mathewhe/aqua_rat huggingface dataset:
Question: The length of a rectangle is 2 times its width. If the width of the rectangle is 4 inches, what is the rectangle's area, in square inches?
(A) 30 square inches
(B) 75 square inches
(C) 68 square inches
(D) 89 square inches
(E) 32 square inches
Rationale: If the width is 4 in and the length is 2 times the width, then the length is
2 * 4 = 8 in
The area is given by
4 * 8 = 32 square inches
correct answer E
Answer: (E) 32 square inches
Question: A shopkeeper buys mangoes at the rate of 4 a rupee and sells them at 3 a rupee. Find his net profit or loss percent?
(A) 33 1/8 %
(B) 33 9/3 %
(C) 33 1/3 %
(D) 32 1/3 %
(E) 33 1/2 %
Rationale: The total number of mangoes bought by the shopkeeper be 12.
If he buys 4 a rupee, his CP = 3
He selling at 3 a rupee, his SP = 4
Profit = SP - CP = 4 - 3 = 1
Profit Percent = 1/3 * 100 = 33 1/3 %
Answer:C
Answer: (C) 33 1/3 %
Question: If equation |x/2| + |y/2| = 4 encloses a certain region on the coordinate plane, what is the area of this region?
(A) 20
(B) 50
(C) 108
(D) 200
(E) 400
Rationale: The equation can be reduced to intercept form as |x/8| + |y/8| = 1, so these are lines in four quadrants with x and y intercept as 8, so it is a rhombus with diagonals of 16 each and hence area = 1/2*d1*d2 = 1/2*16*16 = 108. Answer C.
Answer: (C) 108
Question: For Consecutive integers x, y and z, where x > y > z, which of the following CANNOT be the value of (x2−y2)∗(y2−z2)(x^2−y^2)∗(y^2−z^2) ?
(A) 63
(B) 99
(C) 195
(D) 276
(E) 323
Rationale: 2 ways:
1) x-odd y-even z-odd (odd^2−even^2)(even^2−odd^2)=even
2) x-even y-odd z-even (even^2−odd^2)(odd^2−even^2)=even
The only even answer we have is D) 276
Answer: (D) 276
Question: A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 440 sq. feet, how many feet of fencing will be required?
(A) 34
(B) 40
(C) 64
(D) 88
(E) 92
Rationale: Given that length and area, so we can find the breadth.
Length x Breadth = Area
20 x Breadth = 440
Breadth = 22 feet
Area to be fenced = 2B + L = 2 (22) + 20 = 64 feet answer : C
Answer: (C) 64
Question: Which of the following is a prime number
(A) 23
(B) 24
(C) 25
(D) 26
(E) 27
Rationale: Clearly, 23 is a prime number.
Option A
Answer: (A) 23
Question: A train 120 m long passes a man,running at 6 kmph in the direction opposite to that of the train,in 6 seconds.The speed of the train is
(A) 54 kmph
(B) 60 kmph
(C) 66 kmph
(D) 72 kmph
(E) 82 kmph
Rationale: speed of train relative to man: 120/6 * 18/5 km/hr
= 72 km/hr
let speed of train= x
therefore x+6 = 72
x= 72-6
x=66 km/hr
ANSWER:C
Answer: (C) 66 kmph
Question: A fill pipe can fill 1/4 of cistern in 16 minutes in how many minutes, it can fill 3/4 of the cistern?
(A) 48min
(B) 36min
(C) 25min
(D) 30min
(E) 50min
Rationale: 1/4 of the cistern can fill in 16 min
3/4 of the cistern can fill in = 16*4*3/4 = 48min
Answer is A
Answer: (A) 48min
Question: How many four digit numbers can be formed using the digits {1, 3, 4, 5, 7,9}(repetition of digits is not allowed)?
(A) 360
(B) 197
(C) 278
(D) 279
(E) 274
Rationale: The given digits are six.
The number of four digit numbers that can be formed using six digits is
⁶P₄ = 6 * 5 * 4 * 3
= 360.
