mathewhe/aqua_rat huggingface dataset:
Question: At 1:00 PM, Train X departed from Station A on the road to Station B. At 1:50 PM, Train Y departed Station B on the same road for Station A. If Station A and Station B are p miles apart, Train X’s speed is r miles per hour, and Train Y’s speed is s miles per hour, how many hours after 1:00 PM, in terms of p, r, and s, do the two trains pass each other?
(A) 0.5 + (p - 0.5s)/(r + s)
(B) (p - 0.5s)/(r + s)
(C) 0.5 + (p - 0.5r)/r
(D) (p - 0.5r)/(r + s)
(E) 0.5 + (p - 0.5r)/(r + s)
Rationale: The distance A is going to cover between 1:00 and 1:30
= .5r
now the distance between the two trains = (p-.5r)
the relative velocity = (r-(-s)) = r+s
From 1:30, time is going to take when they meet = (p-.5r)/(r+s)
số thẻ ans is .5+((p-.5r)/(r+s)) [.5 is added for the time from 1:00 tờ 1:30]
ans is A
Answer: (A) 0.5 + (p - 0.5s)/(r + s)
Question: On dividing number by 56, we get 29 as remainder. On dividing the same number by 8, what will be the remainder?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: Let x be the number and y be the quotient.
Then, x = 357 * y + 39
= (17 * 21 * y) + (17 * 2) + 5
= 17 * (21y + 2) + 5.
Required remainder = 5.
ANSWER:B
Answer: (B) 5
Question: In 10 years, A will be twice as old as B was 10 years ago. If A is now 7 years older than B the present age of B is
(A) 37
(B) 38
(C) 39
(D) 40
(E) 41
Rationale: let present age of A be a and B be b
a+10 = 2*(b-10)
=> 2b-a = 30 ......(i)
a = b+7
=>2b-b-7 = 30
b=37
so the present age of b is 37 years
ANSWER:A
Answer: (A) 37
Question: In a class of 60 students 41 are taking French, 22 are taking German. Of the students taking French or German, 9 are taking both courses. How many students are not enrolled in either course?
(A) 6
(B) 15
(C) 24
(D) 33
(E) 54
Rationale: Formula for calculating two overlapping sets:
A + B - both + NOT(A or B) = Total
so in our task we have equation:
41 (french) + 22 (german) - 9 (both) + NOT = 60
54 + NOT = 60
NOT = 60 - 54 = 6
So answer is A
Answer: (A) 6
Question: Which of the following equations is NOT equivalent to 4u^2 = y^2 - 9 ?
(A)  4u^2 + 9 = y^2
(B)  4u^2 - y^2 = -9
(C)  4u^2= (y + 3)(y - 3)
(D)  2u = y - 3
(E) u^2 = (y^2-9)/4
Rationale: 4X^2 = Y^2 - 9
The basic rule when dealing with equations is that you can do ANYTHING to both sides of an equation as long as you do it EQUALLY to BOTH sides. Everything gets a bit more complex when you're dealing with variables in the denominator of a fraction and/or inequalities, but neither of those subjects is a factor in this prompt.
Looking at Answer D, we have....
2u = Y - 3
While you COULD take the square root of both sides of the original equation, it's important to note that the square root of Y^2 - 9 is NOT (Y-3).
Y^2 - 9 can be factored into (Y-3)(Y+3), but neither of these parentheses is the square root of Y^2 - 9.
You can see the proof when you square either of the two parentheses:
(Y-3)^2 = Y^2 - 6u + 9
(Y+3)^2 = Y^2 + 6u + 9
Thus, D is NOT equivalent to the prompt.
Answer: (D)  2u = y - 3
Question: A used cars salesman receives an annual bonus if he meets a certain quota. This year, the salesman has so far sold 1/5 of last year's quota. If this year's quota is reduced by 25 percent from last year, the quantity that he still needs to sell this year in order to receive the annual bonus is what fraction of the preceding year's car quota?
