MU-NLPC/Calc-aqua_rat huggingface dataset:
Company Z spent 1/4 of its revenues last year on marketing and 1/7 of the remainder on maintenance of its facilities. What fraction of last year’s original revenues did company Z have left after its marketing and maintenance expenditures?	Choose the correct choice from the following answers:
A) 5/14 B) 1/2 C) 17/28 D) 9/14 E) 9/11

Solution: Total revenues = x   Spent on marketing = x/4   Remaining amount = x-x/4 = 3x/4   1/7 of the remainder on maintenance of its facilities = 3x/4*1/7 = 3x/28   Amount left = 3x/4-3x/28 = 9x/14   Answer 9/14
Answer: D
A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
Choose the correct choice from the following answers:	A) 40 sec	B) 42 sec	C) 45 sec	D) 48 sec	E) 58 sec

Solution: Speed = 45 * 5/18 = 25/2 m/sec   Total distance covered = 360 + 140= 
360 + 140 = 500
500 m   Required time= 500 * 2/25= 
500 * 2/25 = 40
40 sec   40 secNSWER:40 sec
Answer: A
What is the scope including 1/21+1/22+1/23+......+1/30?
Pick:
A) 1/6~1/5
B) 1/5~1/4
C) 1/4~1/3
D) 1/3~1/2
E) 1/2~1

Solution: For Maximum value : It should be less than 1/21 + 1/21 +1/21... 10 times = 10/21 ~ 1/2   For Minimum Value : It should be greater than 1/30+ 1/30+ 1/30 .. 10 times = 10/30 = 1/3   Thus, the answer should lie between 1/3 and 1/2. Correct ans : 1/3~1/2.
Answer: D
Company A has 13 employees, 9 of whom belong to the union. If 5 people work any one shift, and the union contract specifies that at least 4 union members work each shift, then how many different combinations of employees might work any given shift?
Choose the most appropriate option.
A) 56  B) 231  C) 336  D) 350  E) 756

Solution: Looks easy: -- 9C4*5C1 + 9C5= 756 (756).
Answer: E
A bag contains 5 red, 2 green balls. 3 balls are drawn randomly. What is the probability that balls drawn contain exactly two green balls?  Choose one
A) 1/7	B) 2/9	C) 3/11	D) 4/17	E) 2/3

Solution: Total number of balls = 5+2= 
5+2 = 7
7   n(S)= 7C3 = 7*6*5 / 3*2 = 35   n(E) = 2C2* 5C1 = 5   Probability = 5/35 = 1/7   1/7nswer is 1/7
Answer: A
A woman complete a journey in 20 hours. She travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.	Answers
A) 334 km.	B) 216 km.	C) 314 km.	D) 448 km.	E) 544 km.

Solution: 0.5x/21 + 0.5x/24 = 20   --> x/21 + x/24 = 40   --> x =448 km.   448 km.
Answer: D
The average height in a group of 4 people is 175 cm. If the average height increased when 2 more people were added to the group, which of the following cannot be the heights of the two new people? Options:
A) 179 cm and 172 cm  B) 181 cm and 169 cm  C) 173 cm and 178 cm  D) 176 cm and 176 cm  E) 174 cm and 177 cm

Solution: Denote X as the sum of the heights of the two new people. From the stem it follows that (700+X)6>175. This reduces to X>350. Only the heights from B add up to 350 cm. All other pairs add up to more than 350 cm.   Answer: 181 cm and 169 cm
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 5 years hence?  Choose the correct choice from the following:
A) 70
B) 55
C) 60
D) 65
E) 80

Solution: 70+B=60 70=2B   2B+B=60===>B=20   70=40   5 yrs ages 45 and 25   Sum of their ages = 70   70NSWER 70
Answer: A
Find the number which when multiplied by 15 is increased by 196.
Choose the correct choice from the following answers
A) 14
B) 20
C) 26
D) 28
E) 30

Solution: Let the number be x. Then, 15x - x = 196   <=> 14x = 196 <=> x = 14.   14nswer :14
Answer: A
A number X equals 80% of the average of 5, 7, 14 and a number Y. If the average of X and Y is 26, the value of Y is?	Choose the correct choice:
A) 13
B) 26
C) 39
D) 36
E) None of these