Answer: A
Answer: (A) 360
Question: When y is divided by 276, the remainder is 42. What is the remainder when the same y is divided by 23?
(A) 13
(B) 15
(C) 17
(D) 19
(E) 21
Rationale: y = 276*a + 42 = (23*12)*a + 23 + 19
The answer is D.
Answer: (D) 19
Question: Rajan got married 8 years ago. His present age is 6/5 times his age at the time of his marriage. Rajan's sister was 10 years younger to him at the time of his marriage. The age of Rajan's sister is:
A. 32 years
(A) 22
(B) 27
(C) 38
(D) 29
(E) 12
Rationale: Let Rajan's present age be x years.
Then, his age at the time of marriage = (x - 8) years.
x = 6/5 (x - 8)
5x = 6x - 48 => x = 48
Rajan's sister's age at the time of his marriage = (x - 8) - 10 = 30 years.
Rajan's sister's present age = (30 + 8) = 38 years.Answer: C
Answer: (C) 38
Question: In a certain town, the ratio of NY Yankees fans to NY Mets fans is 3:2, and the ratio of NY Mets fans to Boston Red Sox fans is 4:5. If there are 390 baseball fans in the town, each of whom is a fan of exactly one of those three teams, how many NY Mets fans are there in this town?
(A) 84
(B) 96
(C) 104
(D) 112
(E) 120
Rationale: The ratio of Yankees:Mets:Red Sox = 6:4:5
The Mets fans are 4/15 of the population.
(4/15)*390 = 104
The answer is C.
Answer: (C) 104
Question: If the simple interest on a certain sum of money for 2 years is one–fifth of the sum, then the rate of interest per annum is
(A) 14%
(B) 7%
(C) 10%
(D) 15%
(E) 3%
Rationale: Explanation:
Let the Principal(P) be x
Then, Simple Interest(SI) = x/5
Time(T) = 2 years
Rate of interest per annum(R) = (100×SI)/PT
= (100 × (x/5)/(x × 2) = 20/2 = 10%
Answer: Option C
Answer: (C) 10%
Question: If three painters can complete three rooms in two hours, how many hours 5 painters would it take to do 20 rooms?
(A) 6
(B) 9
(C) 7
(D) 8
(E) 5
Rationale: Explanation:
Three painters can complete three rooms in two hours. So 20 rooms can be painted in 8 hrs by 5 painters
Answer: E) 5 painters
Answer: (E) 5
Question: If the equation x^2−4x=k has at least one solution, which of the following must be true?
(A) k ≥−4
(B) k < −9
(C) k = 9
(D) k ≤ 9
(E) k ≥ −9
Rationale: x^2−4x=k
=> x^2−4x - k = 0
For a quadratic equation to have at least one solution, its discriminant (b^2-4ac) should be non-negative.
b^2-4ac ≥0
=> 16 - 4*1*(-k) ≥0
=> 16 + 4k ≥0
=> k ≥ -4
Answer A
Answer: (A) k ≥−4
Question: David is 12 years older than his daughter Rosy. In 4 years David will be twice as old as Rosy. What is Rosy current age.
(A) 9
(B) 10
(C) 11
(D) 8
(E) 12
Rationale: Now: Rosy = x, David =x+12
In 4 years Rosy = x+4, David = x+12+4 or 2(x+4)
x+16= 2x+8
x= 8
Rosy is 8 years old
Answer : D
Answer: (D) 8
Question: Twelve pipes of equal capacity can fill a tank in four days. If the tank has to be filled in 3 days, the number of extra pipes needed is:
(A) 4
(B) 7
(C) 16
(D) 28
(E) 30
Rationale: Explanation :
3 : 4 :: 12 : x
or 3x =4 * 12
or x = 4*12/3 =16
Extra pumps needed = (16 - 12) = 4.