(A) 4/15
(B) 4/20
(C) 3/4
(D) 11/20
(E) 9/20
Rationale: Let Last year Quota be = 100x
This year Quota = 100x - 25%of100x = 75x
Salesman has so far sold = 1/5(100x) = 20x
Quantity still need to be sold = 75 x - 20x = 55x
Question :: What fraction of 100x is 55x = 55x/100x = 11/20.
Ans:: D
Answer: (D) 11/20
Question: If the average marks of three batches of 56, 60 and 45 students respectively is 50, 55, 60, then the
average marks of all the students is
(A) 54.48
(B) 54.68
(C) 54.65
(D) 54.58
(E) None of these
Rationale: Explanation:
(56Ã—50)+(60Ã—55)+(45Ã—60)/(56+60+46)=54.65
Answer: Option C
Answer: (C) 54.65
Question: A toy store's revenue in November was 3/5 of its revenue in December and its revenue in January was 3/4 of its revenue in November, then the store's revenue in December was how many times the average (arithmetic mean) of its revenues in November and January?
(A)  1/4
(B)  1/2
(C)  2/3
(D)  2
(E)  4
Rationale: Let Dec rev =100
Then Nov rev is 3/5 (100) => 60
Therefore Jan rev = 3/4(Nov rev) = 3/4(60) => 45
Hence Dec rev = x*( Nov rev+Jan rev)/2
100 = x* (60+45)/2
x = 100/52.5 => 1.90=2
Ans) D
Answer: (D)  2
Question: The average age of three boys is 20 years and their ages are in the proportion 2 : 3 : 5. The age of the youngest boy is:
(A) 21 years
(B) 18 years
(C) 15 years
(D) 9 years
(E) None of these
Rationale: Total age of 3 boys = (20 Ã— 3) years = 60 years. Ratio of their ages = 2 : 3 : 3.
Age of the youngest = (60 Ã— 3â„10) years = 18 years.
Answer B
Answer: (B) 18 years
Question: Each student at a certain business school is assigned a 3-digit student identification number. The first digit of the identification number cannot be zero, and the last digit of the identification number must be prime. How many different student identification numbers can the school create?
(A) 9,000
(B) 3,600
(C) 2,700
(D) 360
(E) 1,944
Rationale: The identification number is of the form _ _ _ _
1. First digit cannot be 0
2. Middle digits can be anything
3. Last digit has to be prime - 2, 3, 5, 7
We can have the following number of possibilities for each space
__ __ __ __
9 10 4
Total cases = 360
Answer : D
Answer: (D) 360
Question: The radius of the two circular fields is in the ratio 3: 5 the area of the first field is what percent less than the area of the second?
(A) 84%
(B) 24%
(C) 54%
(D) 64%
(E) 34%
Rationale: r = 3 πr2 = 9
r = 5 πr2 = 25
25 π – 16 π
100 ---- ? => 64%
Answer: D
Answer: (D) 64%
Question: A train 125 m long passes a man, running at 15 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?
(A) 40
(B) 50
(C) 60
(D) 79
(E) 80
Rationale: Speed of the train relative to man = 125/10 = 25/2 m/sec.
= 25/2 * 18/5 = 45 km/hr
Let the speed of the train be x km/hr. Then, relative speed = (x - 15) km/hr.
x - 15 = 45 => x = 60 km/hr.
Answer: Option C
Answer: (C) 60
Question: A train moves at average speed of 40kmph reaches its destination on time.what its average speed becomes 35kmph , then it reaches its destination 15 late. find the length of the journey?
(A) 70km
(B) 85km
(C) 38km
(D) 14km
(E) 1km
Rationale: Difference between timings=15 mis=1/4hr
let the length of the journey be x km.
then x/35-x/40=1/4
8x-7x=70
x=70km
Answer (A)
Answer: (A) 70km
Question: In a sports club with 30 members, 16 play badminton and 19 play tennis and 2 do not play either. How many members play both badminton and tennis?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: Let x play both badminton and tennis so 16-x play only badminton and 19-x play only tennis. 2 play none and there are total 30 students. hence,
(16-x)+(19-x)+x+2=30
37-2x+x=30
37-x=30
x=7
So 7 members play both badminton and tennis.
