MU-NLPC/Calc-aqua_rat huggingface dataset:
For which of the following does f(p)−f(q)=f(p−q) for all values of p and q? Choices:	A) f(a)=a^2	B) f(a)=a/2	C) f(a)=a+5	D) f(a)=2a−1	E) f(a)=|a|

Solution: To solve this easiest way is just put the value and see that if it equals or not.   with option 1. f(p) = p^2 and f(q) = q^2   so L.H.S = p^2 - q^2   and R.H.S = (p-q)^2 ==> p^2 + q^2 -2pq.   so L.H.S not equal to R.H.S   with option 2. f(p) = p/2 and f(q) = q/2   L.H.S = p/2 - q/2 ==> 1/2(p-q)   R.H.S = (p-q)/2   so L.H.S = R.H.S which is the correct answer.   f(a)=a/2
Answer: B
A cyclist covers a distance of 750 meter in 2 minutes 30 seconds. What is the speed in km/hr of cyclist
Select: A) 16 km/hr B) 17 km/hr C) 18 km/hr D) 19 km/hr E) None of these

Solution: ExplanaƟon:   Speed=DistanceTimeDistance=750meterTime=2 min 30   sec=150secSpeed=750150=5m/sec=>5   ∗   185km/hr=18km/hr   Answer: 18 km/hr
Answer: C
The sum of the first k positive integers is equal to k(k+1)/2. What is the sum of the integers from a to b, inclusive, where 0<a<b?	Options:
A) b(b+1)/2 - (a+1)(a+2)/2
B) b(b+1)/2 - a(a+1)/2
C) b(b+1)/2 - (a-1)a/2
D) (b-1)b/2 - (a+1)(a+2)/2
E) (b-1)b/2 - a(a+1)/2

Solution: Or try plug-in method: let b=4 and a=3 --> then b+a=7. Let see which option yields 7.   A. b(b+1)/2 - (a+1)(a+2)/2 = 10-10= 
10-10 = 0
0;   B. b(b+1)/2 - a(a+1)/2= 10-6= 
10-6 = 4
4;   C. b(b+1)/2 - (a-1)a/2= 10-3= 
10-3 = 7
7 --> OK;   D. (b-1)b/2 - (a+1)(a+2)/2= 6-10=-4;   E. (b-1)b/2 - a(a+1)/2 = 6-6= 
6-6 = 0
0.   Answer: b(b+1)/2 - (a-1)a/2.
Answer: C
TATA company has four empty trucks that will head out in the morning, all four to the same destination. The clerk has four different boxes to ship to that same destination. All four boxes could go on any one of the trucks, or the boxes could be split up into any groupings and given to the trucks in any combinations (ie. two to one truck, one to another, and one to another). In how many different ways could the boxes be put on the four trucks?
Options:
A) 16 B) 64 C) 256 D) 576 E) 4096

Solution: MAGOOSHOFFICIAL SOLUTION:   TATA company has four empty trucks that will head out in the morning, all four to the same destination. Where we put one box has absolutely no bearing on where we put any of the other boxes. The placement of the four boxes is completely independent of one another. For each box, we have four choices.   N = 4*4*4*4 = 16*16= 
16*16 = 256
256   Answer= (256)
Answer: C
The average monthly salary of 20 employees in an organisation is Rs. 1500. If the manager's salary is added, then the average salary increases by Rs. 1000. What is the manager's monthly salary ?
Choices:	A) Rs.16003	B) Rs.16029	C) Rs.22500	D) Rs.16108	E) Rs.16011

Solution: Explanation:   Manager's monthly salary Rs. (2500 * 21 - 1500 * 20) = Rs.22500.   Answer: Rs.22500
Answer: C
A can do a piece of work in 10 days and B can do it in 15 days and C can do it 20 days. They started the work together and A leaves after 2 days and B leaves after 4 days from the beginning. How long will work lost?
Pick one
A) 10 2/8  B) 10 2/9  C) 10 2/3  D) 10 2/2  E) 10 2/1

Solution: 2/10 + 4/15 + x/20 = 1   x = 32/3 = 10 2/3   Answer: 10 2/3
Answer: C
76^77 /7
remainder is ? Answers.
A) 5	B) 6	C) 7	D) 8	E) 9

