mathewhe/aqua_rat huggingface dataset:
Question: Two brothers were expected to return here on the same day. Rajat returned 3 days earlier but Rohit returned 4 days later. If Rajat returned on Wednesday, what was the expected day when both the brothers were to return home and when did Rohit Return?
(A) Wednesday, Sunday
(B) Thursday, Monday
(C) Saturday, Wednesday
(D) Monday, Friday
(E) none
Rationale: Rajat returned on Wednesday -i.e. 3 days earlier
so actual day to return home is Saturday.
Rohit returned after days so Wednesday.
ANSWER:C
Answer: (C) Saturday, Wednesday
Question: A is twice as good a work man as B and together they finish the work in 14 days. In how many days A alone can finish the work?
(A) 12
(B) 21
(C) 77
(D) 99
(E) 22
Rationale: WC = 2:1
2x + x = 1/14 => x = 1/42
2x = 1/21
A can do the work in 21 days.
Answer:B
Answer: (B) 21
Question: Total value of the quantity sold for item C is what per cent of the total value of the quantity sold for Item E?
(A) 30
(B) 60
(C) 100
(D) 80
(E) 90
Rationale: E
90
Total value of the quantity sold for item C = Rs(45 × 7.5 × 100)
= Rs 33750
Total value of the quantity sold for item E = Rs(15 × 25 × 100) = Rs 37500
∴ Required percentage = 33750/37500X 100 = 90
Answer: (E) 90
Question: P can do a work in 12 days. Q can do the same work in 9 days and R can do the same in 12 days. Q and R start the work and leave after 3 days. P finishes the remaining work in --- days.
(A) 5
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: Work done by P in 1 day = 1/24
Work done by Q in 1 day = 1/9
Work done by R in 1 day = 1/12
Work done by Q and R in 1 day = 1/9 + 1/12 = 7/36
Work done by Q and R in 3 days = 3Ã—7/36 = 7/12
Remaining work = 1 â€“ 7/12 = 5/12
Number of days in which P can finish the remaining work = (5/12) / (1/12) = 5
Option A
Answer: (A) 5
Question: If m and n are positive integers and m^2 + n^2 = 58, what is the value of m^3 + n^3?
(A) 72
(B) 224
(C) 370
(D) 512
(E) 1,600
Rationale: You need to integers which squared are equal 58.
Which could it be ? Let's start with the first integer:
1^2 = 1
2^2 = 4
3^2 = 9
4^2 = 16
5^2 = 25
6^2 = 36
7^2 = 49
Stop. The integers can't be greater than 7 or we will score above 58.
The second integer need to be picked up the same way.
1^2 = 1
2^2 = 4
3^2 = 9
4^2 = 16
5^2 = 25
6^2 = 36
7^2 = 49
The only pair that matches is 7^2 + 3^2 = 58.
So 7^3 + 3^3 = 370.
Answer C.)
Answer: (C) 370
Question: A man can row downstream at 28 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively?
(A) 2, 9
(B) 4, 9
(C) 8, 9
(D) 19, 9
(E) 7, 9
Rationale: Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.
Given x + y = 28 --- (1)
and x - y = 10 --- (2)
From (1) & (2) 2x = 38 => x = 19, y = 9.
Answer:D
Answer: (D) 19, 9
Question: Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 15 cm?
(A) 272 cm
(B) 786 cm
(C) 285 cm
(D) 186 cm
(E) 179 cm
Rationale: Area of a trapezium
= 1/2 (sum of parallel sides) * (perpendicular distance between them)
= 1/2 (20 + 18) * (15)
= 285 cm
Answer: C
Answer: (C) 285 cm
Question: A man has Rs. 640 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
(A) 33
(B) 38
(C) 37
(D) 120
(E) 28
Rationale: Let number of notes of each denomination be x.
Then x + 5x + 10x = 640
⇒ 16x = 640
∴ x = 40.
Hence, total number of notes = 3x = 120
Answer:D
Answer: (D) 120
Question: The owner of a furniture shop charges his customer 25% more than the cost price. If a customer paid Rs. 4800 for a computer table, then what was the cost price of the computer table?