A
Answer: (A) 7
Question: If (x/y)=(8/5), find the value (x^2+y^2)/(x^2-y^2)
(A) 89/39
(B) 59/11
(C) 51/77
(D) 41/11
(E) None of them
Rationale: = (x^2+y^2)/(x^2-y^2) = ( x^2 /y^2+ 1)/ ( x^2 /y^2-1) = [(8/5)^2+1] / [(8/5)^2-1]
= [(64/25)+1] / [(64/25)-1] = 89/39
Answer is A.
Answer: (A) 89/39
Question: Marginal cost is the cost of increasing the quantity produced (or purchased) by one unit. If the fixed cost for n products is $10,000 and the marginal cost is $200, and the total cost is $40,000, what is the value of n?
(A)  30
(B)  50
(C)  60
(D)  80
(E)  150
Rationale: Total cost for n products = fixed cost for n products + n*marginal cost --> $40,000 = $10,000 + n * $200 --> n = 150.
Answer: E.
Answer: (E)  150
Question: A person can row at 10 kmph and still water. He takes 5 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 2 kmph?
(A) 32 km
(B) 25 km
(C) 28 km
(D) 24 km
(E) 20 km
Rationale: Let the distance between A and B be x km.
Total time = x/(10 + 2) + x/(10 - 2) = 5
=> x/12 + x/8 = 5 => (2x + 3x)/24 = 5 => x = 24 km.
ANSWER:D
Answer: (D) 24 km
Question: If a certain sample of data has a mean of 25.0 and the value 36.0 is more than 2.5 standard deviations from the mean, which of the following could be the standard deviation of the sample
(A) 3.75
(B) 3.5
(C) 3.25
(D) 3.0
(E) 4.35
Rationale: 36.0 is more than 2.5 standard deviations from 25 --> 36 > 25 + 2.5*{SD} --> 2.5*{SD} < 11 --> {SD} < 4.4. Only option E offers the standard deviation less than 4.4.
Answer: E.
Answer: (E) 4.35
Question: The integer x is divisible by both 15 and 25. Which of the following must be an integer?
(A) x/11
(B) x/75
(C) x/84
(D) x/36
(E) x/26
Rationale: Prime factorization of 15 = 5*3
Prime factorization of 25= 5*5
LCM of 15 and 25 = 5^2 * 3 = 75
Therefore x/75 must be an integer
Answer B
Answer: (B) x/75
Question: The H.C.F of 2^4*3^2*5^3*7, 2^3*3^3*5^2*7^2 and 3*5*7*11 is?
(A) 105
(B) 1155
(C) 2310
(D) 27720
(E) None of these
Rationale: H.C.F= Product of lowest power of factors=3*5*7=105
Correct Option: A
Answer: (A) 105
Question: Four brothers Adam, Bill, Charles and David together contributed certain amount of money and purchased a car. The contribution made by Adam is half that of the total contribution made by the other three brothers, contribution made by Bill is one-fourth of the total contribution made by the other three brothers and the contribution made by Charles is two-third of the total contribution made by the other three brothers. If the total price of the car is $9000, find the contribution made by David.
(A) $540
(B) $580
(C) $600
(D) $660
(E) $680
Rationale: Given that A:(B+C+D)= 1:2.
Hence A contributed 1/3rd of the total price.
Given B:(A+C+D)=1:4
Hence B contributed 1/5th of the total price.
Given C:(A+B+D)=2:3
Hence C contributed 2/5th of the total price.
Thus the contribution made by A,B and C= 1/3+1/5+2/5=14/15
So, the remaining 1/15th of the price is contributed by David.
Hence David's contribution= 1/15×9000=$600.
The answer is C.
Answer: (C) $600
Question: The salary of A, B, C, D, E is Rs. 8000, Rs. 5000, Rs. 16000, Rs. 7000, Rs. 9000 per month respectively, then the average salary of A, B, C, D, and E per month is
(A) Rs. 7000
(B) Rs. 8000
(C) Rs. 8500
(D) Rs. 9000
(E) None
Rationale: Answer
Average salary
= 8000 + 5000 + 16000 + 7000 + 9000 / 5
= Rs. 9000
Correct Option: D
Answer: (D) Rs. 9000
Question: How many words can be formed by using all letters of the word ‘COMPUTER’ ?
