MU-NLPC/Calc-aqua_rat huggingface dataset:
Six children â€” A, B, C, D, E, and F â€” are going to sit in six chairs in a row. Child E must be somewhere to the left of child F. How many possible configurations are there for the children?  Choose the correct choice:  A) 60  B) 180  C) 240  D) 360  E) 720

Solution: If we wanted, we could make this one extremely difficult, counting out all kinds of possibilities in several different cases. Instead, we are going to make this ridiculously easy.   First of all, with absolutely no restrictions, how many ways can the six children be arranged on the six chairs? Thatâ€™s a permutation of the 6 items â€”- 6P6 = 6! = 720. Thatâ€™s the total number of arrangements with no restrictions. Of course, those 720 arrangements have all kinds of symmetry to them. In particular, in all of those arrangements overall, itâ€™s just as likely for E to be to the left of F as it is for E to be to the right of F. Therefore, exactly half must have E to the right of F, and exactly half must have E to the left of F. Therefore, exactly (1/2)*720= 
(1/2)*720 = 360
360 of the arrangements have E to the left of F. Answer= 360.
Answer: D
250 men work for 16 days and finish a work. How many men would do a job 3 times the previous one in 20 days?
Choose the correct choice from the following.
A) 700	B) 666	C) 600	D) 400	E) 800

Solution: Number of men needed to finish the required work (variation, proportion method ) =3*16*250/20= 
3*16*250/20 = 600
600 Answer : 600
Answer: C
The food in a camp lasts for 30 men for 40 days. If ten more men join, how many days will the food last?
Select the correct option:
A) 22 days B) 30 days C) 76 days D) 88 days E) 82 days

Solution: one man can consume the same food in 30*40= 
30*40 = 1_200
1200 days.   10 more men join, the total number of men= 40   The number of days the food will last = 1200/40= 
1200/40 = 30
30 days.   Answer: 30 days
Answer: B
In an electric circuit, two resistors with resistances D and E are connected in parallel. In this case, if F is the combined resistance of these two resistors, then the reciprocal of F is equal to the sum of the reciprocals of D and E. What is F in terms of D and E?	Choose the correct choice:
A) DE/(D + E)
B) (D+E)/DE
C) DE
D) D-E
E) NONE OF THESE

Solution: The wording is a bit confusing, though basically we are told that 1/F= 1/D + 1/E, from which it follows that F=DE/(D + E).   DE/(D + E)nswer: DE/(D + E)
Answer: A
If 20% of (x-y) = 14% of (x+y), then what percent of x is y?	Choose the correct choice from the following options:
A) 50.5%  B) 44.4%  C) 22.2%  D) 17.6%  E) 25%

Solution: 20% of (x-y) = 14% of (x+y)   20/100 (x-y) = 14/100 (x+y)   6x = 34y   Required percentage = y/x *100 = 6y/34y * 100 = 17.64%   Answer is 17.6%
Answer: D
If the average marks of three batches of 47, 60 and 45 students respectively is 50, 55, 60, then the
average marks of all the students is Choose the correct choice from the following choices
A) 54.48 B) 54.93 C) 54.6 D) 54.58 E) None of these

Solution: Explanation:   =(47*50+60*55+45*60)/(47+60+45)=54.93   Answer: Option 54.93
Answer: B
Alok ordered 16 chapatis, 5 plates of rice, 7 plates of mixed vegetable and 6 ice-cream cups. The cost of each chapati is Rs.6, that of each plate of rice is Rs.45 and that of mixed vegetable is Rs.70. The amount that Alok paid the cashier was Rs.961. Find the cost of each ice-cream cup?  Choose the correct choice from the following choices:  A) Rs.25  B) Rs.22.50  C) Rs.20  D) Rs.17.50  E) None of these

Solution: Let the cost of each ice-cream cup be Rs.x   16(6) + 5(45) + 7(70) + 6(x) = 961   96 + 225 + 490 + 6x = 961   6x = 150 => x = 25.   Rs.25NSWER:Rs.25
Answer: A
If m and n are whole numbers such that mn = 169, then the value of (m – 1)^(n + 1) is:	Select:  A) 1  B) 13  C) 169  D) 1728  E) 1628

Solution: Clearly, m = 13 and n = 2.   Therefore, (m – 1) n + 1 = (13 – 1)3 = 12³ = 1728.   ANSWER:1728
Answer: D
For any number a, a* is defined as the greatest positive even integer less than or equal to a. What is the value of 5.2 – 5.2*?	Pick:
A) 0.2  B) 1.2  C) 1.8  D) 2.2  E) 4.0

