mathewhe/aqua_rat huggingface dataset:
Question: When p is divided by W, the remainder is 4. All of the following are possible values of W, except for which of the following?
(A) 13
(B) 31
(C) 49
(D) 57
(E) 67
Rationale: The number can be expressed in the form of 9x+4 where x can 0,1,2,3,4....
by evaluating the answer choices carefully we can clearly observe that 57 is the only number which can't be W expressed in the form of 9x+4
In other words we can also say that the (answer - 4) will not be divisible by 9.57 is the number which doesn't follow this condition
Correct Answer - D
Answer: (D) 57
Question: There arr 4 prime numbers in ascending order. The multiplication of 1st 3 is 385 and that of last 3is 1001. what is the last number is
(A) 8
(B) 10
(C) 12
(D) 13
(E) 15
Rationale: Explanation:
abcbcd=3851001=>ad=513
abcbcd=3851001=>ad=513
So d = 13
D
Answer: (D) 13
Question: If n is an integer, then the least possible value of |33 - 5n| is?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: |33 - 5n| represents the distance between 33 and 5n on the number line. Now, the distance will be minimized when 5n, which is multiple of 5, is closest to 33. Multiple of 5 which is closest to 33 is 35 (for n = 7), so the least distance is 2: |33 - 35| = 2.
Answer: C.
Answer: (C) 2
Question: An error 2% in excess is made while measuring the side ofa square. The % of error in the calculated area of the square is?
(A) 4.14%
(B) 4.04%
(C) 4.23%
(D) 4.67%
(E) 4.89%
Rationale: 100 cm is read as 102 cm.
A1 = (100 x 100) cm2 and A2 (102 x 102) cm2.
(A2 - A1) = [(102)2 - (100)2]
= (102 + 100) x (102 - 100)
= 404 cm2.
Percentage error = 404 x 100 % = 4.04%
100 x 100
B
Answer: (B) 4.04%
Question: A single discount equivalent to the discount series of 25%, 20% and 15% is?
(A) 31.8
(B) 31.1
(C) 31.6
(D) 49
(E) 31.9
Rationale: Explanation:
100*(75/100)*(80/100)*(85/100) = 51
100 - 51 = 49
Answer: D
Answer: (D) 49
Question: In a certain archery competition, points were awarded as follows: the first place winner receives 11 points, the second place winner receives 7 points, the third place winner receives 5 points and the fourth place winner receives 2 points. No other points are awarded. John participated several times in the competition and finished first, second, third, or fourth each time. The product of all the points he received was 15400. How many times did he participate in the competition?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: 15400 = 2*2*2*5*5*7*11
John participated 7 times.
The answer is C.
Answer: (C) 7
Question: How many different 9 digit numbers can be formed from the number 223355888 by re-arranging its digits so that the odd digits occupy even position?
(A) 22
(B) 776
(C) 26
(D) 28
(E) 60
Rationale: Odd places are 4 and these are occupied by 3355. So this can be done in 4!/ (2! 2!) = 6
There are 5 even numbers which have to be placed at 5 odd places. So 5!/(2!3!) = 10 ways
so total number of ways of arranging all these numbers are 10 * 6 = 60 ways
Answer:E
Answer: (E) 60
Question: The mass of the sun is approximately 4 × 10^30 kg and the mass of the moon is approximately 8 × 10^12 kg. The mass of the sun is approximately how many times the mass of the moon?
(A) 4.0 × 10^(−18)
(B) 2.5 × 10^17
(C) 5 × 10^17
(D) 2.5 × 10^19
(E) 4.0 × 10^42
Rationale: Mass of sun = x * Mass of moon
x = Mass of sun / Mass of moon = (4 × 10^30) / (8 × 10^12) = 2^2*2^-3*10^18 = 10^18/2= 5*10^17
Ans. C) 2.5 × 10^17
Answer: (C) 5 × 10^17
Question: One train is traveling 45 kmph and other is at 10 meters a second. Ratio of the speed of the two trains is?
