MU-NLPC/Calc-aqua_rat huggingface dataset:
The weight of a glass of jar is 20% of the weight of the jar filled with coffee beans. After some of the beans have been removed, the weight of the jar and the remaining beans is 60% of the original total weight. What fraction part of the beans remain in the jar?  Choose the correct answer:
A) 1/5
B) 1/3
C) 2/5
D) 1/2
E) 2/3

Solution: Let weight of jar filled with beans = 100 g   Weight of jar = 20 g   Weight of coffee beans = 80 g   Weight of jar and remaining beans = 60 g   Weight of remaining beans = 40 g   Fraction remaining = 40/80 = 1/2   Answer is 1/2.
Answer: D
The greatest common factor of 16 and the positive integer n is 4, and the greatest common factor of n and 45 is 3. Which of the following could be the greatest common factor of n and 60?
Choose the correct choice:
A) 5	B) 8	C) 12	D) 15	E) 30

Solution: n includes the factors 2^2 (but not 2^3) and 3 (but not 3^2 or 5)   60 = 4*3*5   The GCF is 12.   The answer is 12.
Answer: C
The batting average of a particular batsman is 60 runs in 46 innings. If the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs, find his highest score.	Choose the correct answer:
A) 179	B) 208	C) 210	D) 223	E) 229

Solution: Explanation:   Total runs scored by the batsman = 60*46= 
60*46 = 2_760
2760 runs   Now excluding the two innings the runs scored= 58*44= 
58*44 = 2_552
2552 runs   Hence the runs scored in the two innings= 2760 – 2552 = 208 runs.   Let the highest score be x, hence the lowest score = x – 150   x + (x - 150) = 208   2x = 358   x = 179 runs   179NSWER 179
Answer: A
A 75-liter solution of cool-drink is made from 10% jasmine water. If 3.5 liters of jasmine and 9.5 liters of water were added to the solution, what percent of the solution is jasmine? Select.
A) 12.5%	B) 14%	C) 15.5%	D) 17%	E) 18.5%

Solution: The percent of jasmine in the resulting solution is: (amount of jasmine) / (total volume)   (0.1(75) + 3.5) / 88 = 11/88 = 1/8 = 12.5%   The answer is 12.5%.
Answer: A
workers decided to raise Rs.3 lacs by equal contribution from each. Had they contributed Rs.50 eachextra, the contribution would have been Rs.3.25 lacs. How many workers were they?	Choose the correct choice from the following options.
A) 250
B) 400
C) 500
D) 560
E) 650

Solution: N * 50 = (325000 - 300000)= 
(325000 - 300000) = 25_000
25000   N= 25000 / 50= 
25000 / 50 = 500
500   500
Answer: C
Carolyn bought 16 gumballs, Lew bought 14 gumballs, and Carey bought X gumballs. The average (arithmetic mean) number of gumballs the three bought is between 19 and 25, inclusive. What is the difference between the greatest number and the smallest number of gumballs Carey could have bought?
Choose the correct choice from the following options:
A) 20  B) 18  C) 24  D) 26  E) 28

Solution: Smallest gumballs = (19-16) + (19-14) +19= 
(19-16) + (19-14) +19 = 27
27   Largest gumballs= (25-16) + (25-14) +25= 
(25-16) + (25-14) +25 = 45
45   Difference= 45 - 27= 
45 - 27 = 18
18   18
Answer: B
In a financial company investment compounds annually at an interest rate of 34.1% What is the smallest investment period by which time the investment will more than triple in value?  Choose one:
A) 1.2
B) 1
C) 2
D) 4
E) 3

Solution: Assume initial amount is x   Annual Interest is 34.1% so after 1 year the amount will become x * (100+34.1)/100 => x*4/3   now we need to find n for x * (4/3)^n = 3x   or in other words n = 4   4
Answer: D
In a group of 12 engineers, 4 engineers have a PHD degree; the others have only an MS or BS degree. A team of 4 engineers is to be chosen which must have at least 1 engineer with a PHD, how many different teams can be chosen? Select the correct option.
A) 495  B) 70  C) 245  D) 425  E) 555

