MU-NLPC/Calc-aqua_rat huggingface dataset:
Kate wanted to buy 2kgs of apples. The vendor kept the 2kg weight on the right side and weighed 4 apples for that. She doubted on the correctness of the balance and placed 2 kg weight on the left side and she could weight 14 apples for 2 kgs. If the balance was correct how many apples she would have got? Choose the correct choice from the following answers.
A) 6	B) 9	C) 8	D) 4	E) 3

Solution: As she got less apples when the weight put on the right side, the left pan has more weight say w kgs.   Now w + 4a = 2   and w+ 2 = 14a   Solving we get a = 2/9 Kgs.   So she gets, 2/(2/9) = 9 apples   Answer:9
Answer: B
How many seconds will a 900 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
Pick: A) 22 B) 54 C) 99 D) 77 E) 12

Solution: Speed of train relative to man = 63 - 3= 
63 - 3 = 60
60 km/hr.= 60 * 5/18 = 50/3 m/sec.   Time taken to pass the man = 900 * 3/50= 
900 * 3/50 = 54
54 sec.   Answer: 54
Answer: B
The ratio between the present ages of P and Q is 5:7. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years?
Choose the correct choice from the following.
A) A)3:4
B) B)8:9
C) C)4:3
D) inadequate
E) of these

Solution: Let P's age and Q's age be 5x and 7x years respectively.   Then, 7x - 5x = 4 => x = 2   Required ratio = (6x + 4) : (7x + 4)   16 : 18= 8:9   ANSWER:8:9
Answer: B
If a rectangle length and width are both doubled,by what percent is the rectangle area increase?
Choose the correct choice from the following options:
A) 100
B) 150
C) 300
D) 200
E) 250

Solution: let length and width are l and b   so area = lb   now after doubling both we will get area = 2l*2b = 4lb   so % increase 2 *2= 
2 *2 = 4
4lb   so % increase= 400-100= 
400-100 = 300
300   ANSWER:300
Answer: C
Traders A and B buy two goods for Rs. 1000 and Rs. 2000 respectively. Trader A marks his goods up by x%, while trader B marks his goods up by 2x% and offers a discount of x%. If both make the same non-zero profit, find x.  Choose the correct choice from the following answers.
A) 25%	B) 12.5%	C) 37.5%	D) 40%	E) 50%

Solution: DETAILED SOLUTION   SP of trader A = 1000 (1 + x).   Profit of trader A = 1000 (1 + x) – 1000.   MP of trader B = 2000 (1 + 2x).   SP of trader B = 2000 (1 + 2x) (1 – x).   Profit of trader B = 2000(1 + 2x) (1 – x) – 2000.   Both make the same profit => 1000(1 + x) – 1000 = 2000(1 + 2x) (1 – x) – 2000   1000x = 2000 – 4000x2 + 4000x – 2000x – 2000   4000x2 -1000x = 0   1000x (4x – 1) = 0   => x = 25%.   25%nswer choice (25%)
Answer: A
The ratio of the present age of Viju to that of Aju is 7:2. Four years from now, the ratio of the ages of Viju to Aju will be 5:2. What was Viju age 2 years ago ? (RBI Assistant 2015)  Choose the correct choice from the following:  A) 24  B) 19  C) 12  D) 15  E) 13

Solution: Let the present age of Viju be 7x years and that of Aju be 2x years.   Then, 4 years from now   7x + 4 / 2x + 4 = 5 / 2   or 4x = 12   or x = 3   Viju present age = 7 * 3= 
7 * 3 = 21
21 years   Viju age 2 years ago= 21 - 2= 
21 - 2 = 19
19 years   answer :19
Answer: B
Speed of boat in water is 12km/hr. and the speed of the stream is 3km/hr. Find the time taken by the boat to go upstream a distance of 45km.
Pick one:
A) 3	B) 4	C) 5 hrs.	D) 6	E) 2