(A) Rs. 3840
(B) Rs. 5270
(C) Rs. 6275
(D) Rs. 6720
(E) None of these
Rationale: CP = SP * (100/(100 + profit%))
= 4800(100/125) = Rs. 3840.
ANSWER:A
Answer: (A) Rs. 3840
Question: M is the sum of the reciprocals of the consecutive integers from 501 to 600, inclusive. Which of the following is true?
(A) 1/3 < M < 1/2
(B) 1/5 < M < 1/3
(C) 1/7 < M < 1/5
(D) 1/6 < M < 1/6
(E) 1/12 < M < 1/9
Rationale: M = 1/501 + 1/502 + 1/503 + ...... + 1/600
If we replace the first 99 terms by 1/600, then we get a sum = 100/600 = 1/6. Since the actual terms are larger than 1/600, the sum is larger than 1/6.
If we replace the all the 100 terms by 1/500, we get a sum = 100/500 = 1/5. Since the actual terms are smaller than 1/500, the sum is less than 1/5.
Therefore 1/6 < M < 1/5
Choice D
Answer: (D) 1/6 < M < 1/6
Question: A train 200 m long passed a pole in 20 sec. How long will it take to pass a platform 610 m long?
(A) 46
(B) 54
(C) 92
(D) 76
(E) 81
Rationale: Speed = 200/20 = 10 m/sec.
Required time = (200 + 610)/10 = 81 sec.
Answer: E
Answer: (E) 81
Question: A bag contains 6 black and 6 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
(A) 3/4
(B) 1/2
(C) 1/7
(D) 1/8
(E) 4/3
Rationale: Let number of balls = (6 + 6) = 12.
Number of white balls = 6.
P (drawing a white ball) =6/12=1/2.
Option B.
Answer: (B) 1/2
Question: Two trains are moving in the same direction at 162 kmph and 18 kmph. The faster train crosses a man in the slower train in 33 seconds. Find the length of the faster train?
(A) 1300
(B) 1310
(C) 1320
(D) 1330
(E) 1340
Rationale: Relative speed = (162 - 18) * 5/18 = 8 * 5
= 40 mps.
Distance covered in 33 sec
= 33 * 40
= 1320 m.
The length of the faster train
= 1320 m.
Answer:C
Answer: (C) 1320
Question: A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30° with the man’s eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes 60°. What is the distance between the base of the tower and the point P?
(A) 4√3 units
(B) 8 units
(C) 12 units
(D) Data inadequate
(E) None
Rationale: Solution
One of AB, AD and CD must have been given.So, the data is inadequate.
Answer D
Answer: (D) Data inadequate
Question: By mixing two brands of coffee and selling the mixture at the rate of $177 per kg. a shopkeeper makes a profit of 18%. If to every 2 kg of one brand costing $200 per kg, 3 kg of the other brand is added, then how much per kg does the other brand cost?
(A) $110.66
(B) $132.66
(C) $116.66
(D) $126.66
(E) $118.66
Rationale: C
$116.66
Let the cost of the brand be $X per kg.
C.P. of 5 kg = (2 * 200 + 3 * x) = $(400 + 3x)
S.P of 5 kg = $(5 * 177) = $885
[885 - (400 + 3x)]/(400 + 3x) * 100 = 18
24250 - 150x = 3600 + 27x
177x = 20650 => x = 116 2/3
So, cost of the other brand = $116.66.
Answer: (C) $116.66
Question: 6 men and 12 boys finish a job in 12 days, 12 men and 12 boys finish it in 10 days. 10 men and 10 boys shall finish it in how many days?
(A) 12 days
(B) 11 days
(C) 14 days
(D) 16 days
(E) 18 days
Rationale: 6M + 12B ----- 12 days
12M + 12B ------- 10 days
10M + 10B -------?
72M + 144B = 120M +120B
24B = 48M => 2M = B
3B + 12B = 15B ---- 12 days
5B + 10B = 15B -----? => 12 days
ANSWER:A
Answer: (A) 12 days
Question: A 260 metres long train runs at a speed of 55 Kmph.How much time will it take to cross a Platform 290 meters long?