(A) 5:4
(B) 9:4
(C) 5:6
(D) 5:0
(E) 2:4
Rationale: Explanation:
45 * 5/18 = 10
25:20 => 5:4
Answer: Option A
Answer: (A) 5:4
Question: The scoring system in a certain football competition goes as follows: 3 points for victory, 1 point for a draw, and 0 points for defeat. Each team plays 20 matches. If a team scored 14 points after 5 games, what is the least number of the remaining matches it has to win to reach the 40-point mark by the end of the tournament?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: To get 40 points as end of season we need another 26 points or more from remaining 15 matches:
Option A= 6*3+9*1=27
hence option A-6
Answer: (A) 6
Question: y = x^2 + bx +64 cuts the x axis at (h, 0) and (k, 0). If h and k are integers, what is the least value of b?
(A) -65
(B) -64
(C) -32
(D) 32
(E) 64
Rationale: As the curve cuts the x-axis at (h,0) and (k,0). Therefore h,k are the roots of the quadratic equation.
For the quadratic equation is in the form ofax^2+bx+c=0,
The product of the roots =c/a= 64/1=256 and the sum of the roots =-b/a=-b
64 can be expressed as product of two numbers in the following ways:
1 * 64
2 * 32
4 * 16
The sum of the roots is maximum when the roots are 1 and 64 and the maximum sum is 1 + 64 = 65.
The least value possible for b is therefore -65.
B
Answer: (B) -64
Question: In a covering a certain distance, the speeds of A and B are in the ratio of 3:4. A takes 30 minutes more than B to reach the destination. The time taken by A to reach the destination is?
(A) 32 hrs
(B) 8 hrs
(C) 2 hrs
(D) 6 hrs
(E) 7 hrs
Rationale: Ratio of speeds = 3:4
Ratio of times taken = 4:3
Suppose A takes 4x hrs and B takes 3x hrs to reach the destination.
Then, 4x - 3x = 30/60 => x = 1/2
Time taken by A = 4x hrs = 4 * 1/2 = 2 hrs.
Answer: C
Answer: (C) 2 hrs
Question: A board of length L feet is cut into two pieces such that the length of piece A is 4 feet less than twice the length of piece B. Which of the following is the length, in feet, of piece A?
(A) (L - 4)/3
(B) (2L + 4)/3
(C) (L + 4)/3
(D) (2L + 2)/3
(E) (2L - 4)/3
Rationale: A+B = L so we know that B = L - A.
A = 2B-4
A = 2(L-A) - 4
3A = 2L - 4
A = (2L-4) / 3
The answer is E.
Answer: (E) (2L - 4)/3
Question: A license plate in the country Kerrania consists of four digits followed by two letters. The letters A, B, and C are used only by government vehicles while the letters D through Z are used by non-government vehicles. Kerrania's intelligence agency has recently captured a message from the country Gonzalia indicating that an electronic transmitter has been installed in a Kerrania government vehicle with a license plate starting with 79. If it takes the police 60 minutes to inspect each vehicle, what is the probability that the police will find the transmitter within three hours?
(A) 18/79
(B) 1/6
(C) 1/300
(D) 1/50
(E) 1/900
Rationale: So there are 900 cars that they have to search.. Each takes 60mins, total of 54000 mins.. Have to find in 180 mins.. Prob180/54000 = 1/300 (ANSWER C)
Answer: (C) 1/300
Question: Shekar scored 76, 65, 82, 67 and 95 marks in Mathematics, Science, Social studies, English and Biology respectively. What are his average marks?
(A) 65
(B) 77
(C) 75
(D) 85
(E) 90
Rationale: Explanation :
Average= (76+65+82+67+95)/5 = 385/5 =77
Hence average=77
Answer : B
Answer: (B) 77
Question: On average, Machine A will produce a completed item once every three minutes, and Machine B will produce a completed item once every thirteen minutes. The number of items Machine A produces in a 24-hour period is approximately what percent greater than the number of items Machine B would produce in that same period?
(A) 500%
(B) 133%
(C) 100%
(D) 166%
(E) 333%
Rationale: Machine A: 1 item in 3 minutes --> 1/3 items in 1 minute;
Machine B: 1 item in 13 minutes --> 1/13 items in 1 minute.
