MU-NLPC/Calc-aqua_rat huggingface dataset:
The average of five consecutive odd numbers is 61. What is the difference between the highest and lowest numbers :  Pick one.
A) 4	B) 8	C) 12	D) 16	E) 20

Solution: Let the numbers be x, x + 2, x + 4, x + 6 and x + 8.Then [x + (x + 2) + (x + 4) + (x + 6) + (x + 8) ] / 5 = 61.or 5x + 20 = 305 or x = 57.So, required difference = (57 + 8) - 57= 
(57 + 8) - 57 = 8
8 Answer : 8
Answer: B
The ratio of the volumes of two cubes is 3375 : 1331. What is the ratio of their total surface areas?  Choose the correct choice from the following answers
A) 225 : 121
B) 221 : 127
C) 225 : 191
D) 181 : 161
E) 81 : 182

Solution: Explanation:   Ratio of the sides = ³√3375 : ³√1331 = 15 : 11   Ratio of surface areas = 15^2 : 11^2 = 225 : 121   225 : 121nswer: Option 225 : 121
Answer: A
If n is the greatest positive integer for which 4^n is a factor of 8!, then n =?  Pick one:
A) 2  B) 4  C) 6  D) 8  E) 10

Solution: 8! = 40320   E. 4^10 = 1048576 (40320/1048576) - this is not a factor of 8!   D. 4^8 = 65536 (40320/65536) - this is not a factor of 8!   C. 4^6 = 4096 (40320/4096) - this is not a factor of 8!   B. 4^4 = 256 (40320/256) - this is not a factor of 8!   A. 4^2 = 16 (40320/16) - this is a factor of 8!
Answer: A
Square ABCD shown above is rotated in a plane about its center in a clockwise direction the minimum number of degrees necessary for C to be in the position where B is now shown. The number of degrees through which ABCD is rotated is	Choose the correct answer: A) 135 degree B) 180 degree C) 225 degree D) 315 degree E) 270 degree

Solution: From the options, I am assuming the positioning of B and C relative to each other to be as shown. To replace B by C, focus on OC. Say, you rotate OC clockwise (and with it the entire square) and bring it in place of OB. How many degrees did you go? You covered 3 right angles i.e. 270 degrees.   Answer : 270 degree
Answer: E
A team of 6 cooks is chosen from 8 men and 6 women. The team must have at least 2 men and at least 3 women. How many ways can this team be created?	Choose the most appropriate option:  A) 1540  B) 320  C) 560  D) 700  E) 840

Solution: Only possible combinations are a team of 2M, 4 W or 3M,3W.   Possible ways to make a team of 2M,4W = 8C2 * 6C4 =28*15= 
28*15 = 420
420   Possible ways to make a team of 3M,3W= 8C3* 6C3 = 56*20= 
56*20 = 1_120
1120   Total possible ways= 420+1120= 
420+1120 = 1_540
1540   1540ns 1540 it is.
Answer: A
The symphony sells two kinds of tickets: orchestra, for $30, and upper tiers, for $12. On a certain night, the symphony sells 90 tickets and gets $1926 in revenue from the sales. How many orchestra tickets did they sell?  Choose the correct option.
A) 35	B) 39	C) 43	D) 47	E) 51

Solution: Let x be the number of orchestra tickets.   Then 90-x is the number of upper tier tickets.   30x + 12(90-x) = 1926   18x = 1926-1080   x = 47   The answer is 47.
Answer: D
A juice manufacturer organized taste-testing sessions featuring four brands of orange juice, A, B, C and D. All customers who participated told the organizer which variety they thought was the most similar to freshly-squeezed orange juice. 61% preferred brand A and exactly half as many preferred brand B. Only 55 chose brand C. Which of the following could be the number of customers who preferred brand D?  Pick.
A) 1	B) 8	C) 19	D) 20	E) 27

