MU-NLPC/Calc-aqua_rat huggingface dataset:
8 men can do a piece of work in 12 days. 4 women can do it in 48 days and 10 children can do it in 24 days. In how many days can 10 men, 4 women and 30 children together complete the piece of work?	Select
A) 5 days	B) 15 days	C) 28 days	D) 4 days	E) 7 days

Solution: Explanation:   1 man’s 1 day’s work = 1/8 × 12 = 1/96   10 men’s 1 day’s work = 1 × 10/96 = 5/48   1 woman’s 1 day’s work = 1/192   4 women’s 1 day’s work = 1/192 × 4 = 1/48   1 child’s 1 day’s work = 1/240   30 children’s 1 day’s work = 1/8   Therefore, (10 men + 4 women + 30 children)’s 1 day’s work = 5/48 + 1/48 + 1/8   =1/4   The required No. of days = 4 days   Answer: Option 4 days
Answer: D
Abi decided to save a certain amount of her monthly salary each month and her salary was unchanged from month to month. If abi's savings by the end of the year from these monthly savings were six times the amount she spent per month, what should be the fraction of her salary that she spent each month?
Choose the most appropriate option
A) 6/9
B) 5/3
C) 2/3
D) 4/3
E) 5/3

Solution: Let Abi 's monthly savings = S   Abi 's monthly pay = P   Abi 's monthly expenditure = P-S   Abi 's savings by the end of the year from these monthly savings were six times the amount she spent per month   12S = 6*(P-S)   =>2S = P-S   => P = 3S   Abi 's monthly expenditure = P-S = 3S-S = 2S   fraction of her salary that Abi spent each month = 2S / 3S=P-S/P = 2/3. Answer is 2/3
Answer: C
A present value of a machine is $148000. Its value depletiation rate is 25% per annum then find the machine value after 3 years?
Choose the correct choice from the following options
A) A)$54000  B) B)$48000  C) C)$36520  D) D)$62437.5  E) E)$42500

Solution: P= $148000   R = 25%   T = 3 years   Machine value after 3years = P/(1-R/100)^T   =148000*3/4 * 3/4 * 3/4= 
148000*3/4 * 3/4 * 3/4 = 124_875/2 = around 62_437.5
$62437.5   Answer is $62437.5
Answer: D
A boat with speed 15 km/hr in standing water goes 30 km downstream and returns in a total of 4.5 hours. What is the speed of current?  Choose the correct answer
A) 8kmph	B) 6kmph	C) 4kmph	D) 5 kmph	E) 1kmph

Solution: Explanation:   Speed of the boat in still water: 15 km/hr   Speed of boat downstream: (15+x)km/hr where x is speed of the current.   The boat travels 30 km downstream and then 30 km upstream and takes 9/2 hours.   Total time= Time taken to travel downstream + Time taken to travel upstream   => 4/5= (30/(15+x))+(30/(15-x))   =>x= 5   ANSWER:5 kmph
Answer: D
How long will a train 100m long travelling at 72kmph take to overtake another train 200m long travelling at 54kmph ?	Choose the correct choice from the following choices
A) 60 sec B) 70 sec C) 80 sec D) 50 sec E) 90 sec

Solution: 72 kmph=72*5/18= 
72*5/18 = 20
20mps.   54 kmph=54*5/18= 
54*5/18 = 15
15 mps.   The train has to travel (200+100)= 
(200+100) = 300
300m to overtake the other one.   Resultant velocity=(20-15)= 
(20-15) = 5
5 mps   time it takes to travel 300m at a velocity of 5 mps is 60 sec..   Ans 60 sec.   60 secNSWER:60 sec
Answer: A
An accurate clock shows 8 o'clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 2 o'clock in the afternoon?
Choose one
A) 180°	B) 154°	C) 160°	D) 170°	E) 150°

Solution: We know that angle traced by hour hand in 12 hrs = 360°   From 8 to 2, there are 6 hours.   180°ngle traced by the hour hand in 6 hours = 6×36012=180°   180°nswer is 180°.
Answer: A
Find the slope of the line perpendicular to the line y = x - 7	Choose the correct choice from the following answers:
A) 1
B) 2
C) -1
D) 4
E) 5

Solution: Two lines are perpendicular if the product of their slopes is equal to -1. The slope of the given line is equal to 1. If m is the slope of the line perpendicular to the given line, then   m × 1 = -1   Solve for m   m = - 1   correct answer -1) -1
Answer: C
In one alloy there is 12% chromium while in another alloy it is 8%. 35 kg of the first alloy was melted together with 40 kg of the second one to form a third alloy. Find the percentage of chromium in the new alloy.	Choose the correct choice.
A) 8.8% B) 9.75% C) 9.2% D) 8.6% E) 8.4%