Solution: Average of 5, 7, 14 and Y = ( 5 + 7 + 14 + Y )/ 4   Therefore, X = 80% of ( 5 + 7 + 14 + y )/ 4   = (80/100) x (26 + Y)/4   => X = (26 + Y)/5   5X - Y = 26----- (i)   Also, (X + Y)/2 = 26 ----- (ii)   From (i)and (ii)   X = 13   Y = 39.   ANSWER:39
Answer: C
A man covers a distance on scooter. Had he moved 3kmph faster he would have taken 40 min less. If he had moved 2kmph slower, he would have taken 40min more. The distance is.  Choose the most appropriate option.
A) 30 km  B) 40 km  C) 45 km  D) 50 km  E) 55 km

Solution: Let distance = x m   Usual rate = y kmph   x/y – x/y+3 = 40/60 hr   2y(y+3) = 9x ---------------------------------(1)   x/y-2 – x/y = 40/60 hr y(y-2) = 3x -----------(2)   divide 1 & 2 equations   by solving we get x = 40 km   Answer : 40 km
Answer: B
The number of livestock in a farm at the beginning of year 2000 was 130,000. During the year, the number increased by p%. During the next year 2001, there was a famine and the number decreased by q%. A census at the end of year 2001 revealed that the number of livestock in the farm was 130,000. Which of the following expressions is correct? Choose the correct answer:  A) With the exception of 1 instance, p will be equal to q  B) q > p  C) p = q  D) p > q  E) There is no relation between p and q

Solution: Number plugging in will be best strategy for this question.   Let p = 5%,   Per the question 100000(1.05)(1-q/100) = 100000 ---> q = 4.7%. Thus p > q and hence p > q is the correct answer.
Answer: D
If 3 men or 4 women can reap a field in 10 days how long will 5 men and 6 women take to reap it?	Pick:
A) 19/60
B) 9/60
C) 2/3
D) 5/18
E) 6/24

Solution: Explanation:   3 men reap 1/10 field in 1 day   1 man reap 1/(3 x 10)   4 women reap 1/10 field in 1 day   1 woman reap 1/(10 x 4)   5 men and 6 women reap (5/(3 x 10)+ 6/(4 x 10)) =19/60 in 1 day   5 men and 6 women will reap the field in 19/60 days   19/60nswer: Option 19/60
Answer: A
What is the greatest possible value of integer n if 100! is divisible by 15^n  Pick one:
A) 20  B) 21  C) 22  D) 23  E) 24

Solution: 15^n = 5^n * 3^n   Highest prime factor will be the limiting factor.   100/5 +100/25 =20+4= 
20+4 = 24
24   ANSW24R:24
Answer: E
Find the invalid no.from the following series 15, 16, 34, 105, 424, 2124, 12756  Choose the correct choice:
A) 15 B) 16 C) 34 D) 105 E) 2124

Solution: 2nd term = (1st term) * 1 + 1 = 15 *1 + 1= 
15 *1 + 1 = 16
16.   3rd term= (2nd term) * 2 + 2 = 16 * 2 + 2= 
16 * 2 + 2 = 34
34   4th term= (3th term) *3 + 3 = 34 * 3 + 3= 
34 * 3 + 3 = 105
105   5th term= (4th term) * 4 + 4 = 105 * 4 + 4= 
105 * 4 + 4 = 424
424   6th term= (5th term) * 5 + 5 = 424 * 5 + 5= 
424 * 5 + 5 = 2_125
2125   6th term should 2125 instead of 2124.   2124
Answer: E
On Monday, a certain animal shelter housed 45 cats and dogs. By Friday, 1/5 of the cats and 1/4 of the dogs had been adopted; no new cats or dogs were brought to the shelter during this period. What is the greatest possible number of pets that could have been adopted from the animal shelter between Monday and Friday?
Select the correct option.
A) 10 B) 11 C) 12 D) 13 E) 14

Solution: To maximize the number of pets adopted, we should maximize the number of dogs adopted since 1/4 > 1/5.   The greatest multiple of 4 less than 45 is 40 (such that the remaining number is divisible by 5), so let's assume there were 40 dogs and 5 cats.   Then the maximum number of adopted pets is 1/4*(40) + 1/5*(5) = 10 + 1= 
10 + 1 = 11
11.   The answer is 11.
Answer: B
A shopkeeper gave an additional 20 per cent concession on the reduced price after giving 30 per cent standard concession on an article. If Arun bought that article for 1,120, what was the original price?  Choose the correct option
A) 3,000 B) 4,000 C) 2,400 D) 2,000 E) None of these

Solution: Original price = 1120 × 100⁄70 × 100⁄80 = 2000   Answer 2,000
Answer: D
The total age of A and B is 10 years more than the total age of B and C. C is how many years younger than A.?
Options
A) 16	B) 12	C) 10	D) 20	E) 10