Solution: Since a* is defined as the greatest positive even integer less than or equal to a, then 5.2* = 4 (the greatest positive even integer less than or equal to 5.2 is 4).   Hence, 5.2 – 5.2* = 5.2 - 4= 
5.2 - 4 = 1.2
1.2   Answer: 1.2.
Answer: B
A two digit number is divided by the sum of its digits. What is the maximum possible remainder?  Choose one:
A) 13	B) 14	C) 15	D) 16	E) 17

Solution: Solution   The maximum possible remainder must be less than 18 as the sum of any two digits can not be greater than 18. So we check when the sum of digits is 18. If the sum of digits is 18 the only possible remainder is 9 in case of 99. Similarly, if the sum of digits is 17 the maximum possible remainder is 14 in case of 98.Similarly, if the sum of digits is 16 the maximum possible remainder is 15 in case of 79. The remainder we have already got is 15 and all other sums of digits will be 15 or less than 15. So 15 has to be the answer. Answer 15
Answer: C
In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither blue nor green?	Select: A) 2/3 B) 8/21 C) 3/7 D) 9/22 E) None of these

Solution: Explanation:   Total number of balls = (8 + 7 + 6)= 
(8 + 7 + 6) = 21
21   Let E= event that the ball drawn is neither blue nor green =e vent that the ball drawn is red.   Therefore, n(E) = 8.   P(E) = 8/21.   Option 8/21
Answer: B
A child has 36 blue marbles and 10 red marbles, and he kept they into a bag. If he asks you to pick up 3 marbles, what is the probability that all the 3 marbles will be red?	Choose the correct choice from the following answers:
A) 1/253
B) 2/253
C) 3/253
D) 1/153
E) 2/153

Solution: There are 10 red marbles in a group of 36 + 10 that is 46. Thus the probability of picking all 3 red marbles is: (10/46)(9/45)(8/44) = 2/253. The correct answer is 2/253.
Answer: B
The average of 5 quantities is 6. The average of 3 of them is 4. What is the average of remaining 2 numbers?	Choose the correct answer:
A) 9	B) 10	C) 8	D) 9.5	E) None of these

Solution: 9NSWER: 9
Answer: A
A train running at the speed of 240 km/hr crosses a pole in 21 seconds. What is the length of the train?
Pick:
A) 1300 m B) 1350 m C) 1400 m D) 1450 m E) 1500 m

Solution: Speed=(240 * 5/18) m/sec   = (200/3) m/sec Length of the train   = (Speed x Time)   = (200/3 * 21)= 
(200/3 * 21) = 1_400
1400 m.   Answer:1400 m
Answer: C
Rhonda picked 2 pen from the table, if there were 7 pens on the table and 5 belongs to Jill, what is the probability that the 2 pen she picked does not belong to Jill?.	Choose the most appropriate option.
A) 5/42
B) 2/42
C) 7/42
D) 2/7
E) 5/7

Solution: Since Jill owns 5 of the pen, the subset from which the 2 pens hould be chosen are the 2 pens not owned by Jill fom the universe of 7.   The first pen can be one of the 2 from the 7 with probability 2/7.   The second pen can be one of the 1 from the 6 remaining with probability 1/6,   The total probability will be 2/7 × 1/6. On cancellation, this comes to 2/42.   Thus, the answer is 2/42 - 2/42.
Answer: B
If a/x = 1/3 and a/y =1/ 4, then (x + y) = Choose one:
A) 2a
B) a/2
C) 6a
D) 7a
E) 9a

Solution: Ratio 1:   3a = x   Ratio 2:   4a = y   x+y = 7a   Answer is 7a
Answer: D
Total 75 cows 25 cow gives each 2 liter milk 25 cow gives each 3/4 liter milk 25 cow gives each 1/4 liter milk this is split into 3 son per each 25 cows & 25 liter milk how?	Select the correct option.
A) 10
B) 12
C) 15
D) 25
E) 18

Solution: 25 cow 2 liter each =50 liter   25 cow 3/4 liter each= 3/4= 
3/4 = 3/4 = around 0.75
0.75*25= 
0.75*25 = 18.75
18.75   25 cow 1/4 liter each= 1/4= 
1/4 = 1/4 = around 0.25
0.25*25= 
0.25*25 = 6.25
6.25   add  50+18.75+6.25= 
 50+18.75+6.25 = 75
75   milk split into 3 son each 25 liter then 75/3= 
75/3 = 25
25   ANSWER:25
Answer: D
Jacob brought a scooter for a certain sum of money. He spent 10% of the cost on repairs and sold the scooter for a profit of Rs. 1100. How much did he spend on repairs if he made a profit of 20%?
Choose the correct option:
A) Rs. 400  B) Rs. 440  C) Rs. 500  D) Rs. 550  E) Rs. 650