Solution: as, 4^3/3=64/3 remainder=1 and also 4/3=1   and 5^3/3 remainder=2 and also 5/3=2   so it does not matter on the power value   so the answer will be 76/7 remainder=6   ANSWER:6
Answer: B
In a simultaneous throw of a pair of dice, find the probability of getting a total more than 11
Answers:
A) 11/25  B) 7/12  C) 5/13  D) 5/12  E) 6/17

Solution: Total number of cases = 10*10= 
10*10 = 100
100   Favourable cases= [(2,10),(3,9),(3,10),(4,8),(4,9),(4,10),(5,7),(5,8),(5,9),(5,10),(6,6),(6,7),(6,8),(6,9),(6,10),(7,5),(7,6),(7,7),(7,8),(7,9),(7,10),(8,4),(8,5),(8,6),(8,7),(8,8),(8,9),(8,10),(9,3),(9,4),(9,5),(9,6),(9,7),(9,8),(9,10),(10,2),(10,3),(10,4),(10,5),(10,6),(10,7),(10,8),(10,9),(10,10)] = 44   So Probability = 44/100 = 11/25   11/25nswer is 11/25
Answer: A
The compound ratio of 2/5, 6/7, 1/3 and 1/8 is given by?  Pick:  A) 7/98  B) 1/70  C) 1/98  D) 1/96  E) 1/68

Solution: 2/5 * 6/7 * 1/3 * 1/8 = 12/840 = 1/70   ANSWER:1/70
Answer: B
On a certain number line, there are 10 marks evenly spaced. If the fifth mark has a value equal to 2.3 and the tenth mark's value is equal to 3.8, then what is the value of the second mark?  Select:
A) 0.3
B) 1.1
C) 1.4
D) 1.5
E) 1.7

Solution: 5th Mark = 2.3   10th Mark = 3.8   Evenly spaced means we have 5 gaps of equal length between 5th and 10th mark.   So, Each gap distance = 3.8 - 2.3 /10 = 0.3   So, 2nd mark will be  2.3 - 3*0.3= 
 2.3 - 3*0.3 = 1.4
1.4   Answer 1.4.
Answer: C
AMOUNT OF BACTERIA PRESENT
Time Amount
1:00 P.M. 20.0 grams
4:00 P.M. x grams
7:00 P.M. 24.4 grams
Data for a certain biology experiment are given in the table above. If the amount of bacteria present increased by the same fraction during each of the two 3-hour periods shown, how many grams of bacteria were present at 4:00 P.M.?
Choose one:  A) 22.0  B) 12.1  C) 12.2  D) 22.3  E) 12.4

Solution: The question says that bacteria increased by same fraction, not by same amount in 2 intervals of 3 hours.   Let X represent the amount of bacteria present at 4:00 PM. Since the fractional increase must remain constant from 1 to 4pm as it is from 4pm to 7pm:   Fractional increase from 1 PM to 4 PM = X / 20.0   Fractional increase from 4 PM to 7 PM = 24.4 / X   X \ 20 = 24.4 \ X   X^2 = 24.4 * 20   X^2 = 444   X = 22   answer : 22.0
Answer: A
Tourist purchased a total of 30 travelers checks in $50 and $100 denominations. The total worth of the travelers checks is $1800. How many checks of $50 denominations can he spend so that average amount (arithmetic mean) of the remaining travelers checks is $62.5? Choose the correct option:  A) 6  B) 12  C) 15  D) 20  E) 24

Solution: you could set-up a quick table and brute force the answer.   6	6	*	50	300 1800	-300	1500 24 62.50   B	16	*	50	600 1800	-600	1200 18 66.67   C	15	*	50	750 1800	-750	1050 15 70.00   D	20	*	50	1000 1800	-1000 800 10 80.00   E	24	*	50	1200 1800	-1200 600 6 100.00   6nswer is 6
Answer: A
There are 15 cans in the refrigerator. 7 of them are red and 8 of them are blue. In how many ways we can remove 8 cans so that at least one red and at least one blue cans to remain the refrigerator. Answers
A) 460  B) 490  C) 493  D) 455  E) 445

