MU-NLPC/Calc-aqua_rat huggingface dataset:
A shopkeeper loses 15%,if an article is sold for Rs. 102. What should be the selling price of the article to gain 20%?  Select the correct option:
A) 221
B) 144
C) 666
D) 888
E) 212

Solution: Given that SP = Rs. 102 and loss = 15%   CP = [100(SP)]/(100 - l%) = (100 * 102)/85 = 20 * 6 = Rs. 120.   To get 20% profit, New SP = [(100 + p%)CP]/100 = (120 * 120)/100 = Rs. 144   Answer:144
Answer: B
If the cost price of 22 articles is equal to the selling price of 16 articles, What is the percentage of profit or loss that the merchant makes?  Choose one:
A) 20% loss  B) 37.5 % profit  C) 37.5 % loss  D) 30.33% loss  E) None of these

Solution: Explanation :   Let Cost price of 1 article be Re.1.   Therefore, Cost price of 22 articles = Rs. 22.   Selling price of 16 articles = Rs. 22   Therefore, Selling price of 22 articles is :-   =>22/16Ã—22   =>30.25.   Therefore, Profit = Selling price - Cost price.   =>30.25âˆ’22=8.25   Hence, the percentage of profit = profit x 100/C.P.   =>8.25/22Ã—100.   =>37.5% Profit.   Answer : 37.5 % profit
Answer: B
The price of 5 kilograms of premium fertilizer is the same as the price of 10 kilograms of regular fertilizer. If the price of premium fertilizer is y cents per kilogram more than the price of regular fertilizer, what is the price, in cents, per kilogram of premium fertilizer? Pick one:
A) y/30 B) 5/6*y C) 6/5*y D) 2y E) 6y

Solution: Usingpfor premium andrfor regular, I got two equations from the question stem:   5p = 10r and p = r+y   Substitute for p: 5(r+y) = 10r   2yistribute: 5r + 5y = 10r   Subtract 5r from both sides: 5y 5  + 5= 
5  + 5 = 10
10r   Subtract 5r from both sides: 5y= 5r   Plug back into the first equation: 5p = 10(y)   2yistribute: 5p = 10y   2yivide both sides by 5: p = 2y   The answer is 2y.
Answer: D
Given that p is a positive even integer with a positive units digit, if the units digit of p^3 minus the units digit of p^2 is equal to 0, what is the units digit of p - 3? Options.
A) 10 B) 8 C) 7 D) 3 E) 11

Solution: p is a positive even integer with a positive units digit--> the units digit of p can be 2, 4, 6, or 8 -->   In order the units digit of p^3 - p^2 to be 0, the units digit of p^3 and p^2 must be the same. Thus the units digit of p can be 0, 1, 5 or 6.   Intersection of values is 6, thus the units digit of p - 3 is  6 - 3= 
 6 - 3 = 3
3.   Answer: 3.
Answer: D
A taxicab fare costs x dollars for the first quarter of a mile and 1/4*x dollars for each quarter of a mile after that. How much will the total cost be for a 3/2 mile ride? Choose the correct choice.
A) 3x	B) 13/4*x	C) 10x	D) 5/4*x	E) 2.5x

Solution: 3/2 miles = 1+1/2 miles   1+1/2 miles have 6 1/4 miles   1st 1/4 mile will cost= x   Remaining 5 1/4 miles will cost= 5/4 x   Total cost = x + 5/4 x= 9/4 x   ANSWER:13/4*x
Answer: B
Find the odd man out. 10,30,50,72,95  Options:	A) 10	B) 30	C) 50	D) 72	E) 95

Solution: All except 72 are multiples of 5   Answer is 72
Answer: D
If in a $120 mln portfolio of stock, twice as much is invested in stock A as is invested in all the other stocks, how much is invested in all the other stocks?	Pick:
A) 40mln  B) 50mln  C) 60mln  D) 70mln  E) 80mln

