MU-NLPC/Calc-aqua_rat huggingface dataset:
What will be the compound interest on a sum of Rs. 45,000 after 3 years at the rate of 12% p.a.? Options:
A) s:10123.19 B) s:10123.29 C) s:10123.20 D) s:18221.76 E) s:10123.12

Solution: Amount   = [45000 * (1 + 12/100)3]   = 45000 * 28/25 * 28/25 * 28/25   = Rs. 63221.76   C.I. = (63221.76 - 45000)= 
(63221.76 - 45000) = 18_221.76
Rs:18221.76   Answer: s:18221.76
Answer: D
x,y are odd and z is even then ((x^2+y^2)z^2)/8 is Select.
A) even  B) odd  C) fraction  D) fractiWQ  E) either even or odd

Solution: As x, y are odd x2+y2x2+y2 is always even. Now if z is a multiple of 4, then z2z2 is divisible by 8, then the equation is even. if z is a not a multiple of 4, but only a multiple of 2, then z2z2 is not completely divisible as it contains only two 2's and other two is cancelled in x2+y2x2+y2 which results in an odd number.   (32+52)428=34×168=34×2(32+52)428=34×168=34×2   (32+52)628(32+52)628 = 34×368=17×9   Answer:either even or odd
Answer: E
'a' and 'b' are positive integers such that their LCM is 20 and their HCF is 1. What is the addition of the maximum and minimum possible values of 'a + b'?
Pick:
A) 28 B) 30 C) 22 D) 20 E) 32

Solution: possible values of a and b can be 5,4; 4,5 (which are same for a+b) and 1,20; 20,1 (same result for a+b)   so 21+9= 
21+9 = 30
30. ans 30.
Answer: B
The present population of a town is 1240. Population increase rate is 4% p.a. Find the population of town after 1 years?	Choose the correct choice from the following answers
A) 990  B) 1215  C) 1345  D) 1142  E) 1290

Solution: P = 1240   R = 4%   Required population of town = P*(1 + R/100)^T   = 1240*(1 + 4/100)   = 1240*(26/25)   = 1290(approximately)   Answer is 1290
Answer: E
Which of the following numbers doesn't have a divisor greater than 1 that is the square of an integer?	Pick one: A) 63 B) 108 C) 25 D) 13 E) 36

Solution: Prime Factorization   63=7*3*3= 7*3^2. Includes the perfect square of 9.   108=2*3*2*3*3=6^2*3. Includes the perfect square of 36.   25=5*5=5^2. A perfect square of 25.   13=13*1. There are no perfect squares as factors.   36=2*2*3*3= 2^2*3^2. Includes the perfect squares of 4 and 9.   Only 13 does not have a perfect square as a factor so the correct answer is 13.
Answer: D
If g and f are both odd prime numbers andg < f, then how many different positive integer factors does2gfhave?  Pick: A) 3 B) 4 C) 6 D) 8 E) 12

Solution: g and f are both odd prime numbers- It means either g or f is not 2   and since prime numbers have only two factors - 1 and the number itself   g and f each will have (1+1)= 
(1+1) = 2
2 factors   Hence 2gf will have (1+1)(1+1)(1+1)= 8 factors   8 is the answer
Answer: D
What is (25^7+25) / 25?	Select: A) 244140626 B) 243120617 C) 242580531 D) 241230438 E) 240760355

Solution: (25^7+25) / 25 =   25*(25^6+1) / 25 =   25^6 + 1   Clearly this is a number which ends with a 6 in the units place.   The answer is 244140626.
Answer: A
A started a business with an investment of Rs. 70000 and after 9 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 76000, then the share of B is?
Options: A) 33008 B) 24000 C) 28000 D) 48000 E) 81122

Solution: Ratio of investments of A and B is (70000 * 12) : (120000 * 3) = 7 : 12   Total profit = Rs. 76000   Share of B = 12/19 (76000) = Rs. 48000   Answer: 48000
Answer: D
If s,t ,and u are positive real numbers such that s(t+u) = 152, t(u+s) =162 , and u(s+t) = 170, then stu is Choose the correct choice from the following answers:  A) a) 672  B) b) 688  C) c) 704  D) d) 720  E) e) 750