Solution: US =speed of the boat - speed of the stream 12-3= 
12-3 = 9
9km/hr. Time taken to cover 45km=45/9= 
45/9 = 5
5hrs. Answer : 5 hrs.
Answer: C
An error 6% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:	Choose the correct answer:
A) 12.36
B) 8.36
C) 9.36
D) 10.36
E) 11.36

Solution: Explanation:   100 cm is read as 106 cm.   12.361 =(100 × 100)cm2 = 10000   and 12.362= (106 × 106)cm2= 11236   (12.362 - 12.361) = 11236-10000= 
11236-10000 = 1_236
1236=> 1236/10000*100= 
1236/10000*100 = 309/25 = around 12.36
12.36   12.36nswer : 12.36
Answer: A
A pharmaceutical company uses 900 gm in place of 1 kg to sell the drug. Find the actual % profit or loss, when the company sells the product on 10% gain on cost price?
Pick one:
A) 20
B) 25
C) 30
D) 35
E) 40

Solution: Selling price of 900gm = 100+10= 
100+10 = 110
$110   Profit= 110-90= 
110-90 = 20
$20   % of profit= 20*100/80= 
20*100/80 = 25
25 %   Answer is 25
Answer: B
A certain cricket team played seven games and scored an average of 180 runs per game. If, in the team’s first five games, it scored 175, 169, 181, 190, and 173 points, what was the average (arithmetic mean) number of points scored over the last two games?  Select the correct option.
A) 165	B) 181	C) 182	D) 186	E) Cannot be determined from the information given.

Solution: Avg runs for total of 7 games = 50   So A+B+C+186+E+F+G/7=180   and A+B+C+186+E+F+G = 1260   Given A+B+C+186+E = 888   So F+G = 372   So average (arithmetic mean) number of runs scored over the last two games is   372/2= 
  372/2 = 186
186   Correct answer is 186) 186
Answer: D
A train 280 m long, running with a speed of 72 km / hr will pass a tree in Pick one
A) 14 sec  B) 15 sec  C) 16 sec  D) 20 sec  E) None

Solution: Sol.   Speed = (72 x 5/18) m/sec.   = 20 m / sec.   Time taken = (280 x 1/20) sec = 14 sec   14 secnswer 14 sec
Answer: A
At what rate of compound interest per annum will a sum of Rs.1200 become Rs.1348.32 in 2 years?	Pick one: A) 6% B) 6.5% C) 7% D) 7.5% E) 8%

Solution: Let the rate be R% p.a. (1+ R )2 = 1348.32. Then, 1200* (1+ (R/100))2 = 1348.32   (1+R/100)2 = 134832/120000 = 11236/10000 :. (1 + R/100) 2 = (106/100)2   1 + R/100 = 106/100. So R = 6%   6%NSWER:6%
Answer: A
The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?  Answers:
A) 80 kg
B) 85 kg
C) 90 kg
D) 100 kg
E) 110 kg

Solution: Total weight increased = (8 x 2.5) kg = 20 kg.   Weight of new person = (65 + 20)= 
(65 + 20) = 85
85 kg.   85 kg)
Answer: B
The sum of a certain number and its reciprocal is equal to 2,9. What is the absolute value of the difference of this number and its reciprocal ?	Select
A) 2,2  B) 1,2  C) 0,3  D) 0,4  E) 2,1

Solution: x + 1/x = 2.9   x-1/x = y   Add two equations   2x = 2.9 + y   So when 2.9 and correct answer choice are added, the final digit should be even   So eliminate A, B and D   Substitute y=0.3   x=1.6   1.6+1/1.6 is not equal to 2.9   Substitute y = 2.1   So x=2.5   2.5+1/2.5= 
2.5+1/2.5 = 2.9
2.9   ANSW2,1R:2,1
Answer: E
In what time will a railway train 70 m long moving at the rate of 36 kmph pass a telegraph post on its way?
Choose the correct option.
A) 5 sec	B) 4 sec	C) 3 sec	D) 7 sec	E) 1 sec