In the same time period, Machine A produces (1/3-1/13)/(1/13)*100=~133% more items than machine B.
Answer: E.
Answer: (E) 333%
Question: The sum of the numbers is 330. 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) 84
(E) 90
Rationale: Let the second number be x. Then, first number = 2x and third number = 2x/3.
2x + x + 2x/3 = 330
11x/3 = 330
x = 90
ANSWER:E
Answer: (E) 90
Question: In a house, there are dogs, cats and parrot in the ratio 3:7:5. If the number of cats was more than the number of dogs by a multiple of both 9 and 7. What is the minimum number of pets in the house?
(A) 945
(B) 630
(C) 252
(D) 238
(E) None of these
Rationale: Explanation :
Let, the number of Dogs, Cat and Parrots be 3k, 7k and 5k respectively.
Then, According to the question,
=>7k−3k=63p. (where p is any positive integer).
As the number is a multiple of both 9 and 7, it has to be multiple of 63.
=>k=63p/4.
Minimum value of p for which k is a natural number is 4.
Thus, k=63.
Hence, the number of pets are (63x5) + (63x3) + (63x7) i.e 315 +189+ 441= 945.
Answer : A
Answer: (A) 945
Question: A certain bakery has 6 employees. It pays annual salaries of $14,000 to each of 2 employees, $16,000 to 1 employee, and $17,000 to each of the remaining 3 employees. The average (arithmetic mean) annual salary of these employees is closest to which of the following?
(A) $15,200
(B) $15,500
(C) $15,800
(D) $16,000
(E) $16,400
Rationale: Let the salary for each person be 14. Thus, the bakery ends up getting 2 + 3*3 = 11 as extra. This again has to be divided among 6 people. 12/6 = 2 which makes it 14+2 =16. Thus, as it is 11/6, it will be somewhere close to 16 and less than that. Also, 1/6 = 0.166. Thus 10/6 = 1.66 which gives the final salary after redistribution as 15.66. Correct answer is C.
_________________
Answer: (C) $15,800
Question: One water pump can fill half of a certain empty tank in 4 hours. Another pump can fill half of the same tank in 4.5 hours. Working together, how long will it take these two pumps to fill the entire tank?
(A) 1 7/13
(B) 4 5/8
(C) 3 1/4
(D) 4 4/17
(E) 3 1/2
Rationale: One pump can fill a tank in 4 hours and another in 4.5 hours
so the rate at which both can half fill the tank is (1/4+1/4.5) => 17/36
Thus half of the tank can be filled in 36/17
so for filling the complete tank => 36/17*2 = 72/17 =4 4/17
ANSWER:D
Answer: (D) 4 4/17
Question: Two numbers are less than third number by 35% and 37% respectively. How much percent is the second number less than by the first
(A) 8%
(B) 10%
(C) 33%
(D) 41%
(E) 42%
Rationale: Let the third number is x.
then first number = (100-35)% of x
= 65% of x =65x/100
Second number is (63x/100)
Difference =65x/100 - 63x/100 = x/50
So required percentage is, difference is what percent of first number
(x/50 * 100/65x * 100 )% = 33% ANSWER :C
Answer: (C) 33%
Question: Which of the following is closest to the difference between sum of all proper fractions (fractions less than 1) in the form 1/x , where x is a positive digit, and the product of all proper fractions in the form y/(y+1), where y is a positive digit?
(A) 2.82
(B) 2.72
(C) 1.82
(D) 1.72
(E) 0.82
Rationale: First term = 1/2 +1/3 +1/4 +1/5 +1/6 +1/7 +1/8 + 1/9
Second term = 1/2 * 2/3 * 3/4 * 4/5 * 5/6 * 6/7 * 7/8 * 8/9 * 9/10 = 1/10
First term - Second term = 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 +1/8 + 1/9 - 1/10
Now rearrange the above equation for simplification:
= (1/2 + 1/5 - 1/10) +( 1/3 + 1/6 + 1/9) + (1/4 + +1/8) +1/7
= 6/10 + 11/18 + 3/8 +1/7
6/10 , 11/18, 3/8 are approximately equal to 0.5
=0.5+0.5+0.5+0.14 = 1.64
The closest answer choice is D
Answer: (D) 1.72
Question: What annual instalment will discharge a debt of Rs 1092 due in 3 years at 12% simple interest?