Solution: I get D, but I'm not sure that my method is sound.   You have A + B + C + D = total testers. Stating the variety they think is most similar to freshly squeezed orange juice means each person should get 1 vote.   x = total number of testers   A + B + C + D   .61x + (.5)(.61x) + 65 + D = x   .61x + .305x + 65 + D = x   I took total testers = 1000 because that gives me nice numbers to deal with. Also, if I use 200 total testers, that gives me A = 122, B = 61, C = 65...that's over 200 without considering D.   x = 400   A = 244, B = 122, C = 65..also over 400   x = 600   A = 366, B = 183 C = 65....also over 600   x = 800   A = 488, B = 244, C = 65...D = 3...not an option on the list.   x = 1000   A = 610 B = 305 C = 65 D = 20....the first time I get an answer that is an option in the question.   19
Answer: C
A sum of Rs. 2730 is lent into two parts so that the interest on the first part for 8 years at 3% per annum may be equal to the interest on the second part for 3 years at 5% per annum. Find the second sum?
Choose the correct choice from the following: A) 1629 B) 1680 C) 1677 D) 1698 E) 1679

Solution: (x*8*3)/100 = ((2730 - x)*3*5)/100   24x/100 = 40950/100 - 15x/100   39x = 40950 => x = 1050   Second sum = 2730 â€“ 1050 = 1680   Answer:1680
Answer: B
Tom can hit a target 3 times in 6 shots, Mike can hit the target 2 times in 6 shots & Johncan hit 4 times in 4 shots. What is the probability that at least 2 shots hit the target ?
Choose the correct choice.
A) 1/4
B) 2/5
C) 2/3
D) 3/7
E) 4/9

Solution: John hits the target definitely, hence required probability that atleast 2 shots hit the target is given by   Mike hits tha target and Raja not hit the target.   or   Mike does not hit the target and Raja hits the target.   or.   Mike hits the target and Raja hits the target   = 2/6 x 3/6 + 4/6 x 3/6 + 2/6 x 3/6   = 24/36 = 2/3   2/3
Answer: C
There are 5 sweets = Jamun, Kaju, Peda, Laddu, Jalebi which can be consumed in 5 consecutive days. Monday to Friday. A person eats one sweet a day, based on the following constraints.
(i)	Laddu not eaten on Monday.
(ii)	If Jamun is eaten on Monday, Laddu should be eaten of Friday.
(iii)	Peda is eaten the day following the day of eating Jalebi.
(iv)	If Laddu eaten on Tuesday, Kaju should be eaten on Monday.
Based on above, Peda can be eaten on any day except:  Choose one:
A) Tuesday
B) Monday
C) Wednesday
D) Friday
E) sunday

Solution: The answer lies in statement (iii)   It is given that peda is eaten the day following the day of eating jalebi.   So peda cannot be eaten on Monday   Answer--> (b) Monday   ANSWER:Monday
Answer: B
The average price of 10 oranges is Rs. 12 while the average price of 8 of these oranges is Rs. 11.75. Of the remaining two oranges, if the price of one orange is 25% more than the price of the other, what is the price of each of these two oranges?
Pick one:
A) Rs 11.5, Rs 14.5
B) Rs 8, Rs 12
C) Rs 10, Rs 16
D) Rs 12, Rs 14
E) None of these

Solution: Explanation :   Total price of the two oranges = Rs. [(12 x 10) (11.75 x 8)]   = Rs. (120 - 94) = Rs. 26.   Let the price of one orange be Rs. x.   Then, the price of other orange = Rs. (x + 25% of x) = Rs. x + 1/4x = Rs. 5x/4   So, x + 5x/4 = 26   9x = 104   x = 11.5   The prices of the two oranges are Rs. 11.5 and Rs. 14.5   Rs 11.5, Rs 14.5nswer : Rs 11.5, Rs 14.5
Answer: A
For all integers a and b, a%b = (a + b)(a - b). If 5%x = 24, then which of the following could be a value of x? Choose the most appropriate option
A) -4
B) -3
C) 2
D) 3
E) 1

