MU-NLPC/Calc-aqua_rat huggingface dataset:
P and Q can do a work in 30 days. Q and R can do the same work in 24 days and R and P in 20 days. They started the work together, but Q and R left after 10 days. How many days more will P take to finish the work?  Choose one
A) 10  B) 15  C) 18  D) 20  E) 22

Solution: Let work done by P in 1 day = p,   Work done by Q in 1 day = q,   Work done by R in 1 day = r   p + q = 1/30   q + r = 1/24   r + p = 1/20   Adding all the above, 2p + 2q + 2r = 1/30 + 1/24+ 1/20 = 15/120 = 1/8   => p + q + r = 1/16   => Work done by P,Q and R in 1 day = 1/16   Work done by P, Q and R in 10 days = 10 × (1/16) = 10/16 = 5/8   Remaining work = 1 = 5/8 = 3/8   Work done by P in 1 day = Work done by P,Q and R in 1 day - Work done by Q and R in 1 day   = 1/16 – 1/24 = 1/48   Number of days P needs to work to complete the remaining work = (3/8) / (1/48)= 
(3/8) / (1/48) = 18
18   Option 18
Answer: C
For which of the following functions does f(−k)=−f(k) for all real number values of x?	Choose the correct choice.
A) k^8  B) −k^6  C) k^5/k^7  D) k^9  E) k^4/k^2

Solution: f(-k) = (-k)^9 = -k*k^8   -f(u) = -u^9   k^9
Answer: D
Sides of a rectangular park are in the ratio 3: 2 and its area is 3750 sq m, the cost of fencing it at 60 ps per meter is?  Select the correct option
A) 287
B) 369
C) 150
D) 279
E) 361

Solution: 3x * 2x = 3750 => x = 25   2(75 + 50) = 250 m   250 * 0.60   = Rs.150   Answer:150
Answer: C
During a trip on an expressway, Ron drove a total of x miles. His average speed on a certain 5-mile section of the expressway was 30 miles per hour, and his average speed for the remainder of the trip was 60 miles per hour. His travel time for the x-mile trip was what percent greater than it would have been if he had traveled at a constant rate of 60 miles per hour for the entire trip?  Choose the most appropriate option.
A) 8.5% B) 50% C) x/12% D) 60/x% E) 500/x%

Solution: so Ron drove (x-5) miles at 60mph and 5 miles at 30mph:   (x-5)/60 + (10/60) = (X+5)/60 - current time to drive the whole distance   if the entire trip @60mph than time = x/60   so to get percent [(X+5)/60 ]/[x/60] x100   =(x+5)/x *100   =100+500/x   so increase of 500/x%[/u]=500/x%
Answer: E
A certain car dealership sells economy cars, luxury cars, and sport utility vehicles. The ratio of economy to luxury cars is 4:3. The ratio of economy cars to sport utility vehicles is 6:5. What is the ratio of luxury cars to sport utility vehicles?	Choose the correct choice
A) 9:10
B) 8:9
C) 3:2
D) 2:3
E) 1:2

Solution: The ratio of economy to luxury cars is 4:3 --> E:L = 4:3 = 24:18.   The ratio of economy cars to sport utility vehicles is 6:5 --> E:S = 6:5 = 24:20.   Thus, L:S = 18:20 = 9:10.   9:10nswer: 9:10.
Answer: A
Simplify 586645 * 9999  Choose one:
A) 5865863355  B) 5665863355  C) 4865863355  D) 4665863355  E) 4556834553

Solution: Explanation:   Although it is a simple question, but the trick is to save time in solving this.   Rather than multiplying it we can do as follows:   586645 * (10000 - 1) = 5866450000 - 586645= 
5866450000 - 586645 = 5_865_863_355
5865863355   5865863355nswer: Option 5865863355
Answer: A
The income of a broker remains unchanged though the rate of commission is increased from 4% to 5%. The percentage of slump in business is :
Choices.
A) 8%
B) 1%
C) 20%
D) 80%
E) None