Solution: st+su = 152 ----------------------------- tu+ts = 162-------------------------------- su+ut= 170---------------------------------------3)   Re-writing equation 3 as follows:   su+ut = 162 + 8   su+ut = tu+ts + 8   su = ts + 8 ............... (4)   Adding (1)(4)   2su = 160   su = 80   stu has to be multiple of 80, only 720 fits in   Answer = d) 720
Answer: D
During a Thanksgiving weekend, a car rental company rented six-tenths of their vehicles, including two-fifths of the 4WDs that it had. If 40% of the vehicles are 4WDs, then what percent of the vehicles that were not rented were not 4WDs? Choose the correct choice from the following options.
A) 20%  B) 30%  C) 40%  D) 50%  E) 60%

Solution: 4/10 of all the vehicles were not rented.   (3/5)(2/5) = 6/25 of all the vehicles are 4WDs that were not rented.   (6/25) / (4/10) = 3/5 is the fraction of non-rented vehicles that were 4WDs   1 - 3/5 = 40% of non-rented vehicles were not 4WDs.   The answer is 40%.
Answer: C
Jack needs to arrive at the flower shop before 2 p.m, and the car rental by 3:30 pm, before he picks Sally up for their date at 5:30. It is now 12 p.m. the flower shop is 1.2 miles from Jacks house. He walks at a pace of 3.1 miles per hour. The flower shop is about .6 miles from the car rental shop, where Jack must walk to next. He can then drive the last 4.3 miles to Sallys house with an approx speed of 35 mph. When should he leave for each destination, in order based on the distance between stops Jack's walking speed, and finally the travel in the car?  Select the correct option
A) 1:56 p.m, 3:21pm, 5:21 p.m	B) 1:59 p.m, 3:17p.m, and 5:24 p.m	C) 1:57 p.m., 3.19 p.m, and 5:26pm	D) 1:52 pm, 3:11 p.m, and 5:18 pm	E) 1:59 p.m, 3:22 p.m, there isn't time to pick up Sally :(

Solution: 1.2 m/3.2 mph= 38 minutes to travel to flower shop   Needs to leave home at: 1:52 pm bc 2pm-38minutes=1:52 pm   Needs to leave flower shop at: .6Ã·3.1=approx 19 minutes 3:30 pm- 19 minutes= 3:11pm   Needs to leave car rental by: 4.3/35mph= approx 12 minutes 5:30-12 minutes= 5:18pm   Correct answer is 1:52 pm, 3:11 p.m, and 5:18 pm
Answer: D
Evaluate: 6302.5 + 630.25 + 63.025 + 6.3025 + 0.63025  Choose the most appropriate option
A) 6819.59775 B) 6981.59775 C) 6918.59775 D) 6198.59775 E) 7002.70775

Solution: 6302.5   630.25   63.025   6.3025   + 0.63025   ---------------   7002.70775   Answer is 7002.70775.
Answer: E
What approximate value should come in place of question mark (?) in the following equation
287.532 + 1894.029 – 657.48 = 743.095 + ?
Choose the correct answer:
A) 870	B) 790	C) 780	D) 770	E) 890

Solution: ? = 285 + 1895 – 655 – 745 or, ? = 780   Answer 780
Answer: C
The cost of producing x tools by a company is given by
C(x) = 1000 x + 5500 (in $)
a) What is the cost of 100 tools?  Choose the correct choice from the following answers: A) 125500 $ B) 125800 $ C) 105900 $ D) 105500 $ E) 122500 $

Solution: Solution   C(100) = 1000*100 + 5500 = 125500 $   Answer 105500 $
Answer: D
A person buys an article at Rs.400. At what price should he sell the article so as to make a profit of 40%?  Choose the correct choice from the following:  A) 600  B) 277  C) 560  D) 261  E) 281