Solution: Let x denote the amount invested in all the other stocks. Then the amount invested in stock A is 2x. As we have the $120 mln portfolio, x+2x=3x=120 mln from where x=40 mln.   40mlnnswer: 40mln
Answer: A
The cost price of 13 articles is equal to the selling price of 11 articles. Find the profit percent? Choose the correct choice from the following options.
A) 67 2/16% B) 45 2/17% C) 18 2/11% D) 23 2/13% E) 14 2/10%

Solution: 18 2/11%   13 18 2/11%P = 11 SP   11 --- 2 18 2/11%P   100 --- ? =>18 2/11%
Answer: C
From the word 'INTENSIFICATION', how many independent words can be made with-out changing the order of the letters and using each letter only once ?  Options.
A) 5 B) 4 C) 3 D) 2 E) 9

Solution: Explanation:   The words formed are   IN, TEN, INTENS and CATION   Answer: 4) 4
Answer: B
If the city centers of New York and London are 3,471 miles apart, which of the following is closest to the distance between the city centers in inches? (There are 5,280 feet in a mile.) Select the correct option
A) 1.75 × 10^7	B) 1.83 × 10^7	C) 2.10 × 10^8	D) 2.10 × 10^9	E) 2.20 × 10^10

Solution: Distance in Miles = 3471   Given 1 mile = 5280 ft   So 3471 miles = 3471 X 5280 feet ~ 3500 x 5300 = 1.855 x 10^7 feet   1 feet is 12 inches, so the answer : 1.855 x 12 x 10^7 ~ 2.2 x 10^8.   Answer 2.10 × 10^8
Answer: C
Every minute, G an type 55 words while H can type 70 in the same amount of time. IF they have 20 minutes to complete a 500 word document, how much time remains when they have finished typing the document? Answer in fractions. Answers.
A) 290/77  B) 1250/77  C) 500/77  D) 154/77  E) 3750/77

Solution: MInutes it takes for G to type 1 word: 1/55   Minutes it takes for H to type 1 word: 1/70   Minutes it takes for G and H to type 1 word: 1/55+1/70=5/154   Minutes it takes for G and H to type 500 words: 500x(5/154)=1250/77   MInutes remaining: 20-1250/77=290/77   290/77nswer is 290/77
Answer: A
At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.20000?  Choose the correct answer
A) 6620
B) 1879
C) 2779
D) 2672
E) 2782

Solution: 6620 = 20000(11/10)3   = 26620   = 20000   ----------   6620   6620nswer: 6620
Answer: A
Simplify: 2005-2000+10	Choose the correct option:
A) 1805 B) 4509 C) 2601 D) 4508 E) None of them

Solution: 2005-2000+10   =2005-(2000/10)   =2005-200= 
2005-200 = 1_805
1805.   1805nswer is 1805
Answer: A
Find the Greatest Number that will devide 43, 91 and 183 so as to leave the same remainder in each case
Choose the correct choice from the following choices
A) 4	B) 7	C) 9	D) 13	E) 15

Solution: Explanation:   Required Number = H.C.F of (91- 43), (183- 91) and (183-43)   = H.C.F of 48, 92, and 140 = 4. 4nswer: 4
Answer: A
I. a^2 + 11a + 30 = 0,
II. b^2 + 6b + 5 = 0 to solve both the equations to find the values of a and b?  Answers.
A) If a < b
B) If a ≤ b
C) If a > b
D) If the relationship between a and b cannot be established
E) If a ≥ b

Solution: Explanation:   I. (a + 6)(a + 5) = 0   => a = -6, -5   II. (b + 5)(b + 1) = 0   => b = -5, -1 => a ≤ b   Option If a ≤ b
Answer: B
For any integer k > 1, the term “length of an integer” refers to the number of positive prime factors, not necessarily distinct, whose product is equal to k. For example, if k = 24, the length of k is equal to 4, since 24 = 2 × 2 × 2 × 3. If x and y are positive integers such that x > 1, y > 1, and x + 3y < 902, what is the maximum possible sum of the length of x and the length of y? Answers:
A) 8	B) 10	C) 12	D) 14	E) 16