Solution: Explanation:   Let the business value changes from x to y.   Then, 4% of x = 5% of y or 4/100×x=5/100×y   or y = 4/5x   20%hange in business = (x−4/5x)=1/5x   Percentage slump in business   = (1/5x×1/x×100)%   20%orrect Option: 20%
Answer: C
A train 110 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?  Choose the most appropriate option.
A) 8 sec	B) 6 sec	C) 3 sec	D) 9 sec	E) 5 sec

Solution: Speed of train relative to man = (60 + 6) km/hr   = 66 km/hr   [66 * 5/18] m/sec   =[55/3] m/sec.   Time taken to pass the man   = [110 * 3/55= 
110 * 3/55 = 6
6 sec   Answer:6 sec
Answer: B
What is the ratio of 5/7 to the product 3*(7/3)? Pick.
A) 3:7	B) 1:3	C) 5:49	D) 1:7	E) 3:49

Solution: 3/7 / 21/3 = 5/49...   IMO option 5:49.
Answer: C
Look at this series: 1000, 200, 40, ... What number should come next?	Choose the correct answer
A) 8	B) 10	C) 15	D) 20	E) 25

Solution: 1000/5= 
1000/5 = 200
200   200/5= 
200/5 = 40
40   40/5= 
40/5 = 8
8   8NSWER:8
Answer: A
A person walking at 10 Kmph reaches his office 10 minutes late. If he walks at 15 Kmph, he reaches there 10 minutes earlier. How far is the office from his house?
Choices.
A) 5km
B) 15km
C) 8km
D) 10km
E) 20km

Solution: Formula = S1*S2/S2-S1 * T1+T2/60   = 10*15/5 * 20/60   = 30 * 20/60= 
30 * 20/60 = 10
10 km   Answer is 10km
Answer: D
How many zeroes are there at the end of the number N, if N = 100! + 200! ?
Choose the correct choice from the following answers:
A) 73
B) 49
C) 20
D) 48
E) 24

Solution: The number of zeroes at the end of 100! will be less than the number of zeroes at the end of 200!   Hence it would be sufficient to calculate the number of zeroes at the end of 100!   Number of zeroes = [100/5] + [100/25] + [100/125] = 20 + 4 + 0= 
20 + 4 + 0 = 24
24   Correct Option: 24
Answer: E
Sixty men can stitch 200 shirts in 30 days working 8 hours a day. In how many days can 45 men stitch 300 shirts working 6 hours a day?  Pick.
A) 33
B) 77
C) 33
D) 80
E) 12

Solution: We have M1 D1 H1 / W1 = M2 D2 H2 / W2 (Variation rule)   (60 * 30 * 8)/ 200 = (45 * D2 * 6) / 300   D2 = (60 * 30 * 8 * 300) / (200 * 45 * 6) => D2 = 80.   Answer:80
Answer: D
The length of a train and that of a platform are equal. If with a speed of 90 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is:	Choose the correct choice from the following options:  A) 700  B) 780  C) 760  D) 750  E) 459

Solution: Speed = [90 * 5/18] m/sec = 25 m/sec; Time = 1 min. = 60 sec.   Let the length of the train and that of the platform be x meters.   Then, 2x/60 = 25 è x = 25 * 60 / 2= 
25 * 60 / 2 = 750
750   Answer: Option 750
Answer: D
The volume of a cube is 1728 cc. Find its surface.  Choose the correct choice from the following answers.
A) 864	B) 277	C) 299	D) 268	E) 191

Solution: a3 = 1728 => a = 12   6a2 = 6 * 12 * 12= 
6 * 12 * 12 = 864
864   864nswer: 864
Answer: A
A is twice as good workman as B, and together they complete a work in 3 days. In how many days can the work be complete by B alone?  Answers
A) 35 days B) 65 days C) 9 days D) 75 days E) 95 days

Solution: B=3A   9 days   9 days
Answer: C
The sum of three integers A, B and C is 240. A is one third of the sum of B and C and B is one fifth of the sum of A and C. What is C?  Choose the correct choice from the following answers:
A) 120
B) 130
C) 125
D) 140
E) 145

