MU-NLPC/Calc-aqua_rat huggingface dataset:
A man spends 35% of his income on food, 25% on children education and 80% of the remaining on house rent. What percent of his income he is left with?	Choose one:  A) 1%  B) 8%  C) 12%  D) 5%  E) 4%

Solution: Let the total income be x   then, income left = (100-80)% of x - [100-(35+25)]% of x = 20% of 40% of x = 8% of x   Answer is 8%
Answer: B
A and B invests Rs.3000 and Rs.8000 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit?
Choose the correct answer:
A) 9:6  B) 9:8  C) 9:16  D) 9:9  E) 9:5

Solution: (3*6 + 6*6): (8*12)   54:96 => 9:16.Answer:9:16
Answer: C
At a summer camp with 2100 participants, 1/2 of the campers are aged 8 to 12. Next year, the number of campers aged 8 to 12 will increase by 1/3. After this change, what percentage of the total 2100 campers will the 8- to 12-year-olds represent?	Choose the correct answer:	A) 62	B) 68	C) 66	D) 64	E) 66 2/3

Solution: Total - 2100 participants   campers are aged 8 to 12 = (1/2)*2100= 
(1/2)*2100 = 1_050
1050   Next year, campers are aged 8 to 12= (4/3)*1050= 
(4/3)*1050 = 1_400
1400   Percentage= (1400/2100)*100 = 66 2/3%   Answer: Option 66 2/3
Answer: E
The sum of the present ages of a father and his son is 42 years. Six years ago, father's age was four times the age of the son. After 6 years, son's age will be:  Choose the correct choice:
A) 14 B) 16 C) 18 D) 20 E) 22

Solution: Let the present ages of son and father be x and (42 - x) years respectively.   Then, (42 - x) - 6 = 4(x - 6)   36 - x = 4x - 24   x = 12   The son's age after 6 years will be 18.   The answer is 18.
Answer: C
For integers x and y, if 91x = 8y, which of the following must be true?
I. x > y
II. y is not an integer
III. The cube root of x is an integer
Choose the correct choice from the following answers.
A) I only B) II only C) III only D) I and II E) II and III

Solution: Statement 1: y>x   When y=x=0, equation holds but y is not greater than x   When x=-8 and y=-91, equation again holds but x>y   TRUE   Statement 2: y is not an integer   Since x and y are integers, 91x and 8y must also be integers.   It is given that 91x=8y   or 13*7*x = 8 y   or 13x = 8y/7   To balance the equation, y must be an integer   NOT TRUE   Statement 3: The cube root of x is an integer   x can be equal to 2*2*2*3 and for this value of x,y will be 13*7*3   So, x may or may not be a cube root.   NOT TRUE   I onlynswer:-I only
Answer: A
In the game of Yahtzee, a "full house" occurs when a player rolls five fair dice and the result is two dice showing one number and the other three all showing another (three of a kind). What is the probability that a player will roll a full house on one roll of each of the three remaining dice if that player has already rolled a pair on the first two? Choose the most appropriate option:  A) 1/3  B) 5/54  C) 5/72  D) 5/216  E) 1/1296

Solution: We have that the player rolled XX on the first two dice. To get a "full house" the next three dice must show YYY or XYY in any combination.   The probability of YYY is 5/6*1/6*1/6 = 5/216.   The probability of XYY is 3*1/6*5/6*1/6 = 15/216 (multiply by 3 because XYY can occur in three ways: XYY, YXY, YYX).   The overall probability is 5/216 + 15/216 = 20/216 = 5/54.   Answer: 5/54.
Answer: B
If the volume of two cubes are in the ratio 64:1, the ratio of their edges is: Pick one:
A) 3:1
B) 3:2
C) 3:5
D) 4:1
E) None of these

Solution: Explanation:   Let the edges be a and b of two cubes, then   a3/b3=64/1   =>(a/b)3=(4/1)3   a/b=4/1   =>a:b=4:1   Option 4:1
Answer: D
If p and q are prime numbers, how many divisors does the product p^4 * q^9 have?	Choose the correct choice from the following options.
A) 30 B) 35 C) 40 D) 50 E) 60