Solution: we know that : x > 1, y > 1, and x + 3y < 902,   and it is given that length means no of factors.   for any value of x and y, the max no of factors can be obtained only if factor is smallest no all factors are equal.   hence, lets start with smallest no 2.   2^1 =2   2^2 =4   2^3=8   2^4=16   2^5=32   2^6=64   2^7=128   2^8=256   2^9=512   2^10 =1024 (it exceeds 1000, so, x can't be 2^10)   so, max value that X can take is 2^9 , for which has length of integer is 9.   now, since x =512 ,x+3y<902   so, 3y<390   ==> y<130   so, y can take any value which is less than 130. and to get the maximum no of factors of smallest integer, we can say y=2^7   for 2^7 has length of integer is 7.   SO, combined together : 9+7= 
9+7 = 16
16.   16
Answer: E
Population of a city in 20004 was 1000000. If in 2005 there isan increment of 15% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city atthe end of the year 2007
Choices:  A) 985645  B) 934556  C) 934578  D) 994213  E) 1083875

Solution: Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100)   = P (1 + 15/100)(1 - 35/100)(1 + 45/100)   = 1083875   1083875
Answer: E
At what rate percent on simple interest will Rs.900 amount to Rs.950 in 5 years?	Choose the correct answer.
A) 1.11%
B) 5.93%
C) 4.33%
D) 5.33%
E) 6.33%

Solution: 50 = (900*5*R)/100   R = 1.11%   1.11%NSWER:1.11%
Answer: A
The area of a triangle will be when a = 1m, b = 2m, c = 3m, a, b, c being lengths of respective sides.	Pick one: A) 3 B) 4 C) 5 D) 6 E) 7

Solution: S = (1 + 2 + 3)/2= 
(1 + 2 + 3)/2 = 3
3=> No triangle exists   3nswer:3
Answer: A
A man can row a boat at 20 kmph in still water. If the speed of the stream is 9 kmph, what is the time taken to row a distance of 60 km downstream?	Choose one
A) 30/18 hours	B) 37/13 hours	C) 80/13 hours	D) 30/13 hours	E) 60/29 hours

Solution: Speed downstream = 20 + 9= 
20 + 9 = 29
29 kmph.   Time required to cover 60 km downstream= d/s = 60/29   = 60/29 hours.   Answer: 60/29 hours
Answer: E
If one-third of one-fourth of a number is 30, then three-tenth of that number is:
A. 35  Choose the correct answer:
A) 23
B) 87
C) 108
D) 54
E) 01

Solution: Explanation:   The number is 1/3 of 1/4 is =15 then 1/3 Ã— 1/4 = 30   Number is 360 then 360 Ã— 3/10 = 108   Answer: 108
Answer: C
A train speeds past a pole in 15 sec and a platform 100 m long in 25 sec, its length is?
Choose the correct choice from the following answers
A) 257 m B) 268 m C) 245 m D) 156 m E) 150 m

Solution: Let the length of the train be x m and its speed be y m/sec.   Then, x/y = 15 => y = x/15   (x + 100)/25 = x/15 => x   = 150 m.   Answer: 150 m
Answer: E
If there are 4 seats and 3 students, in how many ways can they be seated?  Choose the correct answer.
A) 8	B) 10	C) 12	D) 16	E) 24

Solution: The first student has 4 choices, the second student has 3 choices, and the third student has 2 choices. The number of ways to sit is 4*3*2= 
4*3*2 = 24
24.   The answer is 24.
Answer: E
What is the next number in the sequence below?
1 4 9 16 25 36 49 64 81 __ ?  Select
A) 45 B) 81 C) 64 D) 65 E) 100

Solution: as the series of numbers are squares of numbers   1^2=1   2^2=4   3^2=9   and so on   therefore 10^2=100   ANSW100R:100
Answer: E
There are 22 Kids in a classroom. 12 Kids are wearing socks and 8 are wearing Shoes. 6 Kids are wearing both.
How many are Bare Feet ?	Choose the most appropriate option:
A) 10  B) 2  C) 4  D) 5  E) 8

