MU-NLPC/Calc-aqua_rat huggingface dataset:
21 buses are running between two places P and Q. In how many ways can a person go from P to Q and return by a different bus?
Choose the correct choice from the following options:
A) 625
B) 600
C) 576
D) 676
E) 420

Solution: we can go in any bus out of the 21 buses.   Hence He can go in 21 ways.   Since we can not come back in the same bus that he used for travelling,   we can return in 24 ways.   Total number of ways = 21 x 20 = 420   ANSW420R:420
Answer: E
Private Benjamin is a member of a squad of 10 soldiers, which must volunteer 4 of its members for latrine duty. If the members of the latrine patrol are chosen randomly, what is the probability W that private Benjamin will be chosen for latrine duty?	Choose the most appropriate option
A) 1/10  B) 1/5  C) 2/5  D) 3/5  E) 4/5

Solution: Easier way : Desired probability = 1- 'excluded' probability   In this case, Excluded probability = probability of Benjamin not being a part of the 4 volunteers. We can choose 4 out of 9 remaining soldiers in 9C4 ways. total ways possible = 10C4.   Thus excluded probability = 9C4/10C4 = 3/5   Thus, the desired probability W= 1- 3/5 = 2/5. Thus 2/5 is the correct answer.
Answer: C
Donovan took a math test and got 35 correct and 10 incorrect answers.
What was the percentage of correct answers? (Round to the nearest
hundredth)
Choose the correct choice from the following answers:  A) 57.78%  B) 67.78%  C) 77.78%  D) 47.78%  E) 97.78%

Solution: 35 correct answers+10 incorrect answers=45 total answers   Multiple the opposites   100 x 35 = 3500   77.777/3500   77.78% (rounded to hundredth)   correct answer 77.78%
Answer: C
If a choir consists of 2 boys and 4 girls, in how many ways can the singers be arranged in a row, so that all the boys are together? Do not differentiate between arrangements that are obtained by swapping two boys or two girls.  Choose the correct choice from the following answers
A) 120  B) 30  C) 24  D) 11  E) 5

Solution: There are 5 possibilities:   bbgggg   gbbggg   ggbbgg   gggbbg   ggggbb   Think of all 2 boys as a single unit. Together with 4 girls it makes a total of 5 units. The difference between the arrangements is the position of the boys (as a single unit). So the problem reduces to finding the number of unique patterns generated by changing the position of the boys who can occupy 1 of 5 available positions. If the number of available unique positions is 5, then the number of unique patterns equals 5 as well.   Answer: 5.
Answer: E
If the product of two positive integers is 144, which of the following could be the LCM and HCF of the two numbers?
I. LCM : 24; HCF : 6
II. LCM : 18; HCF : 8
III. LCM : 16; HCF : 9  Choose the correct choice from the following answers: A) I only B) II and III only C) I and II only D) I and III only E) I, II and III

Solution: We need to keep two things in mind here:   1. Product of two numbers = LCM*HCF   2. LCM should be a multiple of HCF   Only Statement I follows these two rules.   Correct Option I only
Answer: A
Ramu rides his bike at an average speed of 45 km/hr and reaches his desitination in four hours. Somu covers the same distance in six hours. If Ramu covered his journey at an average speed which was 9 km/hr less and Somu covered his journey at an average speed which was 10 km/hr more, then the difference in their times taken to reach the destination would be (in minutes).  Pick one
A) 23 minutes	B) 30 minutes	C) 87 minutes	D) 16 minutes	E) 19 minutes

Solution: Distance travelled by Ramu = 45 * 4= 
45 * 4 = 180
180 km   Somu travelled the same distance in 6 hours.   His speed= 180/6= 
180/6 = 30
30 km/hr   Hence in the conditional case, Ramu's speed= 45 - 9= 
45 - 9 = 36
36 km/hr and Somu's speed= 30 + 10= 
30 + 10 = 40
40km/hr.   Therefore travel time of Ramu and Somu would be 5 hours and 4.5 hours respectively. Hence difference in the time taken= 0.5 hours = 30 minutes.   Answer: 30 minutes
Answer: B
A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 52 years now, the son's age five years back was?  Choose the correct choice:  A) 16 years  B) 14 years  C) 18 years  D) 21 years  E) 15 years