Solution: 560ost price = Rs.400   profit = 40% of 400 = Rs.160   Selling price = 560ost price + Profit   = 400 + 160= 
400 + 160 = 560
560   Answer: 560
Answer: C
The average of 6 no.'s is 3.95. The average of 2of them is 3.8, while the average of theother 2 is 3.85. What is the average of the remaining 2 no's? Choose the correct choice from the following choices.
A) 4.2  B) 4.4  C) 4.6  D) 5.6  E) 5.7

Solution: Sum of the remaining two numbers = (3.95 * 6) - [(3.8 * 2) + (3.85 * 2)]   = 8.4.   Required average = (8.4 / 2) = 4.2.   4.2
Answer: A
Two MBA admissions committees are to be formed randomly from 6 second year MBAs with 3 members each. What is the probability Q that Jane will be on the same committee as Albert? Choose the correct choice from the following options:
A) 12%
B) 20%
C) 33%
D) 40%
E) 50%

Solution: Total number of ways to choose 3 member committee - 6C3=(6!/3!3!)=20   No. of ways Albert n Jane are in same committee:- (4C1 * 2)= 8   Probability Q= (8/20) *100= 
(8/20) *100 = 40
40%.   +1 for me.. :40%
Answer: D
Find large number from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder	Choose the correct choice from the following options:
A) 1234
B) 1265
C) 1350
D) 1467
E) 1635

Solution: Let the smaller number be x. Then larger number = (x + 1365).   x + 1365 = 6x + 15   5x = 1350   x = 270   Large number = 270+1365= 
270+1365 = 1_635
1635   1635
Answer: E
If z = 343 * 64 * 9 / 63, Find the unit digit of z,
Select the correct option
A) 5	B) 1	C) 3	D) 2	E) 6

Solution: z = 343 * 64 * 9 / 63   z = 7^3 * 4^3 * 3^2 / 3^2 * 7   z = 7^2 * 4^3   z = 3136   Ans: 6
Answer: E
A circular well with a diameter of 4 metres , is dug to a depth of 24 metres. What is the volume of the earth dug out?	Options.
A) 32 m3	B) 36 m3	C) 40 m3	D) 44 m3	E) 301.6

Solution: Solution   Volume	= πr2h   ‹=› (22 /7 ×2×2×24)m3   ‹=›301.6 m3.   Answer 301.6
Answer: E
A car traveling at a certain constant speed takes 10 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 40 kilometers per hour. At what speed, in kilometers per hour, is the car traveling?	Choose the most appropriate option:
A) 35
B) 35.5
C) 36
D) 36.5
E) 37

Solution: 40 * T = 1 km => T = 1/40 km/h   V*(T+10/3600) = 1   V (1/40 + 10/3600) = 1   V (100/3600) = 1   V = 36 km/h   The answer is 36.
Answer: C
A shopkeeper has 280 kg of apples. He sells 40% of these at 20% profit and remaining 60% at 20% profit. Find his % profit on total.  Choose the correct answer:
A) 24%	B) 20%	C) 26%	D) 28%	E) 35%

Solution: If the total quantity was 100   Then 40X 20% + 60 X20%= 20   This profit will remain same for any total quantity unless the % of products remains the same. Hence '20%' is the answer
Answer: B
A shopkeeper purchased 70 kg of potatoes for Rs. 420 and sold the whole lot at the rate of Rs. 6.50 per kg. What will be his gain percent?	Pick
A) 8 1/9 %
B) 8 7/3 %
C) 8 1/3 %
D) 2 1/3 %
E) 8 3/3 %

Solution: C.P. of 1 kg = 420/7 = Rs. 6   S.P. of 1 kg = Rs. 6.50   Gain % = 0.50/6 * 100 = 25/3 = 8 1/3 %.Answer: 8 1/3 %
Answer: C
The average of 25 result is 18.The average of 1st 12 of them is 14 & that of last 12 is 17.Find the 13th result.	Choose the correct choice from the following answers:
A) 18 B) 68 C) 58 D) 78 E) 98