Solution: The amount of chromium in the new 35+45= 
35+45 = 80
80 kg alloy is  0.12*35+0.08*45= 
 0.12*35+0.08*45 = 7.8
7.8 kg, so the percentage is  7.8/80*100= 
 7.8/80*100 = 9.75
9.75%.   Answer: 9.75%.
Answer: B
Look at this series: 55, 55, 40, 40, 25, 25, ... What number should come next?
Answers:
A) 14
B) 15
C) 17
D) 10
E) 11

Solution: In this series, each number is repeated, then 15 is subtracted to arrive at the next number.   The next number should be 10   Answer : 10
Answer: D
In order to obtain an income of Rs. 1250 from 10% stock at Rs. 210, one must make an investment of  Answers.
A) 5363
B) 26250
C) 28678
D) 29002
E) 2732

Solution: To obtain Rs. 10, investment   = Rs. 210.   To obtain Rs. 1250, investment =   = Rs. 26250.   Answer: 26250
Answer: B
In a certain city each of 17 Girl Scout troops is represented by a colored flag. Each flag consists of either a single color or a pair of two different colors. If each troop has a different flag, what is the minimum number of colors needed for the flags. (Assume that the order of colors in a pair on a flag does not matter.)
Select the correct option:	A) 5	B) 10	C) 6	D) 20	E) 40

Solution: B.6:   if we have 5 colors we can choose pairs in 5C2 ways = 10 and single color flags are 5. Therefore total number of flags = 15. This is less than the number of girl scout groups.   if we have 6 colors we can choose pairs in 6C2 ways = 15 and single color flags are 6. Therefore total number of flags = 21.   ANS 6.
Answer: C
A tank can supply water to a village for 60 days. If a leak at the bottom of the tank drains out 10 liters per day, the supply lasts for 45 days only. For how many days will the supply last if the leak drains out 20 liters per day?	Choose the correct choice from the following options:
A) 15  B) 18  C) 20  D) 24  E) 36

Solution: Losing 10 liters per day results in a loss of 450 liters in 45 days. So, those 450 liters were for 15 days, making daily consumption of the village 30 liters per day. Thus the capacity of the tank is  30*60= 
 30*60 = 1_800
1800 liters.   Losing 20 liters plus 30 liters gives 50 liters per day. At this rate the supply will last   1800/50= 
  1800/50 = 36
36 days.   The answer is 36.
Answer: E
Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 36 kmph. Of how many minutes does the train stop per hour? Choose the correct choice from the following:
A) 11
B) 8
C) 12
D) 99
E) 17

Solution: T = 9/45 * 60= 
9/45 * 60 = 12
12   Answer: 12
Answer: C
If the price of gold increases by 50%, find by how much the quantity of ornaments must be reduced, so that the expenditure may remain the same as before?
Choose the correct choice from the following answers.
A) 331/8%
B) 331/3%
C) 338/3%
D) 391/3%
E) 311/3%

Solution: 100   150   ------   150-------50   100-------? => 331/3%   Answer: 331/3%
Answer: B
In a group of ducks and cows, the total number of legs are 48 more than twice the no. of heads. Find the total no.of buffaloes.  Choose the correct choice from the following options.
A) 28  B) 12  C) 24  D) 16  E) 19

Solution: Let the number of buffaloes be x and the number of ducks be y   => 4x + 2y = 2 (x + y) + 48   => 2x = 48 => x = 24   24
Answer: C
66 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be :	Answers:
A) 84 m B) 88 m C) 120 m D) 137 m E) None

Solution: Sol.   Let the length of the wire b h.   Radius = 1/2 mm = 1/20 cm. Then,   22/7 * 1/20 * 1/20 * h = 66 ⇔ = [66 * 20 * 20 * 7 / 22= 
66 * 20 * 20 * 7 / 22 = 8_400
8400cm= 84 m.   84 mnswer 84 m
Answer: A
Calculate the effect changes in dimension of a rectangle will have on its area, if length is increased by 15% and its breadth is decreased by 10%?	Answers.
A) 3.5 percent increase B) 9.5 percent increase C) 1.5 percent increase D) 3.9 percent increase E) 3.5 percent increase