(A) 32240
(B) 36180
(C) 40320
(D) 45860
(E) 48240
Rationale: The word contains 8 different letters.
The number of permutations is 8! = 40320
The answer is C.
Answer: (C) 40320
Question: A side of beef lost 35 percent of its weight in processing. If the side of beef weighed 560 pounds after processing, how many pounds did it weigh before processing?
(A)  191
(B)  355
(C)  737
(D)  861
(E)  1,560
Rationale: Let weight of side of beef before processing = x
(65/100)*x = 560
=> x = (560 * 100)/65 = 861
Answer D
Answer: (D)  861
Question: In a game of 90 points, A can give B 20 points and C 25 points. then how many points can B give C in a game of 80?
(A) 1.71
(B) 6.71
(C) 5.71
(D) 7.71
(E) 3.71
Rationale: In a game of 90 points,A give B 20 points and c 25 points means B=70,C=65
In 70 points B give 5 since 70-65=5
In 80 points B gives=80*5/70=5.71
ANSWER:C
Answer: (C) 5.71
Question: In how much time will a train of length 100 m, moving at 36 kmph cross an electric pole?
(A) 17 sec
(B) 18 sec
(C) 19 sec
(D) 10 sec
(E) 15 sec
Rationale: Convert kmph to mps. 36 kmph = 36 * 5/18 = 10 mps.
The distance to be covered is equal to the length of the train.
Required time t = d/s
= 100/10
= 10 sec.
Answer: D
Answer: (D) 10 sec
Question: If (10^4 * 3.456789)^9 is written as a single term, how many digits would be to the right of the decimal place?
(A) 6
(B) 12
(C) 18
(D) 32
(E) 48
Rationale: 3.456789^9 has 6*9 = 54 decimal places.
10^36 moves the decimal place to the right 36 places.
(10^4 * 3.456789)^9 has 54-36 = 18 digits after the decimal point.
The answer is C.
Answer: (C) 18
Question: A car drove from Town A to Town B without stopping. The car traveled the first 70 miles of its journey at an average speed of 25 miles per hour. What was the car’s average speed, in miles per hour, for the remaining 90 miles if the car’s average speed for the entire trip was 40 miles per hour?
(A) 28
(B) 48
(C) 50
(D) 55
(E) 75
Rationale: KAPLANOFFICIAL SOLUTION:
To solve this problem, you must remember that average speed means total distance divided by total time over an entire journey. This should not be confused with the average of the speeds. The total distance in this problem is 160 miles, but we will need to express the total time in a more complex way.
For the first 70 miles, the car traveled at 25 miles per hour. Therefore, we can say that the time this took was 70/25, because distance divided by rate equals time.
For the last 90 miles, we are trying to solve for the rate, so we can call this speed R. Thus, the time for the final 90 miles is 90/R.
If we put all of this together, knowing that the average speed over the entire journey is 40 miles per hour, we get the equation 160/(70/25 + 90/R) = 40. We can now solve for R and reach our answer.
160/(70/25 + 90/R) = 40
R = 75
75 is choice (E) and that’s our correct answer.
Answer: (E) 75
Question: A train 560 m in length crosses a telegraph post in 16 seconds. The speed of the train is?
(A) 126 kmph
(B) 77 kmph
(C) 54 kmph
(D) 71 kmph
(E) 88 kmph
Rationale: S = 560/16 * 18/5 = 126 kmph
Answer:A
Answer: (A) 126 kmph
Question: A certain car dealership sells economy cars, luxury cars, and sport utility vehicles. The ratio of economy to luxury cars is 6:2. The ratio of economy cars to sport utility vehicles is 5:3. What is the ratio of luxury cars to sport utility vehicles?