(A) 36 seconds
(B) 18 seconds
(C) 60 seconds
(D) 20 seconds
(E) None of these
Rationale: total distance =260m+290m=550m
speed=55*5/18=275/18
therefore time taken=(550/275)*18=36 sec
ANSWER:A
Answer: (A) 36 seconds
Question: For every positive integer n, the nth term of a sequence is the total sum of three consecutive integers starting at n. What is the total sum of terms 1 through 70 of this series?
(A) 6845
(B) 7225
(C) 7665
(D) 8025
(E) 8485
Rationale: Each term of the series has the form (n+n+1+n+2) = 3n+3
Since the series goes from 1 to 70, the sum of the series is:
3(1+2+...+70) + 70(3) =
3(70)(71)/2 + 70(3) =
105*71 + 210 = 7665
The answer is C.
Answer: (C) 7665
Question: A rectangular circuit board is designed to have width w inches, perimeter p inches, and area r square inches. Which of the following equations must be true?
(A) w^2 + pw + r = 0
(B) w^2 - pw + 2r = 0
(C) 2w^2 + pw + 2r = 0
(D) 2w^2 - pw - 2r = 0
(E) 2w^2 - pw + 2r = 0
Rationale: Notice that we can discard options A, and C right away. The sum of 3 positive values Cannot be 0.
Now, assume:
Width =w = 1 inchand length = 1 inch;
Perimeter =p = 4 inches;
Area =r = 1 square inches.
Plug the values of w, p, and r into the answer choices: only for E 2w^2 - pw + 2r = 2 - 4 + 2 = 0.
Answer: E.
Answer: (E) 2w^2 - pw + 2r = 0
Question: The length of a rectangular floor is more thanits breadth by 200%. If Rs.324 is requiredto paint the floor at the rate of Rs.3/sq m, what would be the length of the floor?
(A) 12
(B) 18
(C) 19
(D) 20
(E) 21
Rationale: Let the length and the breadth of the floor be l m and b m respectively.
l = b + 200% of b = l + 2b = 3b
Area of the floor = 324/3 = 108 sq m
l b = 108 i.e., l * l/3 = 108
l2 = 324 => l = 18.
B
Answer: (B) 18
Question: A man invested Rs. 14,400 in Rs. 100 shares of a company at 20% premium. If his company declares 5% dividend at the end of the year, then how much does he get?
(A) 234
(B) 600
(C) 388
(D) 278
(E) 129
Rationale: Explanation:
Number of shares = =120.
Face value = Rs.(100 x 120) = Rs.12000.
Annual income = = Rs. 600
Answer: B) Rs.600
Answer: (B) 600
Question: The greatest common factor of 16 and the positive integer n is 4, and the greatest common factor of n and 45 is 3. Which of the following could be the greatest common factor of n and 90?
(A) 3
(B) 14
(C) 30
(D) 42
(E) 70
Rationale: Greatest common factor n and 16 is 4 = 2*2 * 2*2
Greatest common factor n and 45 is 3 = 3*3 *5
Greatest common factor n and 90 is = 2*3*5 =30
C
Answer: (C) 30
Question: Count the numbers between 10 - 99 which yield a remainder of 3 when divided by 9 and also yield a remainder of 2 when divided by 5?
(A) Two
(B) Five
(C) Six
(D) Four
(E) One
Rationale: Answer = A) Two
Numbers between 10 - 99 giving remainder 3 when divided by 9 = 12, 21, 30, 39, 48, 57, 66, 75, 84, 93
The Numbers giving remainder 2 when divided by 5 = 12, 57 = 2
Answer: (A) Two
Question: Steve gets on the elevator at the 11th floor of a building and rides up at a rate of 87 floors per minute. At the same time Joyce gets on an elevator on the 71st floor of the same building and rides down at a rate of 93 floors per minute. If they continue traveling at these rates, at which floor will their paths cross?
(A) 19
(B) 28
(C) 40
(D) 32
(E) 44
Rationale: Steve gets on the elevator at the 11th floor of a building and rides up at a rate of 87 floors per minute. At the same time Joyce gets on an elevator on the 71st floor of the same building and rides down at a rate of 93 floors per minute. If they continue traveling at these rates, at which floor will their paths cross?