Solution: Answer: 490.
Answer: B
A thief steals at a car at 4.30 p.m. and drives it at 60 km/hr. The theft is discovered at 3 p.m. and the owner sets off in another car at 75 km/hr. When will he overtake the thief? Choose the correct answer:  A) 1 p.m  B) 3 p.m  C) 4 p.m  D) 5 p.m  E) 7 p.m

Solution: E   7 p.m   Suppose the thief is overtaken x hrs after 4.30 p.m.   Then, distance covered by the owner in (x - 1/2) hrs.   60x = 75(x - 1/2) => x = 5/2 hrs.   So, the thief is overtaken at 7 p.m.
Answer: E
The C.P of 16 books is equal to the S.P of 18 books. Find his gain% or loss%?  Choose the correct choice from the following answers:
A) 11 1/9%
B) 16 2/8%
C) 16 2/5%
D) 16 2/1%
E) 16 1/3%

Solution: 16 CP = 18 SP   18 --- 2 CP loss   100 --- ? => 11 1/9% loss.11 1/9%nswer: 11 1/9%
Answer: A
A person buys an article at Rs.480. At what price should he sell the article so as to make a profit of 24%?  Choose the correct answer:	A) 595	B) 882	C) 772	D) 662	E) 521

Solution: Cost price = Rs.480   profit = 24% of 480 = Rs.115   Selling price = Cost price + Profit   = 480 + 115= 
480 + 115 = 595
595   595nswer: 595
Answer: A
A bag contains 12 white and 18 black balls. 2balls are drawn in succession. What is the probability that 1st is white and second is black? Pick one:
A) 12/123
B) 36/145
C) 13/115
D) 1/213
E) 2/231

Solution: The probability that first ball is white:   =12C130C1=12C130C1   =1230=1230   =25=25   Since, the ball is not replaced; hence the number of balls left in bag is 29.   Hence, the probability the second ball is black:   =18C129C1=18C129C1   =1829=1829   Required probability,   =(25)×(1829)=(25)×(1829)   =36/145   36/145
Answer: B
In a jar there are balls in different colors: blue, red, green and yellow.
The probability of drawing a blue ball is 1/6.
The probability of drawing a red ball is 1/5.
The probability of drawing a green ball is 1/10.
If a jar cannot contain more than 50 balls, how many yellow balls are in the Jar?
Choose the most appropriate option
A) 25.  B) 24.  C) 23.  D) 20.  E) 16.

Solution: We need to get some number which is less than 50 and exactly divisible by 6,5 and 10   Lets take LCM of three balls 6,5 and 10 = 30.   The probability of drawing a blue ball is 1/6...For every 8 balls we get 1 BLUE ball then out of 30 balls we get 5 BLUE balls.   The probability of drawing a red ball is 1/5...For every 5 balls we get 1 RED ball then out of 30 balls we get 6 REB balls.   The probability of drawing a green ball is 1/10. For every 10 balls we get 1 GREEN ball then out of 30 balls we get 3 GREEN BALLS.   Then out of 30 - ( 5 + 6 + 3 )= 
30 - ( 5 + 6 + 3 ) = 16
16 YELLOW balls.   IMO option 16. is correct.
Answer: E
P, Q, R, S, T and U are six cities which are in a row in the same order. A bus, b1 travels from P to U and another bus b2 travel from U to P. The bus b1 reaches S at 10:40 and bus b2 reaches Q at 10:35 if the travel time between any two adjacent cities is 40 minutes and the stoppage time at each city is 15 minutes, then at what time do they start at their respective destinations? Pick:  A) 8:00, 7:00  B) 8:00, 7:10  C) 8:10, 7:10  D) 8:15, 7:25  E) 8:10, 7:00

Solution: Explanation:   The bus b1, which started at P, reached S at 10:40, passing through the intermediary cities Q and R.   The time taken to travel from P to S   = 3 * 40 + 2 * 15= 
3 * 40 + 2 * 15 = 150
150minute   (journey)+(stoppage)= 2 hrs 30 minutes.   Hence, b1 started at 10:40 - 2:30 = 8:10 at P.   b2 reached Q, starting at U, through the city T, S and R.   The time taken by it to reach S = 4 * 40 + 3 * 15= 
4 * 40 + 3 * 15 = 205
205 minutes= 3 hr 25 minutes.   Hence, b2 started at, 10:35 - 3:25 = 7:10, at U.   ANSWER IS 8:10, 7:10
Answer: C
X and Y are two towns. Ganesh covers the distance from X to Y at an average speed of 54 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 : Pick.
A) 34	B) 43.2	C) 40	D) 38	E) 29