Solution: The problem asks for a combination, since order doesn't matter. Now, selecting r items from a set of n gives the Combination Formula: nCr= n!/r!(n-r)!   n = 12   r = 4   So, total teams is 12C4 = 12!/(4!(12 - 4)!) = 495, and   n = 12 - 4= 
12 - 4 = 8
8   r= 4   for teams without a PH425 is 8C4 = 8!/(4!(8 - 4)!) = 70,   so, teams with at least 1 PH425 = 495 - 70= 
495 - 70 = 425
425   Answer: 425
Answer: D
The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 4 per square feet if there is one door of dimensions 6 feet * 3 feet and three WINDOWS of dimensions 4 feet * 3 feet each?
Pick.
A) 4000	B) 3624	C) 5673	D) 4530	E) 4566

Solution: Area of the four walls = 2h(l + b)   Since there are doors and WINDOWS, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.   Total cost = 906 * 4 = Rs. 3624   Answer: Option 3624
Answer: B
During the past week, a local fish market tested N fish for two infections. If 1/10 of those tested had infection A and, of those with infection A, 1/5 also had infection B, how many fish did not have both infection A and B?
Choose the correct choice from the following choices.
A) N/15
B) 4N/15
C) 14N/15
D) N/5
E) 49N/50

Solution: 1/10 of tested had infection A, thus N/10 had infection A;   Of those with infection A, 1/5 also had infection B, thus 1/5*N/10 = N/50 had both infections A and B.   Therefore, N - N/50 = 49/50 did not have both infection A and B.   Answer: 49N/50.
Answer: E
Vessel ‘A’ contains 150 litres of mixture of milk and water in the ratio of 3:1. Vessel ‘B’ contains 200 litres of the mixture in the ratio of 5:2. If the mixture from both the vessels are poured into vessel ‘C’, find the ratio of the resulting mixture.
Choose the correct choice:
A) 15 : 7 B) 8 : 3 C) 15 : 2 D) 143 : 53 E) None of these

Solution: Explanation:   As vessel A contains 150 litres of mixture of milk and water in the ratio 3:1, the quantity of milk is 3*150/4 litres, and that of water is 150/4 litres.   Similarly, as vessel B contains 200 litres of mixture of milk and water in the ratio 5:2, the quantity of milk is 5*200/7, and that of water is 2*200/7 litres.   After mixing the total quantity is 350 litres.   The quantity of milk is {(3*150/4) + (5*200/7)} = 7150/28   The quantity of water is {(150/4) + (2*200/7)} = 2650/28   The ratio of the resulting mixture = 7150/2650 = 143 : 53   ANSWER 143 : 53
Answer: D
One packet contains 2 black, 3 white and 2 red rubbers. 2 rubbers are drawn at random. What is the probability that none of the rubbers drawn is red?	Choose the correct option
A) 10/21  B) 21/23  C) 23/25  D) 21/20  E) None

Solution: Total number of rubbers = (2 + 3 + 2)= 
(2 + 3 + 2) = 7
7.   Let S be the sample space.   Then, n(S)= Number of ways of drawing 2 rubbers out of 7   = 7C2 `   =	(7 x 6)   (2 x 1)   = 21.   Let E = Event of drawing 2 rubbers, none of which is blue.   n(E)	= Number of ways of drawing 2 rubbers out of (2 + 3) rubbers.   = 5C2   =	(5 x 4)   (2 x 1)   = 10.   P(E) =	n(E)	=	10/21.   n(S)   10/21
Answer: A
A library has an average of 510 visitors on Sundays and 240 on other day. The average number of visitors in a month of 50 days starting with sunday is
Choices: A) 280 B) 285 C) 171 D) 295 E) 275

Solution: Explanation:   As the month begin with sunday, so there will be five sundays in the month. So result will be:   =(510×5+240×25/30)=(8550/50)= 
(8550/50) = 171
171   Answer: Option 171
Answer: C
A new savings account offers 9 percent annual interest compounded every 6 months. What would be the total balance in an account after 1 year, if the initial amount in the account were $6000? Choose the correct choice from the following answers.
A) $80.00
B) $84.40
C) $360.00
D) $6,360.00
E) $6,552.15

Solution: The interest is compounded every 6 months. To calculate interest, you must take the principal and multiply it by the interest and the length of time (using the unit used in the interest, typically years). At the end of the first 6 months the interest earned is $6,000(.09) (1/2) = $270. (Note: the 6 months are “1/2” in the equation since 9% is a yearly rate, not a bi-yearly one).   Since the interest is compounded, the second six months of the year are not earning interest on just the original $6,000, but on the interest as well, so they are actually earning interest on $6,270. The interest earned during the final 6 months of the year is $6,270(.09)(1/2) = $282.15. Therefore, the total balance is the original amount ($6000) + $270 + $282.15 = $6,552.15.   The correct answer is $6,552.15.
Answer: E
A card board of size 34*14 has to be attached to a wooden box and a total of 35 pins are to
be used on the each side of the card box. find the total number of pins used. Choose the correct choice from the following
A) 135 B) 136 C) 137 D) 138 E) 139