Solution: Let the son's present age be x years.   Then, (52 - x) = x   2x = 52 => x = 26   Son's age 5 years back = (26 - 5)= 
(26 - 5) = 21
21 years.   Answer: 21 years
Answer: D
A car takes 6 hours to cover a distance of 540 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?  Choose the correct choice:
A) 50 Kmph  B) 60 Kmph  C) 65 Kmph  D) 70 Kmph  E) None

Solution: Time = 6   Distence = 540   3/2 of 6 hours = 6 * 3/2= 
6 * 3/2 = 9
9 Hours   Required speed= 540/9= 
540/9 = 60
60 Kmph   60 Kmph)
Answer: B
Increasing the original price of a certain item by 25 percent and then increasing the new price by 25 percent is equivalent to increasing the original price by what percent?	Pick:
A) 31.25
B) 37.5
C) 50.0
D) 52.5
E) 56.25

Solution: Soln:-   X*1.25*1.25 = 1.5625 X   so there is a net increase of 56.25% .   Answer 56.25.
Answer: E
A train 300m long takes 9 sec to cross a man walking at 3kmph in a direction opposite to that of the train. Find the speed of the train? Choose the correct choice from the following options.
A) 100kmph B) 90kmph C) 120kmph D) 117kmph E) 125kmph

Solution: Let the speed of the train be x kmph   Speed of the train relative to man = x+3 = (x+3)*5/18 m/sec   300/[(x+3)*5/18] = 9   9(x+3) = 1080   x = 117kmph   Answer is 117kmph
Answer: D
If a^x = b^y, then  Answers:
A) log a/b= x/y
B) log a/ log b = x/y
C) log a/ log b = y/x
D) log b/a = x/y
E) log b/a = y/x

Solution: a^x = b^y => log a^x = log b^y => x log a = y log b   => log a/ log b = y/x   ANSWER:log a/ log b = y/x
Answer: C
On dividing 23 by a number, the quotient is 7 and the remainder is 2. Find the divisor.  Options.
A) 1  B) 2  C) 3  D) 6  E) 7

Solution: d = (D-R)/Q   = (23 - 2)/7   = 21/7= 
21/7 = 3
3   3
Answer: C
Nitin borrowed some money at the rate of 6% p.a. for the first three years, 9% p.a. for the next five years and 13% p.a. for the period beyond eight years. If the total interest paid by him at the end of eleven years is Rs. 8160, how much money did he borrow? Choose the correct choice:
A) 8000
B) 9289
C) 2689
D) 2769
E) 2992

Solution: Let the sum be Rs. x. Then,   [(x * 6 * 3)/100] + [(x * 9 * 5)/100] + [(x * 13 * 3)/100] = 8160   18x + 45x + 39x = (8160 * 100)   102x = 816000 => x = 8000.   8000nswer:8000
Answer: A
What least number should be subtracted from 13600 such that the remainder is divisible by 87 ?
Choose the correct choice from the following choices.
A) 27  B) 29  C) 28  D) 30  E) 31

Solution: 13600 ÷ 87 = 156, remainder = 28   Hence 28 is the least number which can be subtracted from 13600 such that the remainder   is divisible by 87   Answer is 28
Answer: C
You collect baseball cards. Suppose you start out with 16. Since you're nice, you give John 4 baseball cards. How many baseball cards do you have at the end?  Choose the correct choice from the following answers
A) 11	B) 12	C) 13	D) 14	E) 15