Solution: let L and B be 100 each     100 * 100= 
  100 * 100 = 10_000
10000   L increase by 15%= 115   B decrease by 10% = 90   115 * 90= 
115 * 90 = 10_350
10350   3.5 percent increase   ANSW3.5 percent increaseR:3.5 percent increase
Answer: E
Which of the following is equal to 10^-(-2)^2?
Choose one:	A) 1/(10^6)	B) 1/(10^7)	C) 1/(10^8)	D) 1/(10^9)	E) 1/(10^4)

Solution: 10^-(-2)^2 => 10^-(-2^2) => 10^-(4) = 1/(10^4)   Answer : 1/(10^4)
Answer: E
A credit card number has 6 digits (between 1 to 9). The first two digits are 12 in that order, the third digit is bigger than 6, the forth is divisible by 4 and the fifth digit is 3 times the sixth. How many different credit card numbers exist?  Choose the correct choice from the following answers: A) 27 B) 36 C) 72 D) 18 E) 422

Solution: {1}{2}{greater than 6}{divisible by 4}{3x}{x}:   The third digit can take 3 values: 7, 8, or 9.   The fourth digit can take 2 values: 4, or 8.   The fifth and sixth digits can take 3 values: 31, 62, or 93.   Total = 3*2*3= 
3*2*3 = 18
18.   Answer: 18.
Answer: D
Karen places a bet with Tom that she will beat Tom in a car race by 4 miles even if Karen starts 4 minutes late. Assuming that Karen drives at an average speed of 60 mph and Tom drives at an average speed of 45 mph, how many H miles will Tom drive before Karen wins the bet? Choose the correct choice.
A) 15  B) 18  C) 21  D) 24  E) 27

Solution: Let K and T be the speeds of Karen and Tom respectively.   t be the time that Karen will travel ----> t+4/60 will be the total time Tom will travel by the time the distance between Karen and Tom is 4 miles.   Thus, per the question , K(t) - T(t+4/60) = 4 ---> t = 7/15 hours   Thus the distance traveled by Tom when Karen is 4 miles ahead of him H: T*(t+4/60) = 45 (7/15+4/60) = 24 miles. 24 is the correct answer.
Answer: D
Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 25 percent during the third year. What is the value of the account today?
Choose the correct choice from the following:
A) $10,350
B) $8,662.50
C) $10,500
D) $11,500
E) $12,705

Solution: Value after 1 year: 10,000 * 1.1 = 11,000   Value after 2 years: 11,000 * 1.05 = 11,550   Value today: 11,550 * 0.75 = 10,395   Answer $8,662.50 is correct.
Answer: B
Markov bought shares for a total value of $1000. Next day, the price of shares is reduced by 10%. With the same $1000, he could now buy 10 more shares. Which of the following is closest to the original price per share? Choose the most appropriate option:	A) $10	B) $11	C) $12	D) $13	E) $14

Solution: From the given information,we can conclude that Markov bought x number of shares for $1000. With a 10% reduction in price, he could buy the same x number of shares for  1000*.90= 
 1000*.90 = 900
$900 . With the remaining money ($1000 - $900= $100), he can buy 10 more shares. So, the reduced price per share = $100/10= 
100/10 = 10
$10.   Therefore, if the reduced price of $10 equals the original price * 9/10, then the original price is approximately $11=$11
Answer: B
The first three terms of a proportion are 3, 9 and 12. The fourth term is?	Choose the correct choice:  A) 33  B) 20  C) 28  D) 36  E) 11

Solution: (9*12)/3= 
(9*12)/3 = 36
36   Answer: 36
Answer: D
Out of 15 consecutive numbers, 2 are chosen at random. The probability that they are both odds or both primes is?	Choose the correct choice from the following options:
A) 1/8
B) 1/7
C) 1/0
D) 1/6
E) 1/1

Solution: A leap year has 52 weeks and two days   Total number of cases = 7   Number of favourable cases = 1   i.e., {Saturday, Sunday}   Required Probability = 1/7   Answer: 1/7
Answer: B
Five boys picked up 30 mangoes .In how many ways can they divide them if all mangoes be identical?  Pick one.
A) A)5^30	B) B)2^30	C) C)1^30	D) D)3^30	E) E)6^30

Solution: Each Mango can be given to any one of the five people or in other words..1 mango can be divided into 5 ways...so all 30 can be divided in 5^30 ways   5^30NS:5^30
Answer: A
The value of x + x(xx) when x = 2 is: Select the correct option.
A) 8  B) 10  C) 12  D) 14  E) 16