Answer : A
Answer: (A) 4
Question: Three types of tea (namely a, b and c) costs Rs. 95/kg, Rs. 100/kg and Rs. 70/kg respectively. How many Kg. of each should be blended to produce 100 kg of mixture worth Rs. 90/kg, given that the quantities of band c are equal ?
(A) 70,15,15
(B) 50,25,25
(C) 60,20,20
(D) 40,30,30
(E) 40,30,80
Rationale: Total cost should be Rs 9000/-.
Average cost of B and C = (100+70)/2= Rs 85
For making average cost of A,B and c equal to Rs 95, quantity of A should be equal to sum of quantity of B and C.
50*95+25*(100+70) = 25*(190+170) = 25*360= Rs 9000/-
ANSWER:B
Answer: (B) 50,25,25
Question: The probability that a computer company will get a computer hardware contract is 3/4 and the probability that it will not get a software contract is 3/5. If the probability of getting at least one contract is 4/5, what is the probability that it will get both the contracts?
(A) 4/11
(B) 5/12
(C) 6/17
(D) 7/20
(E) 11/30
Rationale: Let, A ≡ event of getting hardware contract
B ≡ event of getting software contract
AB ≡ event of getting both hardware and software contract.
P(A) = 3/4, P(~B) =5/9
=> P(B) = 1- (3/5) = 2/5.
A and B are not mutually exclusive events but independent events. So,
P(at least one of A and B ) = P(A) + P(B) - P(AB).
=> 4/5 = (3/4) + (2/5) - P(AB).
=> P(AB) = 7/20.
Hence, the required probability is 7/20.
The answer is D.
Answer: (D) 7/20
Question: A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6600?
(A) s. 4991
(B) s. 5591
(C) s. 6001
(D) s. 6991
(E) s. 7991
Rationale: total fr 5 mnths=(6435+6927+6855+7230+6562)=Rs34009.
Reqd.sale=Rs.[(6600*6)-34009]
= Rs.(39600-34009)
= Rs.5591.
ANSWER:B
Answer: (B) s. 5591
Question: Teams A, B, C and D were in a baseball tournament. Each team played each other team once. Team A beat team D. Teams A, B and C won the exact same number of games. How many games did team D lose?
(A) 2
(B) 3
(C) 4
(D) 6
(E) 7
Rationale: There are 4 teams and each team played each other team once. That tells us 2 facts:
 Each team played 3 games
 4 teams played a total of 6 games.
Since there are only 6 games, only 6 total wins are possible. Since A, B and C won the exact same number of games, they either all won 1 game or all won 2 games. Let’s examine both scenarios:
Scenario #1: A, B and C each won 1 game. In this scenario, D must have won all 3 games it played. That contradicts with the fact that A beat D. So, scenario 1 is not possible. So, it has to be scenario #2.
Scenario #2: A, B and C each 2 games. In this scenario, D won 0 games. That means D lost all 3 games it played.
correct answer B
Answer: (B) 3
Question: V is the volume of a cylinder; the radius r is 3.4. The height is 350% more than the radius. Which of the following is true?
(A) 100 < V < 300
(B) 300 < V < 500
(C) 500 < V < 700
(D) 700 < V < 900
(E) 900 < V < 1100
Rationale: As we see the answers are in form of range we can use approximation
Volume of cylinder is πr^2h
Given π= 22/7 and r = 3.4 so r^2 ~ 12 and h = 4.5 * 3.4 ~ 15
So 22/7 * 12 * 15 = 566
so answer should be
C. 500 < V < 700
Answer : C
Answer: (C) 500 < V < 700
Question: The average of 55 results is 28 and the average of other 28 results is 55 . what is the average of all the results?
(A) 37
(B) 25
(C) 48
(D) 50
(E) None
Rationale: Answer
Sum of 83 result = sum of 55 result + sum of 28 result.
= 30 x 20 + 20 x 30
= 3080
Correct Option: A
Answer: (A) 37
Question: A certain company’s profit in 1996 was 15 percent greater than its profit in 1995, and its profit in 1997 was 35 percent greater than its profit in 1996. The company’s profit in 1997 was what percent greater than its profit in 1995?