Solution: total 35 pins are there and 4 sides of card board...so 35X4=140   now in the rectangle 4 vertices have 4 pins which is common to the sides....so 140-4= 
140-4 = 136
136   ANSWER:136
Answer: B
A dealer purchases 15 articles for Rs. 25 and sells 12 articles for Rs. 32. Find the profit percentage?	Select:	A) 80%	B) 50%	C) 59%	D) 40%	E) 60%

Solution: L.C.M of 15 and 12   = 60   CP of 60 articles   = Rs. 100 (25 * 4)   SP of 60 articles   = Rs. 160 (32 * 5)   Profit percentage   = (160 - 100)/100 * 100= 
(160 - 100)/100 * 100 = 60
60%   Answer: 60%
Answer: E
A started a business with Rs. 21,000 and is joined afterwards by B with Rs. 36,000. After how many months did B join if the profits at the end of the year are divided equally? Pick one:  A) 4  B) 5  C) 6  D) 7  E) 8

Solution: Sol.   Suppose B joined after x months.   Then, 21000 * 12 = 36000 * (12 - x) ⇔ 36x = 180 ⇔ x = 5.   Hence, B joined after 5 months.   Answer 5
Answer: B
How many integers n are there such that 1< 5n +5 < 40? Choose the correct choice
A) 2	B) 3	C) 4	D) 5	E) 7

Solution: Solution:   1< 5n + 5 < 40 is a compound inequality. Compound inequalities often need to be manipulated, and we can use the rules of algebra that we already know, to do this. Just as with equations, whatever we do to one part of a compound inequality, we must do to all parts of the compound inequality. Let’s first isolate n within the inequality.   1< 5n + 5 < 40   We first subtract 5 from all three parts of the inequality, and we obtain:   -4 < 5n < 35   Next, we divide both sides of the inequality by 5 and we get:   -4/5 < n < 7   The integers that are greater than -4/5 and less than 4 are 0, 1, 2, and 3. Thus, there are 4 integers that satisfy the inequality 1 < 5n + 5 < 40.   The answer is 7
Answer: E
0---:-|---:--|-:--:-|--:---|-:----1
On the number line above, the segment from 0 to 1 has been divided into fifths, as indicated by the large tick marks, and also into sevenths, as indicated by the small tick marks. What is the LEAST possible distance A between any two of the tick marks? Answers:
A) 1/70
B) 1/35
C) 2/35
D) 1/12
E) 1/7

Solution: divisions are 0 1/7 2/7 3/7 4/7 5/7 6/7 1   1/5 2/5 3/5 4/5 5/5   expressing the same in terms of the lcm of 5,7 ,i.e 35   0 7/35 14/35 21/35 28/35 35/35   5/35 10/35 15/35 20/35 25/35 30/35   by comparing the divisions with each other we can see 1/35 is the shortest possible distance between any two selected divisions.   A=1/35   Answer is 1/35.
Answer: B
Which of the following triples of numbers have the same standard deviation as the numbers m, n and o?
I. m-2, n-2, o-2
II. 0, m-n, o-n
III. m-4, n+5, o-1	Choose the correct option.
A) I only  B) II only  C) I and III only  D) II and I only  E) I, II, and III

Solution: If we add or subtract a constant to each term in a set the standard deviation will not change.   Set {m-2, n-2, o-2} is obtained by subtracting 2 from each term of {m, n, o}.   Set {0, m-n, o-n} is obtained by subtracting s from each term of {m, n, o}.   Set {m-4, n+5, o-1} is totally different from {m, n, o}.   Thus the answer is I and II only.   Answer: II and I only.
Answer: D
There are 11 points in a given plane, no three of which are on the same line. If one of the points is represented as 'A', then how many triangles can be determined with the 11 points that contain the point A?  Pick one.
A) 45	B) 105	C) 182	D) 210	E) 455

Solution: Any 2 points out 10 points will create triangle with third point A, so the answer is 10C2=45.   45nswer: 45.
Answer: A
Alice has a jar of juice, and she drank 1/6 of the juice for lunch. If Alice drank 2/5 of the remaining juice for dinner, what fraction of the juice was left after dinner? Choose the correct choice from the following
A) 1/2 B) 2/3 C) 1/4 D) 2/5 E) 3/5