Solution: Clearly 13th result=(sum of 25 results)-(sum of 24 results)   =(18*25)-(14*12)+(17*12)   =450-(168+204)   =450-372= 
450-372 = 78
78.   ANSWER 78 78
Answer: D
If shares of two persons in profits are Rs.600 and Rs.300 then ratio of their capitals is Choose the correct choice from the following answers:
A) 3:4	B) 2:3	C) 4:3	D) 1:3	E) 2:1

Solution: total profit =1000   ratio=600/300= 
600/300 = 2
2:1   ANSW2:1R:2:1
Answer: E
There are ten players in the basketball team. If the average height of the players is 170 cm, what will be the new average height if a 192 cm player will join the team?	Choose the correct answer
A) 168.	B) 172.2	C) 172	D) 181	E) 184

Solution: Given ( X1 + X2 + .......... X10 ) / 10 =170   Now ( X1 + X2 + .......... X10 ) = 1700 ---> Eq 1.   Now one new person added and the person be A and height is 192 and the total no of players will be 11 and let's say the new average is B.   => ( X1 + X2 + .......... X10 + 192 ) / 11 = B --Eq 2   Sub X1 + X2 + .......... X10 from Eq 1 in Eq 2.   => 1700 + 192 = 11 B   B = 172.   Answer: 172 is the correct option
Answer: C
The speed of a boat in upstream is 60 kmph and the speed of the boat downstream is 90 kmph. Find the speed of the boat in still water and the speed of the stream?	Choices.
A) 15  B) 99  C) 77  D) 55  E) 22

Solution: Speed of the boat in still water = (60+90)/2= 
(60+90)/2 = 75
75 kmph. Speed of the stream= (90-60)/2= 
(90-60)/2 = 15
15 kmph.   15nswer: 15
Answer: A
The total age of A and B is 15 years more than the total age of B and C. C is how many year younger than	Choose the correct choice from the following choices:
A) 14 years
B) 12 years
C) 56 years
D) 66 years
E) 15 years

Solution: Given that A+B = 15 + B + C   => A â€“ C = 15 + B â€“ B = 15   => C is younger than A by 15 years   Answer:15 years
Answer: E
A shopkeeper sold 10articles at the cost price of 8 articles. Then find the profit% or lost% ?	Select the correct option.
A) 10%  B) 15%  C) 25%  D) 30%  E) 20%

Solution: here 10 articles selling price = 8 articles cost price   so the difference = 10-8= 
10-8 = 2
2   % of profit= 2*100/10= 
2*100/10 = 20
20%   correct option is 20%
Answer: E
The total age of A and B is 18 years more than the total age of B and C. C is how many years younger than A ?  Choose the correct choice from the following choices
A) 12 B) 27 C) 21 D) 18 E) 11

Solution: (A+B) - (B+C) = 18   A - C = 18.   C is younger than A by 18 years.   Answer: 18
Answer: D
Working individually, Emma can wrap presents for 6 hours and Troy can wrap presents in 8 hours. If Emma and Troy work together but independently at the task for 2 hours, at which point Troy leaves, how many remaining hours will it take Emma to complete the task alone?
Choose the correct choice from the following.
A) 30/12	B) 5/12	C) 3/4	D) 2/12	E) 3/5

Solution: In first 2 hrs Troy will finish 2/8 = 1/4 of work and Emma will finish 2/6 work so total 1/4 + 1/3 = 7/12 work is finished and 1-7/12 = 5/12 work remaining. Now Emma will take (5/12)*6 = 30/12 hrs to finish it.   So answer is 30/12.
Answer: A
Find the value of (100+ 20/90) × 90 Options:
A) 4520  B) 9100  C) 9150  D) 8120  E) 9020

Solution: (9000+20)/90*90= 
(9000+20)/90*90 = 9_020
9020   Answer : 9020
Answer: E
A rainstorm increased the amount of water stored in State J reservoirs from 124 billion gallons to 140 billion gallons. If the storm increased the amount of water in the reservoirs to 80 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) 51 B) 48 C) 55 D) 63 E) 65