Solution: A is one third of the sum of B and C..   or A=1/3(B+C)...   But A+B+C=240   so 1/3(B+C)+B+C=240   4(B+C)/3= 240   B+C =240*3/4= 
240*3/4 = 180
180   A=240-180= 
240-180 = 60
60   2)B is one fifth of the sum of A and C   or B=1/5(A+C)...   But A+B+C=240   so 1/5(A+C)+A+C=240   A+C=240*5/6= 
240*5/6 = 200
200   but A=60, so C=200-60= 
200-60 = 140
140   Answer :140
Answer: D
The water from one outlet, flowing at a constant rate, can fill a swimming pool in 5 hours. The water from a second outlet, flowing at a constant rate, can fill the same pool in 3 hours. If both outlets are used at the same time, approximately what is the number of hours required to fill the pool? Options
A) 0.22
B) 1.87
C) 2.50
D) 3.21
E) 4.56

Solution: Always remember RT=W i.e Rate*Time = Work   Also remember that rate can be added or subtracted. For e.g if A do a work in 2 day and B do a work in 2 day.   They both of them together will do a work in 1 day.   So now your question first determine both outlets rate.   1st outlet rate = 1/5 (R=W/T here W=1 work, T = 5hrs)   2nd outlet rate = 1/3 (R=W/T here W=1 work, T = 3hrs)   1.87oth of them working together rate = 1st outlet rate + 2nd outlet rate = 1/5+1/3 = 8/15   again apply the formula RT=W   T = W/R = 1/8/15 = 15/8 =1.87   Answer is 1.87.
Answer: B
In a game of 100 points, A can give B 10 points and C 15 points. then how many points can B give C in a game of 70?	Answers:
A) 4.89	B) 3.89	C) 1.89	D) 11.89	E) 5.89

Solution: In a game of 100 points,A give 3.89 10 points and c 15 points means 3.89=90,C=85   In 90 points 3.89 give 5 since  90-85= 
 90-85 = 5
5   In 70 points 3.89 gives=70*5/90=3.89   ANSWER:3.89
Answer: B
If it is true that x > -3 and x < 7, which of the following must be true?	Select the correct option.
A) x > 3
B) x < -7
C) x < 3
D) -3 < x < 7
E) none of the above.

Solution: the range is -3 < x < 7   A. x > 3 - no because x can be between -3 < x < 3   B. x < -7 - no because the values of x are always >-7   C. x < 3 - no because x can be between 3 < x < 7   D. -3 < x < 7 - true because x can be between -3 < x < 7   E. none of the above.   Answer: -3 < x < 7
Answer: D
A certain football coach allows his quarterback to call three plays in a row. If the quarterback can choose from 3 passing plays, 4 running plays, and 2 trick plays, how many different R arrangements of plays can be run, if the same play can’t be run more than once?  Choose the correct choice.
A) 24	B) 125	C) 243	D) 504	E) 729

Solution: Number of R ways to choose the first play: 9   Second play: 8   Third:7   9*8*7= 504.504
Answer: D
The area of a square is equal to five times the area of a rectangle of dimensions 27 cm * 16 cm. What is the perimeter of the square?
Choose the correct choice from the following.
A) 140
B) 240
C) 340
D) 144
E) 122

Solution: Area of the square = s * s = 3(27 * 16)   => s = 9 * 4= 
9 * 4 = 36
36 cm   Perimeter of the square= 4 * 36= 
4 * 36 = 144
144 cm.   Answer: 144
Answer: D
A present value of a machine is $900. Its value depletion rate is 10% per annum then find the machine value after 2 years?
Answers:
A) $900
B) $810
C) $915
D) $715
E) $729

Solution: P= $900   R = 10%   T = 2 years   Machine value after 2 years = P[(1-R/100)^T]   =900*9/10 * 9/10= 
900*9/10 * 9/10 = 729
$729   Answer is $729
Answer: E
How many 7 digit number are there having the digit 3 three times & the digit 0 four times ?	Choose the correct choice from the following.
A) 15 B) 3^3 * 4^4 C) 18 D) 19 E) 25