Solution: when a number N=a^x*b^y, where a and b are prime numbers, and x, y are positive integers, the number of divisors of N=(x+1)(y+1)   Therefore, the answer is D. 5*10=50
Answer: D
Three positive integers a, b, and c are such that their average is 20 and a ≤ b ≤ c. If the median is (a + 13), what is the least possible value of c?	Answers.
A) 21 B) 22 C) 23 D) 24 E) 25

Solution: Solution:   We know that the average value is 20 therefore (a+b+c)/3 = 20   so a+b+c = 60   and b = a + 13   therefore a + (a + 13) + c = 60   The least value of c is when c = b   so take c = a + 13   hence, a + (a + 13) + (a + 13) = 60   i.e., a = 34/3 a non integer therefore c is not equal to b   so take c = b+1 therefore c = a+14   a + (a + 13) + (a + 14) = 60   i.e., a= 33/3= 
33/3 = 11
11   hence, a= 11, b = 24, and c = 25   Answer: 25
Answer: E
The smallest number which when divided by 20, 25, 35, 40 leaves the remainder 6 When divided by
14, 19, 23 and 34 respectively is the difference between divisor and The corresponding remainder is 6.
Choose the correct answer:  A) 1396  B) 1394  C) 1494  D) 1384  E) 1391

Solution: The smallest number which when divided by 20, 25, 35, 40 leaves the remainder 6 When divided by   14, 19, 23 and 34 respectively is the difference between divisor and The corresponding remainder is 6.   = 1400-6= 
1400-6 = 1_394
1394   Answer is 1394
Answer: B
Suppose you work for a manufacturing plant that pays you $12.50 an hour and $.16 for each widget you make. How many widgets must you produce in a 40 hour week to earn $800 (before payroll deductions)? Choose the correct choice from the following:  A) 1800  B) 1825  C) 1850  D) 1855  E) 1875

Solution: Hourly = $12.50/hour   TotalHours = 40   PieceWork = $0.16/widget   TotalPieces = ????   Total Pay = (Hourly * TotalHours) + (PieceWork * TotalPieces)   so, put it all together:   $800 = ($12.50 * 40) + ($0.16 * Total Pieces)   TotalPieces = ($800 - ($12.50*40)) / $0.16 = 1875 Widgets   E. 1875( 800 - ( 12.50*40)) /  0.16= 
( 800 - ( 12.50*40)) /  0.16 = 1_875
1875 Widgets   E. 1875
Answer: E
A certain sum of money at simple interest amounted Rs.680 in 8 years at 3% per annum, find the sum?	Choose one:
A) 548	B) 675	C) 588	D) 678	E) 989

Solution: 680 = P [1 + (8*3)/100]   P = 548   Answer: 588
Answer: C
Find the odd man out
1, 2, 5, 14, 41, 123
Choose the correct answer
A) 2  B) 14  C) 124  D) 123  E) 21

Solution: 1*3-1= 
1*3-1 = 2
2   2*3-1= 
2*3-1 = 5
5   5*3-1= 
5*3-1 = 14
14   14*3-1= 
14*3-1 = 41
41   41*3 -1= 
41*3 -1 = 122
122   ANSWER:123
Answer: D
A car traveling at a certain constant speed takes 5 seconds longer to travel 1 km than it would take to travel 1 km at 75 km/hour. At what speed, in km/hr, is the car traveling?	Choose the correct choice from the following
A) 70
B) 72
C) 74
D) 75
E) 78