Solution: Let total capacity be x   we know 140 = 0.80x   x = 140/0.80= 
140/0.80 = 175
175   Prior to storm, we had 124 bn gallons     175-124= 
  175-124 = 51
51   51nswer : 51
Answer: A
An inspector rejects 15% of the meters as defective. How many will he examine to reject 15?	Choose the correct answer
A) A)100 B) B)120 C) C)250 D) D)200 E) E)160

Solution: Then, 15% of x= 15   (15/100)x = 15   x = (15*100*)/15= 100   100nswer is 100
Answer: A
If f(x) = x - 4, then (f o f)(3) = ? Pick
A) -5	B) -4	C) -6	D) -3	E) -7

Solution: (f o f)(3) = f(f(3)) = f(3 - 4) = f(-1) = - 5   correct answer -5
Answer: A
The sum of all solutions for x in the equation x^2 – 8x + 21 = |x – 4|+ 7 is equal to:	Choose the correct option:
A) –7 B) 7 C) 10 D) 12 E) 16

Solution: x^2 - 8x + 14 = |x-4|   RHS can be -ve or +ve   x^2 - 9x + 18 = 0   x^2 - 7x + 10 = 0   x= 6,5,3,2   We test all 4 values in original equation, all ok.   Thus, Sum = 6 + 5 +3 + 2= 
6 + 5 +3 + 2 = 16
16   Ans (16)
Answer: E
A 40-liter solution of alcohol and water is 5 percent alcohol. If 2.5 liters of alcohol and 7.5 liters of water are added to this solution, what percent of the solution produced is alcohol?	Select the correct option: A) 9% B) 12% C) 15% D) 18% E) 21%

Solution: The percent of alcohol in the solution is (0.05(40) + 2.5) / 50 = 4.5/50 = 9%   The answer is 9%.
Answer: A
Timmy and Tommy Pumpernickel are leaving home for college today. Peter and Patty Pumpernickel stand and wave goodbye as their pride and joy head off to schools at opposite ends of the state. If Timmy drives a slow 45 miles/ hour and Tommy "the lead foot" Pumpernickel drives a jaw dropping 75 miles per hour, how long until they are 500 miles away from one another?
Select:
A) 4 hours
B) 4.5 hours
C) 4.24 hours
D) 4.17 hours
E) 5 hours

Solution: The Pumpernickel brothers are traveling 120 miles per hour in opposite directions.   500 miles/ 120 miles/hour= 4.17 hours   Answer is 4.17 hours
Answer: D
A man has $ 10,000 to invest. He invests $ 4000 at 5 % and $ 3500 at 4 %. In order to have a yearly income of $ 500, he must invest the remainder at
Answers:
A) 6 % B) 6.1 % C) 6.2 % D) 6.3 % E) 6.4 %

Solution: Solution:   Income from $ 4000 at 5 % in one year = $ 4000 of 5 %.   = $ 4000 × 5/100.   = $ 4000 × 0.05.   = $ 200.   Income from $ 3500 at 4 % in one year = $ 3500 of 4 %.   = $ 3500 × 4/100.   = $ 3500 × 0.04.   = $ 140.   Total income from 4000 at 5 % and 3500 at 4 % = $ 200 + $ 140 = $ 340.   Remaining income amount in order to have a yearly income of $ 500 = $ 500 - $ 340.   = $ 160.   Total invested amount = $ 4000 + $ 3500 = $7500.   Remaining invest amount = $ 10000 - $ 7500 = $ 2500.   We know that, Interest = Principal × Rate × Time   Interest = $ 160,   Principal = $ 2500,   Rate = r [we need to find the value of r],   Time = 1 year.   160 = 2500 × r × 1.   160 = 2500r   160/2500 = 2500r/2500 [divide both sides by 2500]   0.064 = r   r = 0.064   Change it to a percent by moving the decimal to the right two places r = 6.4 %   Therefore, he invested the remaining amount $ 2500 at 6.4 % in order to get $ 500 income every year.   Answer: (6.4 %)
Answer: E
There are 6 boxes numbered 1, 2, ... 6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is: Choose the correct choice from the following.
A) 5 B) 6 C) 21 D) 33 E) 60