(A) Rs.325
(B) Rs.545
(C) Rs.560
(D) Rs.550
(E) None of these
Rationale: Explanation:
Let each instalment be Rs.x .
Then, [x + (x × 12 × 1)/100] + [ x + (x × 12 × 2)/100] + x =1092
( 28x/25 ) + ( 31x/25 ) + x = 1092
(28x + 31x + 25x) = (1092 * 25)
x = (1092 × 25)/84= 325
∴ Each instalment = Rs. 325
Answer: A
Answer: (A) Rs.325
Question: Each of the dogs in a certain kennel is a single color. Each of the dogs in the kennel either has long fur or does not. Of the 45 dogs in the kennel, 29 have long fur, 17 are brown, and 8 are neither long-furred nor brown. How many long-furred dogs are brown?
(A) 26
(B) 19
(C) 11
(D) 8
(E) 9
Rationale: No of dogs=45
Long fur=29
Brown=17
Neither long fur nor brown=8
Therefore, either long fur or brown=45-8=37
37=29+17-Both
Both=9
Answer E
Answer: (E) 9
Question: A no. when divided by the sum of 555 and 445 gives 2times their difference as quotient & 30 as remainder. Find the no. is?
(A) 234354
(B) 243435
(C) 243445
(D) 245667
(E) 220030
Rationale: (555 + 445) * 2 * 110 + 30 = 220000 + 30 = 220030
E
Answer: (E) 220030
Question: If (64)2 - (36)2 = 20 x a, then a = ?
(A) 70
(B) 120
(C) 180
(D) 140
(E) 130
Rationale: 20 x a = (64 + 36)(64 - 36) = 100 x 28
a = (100 x 28)/20 = 140
ANSWER:D
Answer: (D) 140
Question: The length of a rope, to which a cow is tied, is increased from 19 m to 30 m. How much additional ground will it be able to graze? Assume that the cow is able to move on all sides with equal ease. Use π = \\frac{22}{7}\\) in your calculations.
(A) 1696 sq m
(B) 1694 sq m
(C) 1594 sq m
(D) 1756 sq.m
(E) 1896 sq.m
Rationale: Explanatory Answer
The cow can graze the area covered by the circle of radius 19m initially, as the length of the rope is 19m.
Area of a circle = π * (radius)2
Therefore, the initial area that the cow can graze = 22/7 * 19(2) sq m.
When the length of the rope is increased to 30m, grazing area becomes = 22/7 * 30(2) sq m.
The additional area it could graze when length is increased from 19m to 30m
= 22/7 * (30square - 19square) sq m.
22/7 * (30 + 19)(30 - 19) = 22/7 * 49 * 11 = 1694 sq m.
Choice B
Answer: (B) 1694 sq m
Question: A producer of tea blends two varieties of tea from two tea gardens one costing Rs 18 per kg and another Rs 20 per kg in the ratio 5 : 3. If he sells the blended variety at Rs 20 per kg, then his gain percent is
(A) 7%
(B) 13%
(C) 14%
(D) 15%
(E) 16%
Rationale: Explanation:
Suppose he bought 5 kg and 3 kg of tea.
Cost Price = Rs. (5 x 18 + 3 x 20) = Rs. 150.
Selling price = Rs. (8 x 20) = Rs. 160.
Profit = 160 - 150 = 10
So, Profit % = (10/150) * 100 = 7%
Option A
Answer: (A) 7%
Question: If a man can cover 24 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?
(A) 118 km
(B) 162 km
(C) 324 km
(D) 1887 km
(E) 177 km
Rationale: 24 m/s = 24 * 18/5 kmph
3 hours 45 minutes = 3 3/4 hours = 15/4 hours
Distance = speed * time = 24 * 18/5 * 15/4 km = 324 km.
Answer: C
Answer: (C) 324 km
Question: If 7 cats can kill 7 rats in 7 minutes, how long will it take 100 cats to kill 100 rats?
