MU-NLPC/Calc-aqua_rat huggingface dataset:
There are 408 boys and 192 girls in a school which are to be divided into equal sections of either boys or girls alone. Find the total number of sections thus formed.	Choose the correct choice from the following choices:  A) 25  B) 32  C) 35  D) 30  E) 45

Solution: Explanation:   HCF (408, 192) = 24   The number of boys or girls that can be placed in a section = 24.   Thus the total number of sections is given by   408/24+192/24 =17+8= 
17+8 = 25
25   25nswer: 25
Answer: A
A tourist purchased a total of $1,400 worth of traveler’s checks in $10 and $50 denominations, During the trip the tourist cashed 7 checks and then lost all of the rest. If the number of $10 checks cashed was one more or one less than the number of $50 checks cashed, what is the minimum possible value of the checks that were lost?	Pick one:  A) $1,430  B) $1,310  C) $1,290  D) $1,170  E) $1,150

Solution: since total cashed checks = 7 ans $10 check cashed = one less or more than $50 checks   Therefore either $10 checks = 3 and $50 checks = 4 OR $10 checks = 4 and $50 checks = 3   using this information 1st option gives us the maximum cashed value therefore if we negate this value from total value we will get minimum value of which checks have lost   Therfore   1400 - 230= 
  1400 - 230 = 1_170
1170 hence answer is $1,170
Answer: D
The visitors of a modern art museum who watched a certain Picasso painting were asked to fill in a short questionnaire indicating whether they had enjoyed looking at the picture and whether they felt they had understood it. According to the results of the survey, all 150 visitors who did not enjoy the painting also did not feel they had understood the painting, and the number of visitors who enjoyed the painting was equal to the number of visitors who felt they had understood the painting. If 3/4 of the visitors who answered the questionnaire both enjoyed the painting and felt they had understood the painting, then how many visitors answered the questionnaire?	Select the correct option:
A) 90	B) 120	C) 160	D) 360	E) 600

Solution: If we exclude those cases and take the question at face value, then it seems straightforward.   Group #1 = (didn't like, didn't understand) = 150   Group #2 = (likeunderstood) = 3/4   (1/4)N = 150   N = 600   Answer =(600)
Answer: E
A fair 2 sided coin is flipped 8 times. What is the probability that tails will be the result at least twice, but not more than 8 times?
Select:
A) 5/8
B) 3/4
C) 7/8
D) 157/64
E) 143/128

Solution: at least twice, but not more than 8 timesmeans exactly 2 times, 3 times, 4 times, 5 times, 6 times, 7 times, 8 times   The probability of getting exactly k results out of n flips is nCk/2^n   8C2/2^8+8C3/2^8+8C4/2^8+8C5/2^8+8C6/2^8+8C7/2^8=143/128   Option: 143/128
Answer: E
A recipe requires 2 1/2 (mixed number) cups of flour 2 3/4 (mixed number) cups of sugar and 1 1/3 (mixed number) cups of milk to make one cake. Victor has 15 cups if flour, 16 cups of sugar and 8 cups of milk. What is the greatest number of cakes William can make using this recipe? Pick
A) 5	B) 6	C) 7	D) 8	E) 9

Solution: Less work up front: Go through each item and see what the greatest number of cakes you can make with each. The lowest of these will be the right answer.   Flour: 15 cups, we need 2.5 cups each. Just keep going up the line to see how many cakes we can make: That means I can make 2 cakes with 5 cups, so 6 cakes overall with 15 cups. I've already got the answer narrowed to either A or B.   Sugar: 16 cups, we need 2.75 cups each. Same principle. I can make 2 cups with 5.5 cups, so to make 6 cakes I'd need 16.5 cups. I don't have that much sugar, so we're limited to 5 cakes. No need to even do milk because we're already at 5. Sugar will be the limiting factor.   answer is 5
Answer: A
In an intercollegiate competition that lasted for 3 days, 150 students took part on day 1, 110 on day 2 and 140 on day 3. If 75 took part on day 1 and day 2 and 25 took part on day 2 and day 3 and 15 took part on all three days, how many students took part only on day 2?
Choose the correct option: A) 50 B) 35 C) 45 D) 25 E) 60