60 floors/180 floors per minute=1/3 minutes
11+87/3=40
71-93/3=40
Answer : C
Answer: (C) 40
Question: Suppose the operation * is dened on the set of integers by a*b = a+2b.
Then for every two integers a and b, the value of a*(b*a) is the same
as
(A) a*b
(B) b*a
(C) (3a)*b
(D) b*(4a)
(E) (5a)*b
Rationale: One checks which of the choices is the same as a(ba) = a(b+2a) = a+2(b+2a) =
a +2b +4a = 5a + 2b. Since (5a) b = 5a + 2b, the answer is (e).
correct answer E
Answer: (E) (5a)*b
Question: What will come in place of the x in the following Number series? 11, 14, 19, 22, 27, 30, 35, 38, 43 , 46 x
(A) 23
(B) 51
(C) 36
(D) 35
(E) 45
Rationale: (B)
The pattern is + 3, + 5, + 3, + 5, …………
So the missing term is = 46 + 5 = 51.
Answer: (B) 51
Question: Heena covers a distance in 40 min , if she drives at a speed of 60 km/h on an average. Find the speed at which she must drive at to reduce the time of the journey by 60%.
(A) 60 km/h
(B) 140.48km/h
(C) 100 km/h
(D) 148.14 km/h
(E) 85 km/h
Rationale: Given Speed = 60 Kmph.
It means Heena covered 60 km in 60 min (1 hour). So, in 40 min he will cover 40 km.
60% time reduced = 40 - 60% of 40 = 16min.
Thus, Heena needs to cover 40 km in 16 min (0.27 hour).
Speed * Time = Distance.
Speed * 0.27 = 40
Speed = 148.14 kmph.
ANSWER : OPTION D
Answer: (D) 148.14 km/h
Question: If a and b are consecutive integers (b>a), which of the following statements could be false? 1. a^4+b is always even number. 2. a^2*b is always even number 3. (a + b) is always an odd number.
(A) III only
(B) II only
(C) I,II only
(D) I,III only
(E) I only
Rationale: 2^4+3 =16+3 = 19 Option I false
2^2 * 3 = 4+3 =7 (odd number). Option II is false
odd + even = odd. Option III is true
Answer : C
Answer: (C) I,II only
Question: a,b,c,d, sitting in a row what is the probability that a & b sitting adjacent.
(A) 9/2
(B) 1/2
(C) 3/2
(D) 5/2
(E) 7/2
Rationale: total number of arrangement is= 4!= 24
Favorable event i.e a and b can be arranged in 2! and the remaining can be arranged in 3! since ab can be in any of the four positions.
so2!*3!/4! = 1/2
ANSWER:B
Answer: (B) 1/2
Question: A classroom has equal number of boys and girls. SEVEN girls left to play kho-kho, leaving twice as many boys as girls in the classroom. What was the total number of girls and boys present initially?
(A) 16
(B) 24
(C) 32
(D) 28
(E) 54
Rationale: after 7 girls left remaining 7 girls
now boys 14 are twice as many as remaining girls.
initially boys=14 and girls=14.
ANSWER:D
Answer: (D) 28
Question: 9 - 3 ÷ 1/3 + 4 = ?
(A) 4
(B) 3
(C) 6
(D) 9
(E) 12
Rationale: 9 - 3 1/3 + 4
=9-3÷1/3+4
=9-(3X3) +4
=9-9+4
=4
CORRECT ANSWER : A
Answer: (A) 4
Question: A cistern is fille in 8 hours and it takes 12 hours when there is a leak in its bottom. If the cistern is full, in what time shall the leak empty it?
(A) 22 hours
(B) 21 hours
(C) 24 hours
(D) 23 hours
(E) 25 days
Rationale: Explanation:
work done by 1 hour by filling pipe = 1/8
work done by 1 hour by the leak and the filling pipe =1/12
work done by 1 hour by the leak = 1/8 – 1/12 =1/24
Hence the leak can empty it in 24 hours.