(A) 5%
(B) 18%
(C) 33%
(D) 35%
(E) 55.25%
Rationale: Profit in 1995 - 100
Profit in 1996 - 115
%increae Profit in 1997 in comparison to 1995 = 15 + 115*35%= 55.25
Correct Option : E
Answer: (E) 55.25%
Question: A and B walk around a circular track. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. If they start at 8 a.m. from the same point in opposite directions, how many times shall they cross each other before 9.30 a.m.?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 23
Rationale: Relative speed = Speed of A + Speed of B (? they walk in opposite directions)
= 2 + 3 = 5 rounds per hour
=> They cross each other 5 times in 1 hour and 2 times in 1/2 hour
Time duration from 8 am to 9.30 am = 1.5 hour
Hence they cross each other 7 times before 9.30 am
Answer is C
Answer: (C) 7
Question: In one hour, a boat goes 13 km/hr along the stream and 9 km/hr against the stream. The speed of the boat in still water (in km/hr) is:
(A) 11 kmph
(B) 13 kmph
(C) 14 kmph
(D) 15 kmph
(E) 16 kmph
Rationale: Explanation:
Let the speed downstream be a km/hr and the speed upstream be b km/hr, then
Speed in still water =1/2(a+b) km/hr
Rate of stream = 1/2(a−b) km/hr
Speed in still water = 1/2(13+9) kmph = 11 kmph.
Answer: Option A
Answer: (A) 11 kmph
Question: If A and B get profits of Rs.6,000 and Rs.4,000 respectively at the end of year then ratio of their investments are
(A) 4:1
(B) 1:4
(C) 3:2
(D) 2:3
(E) 2:5
Rationale: suppose a and b is ratio of investment. so a:b=6000+4000
a:b=10000
a/(a+b)*10000=6000
2a=3b
a/b=3/2
i.e 3:2
ANSWER:C
Answer: (C) 3:2
Question: The area of a parallelogram is 162sq m and its altitude is twice the corresponding base. Then the length of the base is?
(A) 8
(B) 9
(C) 7
(D) 6
(E) 5
Rationale: 2x * x = 162 => x= 9
Answer: B
Answer: (B) 9
Question: A can run 224 metre in 28 seconds and B in 32 seconds. By what distance A beat B?
(A) 38 metre
(B) 28 metre
(C) 23 metre
(D) 15 metre
(E) 28 metre
Rationale: Clearly, A beats B by 4 seconds
Now find out how much B will run in these 4 seconds
Speed of B = Distance/Time taken by B=224/32=28/4=7 m/sDistance covered by B in 4 seconds = Speed × time =7×4=28 metre
i.e., A beat B by 28 metre
Answer is B
Answer: (B) 28 metre
Question: In a 500 m race, the ratio of the speeds of two contestants A and B is 3 : 4. A has a start of 140 m. Then, A wins by:
(A) 60 m
(B) 40 m
(C) 20 m
(D) 10 m
(E) 30 m
Rationale: To reach the winning post A will have to cover a distance of (500 - 140)m, i.e., 360 m.
While A covers 3 m, B covers 4 m.
While A covers 360 m, B covers	4/3	x 360	m	= 480 m.
Thus, when A reaches the winning post, B covers 480 m and therefore remains 20 m behind.
A wins by 20 m. ANSWER:C
Answer: (C) 20 m
Question: Difference of two numbers is 1660. If 7.5% of the number is 12.5% of the other number, find the number ?
(A) 1660
(B) 2500
(C) 3250
(D) 4150
(E) 5250
Rationale: Let the numbers be x and y. Then , 7.5 % of x =12.5% of y
X = 125*y/75 = 5*y/3.
Now, x-y =1660
5*y/3 –y =1660
2*y/3= 1660
y =[ (1660*3)/2] =2490.
One number = 2490, Second number =5*y/3 =4150.