(A) 9:8
(B) 8:9
(C) 6:2
(D) 2:3
(E) 1:2
Rationale: The ratio of economy to luxury cars is 6:2 --> E:L = 6:2 = 30:10.
The ratio of economy cars to sport utility vehicles is 5:3 --> E:S = 5:3 = 30:18.
Thus, L:S = 10:18 = 5:6.
Answer: B.
Answer: (B) 8:9
Question: if log 5 = 0.69897, the number of digits in 5128 is
(A) 90
(B) 39
(C) 88
(D) 28
(E) 11
Rationale: Explanation:
log(5128) = 128log(5) = 128 × 0.69897 ≈ 89.46
ie, its characteristic = 89
Hence, number of digits in 2128 = 89+1 = 90
Answer: Option A
Answer: (A) 90
Question: Suganya and Suriya are partners in a business. Suganya invests Rs. 35,000 for 8 months and Suriya invests Rs.42,000 for 10 months. Out of a profit of Rs.31,570. Suganya's share is
(A) Rs.9471
(B) Rs.12,628
(C) Rs.18,040
(D) Rs.18,942
(E) None
Rationale: Solution
Ratio of their shares	=(35000×8):(42000×10)
= 2 : 3.
Suganya's share	= Rs.(31570 ×2/5)
= Rs.12628.
Answer C
Answer: (C) Rs.18,040
Question: Due to construction, the speed limit along an 5-mile section of highway is reduced from 52 miles per hour to 36 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
(A) A) 3.12
(B) B) 8
(C) C) 10
(D) D) 2.57
(E) E) 24
Rationale: Old time in minutes to cross 5 miles stretch = 5*60/52 = 5*15/13 = 5.76
New time in minutes to cross 5 miles stretch = 5*60/36 = 5*5/3 = 8.33
Time difference = 2.57
Ans:D
Answer: (D) D) 2.57
Question: A set of numbers has an average of 50. If the largest element is 3 greater than 3 times the smallest element, which of the following values cannot be in the set?
(A)  85
(B)  90
(C)  123
(D)  150
(E)  155
Rationale: Ans: E
Solution: we are given the relation between smallest and the largest term. so let the smallest a and largest be 3a+3
so the avg = 50
which tells us that any value of a must be less than 50
so a<50 means, largest value 3a+3 <(3*50)+3
=largest value must be <153
so 155 can not be the value in the set.
Answer: (E)  155
Question: A focus group is currently made up of x men and y women. If 2 men and 4 women are added to the group, and if one person is selected at random from the larger focus group, then what is the probability that a man is selected?
(A) x/(x + 2)
(B) x/(x + y)
(C) (x + 2)/(x + y + 2)
(D) (y + 4)/(x + y + 6)
(E) (x + 2)/(x + y + 6)
Rationale: x men
y women
x+2+y+4 is the total
=x+y+6
x+2 is the number of men
so (x + 2)/(x + y + 6)
E. (x + 2)/(x + y + 6)
Answer: (E) (x + 2)/(x + y + 6)
Question: A train is running with a speed of 60 kmph and its length is 110 metres. Calculate the time by which it will pass a man running opposite with speed of 6 kmph
(A) 2 second
(B) 4 second
(C) 6 second
(D) 8 second
(E) 10 second
Rationale: Explanation:
From the given question,
we will first calculate the speed of train relative to man,
=> ( 60 + 6 ) = 66 km/hr ( we added 6 because man is running opposite )
Convert it in metre/second
=66Ã—5/18
=55/3m/sec
Time it will take to pass man
=110Ã—3/55
=6 seconds
ANSWER IS C
Answer: (C) 6 second
Question: A driver covers a certain distance by car driving at 50 km/hr and returns back to the starting point riding on a scooter at 10 km/hr. What was the average speed for the whole journey?
(A) 12.5 km/h
(B) 14.8 km/h
(C) 16.7 km/h
(D) 17.5 km/h
(E) 18.9 km/h
Rationale: time 1 = d / 50
time 2 = d / 10
total time = d/50 + d/10 = 3d/25
average speed = total distance / total time = 2d / (3d/25) = 16.7 km/h
The answer is C.