Solution: T = 70/36 * 18/5= 
70/36 * 18/5 = 7
7 sec   Answer: 7 sec
Answer: D
In a box of 6 pencils, a total of 2 are defective. If a customer buys 3 pencils selected at random from the box, what is the probability that neither pencils will be defective?	Choose the correct choice
A) 1/2
B) 1/5
C) 2/3
D) 2/5
E) 1/7

Solution: First, there are 4C3 ways you can select 3 good pencils from 4 good ones.   Second, there are 6C3 ways you select 3 pencils from 6 ones in the box.   Then, the probability that neither pen will be defective is: 4C3/6C3=4/20 = 1/5   Answer is 1/5
Answer: B
In a pet shop there are 120 eyes and 172 legs. How many birds are included in these? Choose the correct answer:
A) 33
B) 34
C) 35
D) 36
E) 37

Solution: Let there are x birds and y puppies.   Each bird and puppy has 2 eyes. Each bird has 2 legs and each puppy has 4 legs.   Then 2x+2y = 120 => x+y = 60 (i)   2x+4y = 172 => x+2y = 86 (ii)   Solving (i) and (ii) we get   y = 26 & x = 34   So birds are 34   ANSWER:34
Answer: B
On dividing 109 by a number, the quotient is 9 and the remainder is 1. Find the divisor?	Choices:
A) 10
B) 12
C) 14
D) 16
E) 18

Solution: d = (D-R)/Q   = (109 - 1)/9   = 108/9= 
108/9 = 12
12   12)
Answer: B
The sum of the present ages of two persons A and B is 60. If the age of A is twice that of B, find the sum of their ages 4 years hence?
Select:
A) 22
B) 77
C) 70
D) 68
E) 71

Solution: A + B = 60, A = 2B   2B + B = 60 => B = 20 then A = 40.   4 years, their ages will be 44 and 24.   Sum of their ages = 44 + 24= 
44 + 24 = 68
68.   Answer: 68
Answer: D
If circles x and y have the same area and circle x has a circumference of 18π, half of the radius of circle y is:
Pick:	A) 16	B) 4.5	C) 4	D) 2	E) 1

Solution: x be radius of circle x   y be radius of circle y   given:   pi*x^2 = pi*y^2   also,   2*pi*x = 18*pi   x = 9   thus y =9   y/2 = 4.5   Ans: 4.5
Answer: B
. In digging a pond 18 m * 8 m * 6 m the volumes of the soil extracted will be?
Select:
A) 889
B) 1000
C) 864
D) 989
E) 678

Solution: 20 * 10 * 5 = 864   Answer: 864
Answer: C
The digits of a three-digit number A are written in the reverse order to form another three-digit number B. If B>A and B-A is perfectly divisible by 7, then which of the following is necessarily true? Choose the correct choice:
A) 100<A<299 B) 106<A<305 C) 112<A<311 D) 118<A<317 E) None

Solution: Explanation:   Let A = abc the B = cba   Given, B – A is exactly divisible by 7.   Therefore, 100c + 10b + a – (100a + 10b + c) = 99c – 99a = 99(c – a)   So 99(c – a) should be divisible by 7.   We know that 99 is not divisible by 7. So (c – a) should be divisible by 7 which implies c – a is 0, 7, 14...   c – a = 0 is not possible as c = a implies A = B but given that B > A   c – a = 14 is not possible as the maximum difference between c and a = 9 – 1 = 8 only.   So c – a = 7.   If c = 9, a = 2   c = 8, a = 1   b can take any value from 0 to 9   Therefore, minimum value of abc = 109, maximum value = 299   From the given options, option B satisfies this.   Correct option: 106<A<305
Answer: B
A number x is multiplied with itself and then added to the product of 4 and x. If the result of these two operations is -8, what is the value of x?  Pick:
A) -4  B) -2  C) 2  D) 4  E) Cannot be determined.