(A) 5 minutes
(B) 6 minutes
(C) 7 minutes
(D) 8 minutes
(E) 9 minutes
Rationale: It will take 7 minutes for 100 cats to kill 100 rats.
1 cat can kill 1 rat in 7 minutes, so 100 cats can kill 100 rats in 7 minutes
Answer C
Answer: (C) 7 minutes
Question: An error 2% in excess is made while measuring the side ofa square. The % of error in the calculated area of the square is?
(A) 4%
(B) 4.04%
(C) 4.15%
(D) 4.34%
(E) 5%
Rationale: 100 cm is read as 102 cm.
A1 = (100 x 100) cm2 and A2 (102 x 102) cm2.
(A2 - A1) = [(102)2 - (100)2]
= (102 + 100) x (102 - 100)
= 404 cm2.
Percentage error = 404 x 100 % = 4.04%
100 x 100
B
Answer: (B) 4.04%
Question: A shopkeeper sold an article for Rs 2564.36. Approximately what was his profit percent if the cost price of the article was Rs 2300
(A) 4%
(B) 5%
(C) 6%
(D) 7%
(E) 12%
Rationale: Explanation:
Gain % = (264.36*100/2300) = 11.49 % = 12% approx
Option E
Answer: (E) 12%
Question: A train covers a distance of 12 km in 10 min. If it takes 11 sec to pass a telegraph post, then the length of the train is?
(A) 177 m
(B) 189 m
(C) 220 m
(D) 178 m
(E) 188 m
Rationale: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec
= 20 m/sec.
Length of the train = 20 * 11
= 220 m.
Answer: C
Answer: (C) 220 m
Question: What is the units digit of 17^73 × 13^82 × 11^87?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: To find : the units digit of 17^83 × 13^82 × 11^87
Let's reduce the clutter and simplify the product
(7^83) (3^82) (1^87)
7 has a cyclicity of 4 : the last digit of any positive power of 7 repeats itself after every 4th power
so 7^5 has the same last digit as 7^1, 7^9, 7^13
Thus , 7^83 has the same last digit as 7^3, 7^7, 7^11 i.e.3
3 has a cyclicity of 4 : exactly the same routine as above
Thus , 3^82 has the same last digit as 3^2, 3^6, 3^10 i.e.9
Any power of 1 will result in1as the last digit
So, product of our last digits = 3 x 9 x 1 = 27....last digit is 8
Correct Option : E
Answer: (E) 8
Question: A cricketer scored 152 runs which included 12 boundaries and 2 sixes. What percent of his total score did he make by running between the wickets.
(A) 46.2%
(B) 54.54 %
(C) 60.52%
(D) 70%
(E) None of these
Rationale: Explanation :
Number of runs made by running = 152 - (12 x 4 + 2 x 6)
= 152 - (60)
= 92
Now, we need to calculate 92 is what percent of 152.
=> 92/152 * 100 = 60.52 %
Answer : C
Answer: (C) 60.52%
Question: Michael is interested in dividing all of his boxed food equally among the shelves in his pantry. Unfortunately, the boxes don't divide evenly. It turns out that Michael will need to add three more shelves to the pantry and throw away four boxes of food. Which of the following can describe the initial number of boxes of food and the initial number of pantry shelves (in the order boxes of food; shelves)?
(A) 71; 4.
(B) 28; 6.
(C) 65; 7.
(D) 53; 4.
(E) 45; 6.
Rationale: Option D.) Initially 53 boxes of food then reduced to 49 boxes of food; and Initially 4 pantry shelves then increased to 7 pantry shelves.
49 / 7 = 7 boxes of food per pantry shelf.
Answer: (D) 53; 4.
Question: X and Y are two towns. Ganesh covers the distance from X to Y at an average speed of 44 Km/hr. However, he covers the distance from Y to X at an average speed of 36 Km/hr. His average speed during the whole journey in km/hr. is :
(A) 39.6
(B) 43
(C) 40
(D) 38
(E) 29
Rationale: Solution: Average speed = 2XY / X+Y
= 2*44*36 / 44+36
= 39.6
Answer : A
Answer: (A) 39.6
Question: If
1 = 6
2 = 12
3 = 18
4 = 24
5 = 30
6 = 36
Then 24 = ?