Solution: 5%x = (5+x)(5-x)   25-x^2 = 24   x^2 = 1   x=-1,1   Ans: 1
Answer: E
Stephanie, Regine, and Brian ran a 20 mile race. Stephanie and Regine's combined times exceeded Brian's time by exactly 2 hours. If nobody ran faster than 8 miles per hour, who could have won the race?
I. Stephanie
II. Regine
III. Brian
Choose one:
A) I only
B) II only
C) III
D) only I or II only
E) I, II, or III

Solution: Let’s assume that Stephanie won the race in record time of 2.5 hrs. In that case   B = R + 0.5   Note that even if R took the minimum possible time of (2.6 hrs), then Brian would be 3.1 hrs and Stephanie would be 2.5 hrs. This case is very much possible. So S came first, then R and B came last.   The same is true with   B = S + 0.5   R came first, S and then B.   So we see that B is a loser in any case, however R or S have equal chances to win.   So (only I or II only) is the answer.
Answer: D
A group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 7 with 4 students left over. What is the sum of the two smallest possible values of n? Choices
A) 66  B) 70  C) 74  D) 78  E) 82

Solution: n = 4k+1 = 7j+4   Let's start at 1 = 4(0)+1 and keep adding 4 until we find a number in the form 7j+4.   1, 5, 9, 13, 17, 21, 25 = 7(3)+ 4   The next such number is 25 + 4*7= 
25 + 4*7 = 53
53.   25+53= 
25+53 = 78
78   The answer is 78.
Answer: D
There were two candidates in an election. Winner candidate received 62% of votes and won the election by 408 votes. Find the number of votes casted to the winning candidate?
Choose one
A) 288	B) 1054	C) 788	D) 298	E) 177

Solution: W = 62% L = 38%   62% - 38% = 24%   24% -------- 408   62% -------- ?  62  - 38= 
 62  - 38 = 24
24%   24% -------- 408   62% -------- ?=> 1054   Answer: 1054
Answer: B
The first republic day of the India was celebrated on 26th January,1950. It was	Choose the correct choice from the following answers:
A) 221  B) 28  C) 276  D) 20  E) 22

Solution: 1-1-1 AD fall on Monday. We calculate the number of odd days till 24th december, 1995.   Number of odd days till 1600 years = 0   1601 to 1700 = 5   1701 to 1800 = 5   1801 to 1900 = 5   49 years contains = 37 normal   + 12= 
  + 12 = 12
12 × 2 + 37= 61 odd days = 61/7 = 5 odd days   25th January 1950 = 25/7 = 4 odd days   Total odd days =15 + 5 + 4= 
15 + 5 + 4 = 24
24/7= 3 odd days   So 26th January,1950 is Thursday   Answer:28
Answer: B
A tap can fill a tank in 6 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely ?  Choose the correct option:
A) 3 hrs 15 min	B) 3 hrs 45 min	C) 4 hrs	D) 4 hrs 15 min	E) 4 hrs 45 min

Solution: time taken by one tank to fill half the tank=4*(1/6)   Part filled by the four taps in 1 hour=4*(1/6)   remaining part=1/2   therefore 2/3:1/2::1:x   x=3/4hr=(3/4)*60= 
(3/4)*60 = 45
45min   total time=3 hr 45 min   ANSWER:3 hrs 45 min
Answer: B
How much time does a train 100 metres long running at 72 km/hr take to pass a pole?	Choose the correct choice from the following answers:  A) 7.9s  B) 2.5s  C) 5s  D) 7.6s  E) 7.4s

Solution: Explanation:   72 km/hr = 72 * 5/18= 
72 * 5/18 = 20
20 m/s   Speed= distance/time; v = d/t   20 = 100/t   t = 5s   ANSWER: 5s
Answer: C
The sum of two numbers is 184. If one-third of the one exceeds one-seventh
of the other by 8, find the smaller number Choose the correct choice from the following options:
A) 53 B) 18 C) 68 D) 112 E) 72