Solution: (A+B)-(B-10)=10   A-10=10   Answer is 10
Answer: C
In an election between two candidates, 10% of votes are were declares invalid. First candidate got 3600 votes which were 60% of the total valid votes . The total number of votes enrolled in that election was:
Choose the correct choice from the following answers: A) 9000 B) 98000 C) 20000 D) 11000 E) 12000

Solution: 100 % - 10 % = 90 %   54%-36%=18%   18% ------> 3600 ( 18 × 200   54 -36= 
  54 -36 = 18
18%   18% ------> 3600 ( 18 × 200= 3600)   100% -------> 20000 votes (100 × 200 = 20000)   20000
Answer: C
Find a 8 digit number that if multiplied by the number 9 or any of its multiplications products (18, 27, 36, 45,..) will result in the multiplication factor repeated (n) number of times.	Choose the most appropriate option.
A) 12345679 B) 42345675 C) 22347379 D) 52345673 E) 21345679

Solution: 12345679   The number is: 12345679   12345679 * 9= 
12345679 * 9 = 111_111_111
111111111   12345679 * 18= 
12345679 * 18 = 222_222_222
222222222   12345679 * 27= 
12345679 * 27 = 333_333_333
333333333   12345679nd so on...
Answer: A
A and B invests Rs.3000 and Rs.7000 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit?	Choose the correct choice from the following.
A) 9:6 B) 9:8 C) 9:14 D) 9:9 E) 9:5

Solution: (3*6 + 6*6): (7*12)   54:84 => 9:14.Answer:9:14
Answer: C
A man saves 20% of his monthly salary. If an account of dearness of things he is to increase his monthly expenses by 20%, he is only able to save Rs. 200 per month. What is his monthly salary?  Select the correct option:
A) 5000 B) 2889 C) 2779 D) 6257 E) 5362

Solution: Income = Rs. 100   Expenditure = Rs. 80   Savings = Rs. 20   Present Expenditure 80*(20/100) = Rs. 96   Present Savings = 100 – 96 =Rs. 4   100 ------ 4   ? --------- 200 => 5000   5000nswer: 5000
Answer: A
A boat covers a certain distance downstream in 1 hour, while it comes back in 11â„2 hours. If the speed of the stream be 3 kmph, what is the speed of the boat in still water? Answers
A) 31 kmph  B) 16 kmph  C) 19 kmph  D) 15 kmph  E) 14 kmph

Solution: Let the speed of the water in still water =x   Given that speed of the stream = 3 kmph   Speed downstream =(x+3) kmph   Speed upstream =(xâˆ’3) kmph   He travels a certain distance downstream in 1 hour and come back in 11â„2 hour.   i.e., distance travelled downstream in 1 hour = distance travelled upstream in 11â„2 hour   Since distance = speed Ã— time, we have   (x+3)Ã—1=(x-3)3/2   2(x+3)=3(x-3)   2x+6=3x-9   x=6+9= 
6+9 = 15
15 kmph   Answer: 15 kmph
Answer: D
A and B invests Rs.4000 and Rs.6000 in a business. After 4 months, A withdraws three-fourth of his capital and 4 months later, B withdraws half of his capital. In what ratio should they share the profits at the end of the year?	Choose the correct choice from the following choices
A) 2:5	B) 3:5	C) 4:5	D) 3:7	E) 5:7

Solution: 2:5 : B   (4000*4)+(1000*8) : (6000*8)+(3000*4)   24000 : 60000   2 : 5   2:5nswer: 2:5
Answer: A
0.5, 0.55, 0.65, 0.8, ?	Choose the correct option:
A) 0.7 B) 0.9 C) 0.95 D) 1 E) 2

Solution: The pattern is + 0.05, + 0.10, + 0.15, .....   Answer : 1.
Answer: D
If 15 women or 10 men can complete a project in 55 days, in how many days will 5 women and 4 men working together complete the same project ?  Pick one:
A) 75
B) 8
C) 9
D) 85
E) None of these

Solution: 15 W = 10 M   Now, 5W + 4M = 5W + 4×15/10W = 5W + 6W = = 11 W   If 15 women can complete the project in 55 days,   11 women can complete the same project in   55×15/11=75days   75nswer 75
Answer: A
If n is a positive integer and n^2 is divisible by 450, then what is the largest positive integer that must divide n?  Choose one:  A) 10  B) 20  C) 30  D) 40  E) 50