Solution: Solution: Average speed = 2XY / X+Y   = 2*54*36 / 54+36   = 43.2   Answer : 43.2
Answer: B
The population of a village is 14300. It increases annually at the rate of 15% p.a. What will be its population after 2 years? Choose the most appropriate option:
A) 18911
B) 18788
C) 19898
D) 14000
E) 14400

Solution: Formula :   ( 18911fter =100 denominator   18911go = 100 numerator)   14300 × 115/100 × 115/100 = 18911   18911
Answer: A
Solve for x: 2x – y = (3/4)x + 6.	Answers.
A) (y + 6)/5
B) 4(y + 6)/5
C) (y + 6)
D) 4(y - 6)/5
E) 6(y-4)/5

Solution: 2x – y = (3/4)x + 6.   or, 2x - (3/4)x = y + 6.   or, (8x -3x)/4 = y + 6.   or, 5x/4 = y + 6.   or, 5x = 4(y + 6).   or, 5x = 4y + 24.   or, x = (4y + 24)/5.   Therefore, x = 4(y + 6)/5   correct answer 4(y + 6)/5
Answer: B
On dividing a number by 357, we get 38 as remainder.On dividing the same number by 17, what will be the remainder ?
Choose the correct option.
A) 4  B) 5  C) 8  D) 7  E) 2

Solution: Let x be the number and y be the quotient.Then,   x=357*y+38   =(17*21*y)+(17*2)+4   =17*(21y+2)+4.   Required number =4.   4nswer is 4
Answer: A
If 3^x*4^y = 1,594,323 and x – y = 13, then x = ?	Choose the correct choice.
A) 10 B) 11 C) 12 D) 13 E) 14

Solution: Since 1,594,323 is an odd number, it is not a multiple of 4.   This means that y must equal zero.   Since x - y = 13 and y = 0, then x = 13.   The answer is 13.
Answer: D
The area of a parallelogram is 128sq m and its altitude is twice the corresponding base. Then the length of the base is? Choose the most appropriate option:
A) 8
B) 9
C) 7
D) 6
E) 4

Solution: 2x * x = 128 => x= 8   8nswer: 8
Answer: A
Lines y=√2·x+2 and y=3√2·x−1 intersect at what height above the x axis? Choose the correct choice from the following answers: A) (13√2)/2 B) 13/2 C) 13 D) 2 E) 0

Solution: Solve two equations for y   y=√2·x+2   y=3√2·x−1   Set the two equations equal to each other and solve for x   √2·x+2 = 3√2·x−1   3 = 2√2·x   3/(2√2) = x   Plug x = 3/(2√2) into any one of the original equations to find the y value (height above x axis) where the two lines intersect   y=√2·x+2   y=√2·(3/(2√2))+2   y = 3/2 + 5   y = 3/2 + 10/2   y = 13/2   Final answer:   13/2) 13/2
Answer: B
Calculate how many men are needed to finish a specific task in 35 days if it will take 20 men to complete the same task in 70 days. ? Answers.
A) 40
B) 20
C) 10
D) 30
E) 60

Solution: men required to finish the work in 35 days = 20*70/35= 
20*70/35 = 40
40   40nswer is 40
Answer: A
The length W of a rectangle is decreased by 15% and its width is increased by 40%. Does the area of the rectangle decrease or increase and by what percent?
Choose the correct option.
A) Decreases by 19%	B) Decreases by 25%	C) Increases by 6%	D) Increases by 19%	E) Increases by 25%

Solution: Let the length W of the rectangle be 100x, and width be 100y. Area = 100x * 100y = 10000xy   Now after the change Length 100  * 100= 
100  * 100 = 10_000
10000xy   Now after the change Length= 85x, and width = 140 y. Area = 11900xy   % Change = (11900xy - 10000xy)/(10000xy) = 19 % Increase. Hence Increases by 19%.
Answer: D
The ratio between the speeds of two Bullet trains is 7: 8. If the second Bullet train runs 440 kms in 4 hours, then the speed of the first train is:  Choose the most appropriate option:
A) 89.25 km/hr.	B) 37.25 km/hr.	C) 90.25 km/hr.	D) 94.25 km/hr.	E) 96.25 km/hr.