Solution: 25ay 1&2 = 75; Only 25ay 1&2 (75 -15) = 60,   25ay 2&3 = 25; Only 25ay 2&3 (25 -15) = 10,   Only 25ay 2 = 110 - (60+10+15)= 
110 - (60+10+15) = 25
25   Answer:25
Answer: D
From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first is a red card and the second is a king is?
Choose the correct option.
A) 1/26
B) 1/27
C) 1/87
D) 1/67
E) 1/21

Solution: Let E1 be the event of drawing a red card.   Let E2 be the event of drawing a king .   P(E1 ∩ E2) = P(E1) . P(E2)   (1/26s E1 and E2 are independent)   = 1/2 * 1/13 = 1/26   1/26nswer:1/26
Answer: A
The Average of six numbers is 8. The average of the first two is 11 and the average of the last three is 4. What is the middle number?
Choose the correct choice from the following answers
A) A)15	B) B)8	C) C)6	D) D)14	E) E)9

Solution: The total of six numbers = 6X8 = 48   The total of first 2 and last 3 numbers is = 2 X 11+3 X 4 = 34   So, the middle number is  (48 - 34 )= 
 (48 - 34 ) = 14
14   14
Answer: D
Ravi purchased a refrigerator and a mobile phone for Rs. 15000 and Rs. 8000 respectively. He sold the refrigerator at a loss of 5 percent and the mobile phone at a profit of 10 percent. Overall he make a.	Choices:
A) 50
B) 288
C) 27
D) 200
E) 881

Solution: Let the SP of the refrigerator and the mobile phone be Rs. r and Rs. m respectively.   r = 15000(1 - 5/100) = 15000 - 750   m = 8000(1 + 10/100) = 8000 + 800   Total SP - Total CP = r + m - (15000 + 8000) = -750 + 800 = Rs. 50   As this is positive, an overall profit of Rs. 50 was made.50nswer:50
Answer: A
A began business with 45,000 and was later joined by B with 54,000. When did B join if the profit at the end of the year were divided in the ratio 2 : 1?  Pick
A) 5 months after	B) 10 months after	C) 7 months after	D) 12 months after	E) None of these

Solution: Let B join after ‘x’ month of the start of the business.   ⇒ (45,000 × 12) : 54,000 × (12 – x) = 2 : 1   ∴ (45,000 × 12) × 1 = 54,000 × (12 – x) × 2   ⇒ x = 7   Answer 7 months after
Answer: C
A military commander has to choose 6 soldiers out of a company of 9 for guarding the headquarters. How many different group combinations of 6 does he have to choose from?
Select the correct option:	A) 84	B) 15	C) 16	D) 27	E) 35

Solution: A military commander has to choose 6 soldiers out of a company of 9.   different group combinations of 6   He can do this in 9C6 ways   9*8*7*6*5*4/6*5*4*3*2*1= 84 ways   84NSWER:84
Answer: A
Of all the students in a certain dormitory, 1/2 are first-year students and the rest are second-year students. If 4/5 of the first-year students have not declared a major and if the fraction of second-year students who have declared a major is 1/3 times the fraction of first-year students who have declared a major, what fraction of all the students in the dormitory are second-year students who have not declared a major?	Choose one:
A) 7/15
B) 1/5
C) 4/15
D) 1/3
E) 2/5

Solution: tot students=x   1st year student=x/2----> non majaor=4/5(x/2)-----> maj=1/5(x/2)   2nd year student=x/2---->maj=1/3(1/5(x/2))=1/30(x)--->non major=x/2-1/30(x)=7/15(x)   hence 7/15   7/15
Answer: A
45 workers work 8 hours to dig a hole 30 meters deep. How many extra workers should be hired to dig another hole 55 meters deep by working for 6 hours?  Choose the most appropriate option:
A) 50	B) 55	C) 60	D) 65	E) 70