Solution: Let x be the amount of juice at the beginning.   After lunch, the remaining juice was (5/6)x.   After dinner, the remaining juice was (3/5)(5/6)x = (1/2)x.   The answer is 1/2.
Answer: A
A, B and C invests Rs.4000, Rs.2000 and Rs.6000 in a business. After one year A removed his money; B and C continued the business for two more year. If the net profit after 3 years be Rs.3300, then A's share in the profit is?  Choose the correct choice from the following answers:
A) 6000
B) 4000
C) 2000
D) 600
E) 300

Solution: 4*12 : 2*36 : 4*36   2: 3: 6   2/11 * 3300= 
2/11 * 3300 = 600
600   Answer: 600
Answer: D
A, B and C rent a pasture. If A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing and the rent of the pasture is Rs. 140, then how much amount should C pay as his share of rent? Pick
A) 35
B) 45
C) 25
D) 36
E) 55

Solution: A : B : C   =10×7:12×5:15×3   =2×7:12×1:3×3   =14:12:9   Amount that C should pay   =140×9/35=4×9=36   Answer is 36
Answer: D
If mn represents a positive two digit number, where m and n are single digit integers, which of the following cannot be true?	Choose the most appropriate option.
A) m+n =9 B) (m)(n)=9 C) m-n = 9 D) n-m= 9 E) m/n = 9

Solution: (A) mn = 45 or 63 or 27   (B) mn = 33 or 19   (C) 90   (D) impossible   (E) mn = 91   (D) is impossible because 09 is not a valid two digit number --- if there's a zero in the ten's place, that's just 9, a single digit number. Therefore, no valid two digit number would satisfy (D).   ans n-m= 9
Answer: D
A, B, C and D enter into partnership. A subscribes 1/3 of the capital B 1/4, C 1/5 and D the rest. How much share did C get in a profit of Rs.2430 ?  Choose the correct option:
A) s. 432 B) s. 486 C) s. 822 D) s. 812 E) s. 810

Solution: Let the total amount in the partnership be 'x'.   Then A's share = x/3   B's share = x/4   C's share = x/5   D's share = x - (x/3 + x/4 +x/5) = 13x/60   A : B : C : D = x/3 : x/4 : x/5 : 13x/60 = 20 : 15 : 12 : 13   A's share in the profit of Rs. 2430 = 12 (2430/60) = Rs. 486   Answer: s. 486
Answer: B
A photography dealer ordered 60 Model X cameras to be sold for $250 each, which represents a 10 percent markup over the dealer’s initial cost for each camera. Of the cameras ordered, 6 were never sold and were returned to the manufacturer for a refund of 50 percent of the dealer's initial cost. What was the dealer's approximate profit or loss as a percent of the dealer’s initial cost for the 60 cameras?	Choose the correct option
A) 7% loss B) 13% loss C) 4% profit D) 13% profit E) 15% profit

Solution: Total cost 60*($250/1.1)=54.54*250;   # of cameras sold is  60-6= 
 60-6 = 54
54 total revenue is 54*250;   # of cameras returned is 6 total refund 6*(250/1.1)*0.5;   So, total income 54*250+ 6*(250/1.1)*0.5   The dealer's approximate profit is (54*250+ 6*(250/1.1)*0.5-54.54*250)/(54.54*250)*100=4%   Answer: 4% profit.
Answer: C
Because he’s taxed by his home planet, Mork pays a tax rate of 40% on his income, while Mindy pays a rate of only 30% on hers. If Mindy earned 2 times as much as Mork did, what was their combined tax rate?
Choose the correct choice from the following answers:
A) 32.5%  B) 34%  C) 22.5%  D) 33.3%  E) 37.5%

Solution: Say Morks income is - 100   So tax paid will be 40   Say Mindys income is 2*100= 
2*100 = 200
200   So tax paid is 30% * 200= 60   Total tax paid = 40+60= 
40+60 = 100
100.   Combined tax % will be 100/100+200= 33.3%
Answer: D
Some persons can do a piece of work in 12 days. Two times the number of these people will do half of that work in?	Choose the correct choice from the following answers:
A) 3
B) 4
C) 5
D) 6
E) 8

Solution: 12/ (2 * 2)= 
12/ (2 * 2) = 3
3 days   3nswer:3
Answer: A
If two integers x,y (x>y) are selected from -6 to 6 (inclusive), how many cases are there?
Options:
A) 70 B) 74 C) 78 D) 82 E) 86