Solution: E   96.25 km/hr.   Let the speed of two bullet trains be 7x and 8x km/hr.   Then, 8x = (440/4)= 
(440/4) = 110
110   x= (110/8)= 
(110/8) = 55/4 = around 13.75
13.75   Hence, speed of first bullet train= (7 x 13.75) km/hr = 96.25 km/hr.
Answer: E
In a village of 120 families, 93 families use firewood for cooking, 63 families use kerosene, 45 families use cooking gas, 45 families use firewood and kerosene, 24 families use kerosene and cooking gas, 27 families use cooking gas and firewood. Find how many useall?
Choose the most appropriate option:
A) 120 B) 93 C) 150 D) 15 E) 45

Solution: Let F,K and G represent the sets of students who liked rock music, folk music and classical music respectively.   F=93, K=63, G=45   F and K=45   F and G=27   K and G=24   All= 120-93-63-45+45+27+24= 
120-93-63-45+45+27+24 = 15
15   ANSWER 15
Answer: D
X’s income is 3/4 of Y’s income, and X’s expenditure is 4/5 of Y’s expenditure. If X’s income is 9/10 of Y’s expenditure, find the ratio of X’s savings to Y’s savings ?
Choose the correct choice:  A) 1 : 2  B) 2 : 1  C) 1 : 4  D) 2 : 3  E) 3 : 2

Solution: Let X’s income be 3k then Y’s income is 4k.   Let X’s expenditure be 4g then Y’s expenditure is 5g.   But 3k = 9/10 (5g) or k = 3/2g   X’s saving/Y’s saving = (3k - 4g)/(4k - 5g)   [3 (3 / 2g) - 4g]/[ 4(3 / 2g) - 5g] = 1/2   X’s saving : Y’s saving = 1 : 2   1 : 2NSWER:1 : 2
Answer: A
If 31% of a number is 46.5,the number is ?  Choose one: A) 150 B) 155 C) 160 D) 165 E) None

Solution: 150nswer   Let 31% of 150 = 46.5   ⇒ (31 x 150)/100 = 46.5   ∴ 150 = (46.5 x 100) / 31 = 150   Correct Option: 150
Answer: A
On five consecutive flips of a coin, what is the probability that all five produce the same result?	Choose the correct choice from the following: A) 1/16 B) 1/8 C) 1/4 D) 3/8 E) 1/2

Solution: TTTTT case --> P = (1/2)^5 = 1/32   HHHHH case --> P = (1/2)^5 = 1/32   P(TTTTT or HHHHH) = 1/32 + 1/32 = 1/16   1/16nswer: 1/16
Answer: A
Two trains of length 100 meters and 200 meters are 450 meters apart. They are moving towards each other on parallel tracks, at speeds of 90 km/h and 72 km/h. After how many seconds will the trains meet?
Options.
A) 6  B) 8  C) 10  D) 12  E) 14

Solution: The speeds are 90000/3600= 
90000/3600 = 25
25 m/s and 72000/3600= 
72000/3600 = 20
20 m/s   The relative speed is 45 m/s.   time= 450 / 45= 
450 / 45 = 10
10 seconds   The answer is 10.
Answer: C
In a class of students, the ratio of girls to boys is 2:3. If 3 more girls joined the class, the ratio would be 3:4. How many students are in the class?	Choose the correct choice from the following:
A) 50
B) 55
C) 60
D) 65
E) 70

Solution: Let x be the number of students in the class.   (2/5)*x=(3/7)(x+3)-3   14x=15x+45-105   x=60   The answer is 60.
Answer: C
A candidate got 35% of the votes polled and he lost to his rival by 2250 votes. How many votes were cast?	Choose the correct choice from the following answers
A) 7500 B) 7508 C) 7528 D) 7527 E) 7232

Solution: 35%-----------L   65%-----------W   ------------------   30%----------2250   100%---------? => 7500   7500nswer:7500
Answer: A
The ratio between the sale price and the cost price of an article is 7:5. What is the ratio between the profit and the cost price of that article?
Choose one.
A) 2:9	B) 2:5	C) 3:6	D) 2:0	E) 2:1