Solution: Solution   Start with 16 baseball cards.   John takes 4 baseball cards from you:   16 - 4= 
  16 - 4 = 12
12 baseball cards.   So you have 12 at the end.   Correct answer : 12
Answer: B
If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 2 years the amount to be paid is?	Choose the correct choice from the following options.
A) 3377	B) 2688	C) 2688	D) 8112	E) 1268

Solution: A = 7500(26/25)2 = 8112   Answer: 8112
Answer: D
If x and y are integers and 3^(x-4) = 3^(y-2), what is y in terms of x?  Choose the correct option.
A) x - 6	B) x - 5	C) x - 2	D) x + 2	E) x + 6

Solution: Answer: A   3^(x-4) = 3^(y-2)   Since the base is the same, I isolated the equations and solved for y.   x-4 = y-2   y=x-2   Ans : x - 2
Answer: C
A train 250 m long passed a pole in 25 sec. How long will it take to pass a platform 650 m long?  Choices:	A) 78	B) 43	C) 51	D) 66	E) 90

Solution: Speed = 250/25= 
250/25 = 10
10 m/sec.   Required time= (250 + 650)/10= 
(250 + 650)/10 = 90
90 sec.   Answer: 90
Answer: E
From a group of 5men and 4 women, 3 persons are to be selected to form a committee so that at least 2 men are there are on the committee. In how many ways can it be done? Choose one:
A) 20  B) 50  C) 65  D) 86  E) 96

Solution: We have (2men and 1 woman) or (3men only)   Therefore, Required number of ways= (5C2*4C1) + (5C3)   = (5*4)/(2*1) * 4 + 5C2   = 10*4 + 10   = 40 +10= 
40 +10 = 50
50   ANSWER:50
Answer: B
A man walking at a rate of 10km/hr crosses a bridge in 24 minutes. The length of the bridge is?  Options.
A) 1521	B) 1492	C) 1667	D) 4000	E) 1112

Solution: Speed = 10*5/18 = 50/18 m/sec   4000istance covered in 24 minutes = 50/18 * 24 *60= 
50/18 * 24 *60 = 4_000
4000 m   Answer is 4000
Answer: D
40 is subtracted from 60% of a number, the result is 50. Find the number?  Choose the correct answer:  A) 150  B) 887  C) 769  D) 266  E) 291

Solution: (60/100) * X – 40 = 50   6X = 900   X = 150   150nswer: 150
Answer: A
If Sharon's weekly salary increased by 16 percent, she would earn $406 per week. If instead, her weekly salary were to increase by 20 percent, how much would she earn per week?  Choose one.
A) $420	B) $382	C) $385	D) $392	E) $399

Solution: (406/116)120 =420   In this case long division does not take much time.   (406/116)= 
(406/116) = 7/2 = around 3.5
3.5   35*12= 
35*12 = 420
420(350+70)   $420nswer $420
Answer: A
2 pipes function simultaneously the reservoir will be filled in 12 hrs. One pipe fills reservoir 10 hrs faster thanthe other. How many hours does the faster pipe take to fill the reservoir?  Choose one:
A) 12  B) 20  C) 24  D) 26  E) 29

Solution: 1/x + 1/(x + 10) = 1/12   x = 20   20
Answer: B
A bike covers a certain distance at the speed of 56km/h in 5 hrs. If the bike was to cover the same distance in approximately 7 hrs, at what approximate speed should the bike travel? Select:
A) 39 km/h
B) 35 km/h
C) 55 km/h
D) 40 km/h
E) 50 km/h

Solution: Ans.(D)   Sol. Total distance = 56 × 5 = 280 km   Now speed = 280/7= 
280/7 = 40
40 km/h
Answer: D
A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is:
Choose the correct choice from the following answers
A) 3348 B) 3898 C) 1200 D) 2881 E) 7881

Solution: Answer: 1200) 1200
Answer: C
Lagaan is levied on the 60 percent of the cultivated land. The revenue department collected total Rs. 3,94,000 through the lagaan from the village of Mutter. Mutter, a very rich farmer , paid only Rs.480 as lagaan. The percentage of total land of Mutter over the total taxable land of the village is:	Choose the correct choice from the following.
A) 0.20833
B) 0.14544
C) 0.25632
D) 0.35466
E) 0.20304