Solution: Time to cover 1 kilometer at 80 kilometers per hour is 1/75 hours = 3,600/75 seconds = 48 seconds;   Time to cover 1 kilometer at regular speed is  48 + 5= 
 48 + 5 = 53
53 seconds= 53/3,600 hours = 1/70 hours;   So, we get that to cover 1 kilometer 1/70 hours is needed --> regular speed 70 kilometers per hour (rate is a reciprocal of time or rate=distance/time).   70nswer: 70
Answer: A
A train 120 m long is running with a speed of 62 kmph. In what time will it pass a man who is running at 8 kmph in the same direction in which the train is going  Answers
A) 5 sec B) 6 sec C) 7 sec D) 8 sec E) 9 sec

Solution: Explanation:   Speed of the train relative to man = (62 - 8) kmph   = (54× 5/18) m/sec = 15 m/sec   Time taken by the train to cross the man   = Time taken by It to cover 120 m at 15m / sec   = 120 ×1/15 sec = 8sec   Answer: Option 8 sec
Answer: D
A mixture contains milk and water in the ratio 6:3. On adding 10 litters of water, the ratio of milk to water becomes 6:5. The quantity of milk in the original mixture is? Pick:	A) 90	B) 45	C) 110	D) 40	E) 50

Solution: Explanation:   milk:water = 6:3   6x : 3x + 10 = 6 : 5   5[6x] = 6[3x + 10]   30x = 18x + 60   30x - 18x = 60   12x = 60   x = 5   The quantity of milk in the original mixture is = 6 : 3 = 6 + 3= 
6 + 3 = 9
9   9x= 45   Short cut method - 2 : for Only milk problems   milk : water   6 : 3   6 : 5   milk ratio same but water ratio 2 part incress per 10 liters   2 part of ratio -------> 10 liters   9part of ratio -------> 45 liters   Answer: Option 45
Answer: B
The average of 9 numbers is 7 and the average of 7 other numbers is 10. What is the average of all 16 numbers?  Answers:
A) 9 B) 8 5/16 C) 7 7⁄8 D) 7 1⁄2 E) 7 1⁄4

Solution: The average of 9 numbers is 7....   The sum of those numbers is (9)(7) = 63.   The average of 7 other numbers is 10....   The sum of those numbers is (7)(10) = 70   The sum of ALL 16 numbers is 63+70= 
63+70 = 133
133. The average of those numbers is 133/16= 8 5/16.   Final Answer:   [Reveal]Spoiler:   8 5/16
Answer: B
A, B and C started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of B is Rs. 1500. The difference between the profit shares of A and C is?	Pick one.
A) 8867	B) 299	C) 279	D) 600	E) 2612

Solution: Ratio of investments of A, B and C is 8000 : 10000 : 12000 = 4 : 5 : 6   And also given that, profit share of B is Rs. 1500   => 5 parts out of 15 parts is Rs. 1500   Now, required difference is 6 - 4= 
6 - 4 = 2
2 parts   Required difference= 2/5 (1500) = Rs. 600.Answer: 600
Answer: D
The average salary of a person for the months of January, February, March and April is Rs.8000 and that for the months February, March, April and May is Rs.8300. If his salary for the month of May is Rs.6500, find his salary for the month of January?	Pick:
A) 2177  B) 2876  C) 4500  D) 5300  E) 6711

Solution: Sum of the salaries of the person for the months of January, February, March and April = 4 * 8000= 
4 * 8000 = 32_000
32000 ----(1)   Sum of the salaries of the person for the months of February, March, April and May= 4 * 8300= 
4 * 8300 = 33_200
33200 ----(2)   (2)-(1) i.e. May - Jan= 1200   Salary of May is Rs.6500   Salary of January = Rs.5300.Answer: 5300
Answer: D
What is the product of all the prime factors of 24?	Choose the correct option
A) 36  B) 24  C) 48  D) 12  E) 6

Solution: 24 , factors are 2,3,4,8,6,12. Now again prime Numbers are Only Two i.e 2 and 3 , this time we would have  2*2*2*3= 
 2*2*2*3 = 24
24   Answer : 24
Answer: B
Let p and q be the root of the quadratic equation x2 - (∝ - 2)x - ∝ -1 =0. what is the minimum possible value of p2 + q2 ?  Choose the correct option.
A) 0 B) 3 C) 4 D) 5 E) 6