Solution: A number x is multiplied with itself --> X^2   added to the product of 4 and x --> X^2+4X   If the result of these two operations is -4 --> X^2+4X=-8   i.e X^2+4X+8=0 is the Quadratic equation which needs to be solved.   no solution   IMO Cannot be determined.
Answer: E
Thirty men can do a work in 24 days. In how many days can 20 men can do the work, given that the time spent per day is increased by one-third of the previous time? Choose the correct answer:
A) 27 B) 88 C) 26 D) 55 E) 12

Solution: Let the number of hours working per day initially be x. we have M1 D1 H1= M2 D2 H2   30 * 24 * x = 20 * d2 * (4x)/3 => d2 = (30 * 24 * 3)/(24 * 4) = 27 days.   27nswer:27
Answer: A
What is the smallest positive integer K such that the product of 450 x K is a perfect square?	Choose the correct option
A) 3  B) 9  C) 15  D) 25  E) 63

Solution: A perfect square, is just an integer that can be written as the square of some other integer. For example 16=4^2, is a perfect square.   Now, 450 = 3^2 * 5^2 *3 , so if k=3 then 450k = (3 * 5 * 3)^2, which is a perfect square (basically the least positive value of k must complete only the power of 7 to even power as powers of other primes are already even).   3nswer: 3.
Answer: A
A train 210 m long, running with a speed of 63 km/hr will pass a tree in? Choose the correct choice:	A) 15 sec	B) 16 sec	C) 18 sec	D) 12 sec	E) 25 sec

Solution: Speed = 63 * 5/18 = 35/2 m/sec   Time taken = 210 * 2/35= 
210 * 2/35 = 12
12 sec   ANSWER: 12 sec
Answer: D
The ratio of the number of ladies to gents at a party was 1:2 but when 2 ladies and 2 gents left, the ratio became 1:3. How many people were at the party originally?
Select
A) 278 B) 29 C) 12 D) 17 E) 10

Solution: x, 2x   (x-2):(2x-2) = 1:3   3x-6 = 2x-2   x = 4   x+2x = 3x   => 3*4= 
3*4 = 12
12.Answer:12
Answer: C
What is the area of square field whose side of length 16 m?	Choose the correct answer.
A) 225 B) 777 C) 256 D) 288 E) 261

Solution: 16 * 16= 
16 * 16 = 256
256 sq m   Answer: 256
Answer: C
Einstein walks on an escalator at a rate of 5steps per second and reaches the other end in 10 sec. while coming back, walking at the same speed he reaches the starting point in 40secs. What is the number of steps on the escalator?  Choose the correct choice from the following: A) 40 B) 60 C) 120 D) 80 E) data insufficient

Solution: Let the speed of escaltor be X steps per sec.   And length of escalator be Y.   Einstein's speed = 5 step/ sec   Then,   During upward movement   5-X=Y/10   During downward movement   5+X=Y/40   By solving equations we get Y=80.   ANSWER:80
Answer: D
In a shop, shirts are usually sold at 40% above the cost price. During a sale, the shopkeeper offers a discount of 10% off the usual selling price. If he manages to sell 72 shirts for Rs 13.608, then his cost price per shirt, in Rs, is	Choices:
A) 120 B) 130 C) 140 D) 150 E) 160

Solution: suppose cost price is x   so selling price is 14x/10   now after 10% discount selling price is 126x/100   total selling price is 72*126x/100   72*126x/100=13608   x=150   so the cost price per shirt is 150.   ANSWER:150
Answer: D
The speed of a train is 80 kmph. What is the distance covered by it in 6 minutes? Choose the correct choice.
A) 15 kmph B) 11 kmph C) 18 kmph D) 8 kmph E) 12 kmph

Solution: 80 * 6/60= 
80 * 6/60 = 8
8 kmph   Answer:8 kmph
Answer: D
A train consists of 12 boggies, each boggy 15 metres long. The train crosses a telegraph post in 18 seconds. Due to some problem, two boggies were detached. The train now crosses a telegraph post in	Choose the correct option: A) 18 sec B) 12 sec C) 15 sec D) 20 sec E) None of these