Solution: Let the numbers be x and (184 - x). Then,   (X/3) - ((184 – x)/7) = 8 => 7x – 3(184 – x) = 168 => 10x = 720 => x = 72.   So, the numbers are 72 and 112. Hence, smaller number = 72.   Answer is 72.
Answer: E
If the number 481 * 673 is completely divisible by 9, then the smallest whole number in place of * will be:	Choose the correct choice from the following choices.
A) 2  B) 5  C) 6  D) 7  E) None of these

Solution: Sum of digits = (4 + 8 + 1 + x + 6 + 7 + 3) = (29 + x), which must be divisible by 9.   x = 7.   Answer:7
Answer: D
There is a set consisting of 5 numbers--{1,2,3,4,5}. If all possible subsets including null set are created and one subset is picked up, what is the probability that the subset does not have 5 as its largest number?	Select the correct option:  A) 1/5  B) 1/4  C) 1/3  D) 1/2  E) 4/5

Solution: Total Number of possible subsets [ including Null Subset ] : 2525 -- (A number can occur or not occur in a subset -- 2 ways)   Possible subsets where 5 is not present [will include null subset] : 24∗124∗1.   P = 2424 / 2525 = 1 / 2.   ANSWER:1/2
Answer: D
The number of positive integers valued pairs (x, y) ssatisfying 4x -17y = 1 and x <= 1000 (x is less than or equal to 1000) is Choose the correct answer
A) fifty nine	B) 57	C) 55	D) 58	E) 60

Solution: 4x-17y=1   y=(4x-1)/17   x has to be a positive integer such that 1<=x<=1000(4x-1) is a factor of 17 so that y is also a positive integer   So we need to know how many numbers in the set {3,7,11,15,....,3999} are divisible by 17   Lets try to observe the pattern   1. 3 mod 17 = 3   2. 7 mod 17 = 7   3. 11 mod 17 = 11   4. 15 mod 17 = 15   5. 19 mod 17 = 2   6. 23 mod 17 = 6   7. 27 mod 17 = 10   8. 31 mod 17 = 14   9. 35 mod 17 = 1   10. 39 mod 17 = 5   11. 43 mod 17 = 9   12. 47 mod 17 = 13   13.51 mod 17 = 0   14. 55 mod 17 = 4   15. 59 mod 17 = 8   16. 63 mod 17 = 12   17. 67 mod 17 = 16   ... and after this the remainders will repeat (this is no co-incidence that the cyclicity is also 17)   So the right choices are x=13,13+17,13+17+17,.....   The number of such numbers is 59 (highest one being 999) fifty nine
Answer: A
A man spends on an average Rs 269.47 for the first 7 months and Rs 281.05 for the next 5 months. Find his monthly salary if he saves Rs 308.46 during the whole year. Choose the correct choice from the following choices:
A) Rs 300
B) Rs 500
C) Rs 840
D) Rs 400
E) Rs 600

Solution: Total spending in 12 months = Rs [269.47 x 7 - 281.05 × 5] = Rs 3,291.54   Total income = Spending + Saving   = Rs 3,291.54 + Rs 308.46   = Rs 3,600.00   Monthly salary = Rs 3600/12= 
3600/12 = 300
Rs 300   Rs 300NSWER:Rs 300
Answer: A
At the library, 50 books were checked out that day from the display. 5 copies of Sandry's Book were checked out and 15 copies of Howl's Moving Castle. If only two other books were checked out (Harry Potter and the Lightning Thief) and they were both checked out in equal quantities, how many copies of the Lightning Thief were checked out?	Answers.
A) 5 B) 10 C) 15 D) 20 E) 25

