 = 3
So number of rainy days = 7-3 = 4
B is the answer.
Answer: (B) 4
Question: Two trains of equal length 120 metres move in the same direction. The faster train completely
overtakes the slower one in 15 seconds. If the slower train were to move at half its speed, the over
taking would take in 10 seconds. At what speeds are the 2 trains moving ?
(A) 24,22
(B) 32,16
(C) 30,18
(D) 28,14
(E) None of these
Rationale: Explanation :
The total distance covered for over taking = length of the two trains = 120 +120 = 240
Speed of faster train be x m/s and slower train be y m/s
In the first case Relative speed = x-y
Relative Speed = Distance / Time taken = x-y = 240/15 = 16 m/s(1)
In the second case, the slower train moves at half its speed
Relative Speed = x-0.5y = 240/10 = 24 m/s ..(2)
Solving equation 1 & 2 we get x = 32 and y = 16 .
The speed of the faster and slower trains are 32 m/s and 16 m/s respectively
Answer : B
Answer: (B) 32,16
Question: How many liters of water must be evaporated from 50 liters of a 4 percent sugar solution to get a 10 percent sugar solution?
(A) 15
(B) 20
(C) 25
(D) 28
(E) 30
Rationale: Let x be the amount that needs to be evaporated.
0.04(50) = 0.1(50-x)
0.1x = 5 - 2
x = 3/0.1 = 30 liters
The answer is E.
Answer: (E) 30
Question: Train A left Centerville Station, heading toward Dale City Station, at 3: 00 p.m. Train B left Dale City Station, heading toward Centerville Station, at 2: 20 p.m. on the same day. The trains rode on straight tracks that were parallel to each other. If Train A traveled at a constant speed of 30 miles per hour and Train B traveled at a constant speed of 10 miles per hour, and the distance between the Centerville Station and Dale City Station is 90 miles, when did the trains pass each other?
(A) 4: 45 p.m.
(B) 5: 00 p.m.
(C) 5: 20 p.m.
(D) 4: 20 p.m.
(E) 6: 00 p.m.
Rationale: the distance travelled by the train A in first 20 minutes will be 10.
The distance which will be remaining is 80.
Now both trains are running in opposite direction.Their speed will be added so 40.
Time at which they will meet =80/40=2
time of train B will be 2:20 +2=4:20
Hence answer is D.Hope i am correct
Answer: (D) 4: 20 p.m.
Question: Mrs. Rodger got a weekly raise of $155. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.
(A) $ 145.
(B) $ 146
(C) $ 147
(D) $ 155
(E) None
Rationale: Solution:
Let the 1st paycheck be x (integer).
Mrs. Rodger got a weekly raise of $ 155.
So after completing the 1st week she will get $ (x+155).
Similarly after completing the 2nd week she will get $ (x + 155) + $ 155.
= $ (x + 155 + 155)
= $ (x + 310)
So in this way end of every week her salary will increase by $ 155.
Answer D
Answer: (D) $ 155
Question: A = {0, 1, -3, 6, -8, -10}
B = {-1, 2, -4, 7, 6, -9}
If a is a number that is randomly selected from Set A, and b is a number that is randomly selected from Set B, what is the probability that ab < 0?
(A) 1/4
(B) 1/3
(C) 5/13
(D) 5/12
(E) 1/2
Rationale: For the product of 2 numbers to be negative either of them must be positive or negative:
P(positive, negative) = 2/6*3/6 = 6/36;
P(negative,positive ) = 3/6 * 3/6 = 9/36
P = 6/36 + 9/36
P = 15/36
P = 5/12
Answer: D
Answer: (D) 5/12