Solution: 12 kids wear socks   8 kids wear shoes   6 wear both.   12 â€“ 6 = 6 (wear only socks)   8 â€“ 6 = 2 (wear only shoes)   6 (wear both)   hence, 22 -14 = 8   8 kids are with bare feet.   8
Answer: E
Out of 12 students in a class, 7 are wearing blue shirts, 3 are wearing green shirts, and 2 are wearing red shirts. Four students are to be selected at random. What is the probability that at least one is wearing a green shirt?  Choose the correct choice from the following choices.
A) 25/33  B) 31/44  C) 41/55  D) 53/66  E) 65/77

Solution: Total possible ways to choose 4 students out of 12 = 1241/554 = 495   The number of ways to choose 4 students with no green shirts = 941/554 = 126   P(no green shirts) = 126/495 = 14/55   P(at least 1 green shirt) = 1 - 14/55 = 41/55   The answer is 41/55.
Answer: C
A, B, C, D, E and F are six cities which are collinear in the same order. The distance between any two adjacent cities is equal. A bus starts at A for city F. It takes 25 minutes for the bus to travel from one city to another and stops for 5 minutes at each place. If the bus reaches E at 8:55, then at what time did it reach station B?  Select
A) 7:25 B) 7:30 C) 7:35 D) 7:40 E) 7:50

Solution: Explanation:   Between B and E there are two intermediary stations C and D. For traveling from B to C, from C to D and from D to E it takes   3 * 25= 
  3 * 25 = 75
75 minutes. At each of C and B it halts of 5 minutes. Hence, the time taken to reach E after starting at B is 85 minutes. i.e. one hour 25 minutes. Hence, it started at 7:30 at B.=>it reached B at 7:25.   7:25NSWER IS 7:25
Answer: A
The Pinedale bus line travels at an average speed of 60 km/h, and has stops every 5 minutes along its route. Yahya wants to go from his house to the Pinedale Mall, which is 6 stops away. How far away, in kilometers, is Pinedale Mall away from Yahya's house? Choose the most appropriate option:
A) 20 km B) 30 km C) 40 km D) 50 km E) 60 km

Solution: Number of stops in an hour: 60/5= 
60/5 = 12
12   Distance between stops: 60/12= 
60/12 = 5
5 km   Distance between Yahya's house and Pinedale Mall: 5 x 6= 30 km   IMO, correct answer is "30 km."
Answer: B
What number should replace the question mark?
1, 31, 59, 85, 109, ?  Choose the correct choice from the following options: A) 131 B) 145 C) 165 D) 178 E) 193

Solution: 131   131   131dd 30, 28, 26, 24, 22
Answer: A
The number of bacteria in a petri dish increased by 50 percent every 2 hours. If there were 108 million bacteria in the dish at 3: 00 p.m., at what time were there 32 million bacteria in the dish?  Choices:
A) 6: 00 p.m.	B) 9: 00 p.m.	C) 6: 00 a.m.	D) 8: 00 a.m.	E) 10: 00 a.m.

Solution: Given:   The number of bacteria in a petri dish increased by 50 percent every 2 hours   There were 108 million bacteria in the dish at 2: 00 p.m   Since the bacteria is increasing by 50% every 2 hours, this means that the number is multiplied by 1.5 every 2 hours.   Required: At what time were there 32 million bacteria in the dish?   Assume that there were n intervals of 2 hours between 32 million and 108 million.   32 * (1.5)^n = 108   (3/2)^n = 108/32 = 27/8 = (3/2)^3   Hence n = 3 intervals.   Each interval was of 2 hours. Therefore, the number of hours = 6   Subtracting 6 hours from 3 PM, we get 9 AM as the answer.   Option 9: 00 p.m.
Answer: B
A man can row 8 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?	Choose the correct choice:
A) 5.98  B) 7.98  C) 7.96  D) 5.87  E) 5.82