Solution: Let C.P. = Rs. 5x and S.P. = Rs. 7x.   Then, Gain = Rs. 2x   Required ratio = 2x : 5x = 2:5   Answer:2:5
Answer: B
A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is?  Answers:	A) 281	B) 278	C) 698	D) 277	E) 1911

Solution: S.I. for 1 year = (854 - 815) = Rs. 39   S.I. for 3 years = 39 * 3 = Rs. 117   Principal = (815 - 117) = Rs. 698.   Answer:698
Answer: C
Of the 5 numbers, whose average is 150, the first is one-fourth of the sum of the last 4. The first number is?
Select the correct option.
A) 100  B) 80  C) 70  D) 150  E) 60

Solution: Total of 5 numbers = 5 * 150= 
5 * 150 = 750
750   Let total of last 4 numbers= x   1st number = x/4   x+ x/4 = 750   5x = 3000 => x =600   1st number = 600/ 4= 
600/ 4 = 150
150   Answer : 150
Answer: D
In a rectangular coordinate system, if a line passes through the points (-14,-18), (16,22) and (x,2) then what is the value of x?	Select.
A) 0	B) 1	C) 2	D) 3	E) 4

Solution: The slope of the line m is rise/run = 22-(-18) / 16-(-14) = 4/3   4/3 = 22-2 / 16-x   64-4x = 66-6   x = 1   The answer is 1.
Answer: B
How many 3 digit number contain number 4 ?  Choose one:	A) 352	B) 268	C) 236	D) 252	E) 354

Solution: total 3 digit no. = 9*10*10= 
9*10*10 = 900
900   not containing 4= 8*9*9= 
8*9*9 = 648
648   total 3 digit number contain 4= 900 - 648= 
900 - 648 = 252
252   ANSWER:252
Answer: D
A train speeds past a pole in 15 sec and a platform 130 m long in 25 sec, its length is?	Choose the correct choice from the following
A) 238  B) 150  C) 195  D) 177  E) 171

Solution: Let the length of the train be x m and its speed be y m/sec.   Then, x/y = 15 => y = x/15   (x + 130)/25 = x/15 => x = 195 m.   Answer: 195
Answer: C
A, B and C can do a work in 90, 45 and 6 days respectively. If they work together, in how many days will they complete the work?  Choose the correct answer.
A) 5	B) 6	C) 7	D) 8	E) 11

Solution: One days's work of A, B and C = 1/90 + 1/45 + 1/6   = (1 + 2 + 15)/90 = 1/5   A, B and C together can do the work in 5 days.   5nswer:5
Answer: A
The list price of an article is Rs.70. A customer pays Rs.59.85 for it. He was given two successive discounts, one of them being 10%. The other discount is? Choose the correct choice from the following
A) 8%
B) 7%
C) 10%
D) 6%
E) 5%

Solution: Option 5%   5%xplanation:   70*(90/100)*((100-x)/100) = 59.85   x = 5%
Answer: E
A rectangle the length of which is 8 inches and the width of which is 6 inches is made up 48 1 inch by 1 inch squares. Through how many of the squares does a diagonal of the rectangle pass?
Choose one
A) 6	B) 8	C) 10	D) 12	E) 16

Solution: 1)If the two sides are co-prime, SUM of sides -1..   2)and if not co-prime , Sum of sides - HCF of sides..   the difference is related to the diagonal passing through a vertex of squares at some place..   here 6 and 8 are NOT co-primes, so ans =6+8−HCF(6,8)=14−2=12   ANSWER:12
Answer: D
A person lent a certain sum of money at 4% per annum at simple interest and in 8 years the interest amounted to Rs.340 less than the sum lent. What was the sum lent? Select the correct option.
A) 287 B) 278 C) 296 D) 500 E) 297

Solution: P - 340 = (P*4*8)/100   P = 500   Answer:500
Answer: D
A team bought a total of 450 balls. If each player on the team bought at least 12 balls, then what is the greatest possible number of players on the team?
Choose the correct choice from the following answers.
A) 37
B) 22
C) 23
D) 24
E) 25

Solution: 450/12=37 plus remainder.   The answer is 37.
Answer: A
What is the square root of 168,921?	Choose the correct choice:	A) 476	B) 389	C) 497	D) 411	E) 524