Hint: Its a logic Riddle not a mathematical riddle
(A) 1
(B) 2
(C) 4
(D) 6
(E) 8
Rationale: C
24
As stated
4=24 => 24=4
Answer is C
Answer: (C) 4
Question: What amount does Kiran get if he invests Rs.7680 at 8% p.a. compound interest for two years, compounding done annually?
(A) 8957
(B) 8978
(C) 7890
(D) 3408
(E) 2886
Rationale: A= P{1 + R/100}n
=> 7680{1 + 8/100}2
= Rs.8957
Answer: A
Answer: (A) 8957
Question: A pool which was 3/4 full to begin with, was filled at a constant rate for 5/3 hours until it was until it was 6/7 full. At this rate, how much time would it take to completely fill this pool if it was empty to begin with?
(A) 8 hrs 45 mins.
(B) 9 hrs.
(C) 9 hrs 30 mins.
(D) 11 hrs 40 mins.
(E) 15 hrs 33 mins
Rationale: The pool was 3/4 full initially.
In 5/3 hrs, it was filled to 6/7 of its capacity.
Therefore, in 5/3 hrs, 6/7 - 2/3 was the amount of volume filled.
So, 5/3 hrs = 6/7 - 3/4 = 3/28
Therefore, for filling the vessel from empty to full, you would require 5/3 * 28/3 = 35/4 = 15 Hrs 33 Mins.
Hence E
Answer: (E) 15 hrs 33 mins
Question: If n is a positive integer and the product of all integers from 1 to n, inclusive, is a multiple of 294, what is the least possible value of n?
(A) 8
(B) 10
(C) 12
(D) 14
(E) 16
Rationale: 294 = 2*3*7*7, so n must be at least 14.
The answer is D.
Answer: (D) 14
Question: If y = 30p, and p is prime, what is the greatest common factor of y and 20p, in terms of p?
(A) p
(B) 2p
(C) 5p
(D) 10p
(E) p^2
Rationale: y = 30p = 2*3*5*p
20p = 2^2*5*p
The greatest common factor of 30p and 20p is the product of all the common prime factors, using the lower power of repeated factors. The greatest common factor is 2*5*p = 10p
The answer is D.
Answer: (D) 10p
Question: If A`s salary is 20% less then B`s salary , by how much percent is B`s salary more than A`s ?
(A) 15%
(B) 41%
(C) 37%
(D) 25%
(E) 23%
Rationale: Required percentage = [(20*100)/(100-20)]%=25%.
Answer is D.
Answer: (D) 25%
Question: The average weight of a group of persons increased from 48 kg to 51 kg, when two persons weighing 78 kg and 93 kg join the group. Find the initial number of members in the group?
(A) 76
(B) 28
(C) 23
(D) 98
(E) 32
Rationale: Let the initial number of members in the group be n.
Initial total weight of all the members in the group = n(48)
From the data,
48n + 78 + 93 = 51(n + 2) => 51n - 48n = 69 => n = 23
Therefore there were 23 members in the group initially.
Answer:C
Answer: (C) 23
Question: 15 lts are taken of from a container full of liquid A and replaced with Liquid B. Again 15 more lts of the mixture is taken and replaced with liquid B. After this process, if the container contains Liquid A and B in the ratio 9:16,What is the capacity of the container M?
(A) A:45
(B) B:25
(C) C:37.5
(D) D:36
(E) E:42
Rationale: If you have a 37.5 liter capacity, you start with 37.5 L of A and 0 L of B.
1st Replacement
After the first replacement you have 37.5-15=22.5 L of A and 15 L of B. The key is figuring out how many liters of A and B, respectively, are contained in the next 15 liters of mixture to be removed.
The current ratio of A to total mixture is 22.5/37.5; expressed as a fraction this becomes (45/2) / (75/2), or 45/2 * 2/75. Canceling the 2s and factoring out a 5 leaves the ratio as 9/15. Note, no need to reduce further as we're trying to figure out the amount of A and B in 15 L of solution. 9/15 of A means there must be 6/15 of B.