Solution: First, subtract the number of other books that were checked out from the total:   50-5-15= 
  50-5-15 = 30
30. As the remaining two books were checked out in equal quantities, simply divide 30 by 2: 30/2=15. The answer is 15, 15.
Answer: C
During a clearance sale, a retailer discounted the original price of its TVs by 24% for the first two weeks of the month, then for the remainder of the month further reduced the price by taking 20% off the sale price. For those who purchased TVs during the last week of the month, what percent of the original price did they have to pay? Select the correct option:	A) 40%	B) 45%	C) 55%	D) 60%	E) 62%

Solution: VERITAS PREPOFFICIAL SOLUTION:   D. With percent problems, the key is often to make sure that you take the percent of the correct value. In this case, the initial 25% off means that customers will pay 75% of the original price. Then for the second discount, keep in mind that the discount is taken off of the sale price, not of the original price. So that's 20% off of the 75% that they did pay, which can be made easier by looking at what the customer does pay: 80% of the 75% sale price. Using fractions, that means they pay: 4/5*(3/4) of the original price, which nets to 3/5 of the original price, or 62%.   62%
Answer: E
Twenty percent of the skiers that tried out for the ski patrol were selected. Of those that were not selected, 7 skiers were CPR certified and 17 were not. How many skiers tried out for the ski patrol?	Select the correct option:  A) 30  B) 50  C) 60  D) 70  E) 80

Solution: Not Selected = 80%   If total is x.   Then 0.8x=7+17= 
7+17 = 24
24   x=30   Hence answer is 30.
Answer: A
A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.4 per sq m? Choose the correct choice from the following answers:
A) 675, Rs.1350  B) 575, Rs.1350  C) 1350, Rs.675  D) 675, Rs.2700  E) 1550, Rs.875

Solution: Area = (l + b +2d) 2d   = (75 + 55 +2.5 * 2) 2*2.5 => 675   675 * 4 = Rs.2700   ANSWER:675, Rs.2700
Answer: D
In 60 litres mixture milk and water are in the ratio 3:1. After adding how many liters of water its ratio will become 3:2 Choose the correct choice from the following choices:
A) 1
B) 15
C) 7
D) 5
E) 12

Solution: Milk quantity = 3/4 * 60= 
3/4 * 60 = 45
45   water quantity= 60-45= 
60-45 = 15
15   new ratio of M:W= 45:15+x = 3:2   45+3x = 90   x = 15   Answer is 15
Answer: B
A shopkeeper buys mangoes at the rate of 4 a rupee and sells them at 3 a rupee. Find his net profit or loss percent? Choose the correct option:
A) 33 1/6 %  B) 33 8/3 %  C) 33 1/3 %  D) 73 1/3 %  E) 33 16/3 %

Solution: The total number of mangoes bought by the shopkeeper be 12.   If he buys 4 a rupee, his 33 1/3 %P = 3   He selling at 3 a rupee, his SP = 4   Profit = SP - 33 1/3 %P = 4 - 3= 
4 - 3 = 1
1   Profit Percent= 1/3 * 100 = 33 1/3 %   Answer: 33 1/3 %
Answer: C
From a group of 4 boys and 4 girls, 2 children are to be randomly selected. What is the probability that 1 boy and 1 girl will be selected?	Choose the correct answer:
A) 1/2	B) 2/3	C) 3/5	D) 4/7	E) 5/9

Solution: The total number of ways to choose 2 children from 8 is 8C2 = 28   The number of ways to choose 1 boy and 1 girl is 4*4= 
4*4 = 16
16   P(1 boy and 1 girl)= 16/28 = 4/7   The answer is 4/7.
Answer: D
9 men can do a work in 12 days working 4 hours a day. In how many days can 6 men do the same work, working 8 hours a day?	Choose the correct choice from the following choices:
A) 18 B) 9 C) 10 D) 8 E) 11