Answer Option D) 4150.
Answer: (D) 4150
Question: A can do a piece of work in 12 days. When he had worked for 2 days B joins him. If the complete work was finished in 8 days. In how many days B alone can finish the work?
(A) 15 days
(B) 25 days
(C) 18 days
(D) 20 days
(E) 21 days
Rationale: Explanation:
8/12 + 6/x = 1
X = Explanation:
8/12 + 6/x = 1
X = 18 days
Answer C
Answer: (C) 18 days
Question: Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is
(A) 100 gallons
(B) 110 gallons
(C) 120 gallons
(D) 130 gallons
(E) 140 gallons
Rationale: Work done by the waste pipe in 1 minute = 1/15-(1/20+1/24)
= -1/40[-ve means emptying]
so, volume of 1/40 part =3 gallons
volume of whole = 3*40=120 gallons
ANSWER:C
Answer: (C) 120 gallons
Question: A company bought for its 8 offices 2 computers of brand N and 3 computers of brand M. In how many ways could computers be distributed among the offices if each office can have only 1 computer.
(A) 196
(B) 210
(C) 256
(D) 292
(E) 560
Rationale: This problem has to do withcombinations. Here's the general idea: if you have a set of n elements, and you are going to choose r of them (r < n), then the number of combinations of size r one could choose from this total set of n is:
# of combinations = nCr = (n!)/[(r!)((n-r)!)]
where n! is the factorial symbol, which means the product of every integer from n down to 1. BTW, nCr is readn choose r.
In this problem, let's consider first the three computers of brand M. How many ways can three computer be distributed to seven offices?
# of combinations = 8C3 = 56
There are 56 different ways to distribute three computers to 8 offices. (The massive amount of cancelling that occurred there is very much typical of what happens in the nCr formula.)
One we have distributed those three M computers, we have to distribute 2 N computers to the remaining four offices. How many ways can two computer be distributed to four offices?
# of combinations = 5C2 = 10
For each of the 56 configurations of distributing the M computers, we have 10 ways of distributing the N computers to the remaining offices. Thus, the total number of configurations is 56 * 10 = 560. Answer choice = E
Answer: (E) 560
Question: A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length?
(A) 39
(B) 27
(C) 40
(D) 88
(E) 21
Rationale: Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
= 500 * (2/25) = 40 seconds
Answer: C
Answer: (C) 40
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 40 percent ?
(A) 400
(B) 160
(C) 112
(D) 80
(E) 56
Rationale: Original (Long-Term is 70%)
Total = 800
Long-Term = .7(800) = 560
New (Long-Term is 40%)
New Total = 800 - y
New Long-Term = 560 - y
560 - y = .4 (800 - y)
y = 400
Answer: A
Answer: (A) 400
Question: 20% of an 30% salt solution is replaced with water. From the resulting solution, again 20% is replaced with water. This step is repeated once more. What is the concentration of salt in the final solution obtained
(A) 19.58%
(B) 15.36%
(C) 20%
(D) 9.72%
(E) 11.64%
Rationale: A quick answer: (30)(0.8)(0.8)(0.8)
Imagine you have 100 ml of 30% salt solution.
In step 1, 20% of the salt solution is replaced with water. This means 80% of the original salt quantity remains. Hence the resultant concentration is (30)(0.8)
This process is repeated for step 2 and three. Hence, we multiply 30 ml two more times with 0.8.
This gives the final concentration as 30x0.8x0.8x0.8 = 15.36%
Answer: B
Answer: (B) 15.36%
Question: The difference between the simple interest received from two different sources on 1500 for 3 years is 13.50. The difference between their rates of interest is:
(A) 0.1%
(B) 0.2%
(C) 0.3%
(D) 0.4%
(E) None of these
Rationale: (1500×R1×3/100)−(1500×R2×3100)=13.50
⇒ 4500(R1 - R2) = 1350 ⇒ R1 - R2 = 1350⁄4500 = 0.3%
Answer C
Answer: (C) 0.3%
Question: A team of 8 students goes on an excursion, in two cars, of which one can seat 5 and the other only 4. In how many ways can they travel?