Solution: Explanation :   p + q = α –2 and pq = –α – 1   (p + q)2 = p2 + q2 + 2pq,   Thus (α –2)2 = p2 + q2 + 2(–α – 1)   p2 + q2 = α2 – 4α + 4 + 2α + 2   p2 + q2 = α2 – 2α + 6   p2 + q2 = α2 – 2α + 1 + 5   p2 + q2 = (α – 1)2 + 5   Thus, minimum value of p2 + q2 is 5.   Answer : 5
Answer: D
what is the Max number of rectangular boxes, each measuring 5 inches by 2 inches by 7 inches, that can be packed into a rectangular packing box measuring 15 inches by 20 inches by 35 inches, if all boxes are aligned in the same direction?
Choose the correct answer:
A) 200
B) 350
C) 100
D) 150
E) 120

Solution: The 5 inch side should be aligned to the 15 inch side ( 3 layer)   2 inch side should be aligned to the 20 inch side. (10 layer)   7 inch side should be aligned to the 35 inch side.(5 layer)   Maximum number of rectangles =3*10*5= 
3*10*5 = 150
150   Answer is 150
Answer: D
When a number is divided by 6 &then multiply by 12 the answer is 10 what is the no.?	Pick.
A) 4.5	B) 5	C) 5.6	D) 5.7	E) 6.5

Solution: if $x$ is the number, x/6 * 12 = 10   => 2x = 10   => x = 5   5
Answer: B
In a group of 80 children and 10 youngsters, each child got sweets that are 20% of the total number of children and each youngster got sweets that are 25% of the total number of children. How many sweets were there? Choose the correct choice from the following choices: A) 1140 B) 1160 C) 1280 D) 1200 E) 1210

Solution: Number of sweets each child got = 20% of 80 = 20/100 * 80= 
20/100 * 80 = 16
16.   Number of sweets 80 children got= 80 * 16 = 1080.   Number of sweets each youngster got = 25% of 80 = 25/100 * 80= 
25/100 * 80 = 20
20.   Number of sweets 10 youngsters got= 10 * 20= 
10 * 20 = 200
200.   Total number of sweets= 1080 + 200= 
1080 + 200 = 1_280
1280.   1280)
Answer: C
The average marks of a class of 22 students is 40 and that of another class of 28 students is 60. Find the average marks of all the students?  Choose one:
A) 51.2
B) 59.5
C) 52.8
D) 52.5
E) 52.1

Solution: Sum of the marks for the class of 22 students = 22 * 40= 
22 * 40 = 880
880   Sum of the marks for the class of 28 students= 28 * 60= 
28 * 60 = 1_680
1680   Sum of the marks for the class of 50 students=   880 + 1680= 
880 + 1680 = 2_560
2560   51.2verage marks of all the students= 2560/50= 
2560/50 = 256/5 = around 51.2
51.2   51.2nswer:51.2
Answer: A
If the letters of the word PLACE are arranged taken all at a time, find how many do not start with AE?
Choose the correct choice from the following answers.
A) 94	B) 113	C) 114	D) 121	E) 123

Solution: Total no'of arrangements 5P5 = 5! = 120   no'of arrangements start with AE = 1 × 6 = 6   no'of arrangements which do not start with AE = 120 - 6= 
120 - 6 = 114
114   114)
Answer: C
1600 men have provisions for 28 days in the temple. If after 4 days, 400 men leave the temple, how long will the food last now?	Select:
A) 18	B) 77	C) 32 days	D) 16	E) 12

Solution: 1600 ---- 28 days   1600 ---- 24   1200 ---- ?   1600*24 = 1200*x   x = 32 days   Answer: 32 days
Answer: C
If the probability of rain on any given day in City X is 50%, what is probability that it rains on exactly 4 days in a 5 day period? Answers:
A) 2/5
B) 4/5
C) 3/16
D) 4/32
E) 5/32