Solution: We have, M1D1H1 = M2D2H2   So, 9*12*4= 6*D2*8   D2 = 9*12*4/6*8 = 9   ANSWER:9
Answer: B
Find the cost of fencing around a circular field of diameter 18 m at the rate of Rs.2.50 a meter?	Choose the correct option:
A) 138	B) 132	C) 150	D) 140	E) 222

Solution: 2 * 22/7 * 9 = 56   56 * 2 1/2   = Rs.140   Answer: 140
Answer: D
With out any halt a train travels a certain distance with an average speed of 49 km ph , and with halts it covers the same distance at an average speed of 28 kmph. When it is traveling with halts, how many minutes/per hour does the train halt on an average ?  Pick
A) 48 min.  B) 45min.  C) 15min.  D) 18min.  E) 19min.

Solution: With halt in 1 hour the train travels 60km   With out halt for traveling same distance it take 49/28 = 7/4 = 105 minutes   :. 45 minutes is the halting time per hour   ANSWER:45min.
Answer: B
Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?
Choose the correct choice from the following answers.
A) 3/4
B) 3/8
C) 3/1
D) 3/2
E) 3/9

Solution: Explanation:   In a simultaneous throw of two dice, we have n(S) = (6 x 6) = 36.   Then, E= {(1, 2), (1, 4), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (3,4),(3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 2), (5, 4), (5, 6), (6, 1),6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}   n(E) = 27.   P(E) = n(E)/n(S) = 27/36 = 3/4.   3/4nswer: 3/4) 3/4
Answer: A
In traveling from a dormitory to a certain city, a student went 1/2 of the way by foot, 3/5 of the way by bus, and the remaining 4 kilometers by car. What is the distance, in kilometers, from the dormitory to the city?  Pick.
A) 20
B) 15
C) 40
D) 10
E) 12

Solution: Whole trip = distance by foot + distance by bus + distance by car   x = 1/2x + 3/5x + 4   x - 1/2x - 3/5x = 4   x=20km   Option: 20
Answer: A
When positive integer A is divided by positive integer B, the result is 5.15. Which of the following could be the integer A is ?  Select the correct option.
A) 107	B) 117	C) 103	D) 123	E) 171

Solution: the remainder will be obtained from the decimal part when A is divided by B i.e. 0.15   0.15 = 15/100 = 3/20 so possible remainders are 3,6,12,9,15.   let remainder is 3   Now when we divide option 103 i.e 103/20 = 5 is quotient and remainder is 3   therefore ans - 103
Answer: C
Three positive integers a, b, and c are such that their average is 80 and a ≤ b ≤ c. If the median is (a + 20), what is the least possible value of c?
Select the correct option: A) 88 B) 89 C) 90 D) 92 E) 94

Solution: Solution   Given Data   3 positive integers   Average of a, b, and c = 80   So, a+b+c3a+b+c3 = 240 or a + b + c = 240   a ≤ b ≤ c   Median = (a + 20)   Median of these 3 numbers a, b, and c is ‘b’ because a ≤ b ≤ c   Therefore, b = a + 20   Objective To find the least value of 'c'   Theoretically, the least value of c is when c = b.   Therefore, a + (a + 20) + (a + 20) = 240 (b and c are equal and b, the median, is a + 20)   Or 3a = 200 or a = 66.66   So, b = c = 66.66+ 20= 
66.66+ 20 = 86.66
86.66   However, we know that these numbers are all integers.   Therefore, a, b, and c cannot take these values.   So, the least value for c with this constraint is NOT likely to be when c= b   Let us increment c by 1. Let c = (b + 1)   In this scenario, a + (a + 20) + (a + 21) = 240   Or 3a = 199. The value of the numbers is not an integer in this scenario as well.   Let us increment c again by 1. i.e., c = b + 2   Now, a + (a + 20) + (a + 22) = 240   Or 3a = 198 or a = 66   If a = 66, b = 86 and c = 88.   The least value for c that satisfies all these conditions is 88.   Correct answer is choice 88.
Answer: A
A certain store sells all maps at one price and all books at another price. On Monday the store sold 12 maps and 8 books for a total of $38.00, and on Tuesday the store sold 20 maps and 12 books for a total of $60.00. At this store, how much less does a map sell for than a book?	Choose the correct answer: A) $0.25 B) $0.50 C) $0.75 D) $1.00 E) $l.25