Answer: (C) 16.7 km/h
Question: When 20 is subtracted from a number, it reduces to seven-twelve of the number. What is the sum of the digit of the number
(A) 40
(B) 44
(C) 46
(D) 48
(E) 45
Rationale: Explanation:
Let the number be x. Then,
x - 20 = 7x/12 => x - 7x/12 = 20
5x/12 = 20 => x = 48
Answer: Option D
Answer: (D) 48
Question: A student earned a grade of 80% on a math test that had 20 problems. How many problems on this test did the student answer correctly? (round to the nearest whole number)
(A) 36 problems
(B) 53 problems
(C) 27 problems
(D) 16 problems
(E) 18 problems
Rationale: Multiply the opposites:
80/100=x/20
80 x 20 = 1600
Divide by the remaining number:
16/1600
*100
16 problems
correct answer D
Answer: (D) 16 problems
Question: A train 500 meters long is running with a speed of 44 kmph. The time taken by it to cross a tunnel 230 meters long is?
(A) 287 sec
(B) 288 sec
(C) 48 sec
(D) 61 sec
(E) 17 sec
Rationale: D = 500 + 230 = 730
S = 44 * 5/18 = 12 mps
T = 730/12 = 61 sec
Answer: D
Answer: (D) 61 sec
Question: A man rides at the rate of 50km/hr. But stops 20minutes to change horses at the end of every 25th kilometer. How long will he take to go a distance of 100 kilometers?
(A) 3hr
(B) 6hr 30min
(C) 8hr 10min
(D) 7hr 20min
(E) 9hr
Rationale: speed of man = 50km/hr
number of rests = (100/25)-1 = 3
time taken for the man = (100/50)+3*(20/60) = 3 hr
Answer is A
Answer: (A) 3hr
Question: Consider there is an elevator and you are at the upside and coming down using elevator. You walk 20 steps and then you stop, then you reach to the ground in 10 minutes. If you walk 10 steps and then stop, then you reach to the ground in 20 minutes. What is the speed of the elevator and How many steps are there??
(A) 1 step/min
(B) 2 step/min
(C) 3 step/min
(D) 4 step/min
(E) 5 step/min
Rationale: Let e be the speed of the elevator, n be the no. of steps
n = 20 + 10*e = 10+20*e
e=1
n=30
No. of steps : 30
Speed : 1 step/min
ANSWER:A
Answer: (A) 1 step/min
Question: In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 44, the dividend is:
(A) 5330
(B) 5336
(C) 4884
(D) 5345
(E) 5350
Rationale: Divisor = (5 * 44) = 220
= 10 * Quotient = Divisor
=> Quotient = 220/10 = 22
Dividend = (Divisor * Quotient) + Remainder
Dividend = (220 * 22) + 42 = 4884.
C
Answer: (C) 4884
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 42 minutes. The waste pipe can empty the full cistern in?
(A) 8 min
(B) 7 min
(C) 5 min
(D) 9 min
(E) 4 min
Rationale: 1/10 + 1/15 - 1/x
= 1/42
x = 7
Answer: B
Answer: (B) 7 min
Question: The radius of the wheel of a bus is 175 cms and the speed of the bus is 66 km/h, then the r.p.m. (revolutions per minutes)of the wheel is
(A) 100
(B) 250
(C) 300
(D) 330
(E) None of these
Rationale: Radius of the wheel of bus = 175 cm. Then,
circumference of wheel = 2Ï€r = 350Ï€ = 1100 cm
Distance covered by bus in 1 minute
= 66â„60 Ã— 1000 Ã— 100 cms
Distance covered by one revolution of wheel
= circumference of wheel
= 1100 cm
âˆ´ Revolutions per minute = 6600000/60Ã—1100 = 100
Answer A
Answer: (A) 100
Question: There are three departments having students 72,58,24 .In an exam they have to be seated in rooms such that each room has equal number of students and each room has students of one type only (No mixing of departments). Find the minimum number of rooms required?