Solution: x + x(xx)   Put the value of x = 2 in the above expression we get,   2 + 2(22)   = 2 + 2(2 × 2)   = 2 + 2(4)   = 2 + 8= 
2 + 8 = 10
10   ANSWER : (10) +10
Answer: B
It takes Jim three hours to wash the gym and it takes Julia two hours to wash the gym. Working together, how many minutes will it take them to wash the gym?	Select the correct option
A) 70 B) 72 C) 74 D) 76 E) 78

Solution: Jim can wash (1/3) of the gym per hour.   Julia can wash (1/2) gym per hour.   Together they can wash 1/3+1/2=5/6 of the gym per hour.   1 gym / (5/6) of the gym per hour = 6/5 hours = 72 minutes.   The answer is 72.
Answer: B
If a card is drawn from a well shuffled pack of cards, the probability of drawing a spade or a king is  Choose the correct option:	A) 4/15	B) 4/18	C) 4/16	D) 4/13	E) 4/11

Solution: P(SᴜK) = P(S) + P(K) - P(S∩K), where S denotes spade and K denotes king.   P(SᴜK) = 13/52 + 4/52 - 1/52   = 4/13   Answer: 4/13
Answer: D
Three 6 faced dice are thrown together. The probability that all the three show the same number on them is ?	Select:	A) 1/39	B) 1/36	C) 1/35	D) 1/34	E) 1/32

Solution: It all 3 numbers have to be same basically we want triplets. 111, 222, 333, 444, 555 and 666. Those are six in number. Further the three dice can fall in 6 * 6 * 6= 
6 * 6 * 6 = 216
216 ways.   Hence the probability is 6/216= 1/36   Answer: 1/36
Answer: B
Elvin's monthly telephone bill is the sum of the charge for the calls he made during the month and a fixed monthly charge for Internet service. Elvin's total telephone bill for January was $52 and Elvin's total telephone bill for February was 76$. If Elvin's charge for the calls he made in February was twice the charge for the calls he made in January, what is Elvin's fixed monthly charge for Internet service?
Options.
A) $5  B) $10  C) $14  D) $28  E) $29

Solution: Bill = Fixed Charge + Charge of Calls made   in Jan, Bill = Fixed Charge(Let, y) + Charge of calls made in Jan (Let, x) = $52   in Feb, Bill = Fixed Charge (Let, y) + Charge of calls made in Feb (Then, 2x) = $76   i.e. x+y = 52   and 2x+y = 76   Take the difference if two equations   i.e. (2x+y) - (x+y) = 76 - 52   i.e. x = 24   i.e. Fixed Monthly Charge, y = 28   Answer: Option   $28
Answer: D
If a sum of money doubles itself in 10 years at simple interest, the ratepercent per annum is	Select: A) 10 B) 12.5 C) 13 D) 13.5 E) 14

Solution: Explanation:   Let sum = x then Simple Interest = x   Rate = (100 * x) / (x * 10) = 10   Option 10
Answer: A
A rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m?
Choose the correct choice from the following.
A) 3909
B) 3907
C) 3905
D) 3900
E) 3901

Solution: Area = (l + b – d) d   (80 + 60 – 10)10 => 1300 m2   1300 * 3 = Rs.3900   25. The length of a rectangl.Answer:3900
Answer: D
What is the perimeter of a square with area 4p^2/9 ?  Choose the correct answer.
A) 8p/3
B) 3p^2/4
C) 3p
D) 3p^2
E) 4p/3

Solution: 8p/3rea of square, (side)^2 = (2p/3)^2   Therefore side of the square = 2p/3   Perimeter of square = 4*side = 4* (2p/3) = 8p/3   8p/3nswer is 8p/3.
Answer: A
For what value(s) of n is the following equation satisfied: 2n-6-n = 5n+6-4n
Select
A) a. -5  B) b. 0 only  C) c. 5/2 only  D) d. No value  E) e. Any value

Solution: 2n-6-n = 5n+6-4n   n - 6 = n + 6   -6 = 6, which is false.   So, no n satisfies given equation.   Answer: d. No value.
Answer: D
Ages of two persons differ by 4 years. If 3 years ago, the elder one was 3 times as old the younger one, find their present age	Choose one: A) 5,9 B) 14,18 C) 16,20 D) 18,22 E) 19,23