Solution: Length of train = 12 × 15 = 180 m.   Then, speed of train = 180⁄18 = 10 m/s   Now, length of train = 10 × 15 = 150m   ∴ Required time = 150⁄10 = 15 sec.   Answer 15 sec
Answer: C
How many inches are in 2000 millimeters? (round your answer to the nearest hundredth of of an inch).
Select the correct option:
A) 51.45 inches
B) 86.09 inches
C) 67.34 inches
D) 34.98 inches
E) 78.74 inches

Solution: One inch is the same as 25.4 mm. Let x inches be the same as 1000 mm   x = 1 inch * 2000 mm / 25.4 mm = 78.74 inches   correct answer 78.74 inches
Answer: E
Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 24,500. What was Simran's share in the profit ?  Pick.
A) 13500
B) 10500
C) 9423
D) 8500
E) None of these

Solution: Explanation:   Simran : Nanda =(50000Ã—36):(80000Ã—30)=(50000Ã—36):(80000Ã—30) =3:4=3:4.   Simran's share = Rs. (24500Ã—37)(24500Ã—37) = Rs. 10500.   ANSWER IS 10500
Answer: B
A man can do a job in 20 days. His father takes 20 days and his son finishes it in 25 days. How long will they take to complete the job if they all work together?	Choose the correct option
A) 6.3
B) 6.9
C) 7.1
D) 6.1
E) 6.2

Solution: 1 day work of the three persons = (1/20 + 1/20 + 1/25) = 7/50   So, all three together will complete the work in 300/47 = 7.1 days.   Answer:7.1
Answer: C
If x is an integer, then x(x – 1)(x – k) must be evenly divisible by five when k is any of the following values EXCEPT  Choose the correct option
A) -4
B) -2
C) 2
D) -1
E) 5

Solution: We have the product of 3 integers: (x-1)x(x-k).   Note that the product of 3 integers is divisible by 5 if at least one multiple is divisible by 5. Now, to guarantee that at least one integer out of x, (x – 1), and (x – k) is divisible by 5 these numbers must have different remainders upon division by 5, meaning that one of them should have remainder of 1, another reminder of 2 and the last one remainder of 0, so be divisible by 5.   Next, if k=2 then we'll have (x-1)x(x-k)=(x-1)x(x-2) --> which means that (x-1) and (x-2) will have the same remainder upon division by 5. Thus for k=2 we won't be sure whether (x-1)x(x-k) is divisible by 5.   Answer: 2.
Answer: C
A hen leaps 3 leaps for every 2 leaps of a duck, but 4 leaps of the duck are equal to 3 leaps of the hen. What is the ratio of the speed of the hen to that of the duck? Pick one:
A) 2:1  B) 3:4  C) 4:3  D) 1:4  E) 5:6

Solution: Given;   4 duck = 3 hen;   Or, duck/hen = 3/4;   Let hen's 1 leap = 4 meter and ducks 1 leap = 3 meter.   Then, ratio of speed of hen and duck = 4*3/3*2 = 2:1''2:1nswer: 2:1;
Answer: A
What is the fraction in the simplest form of the terminating decimal 0.0325? Choices:  A) 31/40  B) 41/30  C) 13/40  D) 1/30  E) 1/40

Solution: The fraction of the decimal 0.0325 is 325/10000. Simplifying by dividing the top and bottom by 25 to get 13/40.   Option 13/40
Answer: C
How many multiples of 4 are there between 12 and 104, inclusive? Pick:
A) 21	B) 22	C) 23	D) 24	E) 25

Solution: The multiples of 4 are from 4*3 up to 4*26.   26-3+1= 
26-3+1 = 24
24.   The answer is 24.
Answer: D
How many integers from 101 to 800, inclusive, remains the value unchanged when the digits were reversed? Options: A) 50 B) 60 C) 70 D) 80 E) 90