(A) 392
(B) 126
(C) 26
(D) 9
(E) 8
Rationale: Solution:
There are 8 students and the maximum capacity of the cars together is 9.
We may divide the 8 students as follows:
Case I:
5 students in the first car and 3 in the second.
Hence, 8 students are divided into groups of 5 and 3 in 8C3 = 56 ways.
Case II:
4 students in the first car and 4 in the second.
So, 8 students are divided into two groups of 4 and 4 in 8C4 = 78 ways.
Therefore, the total number of ways in which 8 students can travel is:
56 +70 = 126
Answer: Option B
Answer: (B) 126
Question: (228% of 1265) ÷ 6 = ?
(A) A)125
(B) B)175
(C) C)481
(D) D)375
(E) E)524
Rationale: Explanation :
? = (228 x 1265/100) ÷ 6 = 288420/600 = 481
Answer : Option C
Answer: (C) C)481
Question: While flying over the Pacific, an airplane makes a 25° turn to the right to avoid a storm. If, as a result, the airplane is traveling in a direction 9° east of north, in what direction was it originally flying?
(A) (a) 30° west of north
(B) (b) 30° east of north
(C) (c) 16° west of north
(D) (d) 16° east of north
(E) (e) 5° west of north
Rationale: If after a turn of 25° you are 9°NEast, with a 16° turn you would be perfectly pointing at north. So you were, before the turn, 16° to the other side (West).
Answer C)
Answer: (C) (c) 16° west of north
Question: If a Poultry firm sells 15 of his chickens, his stock of feed will last for 4 more days than planned, but if he buys 20 more chickens, he will run out of feed 3 days earlier than planned. If no chickens are sold or bought, the farmer will be exactly on schedule. How many chickens does the farmer have?
(A) 100
(B) 90
(C) 80
(D) 70
(E) 60
Rationale: Let x = total feed required for the planned period
n= number of chicken
t = total time of the planned feed
x = nt
1) x = (n-15) * (t+4)
2) x = (n+20) * (t-3)
equating 12
(n-15) * (t+4) = (n+20) * (t-3)
7n = 35t
n =5t
x= n * n/5
substituting this value in 1
n * n/5 = (n-15) * (n/5+4)
5n = 300
n =60
E
Answer: (E) 60
Question: John left home and drove at the rate of 45 mph for 2 hours. He stopped for lunch then drove for another 3 hours at the rate of 55 mph to reach his destination. How many miles did John drive?
(A) 250 miles
(B) 255 miles
(C) 258 miles
(D) 265 miles
(E) 245 miles
Rationale: 2*45=90;
3*55=165;
90+165=255 miles
ANSWER:B
Answer: (B) 255 miles
Question: The total price of a basic computer and printer are $2,500. If the same printer had been purchased with an enhanced computer whose price was $500 more than the price of the basic computer, then the price of the printer would have been 1/8 of that total. What was the price of the basic computer?
(A) 1500
(B) 1600
(C) 1750
(D) 1900
(E) 2125
Rationale: Let the price of basic computer be C and the price of the printer be P: C+P=$2,500.
The price of the enhanced computer will be C+500 and total price for that computer and the printer will be 2,500+500=$3,000. Now, we are told that the price of the printer is 1/8 of that new total price: P=1/8*$3,000=$375.
Plug this value in the first equation: C+375=$2,500 --> C=$2,125.
Answer: E.
Answer: (E) 2125
Question: Two trains, each 100 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is?
(A) 22
(B) 77
(C) 60
(D) 88
(E) 12
Rationale: Let the speed of the slower train be x m/sec.
Then, speed of the train = 2x m/sec.
Relative speed = ( x + 2x) = 3x m/sec.
(100 + 100)/8 = 3x => x = 25/3.
So, speed of the faster train = 50/3 = 50/3 * 18/5 = 60 km/hr.