Multiply each respective ratio by 15 to get 9 L of A and 6 L of B in the next 15L removal.
Final Replacement
The next 15L removal means 9 liters of A and 6 liters of B are removed and replaced with 15 liters of B. 22.5-9=13.5 liters of A. 15 liters of B - 6 liters + 15 more liters = 24 liters of B.
Test to the see if the final ratio = 9/16; 13.5/24 = (27/2) * (1/24) = 9/16. Choice C is correct.
Answer: (C) C:37.5
Question: A train 150 m long crosses a platform 130 m long in 20 sec; find the speed of the train?
(A) 50
(B) 60
(C) 55
(D) 45
(E) 53
Rationale: D = 150 + 130 = 280
T = 20
S = 280/20 * 18/5 = 50 kmph.
Answer: A
Answer: (A) 50
Question: If 5 - 5/X = 4 + 4/X, then X =
(A) 1
(B) 9
(C) -1
(D) 5/4
(E) -4/5
Rationale: We're given the equation 5 - 5/X = 4 + 4/X. We're asked for the value of X.
The common-denominator of these 4 numbers is X, so we need to multiply both sides of the equation by X, giving us...
5X - 5X/X = 4X + 4X/X
We can then eliminate that denominator, which gives us....
5X - 5 = 4X + 4
9 = X
B
Answer: (B) 9
Question: A dice is rolled twice. What is the probability of getting sum 9?
(A) 1/9
(B) 1/8
(C) 1/7
(D) 1/5
(E) 1/2
Rationale: Explanation:
Possible event = 6*6 = 36
Favourable outcomes= {(3, 6), {4, 5}, {5, 4}, (6, 3)}
Thus probability; favourable/total
= 4/36
=> 1/9
ANSWER: A
Answer: (A) 1/9
Question: A dishonest grocer professes to sell pure butter at cost price, but he mixes it with adulterated fat and thereby gains 25%. Find the percentage of adulterated fat in the mixture assuming that adulterated fat is freely available?
(A) 20%
(B) 25%
(C) 33.33%
(D) 40%
(E) 35%
Rationale: 100 * (b + f) - 100 * b = (25/100) * 100 * b
b = 4 * f
Percentage of f = (f / (b + f)) * 100 = (f/5f) * 100 = 20%
ANSWER:A
Answer: (A) 20%
Question: What number is obtained by adding the units digits of 734^98 and 347^81?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: The units digit of 734^98 is 6 because 4 raised to the power of an even integer ends in 6.
The units digit of 347^81 is 7 because powers of 7 end in 7, 9, 3 or 1 cyclically. Since 81 is in the form 4n+1, the units digit is 7.
Then 6+7 = 13.
The answer is D.
Answer: (D) 13
Question: If five boxes of fruit contain six different fruit in each box, and a fruit is randomly selected from each box, what is the probability of getting at least one pair of the same fruit?
(A) 31/32
(B) 4/9
(C) 1/2
(D) 5/49
(E) 49/54
Rationale: AT LEAST one pair of matching fruit.
First solve for NO matching fruit:
1st box = any fruit = 6/6
2nd box = not a match to the first = 5/6
3rd box = not a match to the 1st or 2nd = 4/6
4th box = not a match to the 1st, 2nd or 3rd = 3/6
5th box = not a match to the 1st, 2nd, 3rd or 4th = 2/6
(6/6)(5/6)(4/6)(3/6)(2/6) =
(1)(5/6)(2/3)(1/2)(1/3) = 60/648
5/54
5/54 is the probability of NO matching fruit, so...
1 - 5/54 = 49/54 = the probability of getting at least one matching pair of fruit.
Answer: E
Answer: (E) 49/54
Question: If c is 25% of a and 50% of b, what percent of a is b?
(A)  2.5%
(B)  50%
(C)  25%
(D)  35%
(E)  250%
Rationale: Answer = B
25a/100 = 50b/100
b = 25a/50 = 50a/100 =50%
Answer: (B)  50%