Solution: first digit possibilities - 1 through 7 = 7   8 is not possible here because it would result in a number greater than 8 (i.e 808 , 818..)   second digit possibilities - 0 though 9 = 10   third digit is same as first digit   =>total possible number meeting the given conditions = 7 *10= 
7 *10 = 70
70   Answer is 70.
Answer: C
For which of the following functions f is f(a) = f(1-a) for all a?	Select the correct option
A) f (x) = 1 - x B) f (a) = 1 - a^2 C) f (a) = a^2 - (1 - a)^2 D) f (a) = a^2*(1 - a)^2 E) f (x) = x/(1 - x)

Solution: I remember seeing this problem in a GMATprep test. I think choice D should be F(a)=(a^2) (1-a)^2. If that is true then substituting (1-a) for will give us the same function back and the answer choice is f (a) = a^2*(1 - a)^2, where the function is multiplicative
Answer: D
The ratio of a to b to c is 2 to 3 to 4, and a, b, c are positive integers. If the average (arithmetic mean) of the three numbers is 36, what is the value of a?  Choose the most appropriate option.
A) 21  B) 24  C) 25  D) 27  E) 30

Solution: Let a=2k, b=3k, and c=4k.   a+b+c = 2k+3k+4k = 9k   Since the average is 36:   9k/3 2 +3 +4= 
2 +3 +4 = 9
9k   Since the average is 36:   9k/3= 36   3k = 36   k=12   Then a=24.   The answer is 24.
Answer: B
A student has to obtain 50% of the total marks to pass. He got 200 marks and failed by 20 marks. The maximum marks are? Choose the correct choice from the following answers.
A) 510 B) 520 C) 530 D) 540 E) 440

Solution: Let the maximum marks be x   Then, 50% of x = 200+20   50x/100 = 220   50x= 220*100= 
220*100 = 22_000
22000   x= 440   Answer is 440
Answer: E
Three medical experts, working together at the same constant rate, can write an anatomy textbook in 18 days. How many additional experts, working together at this same constant rate, are needed to write the textbook in 9 days?  Choices.
A) 2  B) 3  C) 5  D) 8  E) 15

Solution: Each expert can write 1/54 of the book per day.   To complete the book in 9 days, we need 54/9= 
54/9 = 6
6 experts, thus 3 more experts are needed.   The answer is 3.
Answer: B
A watch was sold at a loss of 10%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price? Choose the correct choice from the following
A) Rs.1000
B) Rs.1009
C) Rs.1007
D) Rs.1006
E) Rs.1002

Solution: Explanation:   90%   104%   --------   14% ---- 140   100% ---- ? => Rs.1000   Rs.1000nswer:Rs.1000
Answer: A
How many words can be formed by using all letters of the word ‘BIHAR’ ? Pick one:
A) 110	B) 120	C) 130	D) 140	E) None of these

Solution: Solution   The word BIHAR contains 5 different letters.   Required number of words = 5P5 = 5 ! = (5 x 4 x 3 x 2 x 1) = 120, Answer 120
Answer: B
Two discounts of 40% and 20% equal to a single discount of? Choose the correct choice from the following answers:  A) 52%  B) 48%  C) 60%  D) 80%  E) 70%

Solution: {[(100-40)/100]*[(100-20)/100]}%=(60*80)/(100*100)%   =48%   single discount is equal to   (100-48)= 
  (100-48) = 52
52%   52%NSWER 52% 52%
Answer: A
In a recent election, James received 5 percent of the 2,000 votes cast. To win the election, a candidate needed to receive more than 50 percent of the vote. How many additional votes would James have needed to win the election?	Choose the correct choice from the following answers:
A) 901
B) 989
C) 990
D) 991
E) 1,001