Solution: 12x+8y=38   20x+12y=60   multiply eq 1 by 5 and eq 2 by 3   60x+40y=38*5   60x+36y=60*3   subtracting 1 from 2   4y=190-180   y=2.5   therefore   x=1.5   difference in price =1   $1.00
Answer: D
David buys an old scooter for Rs. 2400 and spends Rs. 600 on its repairs. If he sells the scooter for Rs. 3600, his gain percent is : Options:
A) 20%	B) 12%	C) 10%	D) 5%	E) None of these

Solution: Explanation :   Solution: C.P. =Rs. (2400+600) =Rs. 3000; S.P. = Rs. 3600.   Gain% = (600*100/3000)= 
(600*100/3000) = 20
20%.   20%nswer : 20%
Answer: A
Mr. George paid $8,000 for 100 shares of stock A and $6,000 for 100 shares of stock B. He later sold the same shares of both stocks, gaining 3/8 the amount he paid for stock B. If the prices he had paid for the stocks had been reversed and everything else remained the same, then the net result would have been: Pick one
A) A loss 1 1/2 times as much.	B) A loss 2 times as much	C) The same.	D) A gain 1 1/2 times as much.	E) A gain 1.33 times as much.

Solution: A = 8000; B = 6000; Profit = (3/8)*6000= 
(3/8)*6000 = 2_250
2250   After prices are reversed:   A= 6000; B =8000; Profit = (3/8)*8000= 
(3/8)*8000 = 3_000
3000   3000 --> Gain of 1.33 times 2250   Answer: A gain 1.33 times as much.
Answer: E
A gold purification process cycle, is able to remove 1/16 of impurities in gold. If we have a 10 grams of gold ore dust containing 16/24 pure gold. How much impurities would have been removed from that old after 4 cycles of purification using that method?  Choices.
A) 0.72 B) 0.74 C) 0.76 D) 0.78 E) 0.82

Solution: X is the initial quantity of impurities in that gold.   After a cycle of purification the quantity of impurities left would be X1=X-1/16X i.e. X1=15/16X   Same thing for X2, X3, X4, respectively representing the quantity of impurities left after 2, 3, 4 cycles of purification.   So we have:   X1=15/16 X   X2=15/16 X1   X3=15/16 X2   X4=15/16 X3   By multiplying both ends of the equations we get:   X1*X2*X3*X4 = (15/16)^4 X*X1*X2*X3   Simplification leaves us with:   X4 = (15/16)^4 X   X4 is the quantity of impurities left after four cycles. So the cumulative quantity of impurities (Q4) which has been removed after 4 cycles is: Q4= X-X4=X-(15/16)^4X i.e. Q4 = X (1-(15/16)^4)   In this case, given X was: X=(1-16/24) * 10 g = 3.33 g (Remember we had 16/24 pure gold)   So we have Q4 = 3.33 * (1-(15/16)^4) = 3.33 * (1-(50625/65536)) = 3.33 * (14911/65536) = 0.757 rounded gives Q4=0.76   Answer: 0.76
Answer: C
The price of a coat in a certain store is $500. If the price of the coat is to be reduced by $200, by what percent is the price to be reduced?	Choose the correct choice from the following choices
A) 10%	B) 15%	C) 20%	D) 25%	E) 40%

Solution: price of a coat in a certain store = $500   the price of the coat is to be reduced by $200   % change = (Final Value - Initial Value)*100 / Initial Value   % Reduction= (Reduction in Price)*100 / Initial Value   i.e. % Reduction= (200)*100 / 500= 
(200)*100 / 500 = 40
40%   Answer: Option 40%
Answer: E