Solution: 450 = 2 * 3^2 * 5^2   If 450 divides n^2, then n must be divisible by   2 * 3 * 5= 
  2 * 3 * 5 = 30
30   The answer is 30.
Answer: C
Two pipes A and B can separately fill a cistern in 10 and 15 minutes respectively. A person opens both the pipes together when the cistern should have been was full he finds the waste pipe open. He then closes the waste pipe and in another 4 minutes the cistern was full. In what time can the waste pipe empty the cistern when fill?  Choose one.
A) 6	B) 8	C) 7	D) 4	E) 1

Solution: 1/10 + 1/15 = 1/6 * 4 = 2/3   1 - 2/3 = 1/3   1/10 + 1/15 - 1/x = 1/3   x = 8   Answer:8
Answer: B
A certain club has 14 members, including Harry. One of the 14 members is to be chosen at random to be the president, one of the remaining 13 members is to be chosen at random to be the secretary, and one of the remaining 12 members is to be chosen at random to be the treasurer. What is the probability that Harry will either be the secretary or the member chosen to be the treasurer?	Choose the correct choice from the following answers:
A) 5/7 B) 4/7 C) 3/7 D) 1/7 E) 2/7

Solution: Each member out of 14, including Harry, has equal chances to be selected for any of the positions (the sequence of the selection is given just to confuse us). The probability that Harry will be selected to be the secretary is 1/14 and the probability that Harry will be selected to be the treasurer is also 1/14. So, the probability that Harry will be selected to be either the secretary or the the treasurer is 1/14+1/14=2/14.   Answer: 1/7.
Answer: D
Afreena walks 8 km towards East and then walks 13 km back, then she turns left and walks 4 km; then walks 5 km after turning left; she turns left again and walks 3 km. How far is she from the starting point ?
Answers:
A) 3 km	B) 2 km	C) 1 km	D) 6 km	E) 7 km

Solution: Explanation:   From given details we know that she walks in square shaped path and will be in 1 km away from starting point.   ANSWER IS 1 km
Answer: C
A coed soccer team has W women and M men on the team. If 4 women and 2 men are added to the team roster, and if one person on the team is selected at random to serve as team captain, then the probability that the team captain will be a woman can be represented as  Choose one:
A) (W + 4)/(W + M + 6)  B) (W + 4)/(W + M + 2)  C) (W + 4)/(M + 2)  D) (W + 4)/(W + M)  E) W/M

Solution: W women and M men..now 4 women and 2 men are added then total women = W+4 and total men = M+2.. if we club both as total one team (W + M + 6)   We need to find the probability that the team captain will be a woman => W+4 / (W + M + 6)..   IMO option (W + 4)/(W + M + 6) is correct answer...
Answer: A
A man is 30 years older than his son. In two years, his age will be twice the age of his son. The present age of the son is Choose the correct choice from the following options:  A) 14 years  B) 28 years  C) 20 years  D) 22 years  E) None

Solution: Solution   Let the son's present age be x years .Then, man's present age	= (x+30)years.   Then	â€¹=â€º(x+30)+2= 2(x+2)   â€¹=â€ºx+32=2x+4   x= 28.   Answer 28 years
Answer: B
Chris mixed 3 pounds of raisins with 3 pounds of nuts. If a pound of nuts costs 3 times as much as a pound of raisins, then the total cost of the raisins was what fraction of the total cost of the mixture?  Choose the most appropriate option.
A) 1/7 B) 1/5 C) 1/4 D) 1/3 E) 3/7

Solution: 1 lbs of raisin = $1   3 lbs of raisin = $3   1 lbs of nuts = $3   3 lbs of nuts = $9   Total value of mixture = 9+3= 
9+3 = 12
12   Fraction of the value of raisin= 3/12 = 1/4   Ans:1/4
Answer: C
A watch which gains uniformly is 2 minutes low at noon on Monday and is 4 min. 48 sec fast at 2 p.m. on the following Monday. When was it correct?	Pick one:
A) 2 p.m. on Tuesday	B) 2 p.m. on Wednesday	C) 3 p.m. on Thursday	D) 1 p.m. on Friday	E) None