Answer: Option C
Answer: (C) 24 hours
Question: A cube is divided into 343 identical cubelets. Each cut is made parallel to some surface of the cube. But before doing that, the cube is painted with green on one set of opposite faces, red on another set of opposite faces, and blue on the third set of opposite faces. How many cubelets are painted with exactly one colour?
(A) 125
(B) 150
(C) 175
(D) 200
(E) 225
Rationale: Each side of the cube has 7 x 7 = 49 cubelets.
Only the interior cubelets are painted one colour.
On each side, 5 x 5 = 25 cubelets are painted one colour.
Since the cube has six sides, the number of cubes with one colour is 6*25 = 150
The answer is B.
Answer: (B) 150
Question: The average (arithmetic mean) of the integers from 25 to 225, inclusive, is how much lower than the average of the integers from 50 to 1050 inclusive?
(A)  450
(B)  375
(C)  500
(D)  425
(E)  400
Rationale: For an AP the mean or average of series is average of first and last term.
So, average of numbers between 50 to 1050, inclusive = (50+1050)/2 = 550
average of numbers between 25 to 225, inclusive = (25+225)/2 = 125
difference = 550 - 125 = 425
Answer is D
Answer: (D)  425
Question: If 10! × 10!/10^n is an integer, what is the largest possible value of n?
(A) 20
(B) 16
(C) 8
(D) 4
(E) 1
Rationale: 10! × 10!/10^n is an integer.
Or 10! × 10!/(1^2n*5^n)
This means we need to find the power of 5 in the numerator. We can safely say that the number of powers of 5 will be lower than the number of powers of 4 in the numerator.
Largest power of 5 in 10! = [10/5] + [10/25] = 2
Since there are 2 20!'s, power of 2 in the numerator = 2*2 = 4
Hence the largest value of b for which 10! × 10!/10^n is integer = 4
Correct Option : D
Answer: (D) 4
Question: What least number mustbe subtracted from 427398 so that remaining no.is divisible by 15
(A) 3
(B) 5
(C) 6
(D) 8
(E) 9
Rationale: Explanation:
On dividing 427398 by 15 we get the remainder 3, so 3 should be subtracted
Option A
Answer: (A) 3
Question: The perimeter of a semi circle is 144 cm then the radius is?
(A) 17
(B) 28
(C) 19
(D) 11
(E) 12
Rationale: 36/7 r = 144 => r
= 28
Answer: B
Answer: (B) 28
Question: A glucose molecule contains 6 carbon, 12 hydrogen and 6 oxygen atoms. During photosynthesis, green plants create glucose daily. If, over a period of 12 days, an eucalyptus plant (a green plant) creates 12,000 molecules of glucose then approximately how many more atoms of hydrogen than carbon are created on average per day?
(A) 60,000
(B) 6,000
(C) 2,500
(D) 250
(E) 0
Rationale: Solution:
We know that 12,000 glucose molecules are created over a period of 12 days. Therefore 12,000/12 = 1,000 glucose molecules are created on average per day.
Each glucose molecule contains 6 carbon atoms and 12 hydrogen atoms. So 1,000 glucose molecules contain 6 × 1,000 = 6,000 carbon atoms and 12 × 1,000 = 12,000 hydrogen atoms. The difference is 12,000 – 6,000 = 6,000.
The correct answer is B.
Answer: (B) 6,000
Question: If (x^2 + 1)y=7, which of the following is not a possible value for y?
(A) 2
(B) 2/3
(C) 4/3
(D) 4
(E) 15/2
Rationale: Its simple
equation is (x^2 +1)y = 7 ===> x^2 = (7/y) - 1 . As , in LHS, it is x^2 the value has to be positive or zero in RHS.
Hence, (7/y) - 1>= 0 ===> y =< 7. Now only option E has greater value of 'y' than 7.
Thus, correct ans is E
Answer: (E) 15/2
Question: Consider the sets Tn = {n, n + 1, n + 2, n + 3, n + 4}, where n = 1, 2, 3,...., 84. How many of these sets contain 6 or any integral multiple thereof (i.e., any one of the numbers 6, 12, 18, ...)?