Solution: 1) Checking the last digits in the answer options A, C, E are out since last digit of the square is known to be 1.   2) B = 389^2 and D = 411^2   B = (400-11)^2 and D = (400 + 11)^2   Since we need the answer less than 160000 => B is out.   Thus we have 411 as the ans.
Answer: D
The sum of the squares of three numbers is 138,while the sum of their products take two at a time is 131.Find the sum?	Choose the correct choice from the following answers.
A) 10
B) 30
C) 20
D) 50
E) 40

Solution: Formula is (a+b+c)^2=(a^2)+(b^2)+(c^2)+2(ab+bc+ca)   =138+(2*131)   The sum of the three numbers a+b+c=√400=20   Answer is option 20
Answer: C
At the beginning of year 1, an investor puts pp dollars into an investment whose value increases at a variable rate of xnxn per year, where nn is an integer ranging from 1 to 3 indicating the year. If 85<xn<11085<xn<110 for all nn between 1 and 3, inclusive, then at the end of 3 years, the value of the investment must be between?	Pick one
A) $p and $2p	B) $2pand $5p	C) $5p and $10p	D) $10p and $ 25p	E) $25p and $75p

Solution: Since the min rate of interest is 86% the min value of investment will be (1+0.86)^3*p = (1.86^3)*p. Similarly max value will be (2.1)^3*p.   2.1^3 is 9.5 or you can guess little over 8 so 10p may be good estimate.   1.86^3 is trickier to estimate. I knew root(3) = 1.73. So 1.86^2 is close to 3 and 3*1.8 is 5.4. So 5p is a close lower bound.   So range is 5p to 10p.   Answer $5p and $10p.
Answer: C
There are 15 balls in a jar. You take out 3 blue balls without putting them back inside, and now the probability of pulling out a blue ball is 1/3. How many blue balls were there in the beginning?
Choose the correct choice from the following:
A) 12.
B) 9.
C) 8.
D) 7.
E) 6.

Solution: 7 = 3 blue balls + 12 / 3   Answer:7.
Answer: D
The value of a 10.5% stock, in which an income of Rs.756 is derived by investing Rs.9000, brokerage being% is :
Choose the correct choice:
A) Rs. 120.41
B) Rs. 134.51
C) Rs. 124.75
D) Rs. 145.89
E) Rs. 155.89

Solution: For an income of Rs.756, investment = Rs.9000   For an income of Rs., investment = = Rs.125   For a Rs.100 stock, investment = Rs.125.   Market value of Rs. 100 stock = = Rs. 124.75   Rs. 124.75
Answer: C
Ajay spends 10 per cent of his salary on house rent, 5 percent on food, 15 percent travel, 10 percent on clothes and the remaining amount of Rs.27000 is saved. What is Ajayâ€™s income?  Select.
A) Rs.60000 B) Rs.80500 C) Rs.60700 D) Rs.45000 E) None of these

Solution: Explanation:   Savings = Income â€“ expenditure   100 â€“ (10+5+15+10) = 60%   60% of income = Rs.27000   :. Income = 27000 x 100/60 = Rs. 45000.   Answer: Option Rs.45000
Answer: D
By selling 33 meters of cloth , one gains the selling price of 11 metres . Find the gain percent . Select:  A) 50  B) 45  C) 40  D) 60  E) 55

Solution: (Selling Price of 33m)-(Cost Price of 33m)=Gain=Selling Price of 11m   Selling Price of 22m = Cost Price of 33m Let Cost Price of each meter be $1 , Then, Cost Price of 22m= $22, Selling Price of 22m=$33.   Gain%=[(11/22)*100= 
(11/22)*100 = 50
50%   50nswer 50) 50.
Answer: A
A driver of auto rickshaw makes a profit of 20% on every trip when he carries 3 passengers and the price of petrol is Rs. 30 a litre. Find the % profit for the same journey if he goes for 4 passengers per trip and the price of petrol reduces to Rs. 24 litres?  Answers.
A) 40%. B) 60%. C) 80%. D) 100%. E) 120%.

Solution: 20% of 30 = 6 rupee profit    36/3= 
 36/3 = 12
12 rupee per passenger     12*4= 
  12*4 = 48
48   48 - 24= 
48 - 24 = 24
24.   so profit= 100%.   ANSWER:100%.
Answer: D