Solution: Solution   Time from 12 p.m. on Monday to 2 p.m. on the following Monday	= 7 days 2 hours.   =170 hours.   The watch gains	= (2 + 4 x4/5)min   = 34 / 5 min.in 170 hrs.   Now,34/5 min are gained in 170 hrs.   2 min are gained in(170x 5/34 x2)hrs.   Watch is correct 2 days 2 hrs. after 12 p.m. on Monday i.e., it will be correct at 2 p.m.on Wednesday.   Answer 2 p.m. on Wednesday
Answer: B
Otto and Han are driving at constant speeds in opposite directions on a straight highway. At a certain time they are driving toward each other and are 40 miles apart. One and a half hours later, they are again 40 miles apart, driving away from each other. If Otto drives at a speed of x miles per hour, then, in terms of x, Han drives at a speed of how many miles per hour?	Choose the most appropriate option
A) a) 80-x B) b) 53.33-x C) c) 80-2x D) d) 120-x E) e) 40-x/2

Solution: Let's say the two cars have speeds V1 and V2. The fact that they are moving in opposite direction means that their relative speed is (V1 + V2). In other words, any gap between them will be changing in size at a rate of (V1 + V2). It doesn't matter whether they are moving toward each other or away from each other. If they are approaching each other, the gap between them is decreasing at a rate of (V1 + V2). If they are moving away from each other, the gap between them is increasing at a rate of (V1 + V2). Either way, the number for the rate of change remains the same.   Here, the two cars approach a distance 40 mi, then move away from each other another distance of 40 miles. That's a total distance of 80 miles in 1.5 hr, which gives a rate of:   R = (80 mi)/(1.5) = 53.33 mph   That's the rate of change of the gap, so it must equal the sum of the speeds of the two cars.   One of the speeds is x, and let's call the other y. We want y.   x + y = 53.33   y = 53.33 - x   Answer =(b) 53.33-x)
Answer: B
The angle between two hands at 3.45 is	Choices:
A) 110 degree
B) 115 degree
C) 112 1/2 degree
D) 117 degree
E) 157 1/2 degree

Solution: theta degree=11/2m-30h   =11/2(45)-30(3)   =247.5-90= 
247.5-90 = 157.5
157.5 or 157 1/2 degree   ANSW157 1/2 degreeR:157 1/2 degree
Answer: E
A jeep takes 4 hours to cover a distance of 620 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time? Options: A) 148 Kmph B) 152 Kmph C) 106 Kmph D) 103 Kmph E) 165 Kmph

Solution: Time = 4   103 Kmphistance = 620   3/2 of 4 hours = 4 * 3/2= 
4 * 3/2 = 6
6 Hours   Required speed= 620/6 = 103 Kmph   103 Kmph)
Answer: D
Find at what time between 8 and 9 o'clock will the hands of a clock be in the same straight line but not together. Choose the most appropriate option:	A) 10x11/10	B) 10x10/11	C) 11x10/11	D) 12x10/11	E) None

Solution: Solution   At 8 o'clock, the hour is at 8 and the minute hand is at 12,i.e. the two hands are 20 min. Spaces apart.   So, the minute hand gain	= (30 - 20)minute   55 minutes will be gained in 60 min.   10 minutes spaces will be gained in (60/55 x10) min.	= 10x10/11 min.   The hands will be in the same straight line but not together at 10x10/11 min.past 8.   Answer 10x10/11
Answer: B
On Sunday morning, Pugsley and Wednesday are trading pet spiders. If Pugsley were to give Wednesday four of his spiders, Wednesday would then have four times as many spiders as Pugsley does. But, if Wednesday were to give Pugsley five of her spiders, Pugsley would now have five fewer spiders than Wednesday had before they traded. How many pet spiders does Pugsley have before the trading game commences?	Choose the correct choice from the following choices:
A) 6  B) 7  C) 8  D) 10  E) 12

Solution: If Pugsley were to give Wednesday four of his spiders, Wednesday would then have five times as many spiders as Pugsley does:   (w + 4) = 4(p - 4)   If Wednesday were to give Pugsley five of her spiders, Pugsley would now have five fewer spiders than Wednesday had before they traded:   p + 5  (  + 4)= 
 (  + 4) = 4
4(p - 4)   If Wednesday were to give Pugsley five of her spiders, Pugsley would now have five fewer spiders than Wednesday had before they traded:   p + 5= w - 5   Solving gives p = 10 and w = 20.   Answer: 10.
Answer: D
To apply for the position of photographer at a local magazine, a photographer needs to include two or three photos in an envelope accompanying the application. If the photographer has pre-selected six photos representative of her work, how many choices does she have to provide the photos for the magazine?	Choose the correct choice from the following options.
A) 32	B) 35	C) 36	D) 40	E) 42