Solution: 45 workers * 8 hours / 30 meters = x * 6 / 55   x = 110 total workers     110 - 45= 
  110 - 45 = 65
65 new workers   The answer is 65.
Answer: D
The product of all the prime numbers less than 22 is closest to which of the following powers of 10?  Choose the correct choice from the following options:
A) a) 10^9	B) b) 10^7	C) c) 10^8	D) d) 10^6	E) e) 10^5

Solution: Group these numbers so as to get product close to a multiple of 10, so they can be rewritten as (2*5)(3*7)(11*19)(13*17) or 10*21*209*221   Now take out power of 10 from each number and rewrite   10*10*100*100*(1*2.1*2.09*2.21) or 10^6*(1*2.1*2.09*2.21)   =9.69*10^6=10^7   b) 10^7
Answer: B
If r = ||s – 3| – 2|, for how many values of s is r = 7?
Choose the correct choice from the following choices
A) 4 B) 5 C) 2 D) 1 E) 3

Solution: r = ||s – 3| – 2| can be 4 only and only when s-3= +/-9. so there are 2 values of s   Answer : 2
Answer: C
What is the place value of 1 in the numeral 1259  Pick one:
A) A)1000
B) B)2800
C) C)2900
D) D)2980
E) E)3000

Solution: 1 * 1000= 
1 * 1000 = 1_000
1000   1000
Answer: A
A grocer buys apples for 81¢ per pound. If 10% of the apples goes bad and he still wants to make a 20% profit over his purchase price, what should be the sales price?  Choose one.
A) 100¢  B) 108¢  C) 110¢  D) 95¢  E) 99¢

Solution: for making calculation simple let us consider he buys 10pounds @ 81/pound=810¢ in total .   10% apples lost...means 9 pounds left.   further he wants 20% profit on 810 ¢   means he wants to earn 972¢   sales price should be   972/9= 
  972/9 = 108
¢ 108   Ans 108¢
Answer: B
In a graduating class of 242 students, 144 took geometry and 119 took biology. What is the difference between the greatest possible number and the smallest possible number of students that could have taken both geometry and biology?  Options.
A) 144  B) 119  C) 113  D) 88  E) 123

Solution: Greatest Possible Number taken both should be 144 (As it is maximum for One)   Smallest Possible Number taken both should be given by   Total - Neither = A + B - Both   Both = A+B+Neither - Total (Neither must be 0 to minimize the both)   So 144 + 119 + 0 - 242= 
144 + 119 + 0 - 242 = 21
21   Greatest - Smallest is  144-21= 
 144-21 = 123
123   So answer must be E. 123
Answer: E
Ram professes to sell his goods at the cost price but he made use of 975 grms instead of a kg, what is the gain percent?  Choose the correct choice from the following answers.
A) 3 22/39%
B) 4 22/39%
C) 2 22/39%
D) 7 22/39%
E) 9 22/39%

Solution: 975 --- 25   25 --- ? =>   25/975 *100   = 2 22/39%   Answer: 2 22/39%
Answer: C
A tradesman fixed his selling price of goods at 30% above the cost price. He sells half the stock at this price, one-quarter of his stock at a discount of 15% on the original selling price and rest at a discount of 30% on the original selling price. Find the gain percentage altogether?	Choose the correct choice:
A) 14.875%  B) 15.375%  C) 15.575%  D) 16.375%  E) 16.5%

Solution: Solution: Let CP = 100; then, marked price=130;   Now,   revenue = [(1/2)*130+(1/4)*0.85*130+(1/4)*0.7*130]   = 65+27.65+22.5 = 115.4;   % profit = 15.4*100/100= 
15.4*100/100 = 15.4
15.4%.   Answer: Option 15.375%
Answer: B
An article is bought for Rs.600 and sold for Rs.500, find the loss percent?
Pick one
A) 18 2/3%
B) 16 7/3%
C) 16 2/8%
D) 16 2/3%
E) 76 2/3%