Solution: One possible way is rain-rain-rain-rain-no rain.   The probability of this is 1/2*1/2*1/2*1/2*1/2 = 1/32   The number of possible ways is 5C4 = 5, so we multiply this by 5.   P(rain on exactly 4 days) = 5*1/32 = 5/32   The answer is 5/32.
Answer: E
Running 3/4th of his usual rate, a man is 12min late. Find his usual time in hours ?
Pick:
A) 6/4 hrs B) 3/5 hrs C) 9/4 hrs D) 3/4 hrs E) 1/4 hrs

Solution: Explanation:   Walking at 3/4th of usual rate implies that time taken would be 4/3th of the usual time. In other words, the time taken is 1/3rd more than his usual time   so 1/3rd of the usual time = 12min   or usual time = 3 x 12 = 36min = 36/60 hrs = 3/5 hrs.   Answer: 3/5 hrs
Answer: B
A sum of Rs. 125000 amounts to Rs. 15500 in 4 years at the rate of simple interest. What is the rate of interest? Choose the most appropriate option.
A) 7%
B) 9%
C) 5%
D) 6%
E) 2%

Solution: S.I. = (15500 - 12500) = Rs. 3000\   Rate = (100 * 3000) / (12500 * 4)= 
(100 * 3000) / (12500 * 4) = 6
6%   Answer: 6%
Answer: D
In a market, a dozen eggs cost as much as a pound of rice, and a half-liter of kerosene costs as much as 8 eggs. If the cost of each pound of rice is $0.36, then how many cents does a liter of kerosene cost? [One dollar has 100 cents.] Choose the correct option:
A) 0.33
B) 0.44
C) 0.48
D) 44
E) 48

Solution: A dozen eggs cost as much as a pound of rice --> 12 eggs = 1 pound of rice = 36 cents;   A half-liter of kerosene costs as much as 8 eggs --> 8 eggs = 1/2 liters of kerosene.   How many cents does a liter of kerosene cost --> 1 liter of kerosene = 16 eggs = 16/12*36= 
16/12*36 = 48
48 cents.   Answer: 48.
Answer: E
The difference between the squares of two consecutive odd integers
is a square<1000 whose root equals the combined sum of the digits
of the two integers. What is the sum of the digits M of the larger integer?
Choices: A) M=2 B) M=5 C) M=8 D) 10 E) 11

Solution: Really hard. But let's start with few concepts:   1. Square of an odd integer will be odd.   2. Difference of odd and odd will be even.   3. Any odd integer can be expressed as difference of two squares.   4. An even integer can be expressed as difference of two squares only if that even integer is a multiple of 4.   Assume two odd integers to be (2x-1) and (2x+1).   Difference of their squares = (2x+1)^2 - (2x-1)^2   = 4x^2 + 1 + 4x - (4x^2 + 1 - 4x)   = 4x^2 + 1 + 4x - 4x^2 - 1 + 4x   = 8x   Now root of 8x needs to be an integer such that it is equal to the sum of the digits of the two odd integers.   8 = 2^3, so x needs to be such that itcompletesa perfect square.   If we find x, we can find the value of 2x+1 (larger integer) and then sum of its digits.   Let's check the options, starting with c.   For sum to be 8, few possibilities are: 17, 35, 53, 71   If we take 17, the pair is 15 and 17, meaning x = 8.   8x = 64   root of 64 = 4 but 4 is not equal to 1+5+1+7.   Reject.   If we take 35, the pair is 33 and 35, meaning x = 17.   8x = 8*17   Reject since perfect square is not possible.   If we take 53, the pair is 51 and 53, meaning x = 26.   8x = 8*26   Reject since perfect square is not possible.   If we take 71, the pair is 69 and 71, meaning x = 35.   8x = 8*35   Reject since perfect square is not possible.   I tried each option and the possibilities and then got lost.   Then, it occurred to me that I was only checking 2-digit integers. What about 3-digits?   Starting with option a, only 2-digit odd integer whose sum is 2 is 101.   If we take 101, the pair is 99 and 101, meaning x = 50.   8x = 8*50= 
8*50 = 400
400   root of 400= 20 which is indeed equal to 9+9+1+1.   M=2nswer (M=2).
Answer: A
How many three digit numbers that do not contain the digit 9 are there?  Select the correct option:
A) 100
B) 200
C) 512
D) 596
E) 648