Solution: Total land of Sukhiya = \inline \frac{480x}{0.6} = 800x   \therefore Cultivated land of village = 394000x   \therefore Required percentage = \inline \frac{800x}{394000}\times 100 = 0.20304   0.20304
Answer: E
Anand and Deepak started a business investing Rs. 22,500 and Rs. 35,000 respectively. Out of a total profit of Rs. 13,800, Deepak's share is? Options
A) 8428	B) 8199	C) 8400	D) 8419	E) 8412

Solution: Ratio of their shares = 22500 : 35000 = 9:14   Deepak's share = 13800 * 14/23   = Rs. 8400.   Answer:8400
Answer: C
A cube of side one meter length is cut into small cubes of side 10 cm each. How many such small cubes can be obtained?	Select:	A) 1278	B) 1728	C) 1000	D) 8732	E) 2881

Solution: Along one edge, the number of small cubes that can be cut   = 100/10= 
100/10 = 10
10   Along each edge 10 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut= 10 * 10 * 10= 
10 * 10 * 10 = 1_000
1000   Answer:1000
Answer: C
A rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m?  Choose the correct answer.
A) 2987 B) 2768 C) 2775 D) 3900 E) 2675

Solution: Area = (l + b – d) d   (80 + 60 – 10)10 => 1300 m2   1300 * 3 = Rs.3900   Answer:3900
Answer: D
Find the value of x from the below equation: x^2−7x+10=0
Choose the correct choice from the following options.
A) 1  B) 2  C) 3  D) 4  E) 5

Solution: Here we need to find out a and b such that a + b = -7 and ab = +10   a = -5 and b = -2 satisfies the above condition.   Hence   x^2−7x+10=(x−5)(x−2)   x2−7x+10=(x−5)(x−2)   x^2−7x+10   =0   ⇒(x−5)(x−2)   =0   x2−7x+10=0⇒(x−5)(x−2)=0   Step 3: Equate each factor to 0 and solve the equations   (x−5)(x−2)   =0   ⇒(x−5)   =0or (x−2)=0   ⇒x= 5 or 2   2
Answer: B
A tank has 5 inlet pipes. Three pipes are narrow and two are wide. Each of the three narrow pipes works at 1/2 the rate of each of the wide pipes. All the pipes working together will take what fraction Y of time taken by the two wide pipes working together to fill the tank?	Choose the correct choice from the following
A) 1/2
B) 2/3
C) 3/4
D) 3/7
E) 4/7

Solution: I always plug in for these questions.. I find them easier   Let 2 large pipes each work fill 10lts/hr   small ones = 1/2*10= 
1/2*10 = 5
5   total 5= 10+10+5+5+5= 
10+10+5+5+5 = 35
35 lts/hrs   now assume the total capacity= 140 lts ( LCM of 20,35)   Qn :All the pipes working together will take what fraction of time taken by the two wide pipes working together to fill the tank   all working together will take 140/35= 
140/35 = 4
4 hrs   two large pipes working will take   140/20= 
  140/20 = 7
7 hrs   hence ratio Y= 4/7 = 4/7
Answer: E
A football player just signed a new contract in which he will earn a 10% raise in base pay from the previous year. Last year, he did not earn a performance bonus; but this year, he will have the chance to earn a performance bonus of up to $20,000. If his new salary is effectively an 11% raise after earning the top performance bonus, what is his new salary? Choose the correct option:
A) 2,120,000  B) 2,170,000  C) 2,210,000  D) 2,220,000  E) 2,360,000