Solution: 600 ---- 100   100 ---- ? => 16 2/3%   Answer:16 2/3%
Answer: D
5 liters of a 20 percent solution of alcohol in water are mixed with 3 liters of a 12 percent alcohol in water solution. What is the percentage of alcohol in the new solution? Select the correct option.
A) 16.7%	B) 17.0%	C) 17.3%	D) 17.6%	E) 17.9%

Solution: The total amount of alcohol is 0.2(5) + 0.12(3) = 1.36 liters.   The percentage is 1.36 / 8 = 136 / 800 = 17 / 100 which is 17%   The answer is 17.0%.
Answer: B
The length, breadth and height of a room are in the ratio 12 : 4 : 4. If the breadth and height are halved while the length is doubled, then the total area of the four walls of the room will
Choose the correct choice from the following options
A) (a) remain the same	B) (b) decrease by 13.64%	C) (c) decrease by 15%	D) (d) decrease by 18.75%	E) (e) decrease by 30%

Solution: Length (L) = 12   Breadth (B) = 4   Height (H) = 4   Total Area of Walls = 2(BH + LH) = 2*(4*4 + 12*4) = 2*(16+48)= 
2*(16+48) = 128
128   Then, Finally   Length (L)= 2*12= 
2*12 = 24
24   Breadth (B)= 4/2= 
4/2 = 2
2   Height (H)= 4/2= 
4/2 = 2
2   Total Area of Walls= 2(BH + LH) = 2*(2*2 + 24*2) = 2*(4+48)= 
2*(4+48) = 104
104   % change in Area of four walls= (Final Area-Initial Area)*100 /Initial Area   i.e. % change in Area of four walls = (104-128)*100 /128=- 18.75% ((d) decrease by 18.75%ecrease)   Answer: Option (d) decrease by 18.75%
Answer: D
A certain number of men complete a piece of work in 60 days. If there were 8 men more, the work could be finished in 10 days less. How many men were originally there?  Choose the correct choice from the following options
A) 30	B) 32	C) 36	D) 40	E) 45

Solution: Originally 1et there be x men.   More men, Less days   (x + 8) : x ∷ 60:50   So, x + 8 / x = 60/50 or x = 40.   ANSWER:40
Answer: D
How many 2's are there between the terms 112 to 375?	Choices
A) A)156 B) B)157 C) C)158 D) D)159 E) E)160

Solution: Let us calculate total 2's in the units place. (122, 132, 142 ... 192), (201, 212, 222, ... 292), (302, 312, ... 372) = 8 + 10 + 8= 
8 + 10 + 8 = 26
26   Total 2's in tenth's place, (120, 121, 122, ..., 129) + (220, 221, ..., 229) + (320, 321, ..., 329)= 30   Total 2's in hundred's place = (200, 201, ... 299) = 100.   Total 2's between 112 and 375 = 26 + 30 + 100= 
26 + 30 + 100 = 156
156   156nswer:156
Answer: A
What is greatest positive integer n such that 2^n is a factor of 12^11?
Choose the correct choice from the following options: A) a)10 B) b)12 C) c)22 D) d)20 E) e)60

Solution: The given number is 12^11   =(2*2*3)^11   =(2^22)*(3^11)   So the greatest possible value for n such that 2^n can be factor of given number is 22.   Answer c)22
Answer: C
Find the amount on Rs.8000 in 9 months at 20% per annum, if the interest being compounded quarterly?  Select the correct option:
A) 9269
B) 9261
C) 9262
D) 9231
E) 9263

Solution: A = 8000(21/20)3 = 9261   Answer:9261
Answer: B
How many liters of water must be evaporated from 50 liters of a 1-percent sugar solution to get a 10-percent solution?
Choose the correct choice from the following choices:  A) 35  B) 40  C) 42  D) 45  E) 48

Solution: 1% of a 50 liter solution is 0.5L which is 10% of the solution at the end.   The solution at the end must be 5 L.   We need to evaporate 45 liters.   The answer is 45.
Answer: D
A fair coin is tossed 13 times. What is the probability of getting more heads than tails in 13 tosses? Choose the most appropriate option
A) 1/2
B) 63/128
C) 4/7
D) 61/256
E) 63/64