Solution: The first digit on the left for 7 digit would always be fixed to 3 (as 0 as first digit will no longer makes it a 7 digit number).   So we are left with 6 places to be filled by number 3 two times and number 2 four time.   So possible arrangements at 6 place for repetitive numbers would be = 6! / 4!*2! = 15   15NSWER:15
Answer: A
If 60% of a number is equal to one half of another number, what is the ratio of first number to the second number?	Choose the correct choice from the following answers.
A) 4:5	B) 5:6	C) 6:5	D) 5:4	E) 2:5

Solution: Let 60% of A = 1/2 B. Then,   60A/100 = 1B/2 => 3A/5 = 1B/2   A/B = (1/2 * 5/3) = 5/6   A:B = 5:6.   Answer: 5:6
Answer: B
How much is 80% of 40 is greater than 4/5 of 30?  Select the correct option.
A) 12  B) 27  C) 8  D) 12  E) 81

Solution: (80/100) * 40 â€“ (4/5) * 30   32 - 24= 
32 - 24 = 8
8   Answer:8
Answer: C
A recipe requires 2 1/2 (mixed number) cups of flour 2 3/4 (mixed number) cups of sugar and 1 1/3 (mixed number) cups of milk to make one cake. Victor has 15 cups if flour, 16 cups of sugar and 8 cups of milk. What is the greatest number of cakes Bil can make using this recipe?  Choose the most appropriate option.
A) 5  B) 6  C) 7  D) 8  E) 9

Solution: Less work up front: Go through each item and see what the greatest number of cakes you can make with each. The lowest of these will be the right answer.   Flour: 15 cups, we need 2.5 cups each. Just keep going up the line to see how many cakes we can make: That means I can make 2 cakes with 5 cups, so 6 cakes overall with 15 cups. I've already got the answer narrowed to either A or B.   Sugar: 16 cups, we need 2.75 cups each. Same principle. I can make 2 cups with 5.5 cups, so to make 6 cakes I'd need 16.5 cups. I don't have that much sugar, so we're limited to 5 cakes. No need to even do milk because we're already at 5. Sugar will be the limiting factor.   answer is 5
Answer: A
If n is an even integer, which of the following must also be an even integer? Select:	A) n^2 + 1^2	B) (n+1)^2	C) n + 1	D) 3n + 1	E) n^2 + 1

Solution: Answer: (n+1)^2   A: 2n = odd   (n+1)^2: -2n + 1 = even   C: -(n^2) = odd   D: 2n - 1 = odd   E: n^3 = odd   Answer: (n+1)^2
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 6 years hence?
Select the correct option
A) 58
B) 59
C) 62
D) 70
E) 72

Solution: Explanation:   A + B = 60, A = 2B   2B + B = 60 => B = 20 then A = 40.   5 years, their ages will be 46 and 26.   Sum of their ages = 46 + 26= 
46 + 26 = 72
72.   72)
Answer: E
Nitin ranks 23th in a class of 60 students. What is rank from the last ?  Select
A) 33  B) 38  C) 32  D) 28  E) 19

Solution: Explanation:   Number students behind the nitin in rank = (60 - 23)= 
(60 - 23) = 37
37   Nitin is 38nd from the last   Answer: 38) 38
Answer: B
Speed of a boat in standing water is 9 kmph and the speed of the stream is 6 kmph. A man rows to place at a distance of 210 km and comes back to the starting point. The total time taken by him is:
Choose the correct answer:
A) 92 hours  B) 24 hours  C) 84 hours  D) 48 hours  E) None

Solution: Sol.   Speed upstream = 3 kmph; Speed downstream = 9 kmph.   ∴ total time taken = [210/3 + 210/9] hours = 84 hours.   Answer 84 hours
Answer: C
If ( log 5 5) (log 4 9) (log 3 2) is equal to
Pick one:  A) 1  B) 3/2  C) 2  D) 5  E) 7