Solution: Let the C.P. be Rs. x. Then, 20% of x = 1100   20/100 * x = 1100 => x = 5500   C.P. = Rs. 5500, expenditure on repairs = 10%   Actual price = Rs. (100 * 5500)/110 = Rs. 5000   Expenditures on repairs = (5500 - 5000) = Rs. 500.   ANSWER:Rs. 500
Answer: C
A box contains TEN bulbs out of which 6 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good?  Choose the correct choice from the following: A) 185/210 B) 195/210 C) 123/210 D) 154/210 E) 178/210

Solution: Required probability=1-6C4/10C4= 1 - 15/210= 195/210Answer:195/210
Answer: B
If r > 1 and s = 2^(r −1), then 4^r =
Choose the correct option:
A) 16s^2 B) 4s^2 C) s^2 D) s^2/4 E) s^2/16

Solution: If r > 1 and s = 2^(r −1), then 4^r   Given r>1, so let's assume r=2   s=2^(r-1) = 2^(2-1) = 2, so s=2   hence, 4^r = 4^2 = 16   only 1 ans. choice can satisfy this:   A) 16s^2 --> clearly > 16   B) 4s^2 --> 4*2^2 = 16(we can stop after this as there can be only 1 right answer)   C) s^2 --> clearly < 16   D) s^2/4 --> clearly < 16   E) s^2/16 --> clearly < 16   Ans. 4s^2) 4s^2
Answer: B
The length of rectangle is thrice its breadth and its perimeter is 104 m, find the area of the rectangle?	Choose the most appropriate option
A) 432 sq m	B) 356 sq m	C) 452 sq m	D) 428 sq m	E) 507 sq m

Solution: 2(3x + x) = 104   l = 39 b = 13   lb = 39 * 13= 
39 * 13 = 507
507   ANSW507 sq mR:507 sq m
Answer: E
The average of four consecutive even numbers is 27. find the largest of these numbers?
Choose the correct choice:
A) 14 B) 17 C) 30 D) 26 E) 24

Solution: Sol: let the numbers be x,x+2,x+4 andx+6. then,   (x+(x+2)+(x+4)+(x+6))/4) = 27   (4x+12)/4 = 27   x+3=27; x=24.   Therefore the largest number=(x+6)=24+6= 
24+6 = 30
30.   Ans: 30
Answer: C
The H.C.F. of two numbers is 11 and their L.C.M. is 7700. If one of the numbers is 275, then the other is: Select:
A) 279  B) 283  C) 308  D) 318  E) 415

Solution: Explanation :   Other number = 11â‹…7700 / 275 = 308   ANSWER IS 308
Answer: C
Mangala completes a piece of work in 8 days, Raju completes the same work in 26 days. If both of them work together, then the number of days required to complete the work is? Select:
A) 8 days
B) 6 days
C) 8 days
D) 10 days
E) 12 days

Solution: If A can complete a work in x days and B can complete the same work in y days, then, both   of them together can complete the work in x y/ x+ y days.   That is, the required No. of days = 8 × 26/34 = 6 days   6 days)
Answer: B
A rainstorm increased the amount of water stored in State J reservoirs from 5 billion gallons to 7.5 billion gallons. If the storm increased the amount of water in the reservoirs to 55 percent of total capacity, approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm?	Choose the correct choice from the following answers:
A) 6.9	B) 1.4	C) 2.5	D) 3.0	E) 4.4

Solution: After the reservoir is filled to 7.5 gallons the amount of water is at 55 % - which means that 45% of the reservoir is empty. To figure out what that 45% is approximate: 7.5 gallons /55 percent = x gallons /45 percent , therefore, x = 6.136 gallons , answer choices E,B,C,D are below 6.136 . We know that the reservoir must be short more than 6.136 gallons, therefore, the only possible choice is 6.9.
Answer: A
A part of certain sum of money is invested at 8% per annum and the rest at 12% per annum, if the interest earned in each case for the same period is equal, then ratio of the sums invested is? Choose the correct choice from the following answers:
A) 3:2 B) 4:8 C) 4:3 D) 4:0 E) 4:9