Solution: M = 8   S = 1.2   DS = 9.6   US = 6.8   x/9.6 + x/6.8 = 1   x = 3.98   D = 3.98 * 2= 
3.98 * 2 = 7.96
7.96   Answer:7.96
Answer: C
On the number line, the number p is twice as many units from -2 as -2 is from 5. If p is less than –2, what is the value of p ?	Choose the correct choice from the following answers:
A) –16
B) –10
C) –6
D) 10
E) 14

Solution: Distance between -2 and 5 = 7   Since number p is twice as many units from -2 as -2 is from 5   , therefore p can be -16 Since , p is less than -2 ,   the value of p = -16   –16nswer –16
Answer: A
At a certain conference, 62% of the attendees registered at least two weeks in advance and paid their conference fee in full. If 20% of the attendees who paid their conference fee in full did not register at least two weeks in advance, what percent of conference attendees registered at least two weeks in advance?	Choose the correct choice from the following options.
A) 18.0%  B) 62.0%  C) 79.2%  D) 77.5%  E) 82.0%

Solution: Refer to the table in the attachment:   Let y= No. of members who have paid in Full   20 % members paid in full and did not register in advance = 0.2y   62 % registerd in advance and paid in full.   So if total No. of members = 100, then 62 members paid Full and registered in advance.   Hence total members who paid full amount = 0.2y + 62 =y   0.8y =62   Hence y = 77.5   i.e. 77.5 out of 100 or 77.5 %   Ans. 77.5%
Answer: D
How many two-digit numbers satisfy the following property given below:
The last digit (unit's digit) of the square of the two-digit number is 8?	Select the correct option
A) 4	B) 12	C) 15	D) 16	E) None of these

Solution: Explanation:   Any number ending in 8 can never be a perfect square. Hence, the answer is none of these.   ANSWNone of theseR None of these
Answer: E
Find the odd man out
2880, 482, 96, 24, 8, 4, 4
Choose the most appropriate option:
A) 482	B) 96	C) 24	D) 8	E) 4

Solution: from the right side   4*1= 
4*1 = 4
4,   4*2= 
4*2 = 8
8   8*3= 
8*3 = 24
24   24*4= 
24*4 = 96
96   96*5= 
96*5 = 480
480 but here given 482 so it's not.   480*6= 
480*6 = 2_880
2880   482NSWER:482
Answer: A
A prize of $500 is to be distributed among 20 winners, each of whom must be awarded at least $20. If 2/5 of the prize will be distributed to 3/5 of the winners, what is the greatest possible individual award?  Choose the correct choice
A) $160 B) $220 C) $280 D) $300 E) $360

Solution: Total value of the prize =$500   Number of people = 20   2/5 of 500 (=$200) should be distributed among 3/5 of 20 (=12 people ) with each getting $20 each. Remaining money = 500-200= 
500-200 = 300
$300. Now in order to 'maximize' 1 prize, we need to minimise the others and we have been given that each should get $20. Thus, minimising the remaining 7 people (=20-12-1. '-1' to exclude 1 that needs to be maximised) = 7*20= 
7*20 = 140
140.   Thus the maximum award can be= 300-140= 
300-140 = 160
$160, hence $160 is the correct answer.
Answer: A
A shopkeeper fixes the marked price of an item 35% above its cost price. The percentage of discount allowed to gain 8% is  Choose one.
A) 18%  B) 20%  C) 22%  D) 24%  E) None of these

Solution: Explanation:   Let the cost price = Rs 100   then, Marked price = Rs 135   Required gain = 8%,   So Selling price = Rs 108   Discount = 135 - 108= 
135 - 108 = 27
27   Discount%= (27/135)*100= 
(27/135)*100 = 20
20%   Option 20%
Answer: B
William earned $3,200 per month as a
teacher for the ten months from September
to June. Then he took a job as a barista at a
local café, where he earned $2,000 per
month during July and August. What was
his average monthly pay for the 12 months? Choose the correct choice from the following answers:
A) $2,400
B) $2,800
C) $2,600
D) $3,000
E) $2,500