(A) (a) 80
(B) (b) 81
(C) (c) 82
(D) (d) 83
(E) (e) 70
Rationale: T1: 1,2,3,4,5
T2: 2,3,4,5,6
T3: 3,4,5,6,7
etc.
means that every multiple of 6 will be involved in 5 sets. We have (84-6)/6+1=14 such multiples.
So, final number of sets is 14*5=70
Answer: E
Answer: (E) (e) 70
Question: Seller selling an apple for Rs.18, a Seller loses 1/6th of what it costs him. The CP of the apple is?
(A) 10
(B) 12
(C) 19
(D) 18
(E) 20
Rationale: SP=18Loss=CP19Loss=CP−SP=CP−18⇒CP19=CP−18⇒18 CP19=18⇒CP19=1⇒CP=19
C
Answer: (C) 19
Question: How many three digit number formed by using 2,3,4,5,6,7 once such that number is divisible by 15.
(A) 8
(B) 13
(C) 12
(D) 20
(E) 22
Rationale: 4*2*1=8
at one's place only 5 will come
and at ten's place 4 and 7 can be placed,
and at 100th place rest of the 4 digits can come...
so the answer is 8
ANSWER:A
Answer: (A) 8
Question: What is the present worth of Rs. 154 due in 2 years at 5% simple interest per annum?
(A) 140
(B) 266
(C) 120
(D) 277
(E) 6123
Rationale: Let the present worth be Rs. x. Then,
S.I. = (154 - x)
(x * 5 * 2) / 100 = (154 - x)
10x = 15400 - 100x
110x = 15400 => x = 140.
Answer: A
Answer: (A) 140
Question: An equilateral triangle T2 is formed by joining the mid points of the sides of another equilateral triangle T1. A third equilateral triangle T3 is formed by joining the mid-points of T2 and this process is continued indefinitely. If each side of T1 is 40 cm, find the sum of the perimeters of all the triangles.
(A) 180 cm
(B) 220 cm
(C) 240 cm
(D) 270cm
(E) 300 cm
Rationale: We have 40 for first triangle, when we join mid-points of first triangle we get the second equilateral traingle then the length of second one is 20 and continues.
So we have 40,20,10,...
We have ratio = 1/2, and it is GP type.
Sum of infinite triangle is a/1-r = 40/1-(1/2) = 80
Equilateral triangle perimeter is 3a = 3*80 = 240.
So option C.
Answer: (C) 240 cm
Question: In what time will a train 120 metres long cross an electric pole, if its speed be 72 km/hr?
(A) 7 sec
(B) 6 sec
(C) 8 sec
(D) 9 sec
(E) 5 sec
Rationale: Solution
Speed	= (72 x 5 /18) m/sec
= 20 m / sec
Time taken	= (120 /20) sec
= 6 sec.
Answer B
Answer: (B) 6 sec
Question: A Cone, a Heme sphere and a Cylinder have equal bases and heights. What is the ratio of their volumes.
(A) 1:2:3
(B) 1:2:4
(C) 3:2:3
(D) 4:2:3
(E) 1:4:3
Rationale: Volume of cone=(1/3)*pi*r^2*h
Volume of hemisphere=(2/3)*pi*r^3
Volume of cylinder=pi*r^2*h
Since base and height of all three figures are same and for hemisphere h=r
So ther volumes are in the ratio (1/3:(2/3):1=1:2:3
ANSWER:A
Answer: (A) 1:2:3
Question: If x and y are different integers, both divisible by 9, then which is not necessarily true?
(A) x^2 + y^2 is divisible by 9
(B) x - y is divisible by 9
(C) xy is divisible by 9
(D) x + y is divisible by 9
(E) x + y is divisible by 18
Rationale: Let x = 9k and let y = 9j.
Then x+y = 9(k+j) and k+j could be even or odd.
Thus 9(k+j) is not necessarily divisible by 18.
The answer is E.
Answer: (E) x + y is divisible by 18
Question: The city of Boston decided to reconstruct its major tunnels. It estimated the job would require 612 mini projects spread evenly over an 18 month plan of completion. Only 108 mini projects had been successfully completed after 7 months. At this time, the construction was behind schedule by how many projects?