Solution: let x = the old salary   (1+.10)*x + 20,000 = (1+.11)*x   1.1x + 20,000 = 1.11x   20,000 = .01x   2,000,000 = x   the new salary is thus (1+.11)*2,000,000 = 1.11*2,000,000 = 2,220,000   2,220,000
Answer: D
On a certain transatlantic crossing, 20 percent of a ship’s passengers held round-trip tickets and also took their cars abroad the ship. If 50 percent of the passengers with round-trip tickets did not take their cars abroad the ship, what percent of the ship’s passengers held round-trip tickets?
Choose one.
A) 30%	B) 40%	C) 50%	D) 60%	E) 65%

Solution: Let T be the total number of passengers.   Let x be the number of people with round trip tickets.   0.2T had round trip tickets and took their cars.   0.5x had round trip tickets and took their cars.   0.5x = 0.2T   x = 0.4T   The answer is 40%.
Answer: B
In how many ways can the letters of wordSOLUTIONbe arranged such that all the Consonants always appear together?
Choose the correct choice from the following answers:
A) 9!  B) 5!*4!  C) 5!*5!  D) 5!*4!*2!  E) 6!*4!

Solution: Let the arrangment be: _ _ _ _ _ _ _ _ _ _ (8 letters, 4 vowels O, U, I, O and 4 consonant S, L, T, N)   For all consonants together, consider them as 1 group {S, L, T, N} O U I O --> this gives us 5! arrangements with {} group considered as 1 . Now {} group can in itself be arranged in 4! ways   Thus total arrangements with all consonants together = 5!*4! --> 5!*4! is the correct answer.
Answer: B
Out of first 50 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is -.  Choose the correct choice from the following:
A) 1/2  B) 16/19  C) 4/5  D) 61/50  E) 3/5

Solution: n(S) = 50   n(Even no) = 25 = n(E)   n(Prime no) = 15 = n(P)   P(EᴜP) = 25/50 + 15/50 - 1/50 = 61/50   ANSWER:61/50
Answer: D
A cistern 12 m long and 14 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:  Choose the correct option.
A) 224 m2 B) 250 m2 C) 220 m2 D) 230 m2 E) 233 m2

Solution: Area of the wet surface	= [2(lb + bh + lh) - lb]   = 2(bh + lh) + lb   = [2 (14 x 1.25 + 12 x 1.25) + 12 x 14] m2   = 233 m2.   answer :233 m2
Answer: E
When 15 is divided by integer u, the remainder is 4. For how many values of u is this be true? Select: A) 1 B) 2 C) 3 D) 4 E) 5

Solution: When 15 is divided by u, the remainder is 4 i.e. 4 mangoes left over after grouping, so u must be greater than 4.   It also means that 11 is completely divisible by u.   Factors of 11 are 1 and 11.   Out of these, u could be 11.   1nswer (1)
Answer: A
in a rectangle 8 vertical and 4 horizontal lines are drawn find the number of rectangle formed ?
Select the correct option
A) 654	B) 664	C) 674	D) 684	E) 694

Solution: 8 vertical lines plus the 2 lines of the existing rectangle(as its mentioned in the question "in a rectangle") accordingly 4 plus 2 horizontal lines.   therefore   106742*66742= 675 and if its asked for the new rectangle formed than   675-1= 
675-1 = 674
674 (excluding the existing rectangle)   ANSWER:674
Answer: C
Two bullet trains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each bullet train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?  Choose the correct choice from the following.
A) 13 sec.	B) 15 sec.	C) 12 sec.	D) 17 sec.	E) 19 sec.