Solution: E. William earned $3,200 × 10 = $32,000 as a teacher, and he earned $2,000 × 2 = $4,000 as a   barista. So he earned $32,000 + $4,000 = $36,000 over the 12 months. Plug these values into   the formula for the mean:   mean=sum of values/number of values=>36.000/12= 
36.000/12 = 3
3.000   correct answer $3,000)$3.000
Answer: D
What is the largest positive integer n for which 3^n divides 44^44? Answers.
A) 0
B) 9
C) 8
D) 7
E) 6

Solution: The digit sum of 44444444 is when remainder obtained 44444444 divided by 9   44444444 = (45−1)44(45−1)44   Each term is a multiple of 9 but the last term which is (−1)44(−1)44 = 1   So the digit sum of 44444444 is 1.   Now the divisibility rule for 3, 9, 27... is the sum of the digits should be divisible by 3, 9, 27 respectively. In each case the digit sum is either multiple of 3 or 9.   So for any value of n > 1, the given expression is not divisible by 3n   0nswer:	0
Answer: A
A fair coin is tossed repeatedly. If heads appears on first 5 tosses what is the probability that tail appears on the next two tosses? Choose the correct choice from the following choices
A) 1/6
B) 1/5
C) 1/3
D) 1/4
E) 1/6

Solution: Explanation :   Like mentioned in the question, the coin is fair. So chance of appearing of head and tail on each toss is same and each toss is independent from the previous one. So the chance of appearing tail on the next two tosses is still 1/2 each.   1/2 * 1/2 = 1/4   Answer : 1/4
Answer: D
If 12 men can reap 120 acres of land in 36 days, how many acres of land can 54 men reap in 54 days? Pick one
A) 277 B) 810 C) 888 D) 166 E) 199

Solution: 12 men 120 acres 36 days   54 men ? 54 days   120 * 54/12 * 54/36   10 * 54 * 3/2   54 * 15= 
54 * 15 = 810
810   Answer: 888
Answer: C
Find the probability that a leap year selected at random will have 53 Sundays
Pick:
A) 6/7	B) 5/7	C) 4/7	D) 3/7	E) 2/7

Solution: There are 366 days in a leap year: 52 weeks and 2 more days. So, 52 Sundays and 2 days.   These 2 days can be: {Mon, Tue}, {Tue, Wed}, {Wed, Thu}, {Thu, Fri}, {Fri, Sat}, {Sat, Sun} and {Sun, Mon} (7 cases). In order to have 53 Sundays we should have either {Sat, Sun} or {Sun, Mon} case.   The probability of that is 2/7.   Answer: 2/7.
Answer: E
What is the unit digit in {(6374)^1793 x (625)^317 x (341)^491)}?  Choices.
A) 0	B) 1	C) 2	D) 3	E) 5

Solution: Unit digit in (6374)1793 = Unit digit in (4)1793   = Unit digit in [(42)896 x 4]   = Unit digit in (6 x 4) = 4   Unit digit in (625)317 = Unit digit in (5)317 = 5   Unit digit in (341)491 = Unit digit in (1)491 = 1   Required digit = Unit digit in (4 x 5 x 1) = 0.   Option 0
Answer: A
Find the least number of complete years in which a sum of money put out at 25% compound interest will be more than double of itself?  Pick one
A) 3	B) 6	C) 9	D) 4	E) 3

Solution: 4 years   Answer: 4
Answer: D
Kramer can pack X boxes of cigarettes per minute. If there are Y boxes of cigarettes in one case, how many cases can Kramer pack in 2 hours?  Options: A) 60X/Y. B) 120X/Y. C) 60Y/X. D) 120Y/X. E) (X + Y)/60.