Solution: Solution   Given expression	=log 9/log 4 ×log 2/log 3   ‹=› log 3²/log 2²×log 2/log 3   = 2 log 3/ 2 log 2×log 2/log3   = 1.   1nswer 1
Answer: A
John has taken four (4) tests that have an average of 84. In order to bring his course grade up to a ‘B’, he will need to have a final average of 87. What will he need to average on his final two tests to achieve this grade? Pick.
A) 87 B) 93 C) 92 D) 94 E) 97

Solution: Traditional Method:   Total scored till now 84*4=328   Total score to avg 87 in 6 tests = 87*6= 
87*6 = 522
522   Total to be scored on 2 tests= 522-336= 
522-336 = 186
186   Avg on 2 tests= 186/2= 
186/2 = 93
93   Answer: 93
Answer: B
When positive integer V is divided by 6 the remainder is 3. Which of the following CANNOT be an even integer?	Choose the correct choice from the following answers:
A) a. k + 1 B) b. k -11 C) c. 4k + 2 D) d. (k-3)/3 +2 E) e. V/3

Solution: When positive integer V is divided by 6 the remainder is 3   So, V could equal 3, 9, 15, 21, etc   let's TEST V =3   a.3+ 1 = 4 (EVEN)   b.3-11 = -8 (EVEN)   c. 4(3) + 2 = 14 (EVEN)   d. (3-3)/3 +2 = 2 (EVEN)   At this point, we can already see the answer must be E.   Let's check e. V/3 forfun   e.3/3 = 1 (ODD)   Great!   Answer: e. V/3
Answer: E
A right triangle ABC has to be constructed in the xy-plane so that the right angle is at A and AB is parallel to x axis. The coordinates of A, B and C are to satisfy the inequalities -1 ≤ x ≤ 7 and 1 ≤ y ≤ 7. The numbers of different triangles that can be constructed with these properties are?
Choose the correct option.
A) 63
B) 336
C) 567
D) 3024
E) 5040

Solution: Choose the (x,y) coordinates for vertex A (right angle): 9C1*7C1;   Choose the x coordinate for vertex B (as y coordinate is fixed by A): 8C1, (9-1=8 as 1 horizontal dot is already occupied by A);   Choose the y coordinate for vertex C (as x coordinate is fixed by A): 6C1, (7-1=6 as 1 vertical dot is already occupied by A).   9C1*7C1*8C1*6C1=3024.   Answer: 3024.
Answer: D
At what rate percent on simple interest will Rs.1500 amount to Rs.2000 in 5 years? Choose the most appropriate option:
A) 8.33 %
B) 3 6/7 %
C) 2 6/7 %
D) 5 %
E) 6 %

Solution: Explanation:   500 = (1500x5xR)/100   R = 8.33 %   8.33 %nswer: Option 8.33 %
Answer: A
How many numbers from 2 to 7 are exactly divisible by 2?	Choose the correct choice from the following options.
A) 3 B) 4 C) 5 D) 8 E) 9

Solution: 2/2= 
2/2 = 1
1 and 7/2= 3   3 - 1= 
3 - 1 = 2
2   2 + 1= 
2 + 1 = 3
3 Numbers   3)
Answer: A
A and B started a business investing Rs. 90,000 and Rs 25,000 respectively. In what ratio the profit earned after 2 years be divided between A and B respectively?
Pick one
A) 9:2  B) 3:2  C) 18:20  D) 18:5  E) 17:4

Solution: A: B = 90000 : 25000   = 90 : 25   = 18 : 5   ANSWER:18:5
Answer: D
How many integers between 500 and 1000 are there such that their unit digit is even?
Pick one:	A) 250	B) 150	C) 500	D) 100	E) 200

Solution: 500 numbers between - 500 and 1000   Out of which half would be even, half odd.   Number of even unit digit number = 250.   correct option is 250
Answer: A
A fruit vendor purchased 20 dozens of bananas at Rs. 15 per dozen. But one-fourth of the bananas were rotten and had to be thrown away. He sold two-third of the remaining bananas at Rs. 22.50 per dozen. At what price per dozen should he sell the remaining bananas to make neither a profit nor a loss? Choose the correct choice from the following answers.
A) 16
B) 15
C) 17
D) 888
E) 99