Solution: C   12 sec.   Speed of the first bullet train = 120/10 m/sec = 12 m/sec.   Speed of the second bullet train = 120/15 m/sec = 8 m/sec.   Relative speed = (12 + 8)= 
(12 + 8) = 20
20 m/sec.   Required time= (120 + 120)/20= 
(120 + 120)/20 = 12
12 sec.
Answer: C
Which of the following is divisible by the first thousand positive even integer multiples of 101?
(i) 55650000
(ii) 234177623000
(iii)11111111111110000000000000000000000000
Choose the most appropriate option:	A) None	B) i only	C) ii only	D) iii only	E) i, ii and iii

Solution: The digits of (iii) add to 13, so (iii) is not divisible by 3, so is not divisible by 3*101, and hence not divisible by the first thousand positive even integer multiples.   A positive integer x is divisible by the first thousand integer multiples of 101 if and only if it is divisible by their least common multiple. There are at least 12 primes greater than 10 but less than 1000 so to be divisible by the first thousand integer multiples of 101 x must be at least 10^12. Consquently, neither (i) not (ii) is divisible by the first thousand integer multiples of 101.   Nonenswer None
Answer: A
A can do a piece of work in 12 days and B can do a piece of work in 18 days how many days will the work be completed if both of them work together?	Choices: A) 15 B) 7.2 C) 7.7 D) 7.4 E) 8

Solution: A's 1 day work=1/12,7.2's 1 day work =1/18;   (A+7.2) 1 day work=1/12+1/18=5/36;   they can finish the work in=36/5= 
36/5 = 36/5 = around 7.2
7.2   ANSWER:7.2
Answer: B
Two trains of equal are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is? Pick
A) 50  B) 99  C) 88  D) 71  E) 65

Solution: Let the length of each train be x m.   Then, distance covered = 2x m.   Relative speed = 46 - 36= 
46 - 36 = 10
10 km/hr.= 10 * 5/18 = 25/9 m/sec.   2x/36 = 25/9 => x = 50.   50nswer:50
Answer: A
Rs. 6000 is lent out in two parts. One part is lent at 7% p.a simple interest and the other is lent at 10% p.a simple interest. The total interest at the end of one year was Rs. 450. Find the ratio of the amounts lent at the lower rate and higher rate of interest? Choose the correct choice.
A) 5:1	B) 5:5	C) 5:8	D) 5:4	E) 5:2

Solution: Let the amount lent at 7% be Rs. x   Amount lent at 10% is Rs. (6000 - x)   Total interest for one year on the two sums lent   = 7/100 x + 10/100 (6000 - x) = 600 - 3x/100   => 600 - 3/100 x = 450 => x = 5000   5:1mount lent at 10% = 1000   Required ratio = 5000 : 1000 = 5:1   5:1nswer:5:1
Answer: A
If BELT is coded as 27 and JUMPED is coded as 54, then CHAIRS is coded as
Choose one:  A) 10  B) 21  C) 40  D) 92  E) None

Solution: BELT= 2+5+12+20= 
2+5+12+20 = 39
39 i.e 3*9=27   JUMPED= 10+21+13+16+5+4= 
10+21+13+16+5+4 = 69
69 i.e 6*9=54   40HAIRS= 3+8+1+9+18+19= 
3+8+1+9+18+19 = 58
58 5*8=40   ANSWER:40
Answer: C
A girl has 7 jeans and 12 shirts. In how many different ways can she select a jeans and a shirts?	Select: A) A)100 B) B)102 C) C)108 D) D)110 E) E)84

Solution: The girl can select one jeans in 7 ways.   The girl can select one shirt in 12 ways.   The number of ways in which he can select one jeans and one shirt is 7 * 12= 
7 * 12 = 84
84 ways.   84
Answer: E
The width of a rectangular hall is ½ of its length. If the area of the hall is 800 sq.m, what is the difference between its length and breadth?  Choose the correct choice from the following answers.
A) 8m B) 10m C) 12m D) 20m E) 17m

Solution: Let the length of the hall be x m   Breadth of the hall = 1x/2 m   Area of the hall = Length * Breadth   800 = x * 1x/2   x² = 1600   x =40   20mifference between the length and breadth of the hall = x - 1x/2 = x/2   =40/2= 
40/2 = 20
20m   ANSWER:20m
Answer: D
60% of a number is added to 150, the result is the same number. Find the number?	Choose the correct choice from the following options:
A) 375  B) 277  C) 266  D) 99  E) 121