Solution: 12:8   = 3:2   3:2nswer: 3:2
Answer: A
Find the numbers which are in the ratio 3:2:4 such that the sum of the first and the second added to the difference of the third and the second is 21?  Answers
A) 4,3,22	B) 4,4,22	C) 9,3,32	D) 9,6,12	E) 9,2,23

Solution: Let the numbers be a, b and c.   a:b:c = 3:2:4   Given, (a + b) + (c - b) = 21   => a + c = 21   => 3x + 4x = 21 => x = 3   a, b, c are 3x, 2x, 4x   a, b, c are 9, 6, 12.   Answer:9,6,12
Answer: D
A rectangle has 20 meter length and 15 meter breadth. Find ratio between area of rectangle and square whose side is same with rectangle's length.
Select.
A) 3 : 2	B) 3 : 4	C) 4 : 5	D) 2 : 3	E) 2 : 5

Solution: Area of rectangle = 20*15= 
20*15 = 300
300   Area of square= 20^2 = 400   Ratio of rectangle' area and square's area = 300 : 400 = 3 : 4   Answer: 3 : 4
Answer: B
Of the science books in a certain supply room, 40 are on botany, 65 are on zoology, 90 are on physics. 50 are on geology, and 110 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same science? Choose the most appropriate option
A) 81	B) 159	C) 166	D) 314	E) 324

Solution: First, you can take all 40 Botany books, all 65 zoology books and all 50 geology books because you're sure to never pick 80 of them.   There are still 90 on physics and 110 on chemistry   The worst case could be that we pick 79 physics and 79 chemistry. So that the next book picked will necessary complete 80 books picked, either in physics or chemistry.   Minimum number of books picked to reach 80 in the same science should be : 40 + 65 + 50 + 79 +79 + 1= 
40 + 65 + 50 + 79 +79 + 1 = 314
314   314
Answer: D
Amanda sees a sale for 30% off all items, she sees a dress on sale that originally cost $50. How much will it cost Amanda to buy the dress after the sale amount of 30% has been take off? Choose the correct choice from the following options.
A) $40 B) $35 C) $50 D) $65 E) $15

Solution: Final number = original number - 30%(original number) = 50 - 30%(50) = 50 - 15= 
50 - 15 = 35
$35.   Answer $35
Answer: B
A car rental company charges for mileage as follows: x dollars per mile for the first n miles and x + 1 dollars per mile for each mile over n miles. How much will the mileage charge be, in dollars, for a journey of d miles, where d > n ?
Choose the correct choice from the following choices
A) d( x + 1) – n
B) xn + d
C) xn + d( x + 1)
D) x( n + d) – d
E) (x + 1)( d – n)

Solution: Cost of mileage for the first n miles = nx   Cost of mileage for the next d-n miles = (d-n)(x+1)   Total cost   = nx + (d-n)(x+1)   = nx + dx+d-nx-n   = dx+d-n   = d(x+1) - n   d( x + 1) – nnswer d( x + 1) – n
Answer: A
What is the smallest possible common multiple of three integers, all larger than 53?
Choose the correct choice from the following answers:
A) 27.	B) 54.	C) 846.	D) 19,656.	E) 21,924.

Solution: The Least common positive multiple would be for the immediate least number(s) after 53 i.e 54.   Since nowhere is it stated that the three integers must be different, the integers could be 54,54 and 54... leading to least possible positive common multiple to be 54. Answer 54..
Answer: B
John makes $60 a week from his job. He earns a raise and now makes $80 a week. What is the % increase?	Pick:
A) 16% B) 33.33% C) 17% D) 17.61% E) 17.56%

Solution: Increase = (20/60)*100 = (2/6)*100 = 33.33%.   33.33%
Answer: B
125.62+6.325+14.4=?	Choose the correct option:
A) 222.569 B) 287.36 C) 146.345 D) 125.69 E) 784.36

Solution: 125.62   6.325   14.4   ----------   146.345   Answer is 146.345
Answer: C
The ratio of the incomes of A and B is 2:3 and the ratio of their expenditure is 1:2. If at the end of the year, each saves $500 then the income of A is?
Choose the correct option:
A) $1000	B) $1500	C) $1200	D) $900	E) $1100

Solution: Let the income of $1000 and B be $2x and $3x   Let their expenditures be $y and $2y   2x-y = 500-------1)   3x-2y = 500-------2)   From 1) and 2)   x = 500   $1000's income = 2x = 2*500= 
2*500 = 1_000
$1000   $1000nswer is $1000
Answer: A
John has 10pairs of dark blue socks and 10pairs of black socks. He keeps them all in the same bag. If he picks out 3socks at random, then what is the probability thathe will get a matching pair? Choose the correct choice from the following answers.
A) 0	B) 1	C) 2	D) 3	E) 4