Solution: On each toss, the probability of getting a head is 1/2 and the probability of getting a tail is 1/2.   There is no way to get the same number of heads and tails on an odd number of tosses.   There will either be more heads or more tails.   Then there must be more heads on half of the possible outcomes and more tails on half of the possible outcomes.   P(more heads) = 1/2   The answer is 1/2.
Answer: A
N is a positive integer. When N + 1 is divided by 6, the remainder is 4. What is the remainder when N is divided by 2?
Choose the correct choice from the following answers
A) 6
B) 5
C) 1
D) 3
E) 2

Solution: N+1 = 6a+4   i.e. N+1 = 10, 16, 22, 28, ... etc.   i.e. N = 9, 15, 21, 27, ... etc.   When N is divided by 2 Remainder is always 1   Answer: 1
Answer: C
A man sitting in a train which is traveling at 70 kmph observes that a goods train, traveling in opposite direction, takes 9 seconds to pass him. If the goods train is 280 m long, find its speed.? Options.
A) 50 kmph	B) 58 kmph	C) 62 kmph	D) 65 kmph	E) 42 kmph

Solution: Relative speed = 280/9 m / sec = ((280/9)*(18/5))= 
((280/9)*(18/5)) = 112
112 kmph.   Speed of goods train= (112 - 70)= 
(112 - 70) = 42
42 kmph.   Answer : 42 kmph
Answer: E
The radius of a circular wheel is 1.75 m, how many revolutions will it make in traveling 1 km? Choose the correct choice from the following options: A) 100 B) 277 C) 288 D) 267 E) 281

Solution: 2 * 22/7 * 1.75 * x = 11000   x = 1000   100nswer: 100
Answer: A
A man bought 20 shares of Rs. 50 at 5 discount, the rate of dividend being 13. The rate of interest obtained is: Choose one:
A) 12	1/2	%
B) 13 1/2%
C) 15%
D) 16 2/3%
E) None of these

Solution: Explanation:   Investment = Rs. [20 x (50 - 5)] = Rs. 900.   Face value = Rs. (50 x 20) = Rs. 1000.   Dividend = Rs.27/2 * 1000/100 =Rs. 135.   Interest obtained =(135/900 *100)= 
(135/900 *100) = 15
15%   ANSWER IS 15%
Answer: C
The variables a and b are non-zero integers F. If a = 2b^3/c, what happens to c when a is halved and b is doubled? Choose the correct choice from the following:
A) c is not changed.
B) c is halved.
C) c is doubled.
D) c is multiplied by 4.
E) c is multiplied by 16.

Solution: a =2b^3/c   c =2b^3/a   when a is halved and b is doubled   c=2(2b)^3/(a/2)   c=16*2b^3/a   Ans. c is multiplied by 16. c is multiplied by 16.
Answer: E
In the coordinate plane, points (x, 1) and (4, y) are on line k. If line k passes through the origin and has slope 1/4, then x + y =  Select
A) 1 B) 2 C) 4 D) 5 E) 7

Solution: Line k passes through the origin and has slope 1/4 means that its equation is y=1/4*x.   Thus: (x, 1)=(4, 1) and (4, y) = (4,1) --> x+y=4+1= 
4+1 = 5
5.   Answer: 5
Answer: D
If 76 is divided into four parts proportional to 7, 5, 3, 4, then the smallest part is:	Pick one
A) 12	B) 15	C) 16	D) 19	E) None of these

Solution: Explanation:   Given ratio = 7 : 5 : 3 : 4, Sum of ratio terms = 19.   Smallest part =(76 x 3/19) = 12   12nswer: 12
Answer: A
If 1/(m – 2) = 1/(m + 2) + 1/(m – 1), which of the following is a possible value of m?	Choose the most appropriate option
A) 0  B) -1  C) -2  D) 1  E) 2