Solution: CP of 20 dozen of bananas = 15 * 20 = Rs. 300   Number of bananas which are rotten = 1/4 * 20= 
1/4 * 20 = 5
5 dozen.   SP of two-third of remaining bananas= (2/3 * 15) * 22.5 = Rs. 225   SP of remaining 5 dozens of bananas to make no profit and no loss =(300 - 225) = Rs. 75.   SP of 1 dozen bananas = 75/5 = Rs. 15.   Answer: 15
Answer: B
What is the probability of getting a sum 9 from two throw of a dice?  Pick.
A) 1/6
B) 1/8
C) 1/9
D) 1/12
E) 1/13

Solution: In two throws of die, n(S)=36   Let E =event of getting a sum 9   ={(3,6), (4,5),(5,4),(6,3)}   P(E)=4/36=1/9   ANSWER 1/9 1/9
Answer: C
The length of a rectangular garden is three times its width. If the area of the rectangular garden is 507 square meters, then what is the width of the rectangular garden?	Choose the correct option:
A) 10
B) 11
C) 12
D) 13
E) 14

Solution: Let x be the width of the garden.   3x^2 = 507   x^2 = 169   x = 13   The answer is 13.
Answer: D
The goalkeeper of a Hockey team is 31 years old and the captain is 4 years older and the team size is 11. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?  Choose the correct answer.
A) 28.5 years B) 24 years C) 25 years D) none of the above E) Cannot be determined

Solution: Explanation :   Let the average age of the whole team by x years.   => 11x - (31 + 35) = 9(x -1)   => 11x - 9x = 57   => 2x = 57   => x = 28.5.   So, average age of the team is 28.5 years.   28.5 yearsnswer : 28.5 years
Answer: A
The difference between compound interest and simple interest on a sum for 3 years at 10% p.a. is Rs.124 Find the sum. Choices
A) Rs.5000  B) Rs.4000  C) Rs.6000  D) Rs.8000  E) Rs.7000

Solution: For 3 years, we know   C.I-S.I= p(R/100)^3+3(R/100)^2   so, putting all values we have,   124=p((10/100)^3+3(10/100)^2)= 4000   ANSWER:Rs.4000
Answer: B
Points X, Y, and Z lie, in that order, on a straight railroad track. The distance from point X to point Y is twice the distance from point Y to point Z. A train traveled from point X to point Z without stopping. The train's average speed when traveling from point X to point Y was 100 miles per hour and the train's average speed when traveling from point Y to point Z was 75 miles per hour. What was the train's average speed, in miles per hour, when traveling from point X to point Z?	Choices
A) 90 B) 85 C) 85.5 D) 70 E) 90

Solution: Average speed = distance/time   Because we are looking for average speed we can pick a distance for the variable D.   Speed X-Y = 100   Speed Y-Z = 75   90verage Speed = total distance/total rate   rate = distance/time   X====================Y==========Z   If X-Y is twice the length of Y-Z then let X-Y = 2d and let Y-Z= d   90verage speed = 3d/(2d/100) + (d/75)   3d/(6d/300) + (4d/300)   3d/(10d/300)   900d/10d   90verage speed = 90   90NSWER: 90
Answer: A
The mass of 1 cubic meter of a substance is 700 kilograms under certain conditions. What is the volume, in cubic centimeters, of 1 gram of this substance under these conditions? (1 kilogram = 1,000 grams and 1 cubic meter = 1,000,000 cubic centimeters)	Choose the correct choice
A) 0.8  B) 1.42  C) 8.0  D) 12.5  E) 80.0