Solution: Applying combinations....8 * 9 * 9 = 648...   8 for first digit...cant be 0 or 9   9 and 9 for 2nd and 3rd....cant be 9   ANSW648R: 648
Answer: E
The difference between a number and its three-fifth is 50. What is the number?	Select the correct option
A) 185
B) 190
C) 160
D) 120
E) 125

Solution: Let the number be x. Then,   x - 3/5 x = 50 => 2/5 x = 50   x = (50 * 5)/2= 
(50 * 5)/2 = 125
125.   ANSW125R: 125
Answer: E
One side of a rectangular field is 15 m and one of its diagonals is 17 m. Find the area of the field in meter square
Choose the correct choice from the following
A) 100
B) 110
C) 120
D) 130
E) 140

Solution: Other side = ((17) 2- (15)2)(1/2)   = (289- 225)(1/2)   = (64)(1/2)   = 8 m.   Area = (15 x 8) m2 = 120 m2.   Option 120
Answer: C
A class contains five juniors and five seniors. If one member of the class is assigned at random to present a paper on a certain subject, and another member of the class is randomly assigned to assist him, what is the probability E that both will be juniors?	Select the correct option: A) 1/10 B) 1/5 C) 2/9 D) 2/5 E) 1/2

Solution: I think you're right. The other way to do it (but the long way) is to figure out the probability that it is not two Juniors.   2 seniors = P(Senior) * P(Senior) = 2/9   1 Senior and 1 Junior = (1/2) *(5/9)*2 = 5/9   Probability that it is not two Juniors is 5/9+2/9 = 7/9 so the probability E that it is two juniors is 1- (7/9) = 2/9.2/9
Answer: C
The length of the rectangular field is double its width. Inside the field there is square shaped pond 8m long. If the area of the pond is 1/8 of the area of the field. What is the length of the field? Select.
A) 26
B) 32
C) 72
D) 88
E) 82

Solution: A/8 = 8 * 8 => A = 8 * 8 * 8   x * 2x = 8 * 8 * 8   x = 16 => 2x = 32   Answer: 32
Answer: B
A rectangular tiled patio is composed of 126 square tiles. The rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles. After the change in layout, the patio will still have 126 tiles, and it will still be rectangular. How many rows are in the tile patio before the change in layout?  Choose one: A) 5 B) 6 C) 9 D) 13 E) 28

Solution: Suppose there are c columns and there are r rows   Original Situation   So, Number of tiles = c*r = 126   Also. Reach column has r tiles and each row has c tiles   New Situation   Number of tiles in each column is r-2 and number of tiles in each row is c+4   So, number of rows = r-2 and number of columns is c+4   So, Number of tiles = (r-2)*(c+4) = 126   9omparing both of them we get   c*r = (r-2)*(c+4)   => 4r -2c = 8   c = 2r - 4   Putting it in c*r=126   (2r-4)*r = 126   2r^2 - 4r - 126=0   r cannot be negative so r = 9   and c = 14   So, Answer will be 9
Answer: C
Two numbers are in the ratio of 3:8. If 24 be subtracted from each, they are in the ratio of 4:9. Find the numbers?	Select the correct option: A) 60,89 B) 60,88 C) -27,-128 D) 60,84 E) -72,-192

Solution: (3x-24):(8x-24) = 4:9   x = -24=> -72,-192   Answer: -72,-192
Answer: E
Which of the following is closest to (-6/7)^199？  Choose the correct option
A) -1  B) -1/2  C) 0  D) 1  E) 2