Solution: :   (60/100) * X + 150 = X   2X = 750   X = 375   375nswer: 375
Answer: A
Tough and Tricky questions: Distance/Rate.
On a reconnaissance mission, a state-of-the-art nuclear powered submarine traveled 600 miles to reposition itself in the proximity of an aircraft carrier. This journey would have taken 2 hour less if the submarine had traveled 10 miles per hour faster. What was the average speed, in miles per hour, for the actual journey?
Answers
A) 20	B) 40	C) 60	D) 50	E) 100

Solution: Say, if speed is 50, 600/50 = 12 hrs and 600/60= 
600/60 = 10
10 hrs (a reduction of 2 hr -> Correct answer)   Answer (50)
Answer: D
After 57 liters of petrol were poured into the tank, it was still 5% empty. How much petrol must be poured into the tank in order to fill it?  Select the correct option:
A) 7 liters  B) 4 liters  C) 3 liters  D) 2 liters  E) 6 liters

Solution: 95% ----------- 57   5% ------------ ?   => 3 liters   Answer: 3 liters
Answer: C
A sum of money becomes Rs. 2200 after three years and Rs. 4400 after six years on compound interest. The sum is  Pick:
A) Rs. 1400 B) Rs. 1100 C) Rs. 1000 D) Rs. 1200 E) Rs. 1400

Solution: Explanation:   Let the sum be P and rate of interest be R% per annum.   Amount after 3 years = 2200   P(1 + R/100)T = 2200   P(1 + R/100)3 = 2200 --- ( 1)   Amount after 6 years = 4400   P(1+R/100)T = 4400   P(1 + R/100)6 = 4400 --- (2)   (2) ÷ (1) => [P(1+R/100)6]/[P(1+R/100)3] = 4400/2200= 
4400/2200 = 2
2=> (1+R/100)3 = 2 (Substituting this value in equation 1)   => P × 2 = 2200   P = 22002 = 1100   Answer: Option Rs. 1100
Answer: B
The greater of two numbers is twice the less, and the sum of the numbers is 96. What are the numbers? Pick one.
A) 64	B) 68	C) 70	D) 79	E) 80

Solution: Let x = the less number   2x = the greater number   The sum of the numbers is 96   x+2x=96   3x=96   x=32   2x=64   Option 64
Answer: A
A man can row upstream at 15kmph and downstream at 17kmph. Find man's rate in still water ? Options:
A) 5km/hr
B) 15km/hr
C) 10km/hr
D) 20km/hr
E) 16km/hr

Solution: Rate in still water = 1/2 (15+17) = 16km/hr   Answer is 16km/hr
Answer: E
The value of (2.75)3 - (2.00)3 - (0.75)3 is Pick
A) 12.375
B) 6
C) 9
D) 8
E) 2

Solution: Explanation:   (2.75)3 - (2.00)3 - (0.75)3   a^3 + b^3 + c^3 = (a + b + c)(a^3 + b^3 + c^3 - ab - bc - ca)   If a + b + c = 0 then a^3 + b^3 + c^3 = 3abc   Hence 2.75 - 2.00 - 0.75= 
2.75 - 2.00 - 0.75 = 0
0   So, (2.75)3 - (2.00)3 - (0.75)3= 3 * 2.75 * 2 * 0.75 = 3 * 1.5 * 2.75   = 4.5 * 2.75= 
4.5 * 2.75 = 12.375
12.375   12.375
Answer: A
If a copier makes 10 copies every 5 seconds, then continues at this rate, how many minutes will it take to make 10,000 copies?  Choose the most appropriate option.
A) 82.33	B) 81.33	C) 84.33	D) 83.33	E) 85.33

Solution: 10 copies 5 seconds   10000 copies = (10000*5)/10= 
(10000*5)/10 = 5_000
5000/60 minutes= 83.33 minutes   Answer : 83.33
Answer: D