Solution: There are 13 integers from -6 to 6 inclusive.   13C2 = 78.   The answer is 78.
Answer: C
A and B can do a work in 18 day, B and C in 30 days, A and C in 22 (1/2) days. In how many days can A,B and C individually do the work?
Select the correct option
A) 60,90,128	B) 60,90,120	C) 60,90,127	D) 60,90,118	E) 60,90,121

Solution: (A+B+C)'s two days work = 1/18 + 1/30 + 2/45   = (5 + 3 + 4)/90 = 2/15   (A+B+C)'s one day work = 2/15 * 1/2 = 1/15   A's one day's work = 1/15 - 1/30 = 1/30   B's one day's work = 1/15 - 2/45 = 1/45   C's one day's work = 1/15 - 1/18= 1/90   So, A,B and C can individually do the work in 30, 45 and 90 days.   Answer:60,90,120
Answer: B
A train has a length of 150 meters . it is passing a man who is moving at 3 km/hr in the same direction of the train, in 3 seconds. Find out the speed of the train.	Options:	A) 182 km/hr	B) 180 km/hr	C) 152 km/hr	D) 169 km/hr	E) 183 km/hr

Solution: 183 km/hrxplanation:   Length of the train, l = 150m   Speed of the man , Vm= 3 km/hr   Relative speed, Vr = total distance/time = (150/3) m/s = (150/3) × (18/5) = 180 km/hr   Relative Speed = Speed of train, Vt - Speed of man (As both are moving in the same direction)   => 180 = Vt - 3   => Vt = 180 + 3= 
180 + 3 = 183
183 km/hr   Answer: Option 183 km/hr
Answer: E
In how many ways can the letters of word BISECTION be arranged such that NO two vowels appear together? Choose the correct choice from the following answers:
A) 9! B) 5!*4! C) 4!*5! D) 5!*4!*2! E) 6!*4!

Solution: No 2 vowels together = the only arrangement possible will be C V C V C V C V C (with V=vowel, C=consonant). This is true as we have 4 vowels and 5 consonants and any other combination will force us to pair 2 vowels together.   Thus, the number of arrangements possible : 5 *4 *4 *3 *3 *2 *2*1 = 4!*5! ----> 4!*5! is the correct answer.
Answer: C
If a, b, and c are consecutive even integers and a < b < c, all of the following must be divisible by 4 EXCEPT Answers:	A) a + c	B) b + c	C) ac	D) (bc)/2	E) (abc)/4

Solution: Let integers be a= x-2, b= x, c= x+2   Now by options   a+c = 2x (has to be divisible by 4 as x is an even no.)   b+c = 2x +2 = 2(x+1) as x is an even no. x+1 is odd, so eq. becomes 2 * odd hence cannot be divisible by 4   ANSWER:b + c
Answer: B
A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 3600 interest only for the period. The principal amount borrowed by him was: Answers:
A) s. 2000 B) s. 10,000 C) s. 15,000 D) s. 18,000 E) s. 20,000

Solution: Principal = Rs. (100 x 3600)/(12X3) = Rs. 10000. Answer: Option s. 10,000
Answer: B
To be eligible for retirement benefits at the Mankind Corporation, the sum of an employee's age, in years, and the number of years employment must be at least 60. If a, where a <60, is a certain employee's age when hired and b is the minimum number of years of employment required for the employee to be eligible for retirement benefits, which of the following equations represents the relationship between a and b?  Select the correct option.
A) 2a+2b=60	B) ab=60	C) a+2b=60	D) a+b=60	E) 2a+b=60

Solution: We are told that when a certain employee was hired he was a years old and that the he needed minimum b years to be eligible for benefits.   Now,after b years of employment, when the employee will be be eligible for benefits, the employee will be a+b years old and will have b years of employment, thus{age after b years}+{employment years}=(a+b)+b=a+2b=60   Answer: a+2b=60
Answer: C
The set X = {11,12,13,14,15}. The set Y = {2,3,4,5}. We will randomly choose one element x from set X and one element y from set Y. What is the probability that x / y will be an integer? Choices
A) 11/20 B) 7/20 C) 3/20 D) 7/10 E) 3/10

Solution: The total number of x and y pairs is 5*4= 
5*4 = 20
20.   There are six pairs such that x / y is an integer.   The probability that x / y is an integer is 6/20=3/10.   The answer is 3/10.
Answer: E
A boat takes 19 hours for travelling downstream from point A to point B and coming back to a point C which is at midway between A and B. If the velocity of the stream is 4 kmph and the speed of the boat in still water is 14 kmph, what is the distance between A and B ? Choose the correct choice.
A) 180 km  B) 127 km  C) 178 km  D) 188 km  E) 111 km