Solution: 6 Green - 1 way   5 green - 2 ways   4 green - 3 ways   3 green - 4 ways   2 green - 5 ways   1 green - 6 ways   total = > 21 ways   Answer 21
Answer: C
If 20 men can build a wall 112 metres long in 6 days, what length of a similar wall can be built by 15 men in 3 days? Choose the most appropriate option
A) 65mtr. B) 52mtr C) 70mtr. D) 78mtr. E) 42mtr.

Solution: 20 men is 6 days can build 112 metres   15 men in 3 days can build = 112*(15/20)x(3/6)   = 42 meters   Answer: 42mtr..
Answer: E
A palindrome is a number that reads the same forward and backward, such as 242. How many even thirteen-digit numbers are palindromes?	Pick one.
A) 40	B) 400	C) 500	D) 5,000	E) 40,000,000

Solution: if the palindrome must be even, it must begin and end in 2,4 6 and 8 ( 4 ways) e.g 22122,44144.   The middle number in the thirteen-digit could be 0-9 ( 10 ways), e.g 2222225222222, 2864228224682   The 2nd and fourth numbers , the 3rd and 5th, 4th and 6th, 5th and 7th must also be same i.e 0-9( 10 ways)   we thus have, 4 *10*10*10*10 *10*10= 4000000.40,000,000
Answer: E
A rectangular table seats 8 people on each of two sides, with every person directly facing another person across the table. If 16 people choose their seats at random, what is probability that person P directly faces person Q? Choose the correct choice from the following answers:
A) 1/14  B) 3/7  C) 1/16  D) 2/11  E) 1/15

Solution: Person P will be seated somewhere at the table.   Each of the other 15 people has an equal chance of sitting opposite person P.   The probability that person Q sits across is 1/15.   The answer is 1/15.
Answer: E
A certain stock exchange designates each stock with a 1, 2 or 3 letter code, where each letter is selected from the 8 letters of the alphabet. If the letters may be repeated and if the same letters used in a different order, constitute a different code, how many diff stocks is it possible to designate with these codes?	Choices
A) 258 B) 584 C) 774 D) 624 E) 523

Solution: Pretty simple actually   Number of 1 letter symbols = 8   Number of 2 letter symbols = 8*8   Number of 3 letter symbols = 8*8*8   The answer is sum of the 3. =584   So the answer is 584.
Answer: B
What approximate value should come in place of the a in the following equation?
10% of 6275 + 20% of 7584 = a	Choices:
A) 2180 B) 2160 C) 2140 D) 2130 E) 2120

Solution: a = 10% of 6275 + 20% of 7584   a = 10/100* 6275 + 20/100* 7584= 
10/100* 6275 + 20/100* 7584 = 21_443/10 = around 2_144.3
2144.3   ≈ 2140   Answer 2140
Answer: C
The mark up between "normal plan" price and "premium plan" price is 30 percent of the "normal plan" price. The markup is what percent of the "premium plan" price ?
(markup = difference between normal and premium price plans)  Choose the correct option:	A) 8%	B) 20%	C) 33 1/3%	D) 45%	E) 56 2/3%

Solution: A = price for normal plan   B = price for premium plan   MP = 0.5 A   B = A + 0.5 A = 1.5 A   hence Markup = B-A = 0.5/1.5 B = 1/3 B. Hence MP is 33.33% of B   Answer 33 1/3%
Answer: C
Car X began traveling at an average speed of 35 miles per hour. After 72 minutes, car Y began traveling at an average speed of 42 miles per hour. When both cars had traveled the same distance, both cars stopped. How many miles did car X travel from the time car Y began traveling until both cars stopped?	Choose the correct choice
A) 105	B) 140	C) 175	D) 210	E) 245