(A) 34
(B) 96
(C) 130
(D) 204
(E) 504
Rationale: Project/month : 612/18 = 34
Project in 6 month to be completed = 34*7 =238
Lag :238-108 = 130
C is the answer
Answer: (C) 130
Question: In how many ways can 6 black and 2 white chess pieces be arranged in a row such that they occupy alternate places? Assume that the pieces are distinct.
(A) 12
(B) 1440
(C) 720
(D) 360
(E) 180
Rationale: 6 black chess pieces can be arranged in 6! ways and 2 white pieces can be arranged in 2! ways.
W_W_W_W
Number of ways = 6!*2! = 720 * 2 = 1440
Answer B
Answer: (B) 1440
Question: Company workers decided to raise Rs. 3 lakhs by equal contribution from each. Had they contributed Rs. 50 each extra, the contribution would have been Rs. 3.25 lakhs. How many workers were they?
(A) 300
(B) 400
(C) 500
(D) 600
(E) 700
Rationale: Explanation:
N * 50	= (325000 - 300000) = 25000
N = 25000 / 50
= 500
Option C
Answer: (C) 500
Question: A corporation that had $120 billion in profits for the year paid out $200 million in employee benefits. Approximately what percent of the profits were the employee benefits? (Note: 1 billion = 10^9)
(A) 50%
(B) 20%
(C) 5%
(D) 4%
(E) 0.17%
Rationale: required answer = [employee benefit/profit] *100
=[(200 million)/(120 billion)]*100
=[(200*10^6)/(120*10^9)]*100
=(1.7/1000)*100
=0.17%
So answer is (E)
Answer: (E) 0.17%
Question: On dividing a number by 357, we get 37 as remainder.On dividing the same number by 17, what will be the remainder ?
(A) 4
(B) 3
(C) 8
(D) 7
(E) 2
Rationale: Let x be the number and y be the quotient.Then,
x=357*y+37
=(17*21*y)+(17*2)+3
=17*(21y+2)+3.
Required number =3.
Answer is B
Answer: (B) 3
Question: A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 36 km/hr. What is the length of the platform?
(A) 160
(B) 240
(C) 288
(D) 277
(E) 221
Rationale: Speed = 36 * 5/18 = 10 m/sec.
Length of the train = 10 * 20 = 200 m.
Let the length of the platform be x m . Then,
(x + 200)/36 = 10=> x = 160 m.
Answer: A
Answer: (A) 160
Question: B can be divided by 11 with no remainder. Which of the following expressions could be divided by 11 leaving a remainder of 1?
(A) B-20.
(B) B-12.
(C) B-9.
(D) B-10.
(E) B-13.
Rationale: We could use the following logic:
since Bis a multiple of 11, we could very well say B= 11K (where K is 1,2...n).
The condition here should now be
11K + 1 = <operation> such that it gives us an integer
11k +1 = B-20 => B= 11K + 21 Not divisible by 11
11K +1 = B-12 => B= 11K + 31 Not Divisible by 11
11K +1 = B -9 => B= 11K + 10 Not Divisible by 11
11K +1 = B-10 => B= 11K + 11Divisible by 11
11K +1 = B-13 => B= 11K + 14 Not Divisible by 11
Answer therefore is B-10 (D)
Answer: (D) B-10.
Question: How many three letter words are formed using the letters of the word MARCH?
(A) A)150
(B) B)140
(C) C)130
(D) D)120
(E) E)110
Rationale: The number of letters in the given word is five.
The number of three letter words that can be formed using these four letters is 5P4
= 5 * 4 *3* 2 = 120.
Answer:D
Answer: (D) D)120
Question: Two persons starting from the same place walk at a rate of 5kmph and 5.5kmph respectively. What time will they take to be 8.5km apart, if they walk in the same direction?
(A) 18
(B) 28
(C) 21
(D) 17
(E) 19
Rationale: D
17 hrs
The relative speed of the boys = 5.5kmph – 5kmph
= 0.5 kmph
Distance between them is 8.5 km
Time= 8.5km / 0.5 kmph = 17 hrs
Answer: (D) 17