Solution: If he draws any combination of 3 socks he will definitely have the matching pair of either colour.   1
Answer: B
John and Cindy were each given X dollars in advance for each day they were expected to perform at a community festival. John eventually performed on all 20 days of the festival, while Cindy performed on 5 fewer days than John performed. If Cindy gives John y dollars of her advance payment so that they would have each received the same daily rate, what was John paid in advance, in terms of Y? Answers
A) 8Y  B) 7Y  C) 10Y  D) 12Y  E) 5Y

Solution: 7Yoth of them were given X $ each   Cindy to adjust Y $ in advance to John   So Cindy now has (X-Y)$ and John has (X+Y) $ such that their daily rate becomes same   So Rate of CIndy= Rate of John   Also , Cindy works for 15 days and John works for full 20 days   (X-Y) / 15 = (X+Y) / 20   Solving 20x-20y=15x+15y =>5x=35y => x=35/5= 
35/5 = 7
7Y   Answer : 7Y
Answer: B
A student completes a 3 part exam as follows. The student completes sections A in 18 minutes and takes an equal time to complete the two remaining sections. What is the ratio of time spent on section C to section A if the total duration is 1 hour?	Choose the correct answer.
A) 4:3
B) 5:4
C) 6:5
D) 7:6
E) 8:7

Solution: The time spent on section B and section C is 21 minutes each.   The ratio of C to A is 21:18 = 7:6   The answer is 7:6.
Answer: D
The ages of Patrick and Michael are in the ratio of 3 : 5 and that of Michael and Monica are in the ratio of 3 : 5. If the sum of their ages is 145, what is the difference between the ages of Patrick and Monica? Choose the correct choice from the following answers.
A) 27  B) 48  C) 45  D) 72  E) 18

Solution: Ages of P and Mi=3x+5x   Ages of Mi and Mo=3x:5x   Rationalizing their ages. ratio of their ages will be 9x:15x:25x   Sum=47x=145   x=3   Difference if ages of Pa and Mo=25x-9x=16x25 -9= 
25 -9 = 16
16x=16*3= 
16*3 = 48
48   Answer 48
Answer: B
Adam's mother is 26 years older than him. Next year, however, she will be 3 times older than her son. How old is Adam's mother?
Choose the correct choice from the following:  A) 35 years  B) 36 years  C) 37 years  D) 38 years  E) 39 years

Solution: At the present   Adam is x years old.   Adam's mother is y=x+26 years old.   Next year   Adam will be x+1 years old.   Adams mother will be y+1=3 (x+1) years old.   If we combine the two equations,   y=x+26, and   y+1=3 (x+1), then   x+26+1=3x+3   2x=27-3   2x=24   x=12   This is Adam's age at the moment. Since his mother is 26 years older than him, her age is 12+26= 
12+26 = 38
38.   ANSWER: 38 years
Answer: D
If 'y' is a positive integer exactly divisible by 4 or 5 but not divisible by 8.What could possibly be the value of 'y' ? Choose the correct choice from the following choices:	A) 40	B) 80	C) 20	D) 24	E) 36

Solution: 40 and 80 are both divisible by 4 and 5 but also by 8. so they are not the right answer.   24 and 36 are both clearly not divisible by 5(not correct)   20 is both divisible by 4 and 5 but not by 8.   answer : (20)
Answer: C
Lola has $240.00 in her checking account. She spent $180.00. What percentage does she have left in her account ?  Choose the correct choice from the following answers
A) 75 %  B) 50 %  C) 40 %  D) 55 %  E) None of these

Solution: None of thesexplanation :   Amount left : 240 - 180= 
240 - 180 = 60
60   Amount left percentage= (60/240 x 100) %   = 25 %   Answer : None of these
Answer: E
Solution Y is 20 percent liquid X and 80 percent water. If 2 kilograms of water evaporate from 8 kilograms of solution Y and 2 kilograms of solution Y are added to the remaining 6 kilograms of liquid, what percent of this new solution is liquid X?	Select the correct option:  A) 20%  B) 21 1/2%  C) 22%  D) 24%  E) 25%