Solution: Multiply by (m-2)*(m+2)*(m-1) throughout to get:   (m+2)*(m-1) = (m-2)*(m-1) + (m+2)(m-2)   Of the given options, only m=0 satisfies this.   0nswer : 0
Answer: A
The sum of squares of three numbers is 764 and sum of their products taken two at a time is 500. What is their sum?  Choose one:
A) 48
B) 42
C) 52
D) 32
E) 33

Solution: Description :   Let the numbers be x,y,z.   => x2+y2+z2=764   => 2(xy+yz+xz)=2*500= 
2*500 = 1_000
1000=> (x+y+z)2=(x2+y2+z2)+2(xy+yz+xz)=1764   => (x+y+z)=sqrt(1764)=42   Answer 42
Answer: B
A, B and C enter into a partnership by investing $7000, $11000 and $18000 respectively. At the end of 8 months, B receives $880 as his share. Find the share of A. Pick one
A) $320 B) $440 C) $560 D) $670 E) $780

Solution: The ratio of capital of A, B and $560 = 7000 : 11000 : 18000 = 7 : 11 : 18   A's share = (7/11)*880= 
(7/11)*880 = 560
$560   The answer is $560.
Answer: C
A man rows 750 m in 675 seconds against the stream and returns in 7 and half minutes. His rowing speed in still water is	Select the correct option:  A) 4 kmph  B) 5 kmph  C) 6 kmph  D) 7 kmph  E) None of these

Solution: Explanation:   Rate upstream = (750/675) = 10/9 m/sec   Rate downstream (750/450) m/sec = 5/3 m/sec   Rate in still water = (1/2)*[(10/9) + (5/3)] m/sec.   = 25/18 m/sec   = (25/18)*(18/5)= 
(25/18)*(18/5) = 5
5 kmph   Option 5 kmph
Answer: B
The sale price of an article including the sales tax is Rs. 616. The rate of sales tax is 10%. If the shopkeeper has made a profit of 16%, then the cost price of the article is:
Choose the correct answer
A) 500  B) 334  C) 531  D) 664  E) 5598

Solution: 110% of S.P. = 616   S.P. = (616 * 100)/110 = Rs. 560   C.P = (110 * 560)/116 = Rs. 531   Answer: Option 531
Answer: C
Find the value of e from (14)^2 x 5^3 Ã· 568 = e.	Select the correct option
A) 13.1 B) 43.1 C) 40.1 D) 23.1 E) 45.1

Solution: Given Exp. =(14)^2 x 5^3 Ã· 568 = e   = 196 x 125 Ã· 568   43.1   43.1
Answer: B
In how many ways can the letters of the word 'LEADER' be arranged?	Choose the correct choice from the following answers:
A) 28 ways B) 35 ways C) 670 ways D) 230 ways E) 360 ways

Solution: The word 'LEADER' contains 6 letters, namely 1L, 2E, 1A, 1D and 1R.   Required number of ways =6!/(1!)(2!)(1!)(1!)(1!)= 360   =360 ways.   Answer:360 ways
Answer: E
Evaluate:58- 12*3*2 =?
Select: A) 42 B) 50 C) 62 D) 72 E) 82

Solution: According to order of operations, 12?3?2 (division and multiplication) is done first from left to right   12**2 = 4* 2= 
4* 2 = 8
8   Hence   58- 12*3*2= 58- 8= 
58- 8 = 50
50   correct answer 50
Answer: B
A spike is hammered into a train rail. You are standing at the other end of the rail. You hear the sound of the hammer strike both through the air and through the rail itself. These sounds arrive at your point six seconds apart. You know that sound travels through air at 1100 feet per second and through steel at 16,500 feet per second. How far away is that spike? Select the correct option
A) 7070.25 ft B) 7080.25 C) 6070.25 D) 8070.25 E) 7170.25