Solution: Explanation:   Speed in downstream = (14 + 4) km/hr = 18 km/hr;   Speed in upstream = (14 â€“ 4) km/hr = 10 km/hr.   Let the distance between A and B be x km. Then,   x/18 + (x/2)/10 = 19 â‡” x/18 + x/20 = 19 â‡’ x = 180 km.   180 kmnswer: 180 km
Answer: A
Find the area of the square field if a train 800 metres long passes the field with a speed of 120 kmph in one minute. Choose the correct choice
A) 1.48 sq. km
B) 2.44 sq. km
C) 7.44 sq. km
D) 1.45 sq. km
E) 1.44 sq. km

Solution: Explanation:   120 km/hr = 120 * 5/18 = 33.33 m/s   v = d/t ; 33.33 = d/60   d = 2000 m   Hence, in one minute the train travels 2000 m. But, as the train is 800 m long and it passes the field, the length of the field is 2000 – 800 = 1200 m.   Area = 1200 * 1200 = 1.44 sq. km   ANSW1.44 sq. kmR: 1.44 sq. km
Answer: E
Two cars are driving toward each other. The first car is traveling at a speed of 90 km/h, which is 50% faster than the second car's speed. If the distance between the cars is 975 km, how many hours will it take until the two cars meet? Choose the correct answer.
A) 6	B) 6.5	C) 7	D) 7.5	E) 8

Solution: The speed of the first car is 90 km/h.   The speed of the second car is  90 / 1.5= 
 90 / 1.5 = 60
60 km/h.   The two cars complete a total of 150 km each hour.   The time it takes the cars to meet is   975 / 150= 
  975 / 150 = 13/2 = around 6.5
6.5 hours.   The answer is 6.5.
Answer: B
Twenty four men can do a work in 35 days. How many men are required to complete the work in 21 days? Choose the correct choice from the following answers:
A) 20
B) 10
C) 50
D) 40
E) 60

Solution: 40   40   We have M1 401 = M2 402   So, 24 * 35 = M2 * 21 => M2 = 40.
Answer: D
If a + b > 0 and a * b < 0, which of the following must be true?
I. a > 0 or b > 0
II. a < 0 or b < 0
III. a and b have the same sign  Choose the correct choice from the following answers.
A) I only
B) II only
C) III only
D) I and II only
E) I, II, and III

Solution: I. True, for the sum to be greater than 0, at least one of a or b has to be positive   II. True, for the product to be less than 0, one of a or b has to be negative   III. Not true, by the previous two, one of a or b has to be positive and the other has to be negative   I and II only
Answer: D
Three printing presses, P, S, and T, working together at their respective constant rates, can do a certain printing job in 4 hours. S and T, working together at their respective constant rates, can do the same job in 5 hours. How many hours would it take P, working alone at its constant rate, to do the same job?  Choose the correct choice.
A) 8	B) 10	C) 12	D) 15	E) 20

Solution: =1/4-1/5=1/20   P can do 1/20 job in 1 hour   P can do the whole job in 20 hours=20
Answer: E
what is the value of y if the greatest common divisor of (e+5)!,(e-2)!, and (e+2)! is 24.	Choose the correct choice.
A) 5  B) 7  C) 4  D) 66  E) 6

Solution: GCD of (e+4)!,(e-2)!, and (e+2)! is 24. Find x.   Best way to find n is substitute each of the answer and find out the correct one.   Only option E gave the correct answer.   Try 6 and find GCD or 10!, 4! and 8!. 4! itself is 24 and 4! which is contained in the other two factorials. This satisfies the condition, hence answer is 6.   Answer is 6.
Answer: E
What is the sum of the different positive prime factors of 640?	Choose the correct answer
A) 5 B) 7 C) 10 D) 15 E) 17

Solution: The prime factorization of 640   = 64 * 10   = 2^6 * 2*5   The sum of the different positive prime factors = 2+5= 
2+5 = 7
7   The answer is 7.
Answer: B
If two painters can complete two rooms in two hours, how many rooms painted if 10 painters work for 6 hours? Choose one:
A) 35 B) 25 C) 20 D) 30 E) 15

Solution: Explanation:   Two painters can complete two rooms in two hours.So 30 rooms can be painted in 6 hrs by 10 painters   Answer: 30) 10 painters
Answer: D