Solution: Explanation:   Let the age of the younger person be x,   Then the elder person's age is (x+4)   => 3(x-3) = (x+4-3) [3 years before]   => 3x-9 = x+1   => x = 5.   So the elder person's age is x + 4 = 9   5,9nswer: Option 5,9
Answer: A
If the Average of 10 consecutive integers is 19.5 then the 10th integer is :- Choose the correct choice from the following: A) 15 B) 20 C) 23 D) 24 E) 25

Solution: The average falls between the 5th and 6th integers,   integer 5 = 19, integer 6 = 20.   Counting up to the tenth integer   we get 24.   ANSWER:24
Answer: D
Together, 15 type A machines and 7 type B machines can complete a certain job in 4 hours. Together 8 type B machines and 15 type C machines can complete the same job in 11 hours. How many W hours would it take one type A machine, one type B machine, and one type C machine working together to complete the job (assuming constant rates for each machine)?	Choose the correct choice from the following.
A) 22 hours  B) 30 hours  C) 44 hours  D) 60 hours  E) It cannot be determined from the information above.

Solution: Say the rates of machines A, B and C are a, b, and c, respectively.   Together 15 type A machines and 7 type B machines can complete a certain job in 4 hours --> 15a + 7b = 1/4;   Together 8 type B machines and 15 type C machines can complete the same job in 11 hours --> 8b + 15c = 1/11.   Sum the above: 15a + 15b + 15c = 1/4 + 1/11 = 15/44 --> reduce by 15: a + b + c = 1/44 --> so, the combined rate of the three machines is 1/44 job/hour --> time is reciprocal of the rate, thus machines A, B and C can do the job W in 44 hours.   Answer: 44 hours.
Answer: C
The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?  Answers.
A) 140 sq.units	B) 556 sq.units	C) 155 sq.units	D) 146 sq.units	E) 142 sq.units

Solution: Given that the area of the square = 1225 sq.units   => Side of square = √1225 = 35 units   The radius of the circle = side of the square = 35 units Length of the rectangle = 2/5 * 35= 
2/5 * 35 = 14
14 units   Given that breadth= 10 units   140 sq.unitsrea of the rectangle = lb = 14 * 10= 
14 * 10 = 140
140 sq.units   140 sq.unitsnswer:140 sq.units
Answer: A
The compound interest earned by Sunil on a certain amount at the end of two years at the rate of 8% p.a. was Rs.2828.80. Find the total amount that Sunil got back at the end of two years in the form of principal plus interest earned.  Select:
A) 19828.89  B) 19828.8  C) 19828.37  D) 19828.82  E) 19828.87

Solution: Let the sum be Rs.P   P{ [ 1 + 8/100]2 - 1 } = 2828.80   P(8/100)(2 + 8/100) = 2828.80 [a2 - b2   = (a - b) ( a + b)] P = 2828.80 / (0.08)(2.08)   = 1360/0.08= 
1360/0.08 = 17_000
17000 Principal + Interest= Rs.19828.80   Answer: 19828.8
Answer: B
The average age of three boys is 12 years and their ages are in proportion 4:5:9. What is the age in years of the youngest boy?	Choose the correct choice.
A) 6 B) 9 C) 8 D) 4 E) 2

Solution: 4x + 5x + 9x = 36   x =2   4x = 8   Answer: 8
Answer: C
If f(a)=a^2 and a is a positive integer, which of the following CANNOT be the value of f(f(a))?
Choose the correct choice from the following.
A) 256
B) 16
C) 81
D) 1
E) 165

Solution: f(a)=a^2   f(f(a)) = (a^2)^2 = a^4   Therefore f(f(a)) will be numbers that are 4th power of other numbers.   Checking the options:   1 = 1^$   16 = 2^4   81 = 3^4   165. This cannot be written as the 4th power of any number   256 = 4^4   Answer: 165
Answer: E
How many times in a day, the hands of a clock are straight?
Choices:
A) 22 B) 24 C) 44 D) 48 E) 46

Solution: In 12 hours, the hands coincide or are in opposite direction 22 times.   In 24 hours, the hands coincide or are in opposite direction 44 times a day.   ANSWER:44
Answer: C
The moon revolves around the earth at a speed of approximately 1.03 kilometers per second. This approximate speed is how many kilometers per hour?	Choose the correct choice from the following choices.
A) 60 B) 61.2 C) 62.5 D) 3,708 E) 3,672