(A) 73
(B) 74
(C) 75
(D) 76
(E) 77
Rationale: WE NEED TO TAKE GCD WHICH IS 2
THUS ALL THE ROOMS WILL HAVE 2 STUDENTS OF THE SAME DEPT
1) 72/2 = 36
2) 58/2 = 29
3) 24/2 = 12
TOTAL NO. OF MIN ROOMS REQD = 36+12+29 = 77
ANSWER:E
Answer: (E) 77
Question: Tough and Tricky questions: Mixture Problems.
A drink holding 6 ounces of an alcoholic drink that is 1 part rum to 2 parts coke is added to a jug holding 30 ounces of an alcoholic drink that is 1 part rum to 3 parts coke. What is the ratio of rum to coke in the resulting mixture?
(A) 2:5
(B) 5:14
(C) 3:5
(D) 4:7
(E) 14:5
Rationale: Answer = E) 5:10
........................ Rum ..................... Coke ................. Total
First Drink ........... 2 ............................ 4 ..................... 6 (Ratio 1:2)
Second Drink ....... 8 ............................. 24 ................... 32 (Ratio 1:3)
Total .................. 10 ............................. 28 .................... 38
Ratio = 10:20 = 5:10
E
Answer: (E) 14:5
Question: A candidate got 35% of the votes polled and he lost to his rival by 2250 votes. How many votes were cast?
(A) 7500
(B) 2327
(C) 2997
(D) 2662
(E) 7121
Rationale: 35%-----------L
65%-----------W
------------------
30%----------2250
100%---------? => 7500
Answer: A
Answer: (A) 7500
Question: 12 men take 18 days to complete a job whereas 12 women in 18 days can complete 3⁄4 of the same job. How many days will 10 men and 8 women together take to complete the same job?
(A) 6
(B) 13 1⁄2
(C) 12
(D) Data inadequate
(E) None of these
Rationale: 12 M × 18 = 12 W × 18 × 4⁄3
\ w = 3/4 M
10M + 8W = 10M + 8 × 3⁄4M = 16 M
\16 men can complete the same work
in 12×18/16=27/2=13 1/2days
Answer B
Answer: (B) 13 1⁄2
Question: Three small cruise ships, each carrying 10 passengers, will dock tomorrow. One ship will dock at Port A, another at Port B, and the third at Port C. At Port A, two passengers will be selected at random; each winner will receive one gift certificate worth $50. At Port B, one passenger will be selected at random to receive a gift certificate worth $35, and at Port C, one passenger will be selected at random to receive a gift certificate worth $25. How many different ways can the gift certificates be given out?
(A) 270
(B) 450
(C) 2,700
(D) 4,500
(E) 27,000
Rationale: Number of ways 3 ships can go to 3 ports = 3! =6
Let ship A goes to dock A . Thus, the number of ways of selecting 2 winners out of 10 passengers = 10C2 = 45
Let ship B goes to dock B . Thus, the number of ways of selecting 1 winner out of 10 passengers = 10C1 = 10
Let ship C goes to dock C . Thus, the number of ways of selecting 1 winner out of 10 passengers = 10C1 = 10
Thus the total number of arrangements possible = 6*45*10*10 = 27000, thus E is the correct answer.
Answer: (E) 27,000
Question: What is the square root of 121?
(A) 11
(B) 12
(C) 16
(D) 18
(E) 25
Rationale: 11X11 = 121
ANSWER A
Answer: (A) 11
Question: A bag of P peanuts can be divided into 9 smaller bags with 6 peanuts left over. Another bag of m peanuts can be divided into 12 smaller bags with 4 peanuts left over. Which of the following is the remainder when Pm is divided by 18?
(A) 6
(B) 4
(C) 2
(D) 8
(E) 5
Rationale: P = 9x + 6
m = 12y + 4
Pm = (9x + 6)*(12y + 4) = 108xy + 36x + 72y + 24
Remainder of nm/18 = (108xy + 36x + 72y + 24)/18
Observe that the first three terms are a multiple of 18
24 when divided by 18 leaves remainder 6
Hence mn/18 will leave remainder 6
A
Answer: (A) 6