Solution: In 72 minutes, car X travels 42 miles.   Car Y gains 7 miles each hour, so it takes 6 hours to catch car X.   In 6 hours, car X travels 210 miles.   The answer is 210.
Answer: D
The ratio between the school ages of Neelam and Shaan is 5:6 respectively. If the ratio between the one-third age of Neelam and half of Shaan's age of 5:9, then what is the school age of Shaan?
Select the correct option
A) 17 B) 16 C) 18 D) 15 E) 19

Solution: Let the school ages of Neelam and Shaan be 5x and 6x years respectively.   Then, (1/3 * 5x)/(1/2 * 6x) = 5/9   15 = 15   Thus, Shaan's age cannot be determined.   Answer:15
Answer: D
let p be the product of the positive integers between 1 and 7 inclusive. How many distinct prime factors does p have?
Choices.
A) 1 B) 2 C) 3 D) 4 E) 5

Solution: There are 4 primes between 1 and 7, inclusive: 2, 3, 5, and 7, therefore p=1*2*...*7=7! has 4 distinct prime factors.   Answer: 4.
Answer: D
The ratio of investments of two partners P and Q is 7:5 and the ratio of their profits is 7:10. If P invested the money for 5 months, find for how much time did Q invest the money? Choices.
A) 19 months	B) 10 months	C) 11 months	D) 81 months	E) 12 months

Solution: 7*5: 5*x = 7:10   x = 10   Answer: 10 months
Answer: B
For each of her sales, a saleswoman receives a commission equal to 20 percent of the first $500 of the total amount of the sale, plus 40 percent of the total amount in excess of $500. If the total amount of one of her sales was $800, the saleswoman’s commission was approximately what percent of the total amount of the sale? Choices
A) 22%
B) 24%
C) 25%
D) 27%
E) 28%

Solution: Total sales =800   Comission = (20/100)*500+ (40/100)*300   =100 + 120= 
100 + 120 = 220
220   %Comission=(220/800)*100= 
(220/800)*100 = 55/2 = around 27.5
27.5~ 28%   Answer is 28%
Answer: E
If abc ≠ 1 and the sum of the reciprocals of a, b, and c equals the reciprocal of the product of a, b, and c, then a =  Options.
A) (1 + bc)/(b + c)
B) (1 – bc)/(b + c)
C) (1 + b + c)/(bc)
D) (1 – b – c)/(bc)
E) (1 – b – c)/(b + c)

Solution: Answer is (1 + b + c)/(bc) though it took me around 4 minutes to get that.
Answer: C
g(x) is defined as the product of all even integers k such that 0 < k ≤ x. For example, g(14) = 2 × 4 × 6 × 8 × 10 × 12 × 14. If g(z) is divisible by 4^11, what is the smallest possible value for z?  Choices:
A) 22
B) 24
C) 28
D) 32
E) 44

Solution: g(z)=4^11=2^22. So we have to find a product with atleast 22 2's in it.   in option 1 22 the total no of 2's = [22/2] + [22/4] +[22/8] +[22/16] = 11+5+2+1= 
11+5+2+1 = 19
19   in option 2 24 the total no of 2's= [24/2] + [24/4] +[24/8] +[24/16] = 12+6+3+1= 
12+6+3+1 = 22
22 . Hence 24
Answer: B
A certain list of 300 test scores has an arithmetic mean of 75 and a standard deviation of d, where d is positive. Which of the following two test scores, when added to the list, must result in a list of 301 test scores with a standard deviation less than d?  Choose the correct choice from the following answers:  A) 75 and 80  B) 80 and 85  C) 70 and 75  D) 75 and 75  E) 74 and 74

Solution: Deviation means spreading of the numbers from one median point value..   as the set is already established and we need to add only two numbers, this means we can only add numbers which are closer to the median to reduce the deviation.   so 75 and 75 are the most close numbers and they will increase the number of elements in the set without changing the median value.   75 and 75
Answer: D