Solution: Density is mass divided by volume. So density of the given substance will be mass/volume=700kg/1m^3=700 kg/m^3 or 1g/1.42cm^3=0.7 g/cm^3.   Next, ask yourself if 700,000 g is equivalent to 1,000,000 cubic centimeters then 1 g is equivalent to how many cubic centimeters? --> 1 g - 1,000,000/700,000 = 10/8 = 1.42 cubic centimeters.   Answer is 1.42
Answer: B
An engagement team consists of a project manager, team leader, and four consultants. There are 2 candidates for the position of project manager, 3 candidates for the position of team leader, and 9 candidates for the 4 consultant slots. If 2 out of 9 consultants refuse to be on the same team, how many different teams are possible?
Choose the correct choice from the following answers:  A) 540  B) 630  C) 740  D) 820  E) 980

Solution: Answer= Total number combinations - Total number of combinations with constraints   Total number of combinations = 2C1*3C1*9C4= 756   Total number of combinations with constraints = 2C1*3C1*7C2=126   Answer=756-126= 
756-126 = 630
630   ANSWER: 630
Answer: B
Baker Raj is storing cake boxes in cartons that measure 25 inches by 42 inches by 60 inches. If the measurement of each cake box is 8 inches by 7 inches by 5 inches, then what is the maximum number of cake boxes that can be placed in each carton?
Pick
A) 330
B) 300
C) 252
D) 225
E) 210

Solution: Baker Raj is storing cake boxes in cartons The dimensions of the carton are 25x 42x 60and those of each cake box are 8x 7x 5.   To maximize number of boxes try and fit maximum into the base of the box. If you take the base as 25x 42and fit 5 x 6 boxes of 5x 7, then the total number of boxes is 5 x 6 x integer(60/8) = 5 x 6 x 7 = 210.   Alternatively you could try taking the base as 60x 42and fit 12 x 6 boxes of 5x 7, then the total number of boxes is 12 x 6 x integer(25/8) = 12 x 6 x 3 = 216. But since that is not an answer option, I go with (210) 210.
Answer: E
Three partners A, B, C in a business invested money such that 3(Aâ€™s capital) = 6(Bâ€™s capital) = 9(Câ€™s capital) then, The ratio of their capitals is Choose the correct choice from the following.
A) 63 : 45 : 34  B) 6 : 3 : 2  C) 36 : 54 : 28  D) 63 : 45 : 35  E) None of these

Solution: Explanation:   Let3(Aâ€™s capital) = 6(Bâ€™s capital) = 9(Câ€™s capital) = Rs.x   Then, Aâ€™s capital = Rs x/3, Bâ€™s capital = Rs. x/6 and Câ€™s capital = Rs. x/9.   A : 6 : 3 : 2 : C = x/3 : x/6 : x/9   6 : 3 : 2   Answer: Option 6 : 3 : 2
Answer: B
What will be the compound interest on a sum of Rs. 25,000 after 3 years at the rate of 12 p.c.p.a.?
Choose the correct choice from the following choices:
A) Rs. 9000.30  B) Rs. 9720  C) Rs. 10123.20  D) Rs. 10483.20  E) None of these

Solution: Explanation:   Amount   = Rs.[25000 x (1 + 12/100)3]=Rs. 35123.20   C.I. = Rs. (35123.20 - 25000) = Rs. 10123.20   ANSWER IS Rs. 10123.20
Answer: C
if log 7 = 0.845098, the number of digits in 7128 is  Choose the correct choice from the following:
A) 100
B) 120
C) 109
D) 280
E) 110

Solution: Explanation:   log(7128) = 128log(7) = 128 × 0.845098 ≈ 108.17   ie, its characteristic = 108   Hence, number of digits in 2128 = 108+1= 
108+1 = 109
109   Answer: Option 280
Answer: D
1. Mrs. Rodger got a weekly raise of $145. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.  Choose the correct choice from the following answers
A) $140	B) $125	C) $145	D) $135	E) $155

Solution: Let the 1st paycheck be x (integer).   Mrs. Rodger got a weekly raise of $ 145.   So after completing the 1st week she will get $ (x+145).   Similarly after completing the 2nd week she will get $ (x + 145) + $ 145.   = $ (x + 145 + 145)   = $ (x + 290)   So in this way end of every week her salary will increase by $ 145.   ANSWER : OPTION $145 =$145
Answer: C