Solution: In 8 kilograms of solution Y there are   0.2*8= 
  0.2*8 = 1.6
1.6kilograms of solution X;   After 2 kilograms of water are replaced by 2 kilograms of solution Y, to the existing 2.4 kilograms of solution X, 0.2*2=0.4 kilograms of solution X are added, so in the new solution of 8 kilograms there are 1.6+0.4= 
1.6+0.4 = 2
2 kilograms of solution X, which is  2/8*100= 
 2/8*100 = 25
25% of this new solution.   Answer: 25%.
Answer: E
After harvest, out of a total of N apples from an orchard, if 1/4 of those tested had infection A and, of those with infection A, 1/2 also had infection B, how many apples did not have both infection A and B?
Select the correct option:
A) N/15  B) 7N/8  C) 14N/15  D) N/5  E) 4N/5

Solution: 1/4 of tested had infection A, thus N/4 had infection A;   Of those with infection A, 1/2 also had infection B, thus 1/2*N/4 = N/8 had both infections A and B.   Therefore, N - N/8 = 7N/8 did not have both infection A and B.   Answer: 7N/8.
Answer: B
Of the numbers, average of the first five is 16 and that of the last five is 20. if the last number is 20. find the first number?  Choose the correct choice from the following options:
A) 20	B) 0	C) 24	D) 26	E) 28

Solution: Explanation :   Solution: Let the 6 numbers be a, b, c, d, e and 20. then, given   => a + b + c + d + e/5 =16   => b + c + d + e + 20/5 =20   Solve those two equations then we will get a = 0.   .'. first number = 0.   Answer : 0
Answer: B
Mixture A is 10 percent alcohol, and mixture B is 40 percent alcohol. If the two are poured together to create a 4-gallon mixture that contains 20 percent alcohol, approximately how many gallons of mixture A are in the mixture?
Choose the most appropriate option
A) 1.6  B) 1.7  C) 1.8  D) 1.9  E) 2.0

Solution: (40-20)/(20-15) = Qa/Qb   20/10 = Qa/Qb   2/1 = Qa/Qb   Qa = (2/5) * 4 = 8/5= 
8/5 = 8/5 = around 1.6
1.6 approx   1.6nswer : 1.6
Answer: A
In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there? Choose the correct option:  A) 200  B) 205  C) 204  D) 209  E) 300

Solution: We may have (1 boy and 3 girls) or (2 boys and 2 girls) or (3 boys and 1 girl) or (4 boys).   Required number   of ways	= (6C1 x 4C3) + (6C2 x 4C2) + (6C3 x 4C1) + (6C4)   =>209   ANSWER 209
Answer: D
A wholesale tea dealer 408 kilograms, 468 kilograms and 516 kilograms of three different qualities of tea. He wants it all to be packed into boxes of equal size without mixing. Find the capacity of the largest possible box?  Choose the correct choice from the following answers.
A) 50
B) 36
C) 24
D) 12
E) 20

Solution: HCF of 408, 468, 516 = 12   ANSWER:12
Answer: D
If $10,000,000 is the initial amount placed in an account that collects 7% annual interest, which of the following compounding rates would produce the largest total amount after two years?
Choose the correct answer: A) compounding annually B) compounding quarterly C) compounding daily D) compounding monthly E) All four of these would produce the same total

Solution: Answer = C Compounding daily   This will produce the maximum yield as the interest accured each day will be added the very next day to the Principal amount for further computation of interest.   This process will be repeated every day till the amount matures   compounding dailyompounding annually will give least returns
Answer: C
What is the probability that the sum of two dice will yield a 9, and then when both are thrown again, their sum will again yield a 9? assume that each die has 8 sides with faces numbered 1 to 8.
Choose the correct choice from the following options: A) 1/64 B) 1/36 C) 1/12 D) 1/6 E) 1/3

Solution: Solution -   Rolling dices is an independent event.   The combinations to get 9 are (1,8), (8,1), (2,7), (7,2), (3,6), (6,3), (4,5), (5,4), and total combinations of both dices is 64.   The probability of getting 9 in first attempt is 8/64=1/8.   Probability of getting 9 again in second attempt = (1/8)*(1/8) = 1/64. 1/64NS 1/64
Answer: A
The greatest number of four digits which is divisible by 7, 10, 40 and 60 is:
Choices: A) 9200 B) 9300 C) 9400 D) 8400 E) 7400

Solution: Greatest number of 4-digits is 9999.   L.C.M. of 7, 10, 40 and 60 is 4200.   On dividing 9999 by 4200, the remainder is 1599.   Required number  (9999 - 1599)= 
 (9999 - 1599) = 8_400
8400.   ANSWER :8400
Answer: D