Solution: moon revolves around the earth at a speed of 1.02kilometers per second.   one hour equal to 60 minutes.   one minute equals to 60 seconds. so one hour equals to 3600seconds.   so one hour, speed= 1.03*3600= 
1.03*3600 = 3_708
3708kilometers per hour.   Option 3,708 is correct
Answer: D
The slant height of a cone is 12 cm and radius of the base is 4cm, find the curved surface of the cone.
Choose the correct option:  A) 48 pi cm2  B) 30 pi cm2  C) 35 pi cm2  D) 40 pi cm2  E) 45 pi cm2

Solution: Ï€ * 12 * 4 = 48   48 pi cm2NSWER 48 pi cm2
Answer: A
A survey of employers found that during 1993 employment costs rose 3.5 percent, where employment costs consist of salary costs and fringe-benefit costs. If salary costs rose 3 percent and fringe-benefit costs rose 9.5 percent during 1993, then fringe-benefit costs represented what percent of employment costs at the beginning of 1993 ?
Choose the correct choice.
A) 16.5% B) 8% C) 35% D) 55% E) 65%

Solution: The amount by which employment costs rose is equal to 0.035(salary costs + fringe benefit costs);   On the other hand the amount by which employment costs rose is equal to 0.03*salary costs + 0.095*fringe benefit costs;   So, 35(S+F) = 30S+95F --> S = F --> F/S = 1/12 --> F/(S+F) = 1/(1+12) = 1/13 = 0.08.   Answer: 8%.
Answer: B
When positive integer N is divided by positive integer P, the quotient is 18, with a remainder of 7. When N is divided by (P + 2), the quotient is 15 and the remainder is 1. What is the value of N? Select the correct option:  A) 151  B) 331  C) 511  D) 691  E) 871

Solution: Use the rule dividend = (integer quotient)*(divisor) + remainder to translate each sentence.   The first sentence becomes N = 18P + 7. The second equation becomes N = (P + 2)*15 + 1, which simplifies to N = 15P + 31. These are ordinary simultaneous equations Since they both equal N already, let’s set them equal and solve for P.   18P + 7 = 15P + 31   3P + 7 = 31   3P = 24   P = 8   Now that we know P = 8, we can just plug in. The product 15*8 is particularly easy to do, without a calculator, by using the “doubling and halving” trick. Double 15 to get 30, and take half of 8 to get 4 —- 15*8 = 30*4= 
30*4 = 120
120. So   N= 15(8) + 31 = 120 + 31= 
120 + 31 = 151
151   N= 151, answer = 151.
Answer: A
If P represents the product of the first 18 positive integers, then P is NOT a multiple of Choose the correct choice from the following choices:  A) 99  B) 84  C) 72  D) 65  E) 95

Solution: Answer is E.   Since prime factor of 95 is 5x19. 19 is a prime number and not part of the first 18 positive integers.   A) 9 x 11   B) 12 x 7   C) 12 x 6   D) 13 x 5   95) 3 x 19
Answer: E
how many zeros are there in 50! Choose the correct choice from the following options
A) 10  B) 11  C) 12  D) 13  E) 14

Solution: To find the number of trailing zeroes in 50! factorial we must find the number of integral values in :   50/5 + 50/5^2 + 50/5^3 +.........   = 10+2+0+0....   =12   ANSWER:12
Answer: C
There are two numbers. If 40% of the first number is added to the second number, then the second number increases to its five-fourth. Find the ratio of the first number to the second number? Choose the correct choice from the following:
A) 8 : 25  B) 25 : 8  C) 8 : 5  D) 5 : 8  E) None of these

Solution: Let the two numbers be x and y.   40/100 * x + y = 5/4y   => 2/5 x = 1/4 y => x/y = 5/8   ANSWER:5 : 8
Answer: D
In 1995 a certain store had 1800 tools in stock that had been purchased for $30 each. If 1,000 of these tools were sold in 1995 for $50 each and the remaining 800 were sold in 1996 for $70 each, how many greater was the gross profit on the tools sold in 1996 than the gross profit on those sold in 1995?  Choose the correct answer:
A) $12,000	B) $6,000	C) $8,000	D) $32,000	E) $40,000

Solution: The keyword here isGross Profit:   Gross Profit = (Selling Price - Original Price)*(# of Items Sold)   So lets figure out what the Gross Profit for 1995:   GP1995 = (50-30)*(1000)= 
(50-30)*(1000) = 20_000
20000   $12,000nd the Gross Profit for 1996:   GP1996= (70-30)*(800)= 
(70-30)*(800) = 32_000
32000   So the difference would be:   32000-20000= 
32000-20000 = 12_000
12000   $12,000NSWER: $12,000 12000
Answer: A