Solution: d = 1100(t + 6 ), d = 16500t, so 1100(t + 6) = 16500t   1100t + 6600 = 16500t, 1100t - 1100t + 6600 = 16500t-1100t, 6600 = 15400t   6600/15400 = 15400t/15400, 0.4285 = t, 1100(.4285 + 6) = 7071.35, 16500(.4285) = 7070.25   7070.25 ftNSWER:7070.25 ft
Answer: A
How many positive factors of 42 are not factors of 56?
Choose the correct answer:  A) 1  B) 2  C) 3  D) 4  E) 5

Solution: 42=2*3*7.   So, total number of factors for 42 = 2*2*2= 
2*2*2 = 8
8   factors for 42= 1,2,3,6,7,14,21 and 42   56=2*2*2*7   So, total number of factors for 56 = 4*2= 
4*2 = 8
8   factors of 56= 1,2,4,7,8,14,28 and 56.   Factors same in 42 and 56 are 1,2,7 and 14.   Hence, answer will be 4.
Answer: D
The total of 334 of 20 paise and 25 paise make a sum of Rs. 71. The no of 20 paise coins is	Choose the correct choice from the following answers:
A) 250  B) 277  C) 278  D) 200  E) 288

Solution: Explanation:   Let the number of 20 paise coins be x. Then the no of 25 paise coins = (334 - x).   0.20 * (x) + 0.25 (334 - x) = 71 => x = 250..   250nswer: 250) 250
Answer: A
The least number which should be added to 2497 so that the sum is exactly divisible by 5, 6, 4 and 3 is:  Select the correct option:
A) 3	B) 13	C) 23	D) 33	E) 43

Solution: L.C.M of 5, 6, 4 and 3 = 60.   On dividing 2496 by 60, the remainder is 37. Number to be added = 60 - 37= 
60 - 37 = 23
23.   ANSWER:23
Answer: C
The average (arithmetic mean) of four different positive integers is 15. If the first of these integers in 3 times the second integer and the second integer is 2 less than the third integer, what is the least possible value of the fourth integer?
Choose the correct choice.
A) 8
B) 4
C) 3
D) 2
E) 1

Solution: Let the second integer be x and the fourth be a.   Then [3x + x + (x+2) + a]/4 =15   => 5x + 2 + a = 60   => 5x + a = 58   => a = 58 - 5x   From the above equation we can see that a is minimum when x is maximum, provided both are positive   The maximum value that x can take in the above equation while still keeping a positive is x=10   This gives us a= 58 - 50= 
58 - 50 = 8
8   Therefore the minimum value that the fourth integer can have is 8. Option 8.
Answer: A
Country X imported approximately $1.20 billion of goods in 1996. If Country X imported $288 million of goods in the first two months of 1997 and continued to import goods at the same rate for the rest of the year, by how much would Country Xs 1997 imports exceed those of 1996?  Pick one
A) $24 million
B) $120 million
C) $144 million
D) $240 million
E) $528 million

Solution: Convert units to millions as answer is in millions   1996 Imports = $1.20 bill = $1200 mill   i.e. 1200/12 = $100 mill/month   1997 Imports = $288 mill/2 month   i.e. $144 mill/month   Difference/month = 144-100= 
144-100 = 44
44   Difference/year= $44 mill * 12 = $528 mill   ANSW$528 millionR: $528 million
Answer: E
What is the maximum number of pieces of birthday cake of size 2” by 2” that can be cut from a cake 20” by 20”? Choose the most appropriate option.
A) 5	B) 100	C) 16	D) 20	E) 25

Solution: The prompt is essentially asking for the maximum number of 2 x 2 squares that can be cut from a larger 20 by 20 square. Since each 'row' and each 'column' of the larger square can be sub-divided into 10 'pieces' each, we have (10)(10) = 100 total smaller squares (at maximum).   100
Answer: B
How many litres of pure salt are there in 12 litres of a 25% solution?
Choose the correct choice from the following answers:
A) 1.14 litres  B) 1.41 litres  C) 2.56 litres  D) 3 litres  E) 34litres

Solution: Explanation :   Quantity of pure salt = 25% of 12 litres   = (25/10012)litres   = 3 litres   Answer : 3 litres
Answer: D