Solution: (-6/7)^4 = 1296/2401 which is already close to 1/2.   For larger exponents, the expression will get closer and closer to zero.   The answer is 0.
Answer: C
In a partnership between A, B and C. A's capital is Rs.8000. If his share of a profit of Rs.800 is Rs.200 and C's share is Rs.130, what is B's capital?	Choose the correct choice from the following answers.
A) 23676 B) 19766 C) 29172 D) 18800 E) 11267

Solution: Explanation:   200 + 130= 
200 + 130 = 330
330   800 - 330= 
800 - 330 = 470
470   200 ---- 8000   470 ---- ?=> 18800   Answer:18800
Answer: D
If 4 (P's Capital ) = 6 ( Q's Capital ) = 10 ( R's Capital ) , then out of the total profit of Rs 4340 , R will receive  Choose the most appropriate option
A) 600 B) 700 C) 840 D) 900 E) None of these

Solution: Explanation :   Let P's capital = p, Q's capital = q and R's capital = r   Then   4p = 6q = 10r   => 2p = 3q = 5r   =>q = 2p/3   r = 2p/5   P : Q : R = p : 2p/3 : 2p/5   = 15 : 10 : 6   R's share = 4340 * (6/31) = 140*6= 
140*6 = 840
840. Answer : Option 840
Answer: C
If w and b are positive numbers, and w^3 + b^3 = 75, then the greatest possible value of w is between:
Choose the most appropriate option.
A) 0 and 3
B) 3 and 5
C) 4 and 5
D) 5 and 7
E) 6 and 9

Solution: Yes the question is ambiguous, and the answer is certainly not C between 4 and 5 .   The question stated: w and b are positive numbers but not positive integers.   so fractions are allowed to be a part of calculation.   So if the answer is C then the value 4.5 = 9/2 must comply the equation.   (9/2)^3 + b^3 = 75   so, b^3 = -129/8 , which is not possible according to the question.   Moreover the question didn't mentioninclusive or not, so we can't assume that b is 4 .   hi asif,   question is correct IMO.   Sincemaximumvalues areuniqueso you cant take any value and make it satisfy with equation   question is asking that maximum value ofa(means that unique value ofa) is between...   its not saying all value of that range will satisfy.
Answer: C
Peter's average (arithmetic mean) test score on 4 tests is 78. What must be the student's score on a 5th test for the Peter's average score on the 5 tests to be 80?
Choose the correct choice from the following answers
A) 80	B) 82	C) 84	D) 86	E) 88

Solution: E. 88   Peter must score at least an 80 for sure. If he scores an 8, then he will need to score 2 pots for each of the 4 other tests tomake upthe difference. They each were at 78 (at least the average is, but this is a small point and doesn't matter to the answer). So 4 tests that were each 2 points short of the 80 average that is desired means the next test must be 8 points higher than the desired average, so  80+8= 
 80+8 = 88
88.
Answer: E
When 75% of a number is added to 75, the result is the same number. The number is
Choose the correct choice from the following options:
A) 150	B) 150	C) 100	D) 450	E) None of these

Solution: Let the number be equal to x.   3x/4 +75 = x   Hence x=300   Answer: 150.
Answer: B
Two employees A and B are paid a total of Rs. 550 per week by their employer. If A is paid 120 percent of the sum paid to B, how much is B paid per week?	Pick one:
A) Rs.150  B) Rs.190  C) Rs.200  D) Rs.250  E) Rs.300

Solution: Let the amount paid to A per week = x   and the amount paid to B per week = y   Then x + y = 550   But x = 120% of y = 120y/100 = 12y/10   ∴12y/10 + y = 550   ⇒ y[12/10 + 1] = 550   ⇒ 22y/10 = 550   ⇒ 22y = 5500   ⇒ y = 5500/22 = 500/2 = Rs.250   Rs.250)
Answer: D
A trader bought a car at 20% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price? Choose one: A) 10% B) 12% C) 14% D) 20% E) 22%

Solution: Original price = 100   CP = 80   S = 80*(140/100)= 
80*(140/100) = 112
112   100 - 112= 12%   12%)
Answer: B