Solution: James = (5/100)*2000= 
(5/100)*2000 = 100
100   Votes to win= (50/100)*Total Votes +1 = (50/100)*2000 +1= 
(50/100)*2000 +1 = 1_001
1001   Remaining Voted needed to win election= 1001 - 100= 
1001 - 100 = 901
901   901nswer: option 901
Answer: A
In a certain pond, 70 fish were caught, tagged, and returned to the pond. A few days later, 50 fish were caught again, of which 2 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what is the approximate number of fish in the pond?
Select
A) 400 B) 625 C) 1,750 D) 2,500 E) 10,000

Solution: This is a rather straight forward ratio problem.   1. 70 fish tagged   2. 2 out of the 50 fish caught were tagged thus 2/50   2/50=70/x   thus, x=1750   Think of the analogy: 2 fish is to 50 Fish as 50 fish is to ...?   You've tagged 50 fish and you need to find what that comprises as a percentage of the total fish population - we have that information with the ratio of the second catch.   1,750
Answer: C
Three unbased coins are tossed. the probability of getting at most three head is ?  Choose one:
A) 1/2 B) 7/8 C) 3/4 D) 1/5 E) 1/8

Solution: S={TTT,TTH,THT,HTT,THH,HTH,HHT,HHH}   1/8 be the event of getting at least two head is {HHH}   P(1/8)=n(1/8)/n(S)=1/8   Answer(1/8)
Answer: E
If pqr = 1, the value of the expression (1 / ( 1 + p + q-1)) + (1 / ( 1 + p + r-1)) + (1 / ( 1 + p + p-1))  Pick one:
A) p + q + r
B) 1/ (p + q + r )
C) 1
D) p ^ (-1) + q ^ (-1) + r ^ (-1)
E) None

Solution: Explanation :   If p = q = r = 1, then expression = 1   Check the choice only, one choice gives the value of expression = 1.   Answer : 1
Answer: C
How many different numbers can we have by changing the position of the digits of the number 718844?	Options.
A) 15 B) 90 C) 180 D) 360 E) 720

Solution: Permutation in a group where there are repeated elements = n!/(p! * p2! *...*pn!); where p1, p2, .., pn are the number of times the element is repeated.   So, here required numbers = 6!/(2! * 2!) since we have 6 digits and 8 and 4 are each repeated twice.   = 180   Hence option 180
Answer: C
A and B invest in a business in the ratio 3: 2. Assume that 5% of the total profit goes to charity. If A's share is Rs. 855, what is the total profit?	Choices:
A) 1400
B) 1500
C) 1600
D) 1200
E) 1800

Solution: Explanation:   Assume that the total profit is xx   since 5% goes for charity, 95% of xx will be divided between A and B in the ratio 3:2   Therefore, A's profit =95x 100×35   Given that A's share is Rs. 855. Therefore,   95 x 100×35=855   ⇒95x100=855×53=285×5=1425   ⇒x=1425×10095=285×10019=1500   Hence the total profit = 1500   Answer: Option 1500
Answer: B
A,B,C can complete a piece of work in 16,6,12 days. Working together, they complete the same work in how many days? Choose the correct choice
A) 2
B) 48/15
C) 7/9
D) 10
E) 24/7

Solution: A+48/15+C 1day work = 1/16 + 1/6 + 1/12 = 15/48   A,48/15,C together will complete the job in 48/15 days   Answer is 48/15
Answer: B
The diameters of two spheres are in the ratio 1:2 what is the ratio of their volumes?
Choose the correct option:
A) 1:9	B) 1:2	C) 1:8	D) 1:1	E) 1:6

Solution: 1:8   Answer:1:8
Answer: C
A train 700 m long can cross an electric pole in 20 sec and then find the speed of the train?  Choose the correct choice:
A) 117 Kmph
B) 178 Kmph
C) 126 Kmph
D) 118 Kmph
E) 119 Kmph

Solution: Length = Speed * time   Speed = L/T   S = 700/20= 
700/20 = 35
35 M/Sec   Speed= 35*18/5 (To convert M/Sec in to Kmph multiply by 18/5)   Speed = 126 Kmph   Answer: 126 Kmph
Answer: C