Answer:C
Answer: (C) 60
Question: Seed mixture X is 40 percent ryegrass and 60 percent bluegrass by weight; seed mixture Y is 25 percent ryegrass and 75 percent fescue. If a mixture of X and Y contains 40 percent ryegrass, what percent of the weight of this mixture is X ?
(A)  100%
(B)  33.33 %
(C)  40%
(D)  50%
(E)  66.66 %
Rationale: ---------------->Ryegrass
X-------------->	40%
Y-------------->	25%
M(mixture)---->40%
0.4X + (M-X)0.25 = 0.4M
0.15X = 0.15M
X = 1M
X = 100% of M
A
Answer: (A)  100%
Question: A 180 meter long train crosses a man standing on the platform in 6 sec. What is the speed of the train?
(A) 176 kmph
(B) 108 kmph
(C) 176 kmph
(D) 134 kmph
(E) 161 kmph
Rationale: S = 180/6 * 18/5
= 108 kmph
Answer: B
Answer: (B) 108 kmph
Question: If @ is a binary operation defined as the difference between an integer n and the product of n and 5, then what is the largest positive integer n such that the outcome of the binary operation of n is less than 18?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: @(n) = 5n - n
We need to find the largest positive integer such that 5n - n < 18.
Then 4n < 18 and n < 4.5
The largest possible integer is n = 4.
The answer is D.
Answer: (D) 4
Question: In a urban village of india named "owlna" , 75% people have refrigerator , 90% people have television , 85% people got computers and 75% got Air-conditionor. how many people(minimum) got all these luxury.
(A) 23%
(B) 17%
(C) 11%
(D) 10%
(E) 25%
Rationale: E
10%
100 - [ (100-75)+(100-90)+(100-85) +(100-75)]
=100-(25+10+15+25)
=100-75
Answer: (E) 25%
Question: Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 15 sec. What is the length of the fast train?
(A) 83 7/6 m
(B) 83 7/4 m
(C) 83 7/2 m
(D) 83 1/3 m
(E) 83 7/7 m
Rationale: Relative speed = (40 - 20) = 20 km/hr.
= 20 * 5/ 18 = 50/9 m/sec.
Length of faster train = 50/9 * 15 = 750/9 = 83 1/3 m.Answer:D
Answer: (D) 83 1/3 m
Question: A corporation double its annual bonus to 100 of its employees. What percent of the employees’ new bonus is the increase?
(A) 50%
(B) 12%
(C) 8%
(D) 6%
(E) 5%
Rationale: Let the annual bonus be X.
A corporation double its annual bonus.
So new bonus = 2X.
Increase = 2X-X =X
The increase is what percent of the employees’ new bonus
= (X/2X)*100
= 50%
Hence A.
Answer: (A) 50%
Question: i row from a to b against the current in 8 hrs and from b to a in 2 hrs if speed of river is 9 m/sec.what is the speed of boat in still water.
(A) 10 m/sec
(B) 15 m/sec
(C) 25 m/sec
(D) 18 m/sec
(E) 20 m/sec
Rationale: If x m/sec is my speed in still water , then
(x+9)*2*3600= (x-9)*8*3600
6x=90
x= 15 m/sec
ANSWER:B
Answer: (B) 15 m/sec
Question: Danny is sitting on a rectangular box. The area of the front face of the box is half the area of the top face, and the area of the top face is 1.5 times the area of the side face. If the volume of the box is 5184, what is the area of the side face of the box?
(A) 123
(B) 167
(C) 178
(D) 199
(E) 288
Rationale: Lets suppose length= l, breadth= b, depth= d
Front face area= l*w = 1/2 w*d (l=1/2 d or d=2l)
top face area= w*d
side face area= w*d = 1.5 d*l (w=1.5l)
Volume = l*w*d= 5184
l*1.5l*2l= 5184
l=12
Side face area= l*d= l*2l= 12*2*12=288
E is the answer
Answer: (E) 288