Solution: Kramer can pack X boxes per min.   Therefore in 2 hrs(120 mins)he can pack 120X boxes.   If there are Y boxes in one case then then the total number of cases packed by Kramer = 120X/Y   ANSWER:120Y/X.
Answer: D
If w/x = 1/3 and w/y = 3/4, then (x + y)/y =
Select.
A) 13/4
B) 6/5
C) 7/5
D) 8/5
E) 9/5

Solution: W/X = 1/3=>x=3w and W/Y = 3/4=>y=(4/3)w   (X+Y)/Y = (3w+4/3w)/(4/3w)=(13/3w)/(4/3w)=13/4   Correct Option: 13/4
Answer: A
There are deer and peacocks in a zoo. By counting heads they are 80. The number of their legs is 200. How many peacocks are there ?
Choose the correct choice from the following
A) 20
B) 30
C) 50
D) 60
E) 80

Solution: Explanation:   Let x and y be the number of deer and peacocks in the zoo respectively. Then,   x + y = 80 ...(i) and   4x + 2y = 200 or 2x + y = 100 ...(ii)   Solving (i) and (ii), we get) x = 20, y = 60.   Answer: 60
Answer: D
How many different three-digit multiples of 5 can be composed of digits 1, 2, 3, 4, and 5 if none of the digits is repeated?  Pick:
A) 3
B) 6
C) 8
D) 12
E) 18

Solution: can you explain your method. i solved it differently   XYZ, where Z must be 5. therefore 1 variation of digit in Z.   Y can be any of the 4 possible choices.   X can be any of the 3 possible choices.   4+3+1= 
4+3+1 = 8
8   8
Answer: C
An empty pool being filled with water at a constant rate takes 8hours to fill to 2/5 of its capacity.how much more time will it take to finish filling the pool?
Choose the correct choice:	A) 5hr 30min	B) 5hr 20min	C) 4hr 48min	D) 3 hr 12min	E) 2hr 40 min

Solution: As pool is filled to 2/5 of its capacity then 2/5 of its capacity is left to fill.   To fill 3/5 of the pool took 8 hours --> to fill 2/5 of the pool will take 8/(3/5)*2/5=16/3 hours = 5 hours 20 minutes (because if t is the time needed to fill the pool then t*3/5=8 --> t=8*5/3 hours --> to fill 2/5 of the pool 8*5/3*2/5=16/3 hours will be needed).   Or plug values: take the capacity of the pool to be 5 liters --> 3/5 of the pool or 3 liters is filled in 8 hours, which gives the rate of 3/8 liters per hour --> remaining 2 liters will require: time = job/rate = 2/(3/8) = 16/3 hours = 5 hours 30 minutes.   5hr 30minnswer: 5hr 30min.
Answer: A
Three investors, A, B, and C, divide the profits from a business enterprise in the ratio of 5 : 7 : 8, respectively. If investor A earned $ 5,000, how much money did investors B and C earn in total? Pick.
A) $15,000  B) $4,900  C) $5,600  D) $9,500  E) $10,500

Solution: Let profit for $15,000 = 5x   profit for B = 7x   profit for C = 8x   Investor $15,000 earned = 5000   5x = 5000=>x=1000   Total profit for B and C = 7x+ 8x = 15x   Therefore , 15x 7 + 8= 
7 + 8 = 15
15x   Therefore , 15x=15*1000= 15,000   $15,000nswer $15,000
Answer: A
If 18!/3^x is an integer, what is the greatest possible value of x?
Choose one:
A) 3 B) 4 C) 5 D) 6 E) 8

Solution: 18 - 3*3*2   15 - 5*3   12 - 4*3   9 - 3*3   6 - 2*3   3 - 1*3   Hence max of 3^8 is allowed. IMO 8.
Answer: E
A computer program assigns consecutive numbers to the days of the week. Sunday is 1, Monday is 2, ..... and Saturday is 7. Every day, the computer program calculates the value of parameter D according to the following definition: D is the number of the day times the value of D on the previous day. If the computer calculated D to be 24 on Wednesday, what would be the value of D calculated on the following Saturday?
Choose the correct choice from the following
A) 3450  B) 3860  C) 4220  D) 4670  E) 5040

Solution: On Saturday, the value would be   7*6*5*24= 
  7*6*5*24 = 5_040
5040   The answer is 5040.
Answer: E