Solution: 6C2 + 6C3 = 15 + 20= 
15 + 20 = 35
35   The answer is 35.
Answer: B
If x is an integer and y = 3x + 2, which of the following CANNOT be a divisor of y?	Choose the correct choice:
A) 4
B) 5
C) 6
D) 7
E) 8

Solution: Just to add some more to Bunuel's explanation, if a number is a multiple of 3, it will be in a form:   n = 3*k, where k is an integer   And if a number is a multiple of 6, it will be in a form :   m = 6*l, where l is an integer   so m = 2 * 3 * l = (2*l) * 3 = 3 * p, where p is an integer.   In other words, the prime factorization of m must have 3 as a factor, if it's a multiple of 6, but the expression can't have that (as explained by Bunuel), so it can't be a multiple of 6 either   ANSWER:6
Answer: C
A book store bought copies of a new book by a popular author, in anticipation of robust sales. The store bought 400 copies from their supplier, each copy at wholesale price W. The store sold the first 150 copies in the first week at 80% more than W, and then over the next month, sold a 100 more at 20% more than W. Finally, to clear shelf space, the store sold the remaining copies to a bargain retailer at 40% less than W. What was the bookstore’s net percent profit or loss on the entire lot of 400 books?  Pick one:
A) 30% loss	B) 10% loss	C) 10% profit	D) 20% profit	E) 60% profit

Solution: C.P. = 400W   S.P. = 1.8W*150 + 1.2W*100 + 0.6W*150 = 480W   Since, S.P. > C.P., there is net profit.   Profit 1.8 *150 + 1.2 *100 + 0.6 *150= 
1.8 *150 + 1.2 *100 + 0.6 *150 = 480
480W   Since, S.P. > C.P., there is net profit.   Profit= S.P. - C.P. = 480W - 400W = 80W   Profit % 480  - 400= 
480  - 400 = 80
80W   Profit %= (Profit/C.P.)*100 = (80W/400W)*100 = 20%   So, the correct answer is 20% profit.(80 /400 )*100= 
(80 /400 )*100 = 20
20%   So, the correct answer is 20% profit.
Answer: D
A committee of 2 people is to be selected out of 3 teachers and 4 preachers. If the committee is selected at random, what is the probability that the committee will be composed of at least 1 preacher?
Choose the correct choice from the following answers
A) 1/4 B) 1/3 C) 2/3 D) 6/7 E) 8/9

Solution: Total no of ways in which you can select a committee of 2 people out of 7 people is 7C2 ways= 21 ways   Requirement is at-least 1 preacher= 4C1*3C1+4C2 or 7C2-3C2=18 ways   Probability= 18/21 = 6/7   ANSWER:6/7
Answer: D
If 73! has 16 zeroes at the end, how many zeroes will 80! have at the end? Choose the correct choice from the following answers:
A) 16
B) 17
C) 18
D) 19
E) 20

Solution: Prime Factoring: you need a 2 and a 5 to make a 10 (a "zero"), and there are TONS of 2's so let's skip these and focus on the (rarer) 5s:   80! = 1*2*3*4*5*6...*78*79*80   Since there are 80 consecutive numbers, there are 16 multiples of 5 in there, but if we're prime factoring, we need to remember that SOME multiples of 5 actually contain more than just one 5. Which? 25 comes to mind -- it's got two of them! So all the multiples of 25 actually contain two 5's (ie: 50 and 75)   So, to recap, we have 16 of them, plus 3 more (the additional 5's in 25, 50, and 75), so that makes 19, and since we have more than enough 2's, we know our number will have exactly 19 zeros at the end.   ANSWER:19
Answer: D
Mary's income is 60 percent more than Tim's income, and Tim's income is 40 percent less than Juan's income. What percent of Juan's income is Mary's income? Choose the correct answer
A) 124% B) 120% C) 96% D) 80% E) 64%

Solution: Juan's income = 100 (assume);   Tim's income = 60 (40 percent less than Juan's income);   Mary's income = 96 (60 percent more than Tim's income).   Thus, Mary's income (96) is 96% of Juan's income (100).   Answer: 96%
Answer: C
Y and Z start a business with Rs.3000 and Rs.6000 respectively. How should they share their profits at the end of one year?	Choose the correct choice from the following answers.
A) 4:1  B) 1:3  C) 1:4  D) 1:5  E) 1:2

Solution: They should share the profits in the ratio of their investments.   The ratio of the investments made by Y and Z =   3000 : 6000 => 1:2 .   Answer:1:2
Answer: E