MU-NLPC/Calc-aqua_rat huggingface dataset:
There are 6 girls and 6 boys. If they are to be seated in a row, what is the probability that no two boys sit together?  Choose the correct choice from the following choices
A) A)1/12!
B) B)6!5!/12!
C) C)6!6!/12!
D) D)2∗6!/12!
E) E)none of these

Solution: If girls are alternate, then only no 2 boys can be together.   So among 12 places, boys can be seated in 6 alternate places in 6! ways.   And girls can be seated in the remaining 6 places in 6! ways.   Therefore total number of ways = 6! * 6!   But there could be 2 such arrangements-->   1. When first place is filled by a girl   2. When first place is filled by a boy   Therefore total number of ways = 2*6! * 6!   Also total number of ways to fill 12 places = 12!   Hence probability =2∗6!6!/12!   Answer:none of these
Answer: E
A restaurant meal cost $38.75 and there was no tax. If the tip was more than 20 percent but less than 25 percent of the cost of the meal, then the total amount paid must have been between Choose the correct choice from the following options:
A) $40 and $42
B) $39 and $41
C) $38 and $40
D) $37 and $39
E) $46 and $48

Solution: The total amount for the meal was between 38.75*1.2= 
38.75*1.2 = 46.5
46.5 and 38.75*1.25=~48.43. Only option which covers all possible values of the meal is E.   Answer: $46 and $48
Answer: E
A cloth, when bleached, was found to have lost 20% of its length and 10% of its breadth. The percentage of decrease in area is: Pick one
A) 20%  B) 25%  C) 28%  D) 30%  E) 35%

Solution: length = x   decrease = xy = 80/100 * 90/100 y   xy - 18/25 xy   =7/25 xy   dec % = 7/25*1/xy*100 = 28   ANSWER 28%
Answer: C
A clothing store originally bought 100 jackets at a total cost of j dollars. If each jacket was sold for 40 percent more than its original cost, what was the individual price, in terms of j, of each jacket sold?	Choices
A) j/140 B) 7j/500 C) 140j D) j/100+40 E) 140j/100

Solution: cost of 100 jackets = j dollars   each jacket costing 40% more is same as   all costing 40% more.   therefore over all price = 1.40j   price for each = 1.40j/100 => 14j/1000=7j/500   ANSWER:7j/500
Answer: B
The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?	Choose the correct choice.
A) 2 B) 4 C) 5 D) 6 E) 7

Solution: 65*(90/100)*((100-x)/100) = 56.16   x = 4%   Answer:4
Answer: B
If P(A) = 2/15, P(B) = 4/15, and P(A âˆª B) = 11/15 Find P(A|B)	Select the correct option.
A) 11/4 B) 2/3 C) 3/2 D) 4/5 E) 4/7

Solution: P(A|B) = P(A âˆª B)/P(B)   P(A|B) = (11/15)/(4/15) = 11/4.   11/4
Answer: A
A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it take 4 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?	Choose the correct choice from the following answers:
A) 1:3 B) 3:8 C) 6:3 D) 8:3 E) None

Solution: Sol.   Let the man rate upstream be x kmph and that downstream be y kmph. Then,   Distance coverd upstream in 8 hrs 48 min. = Distance coverd downstream in 4 hrs.   ⇒ [x 8 4/5] = (y * 4) ⇒ 44/5 x = 4y ⇒ y = 11/5 x.   ∴ Required ratio = [y + x / 2] : [6x / 5 * 1/2] : [6x / 5 * 1/2]   = 8/5 : 3/5 = 8:3.   Answer 8:3
Answer: D
In the coordinate plane, points (x, 1) and (10, y) are on line k. If line k passes through the origin and has slope 1/4, then x + y = Select the correct option:
A) 6.5 B) 7 C) 8 D) 11 E) 12

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 (10, y) = (10,2.5) --> x+y=4+2.5= 
4+2.5 = 6.5
6.5   6.5nswer: 6.5.
Answer: A
If s is the product of the integers from 70 to 80 inclusive, and if t is the product of the integers from 70 to 81 inclusive, what is 1/s + 1/t in terms of t? Choose the correct option
A) 32/t B) 42/t C) 52/t D) 62/2t E) 82/t

Solution: Similarly in the actual problem   s =t/81. 1/s = 1/(t/81) or 1/s = 81/t   1/s + 1/t = 81/t + 1/t = 82/t   82/t
Answer: E
Three candidates contested an election and received 1136, 7636 and 13000 votes respectively. What percentage of the total votes did the winning candidate get?
Choose one.
A) 46%  B) 60%  C) 74%  D) 63%  E) 68%

Solution: 60%   13000/(1136 + 7636 + 13000) = 60%.
Answer: B
In the county of Veenapaniville, there are a total of 50 high schools, of three kinds: 25 public schools, 17 parochial schools, and 8 private independent schools. These 50 schools are divided between three districts: A, B, and C. District A has 18 high schools total. District B has 17 high schools total, and only two of those are private independent schools. If District C has an equal number of each of the three kinds of schools, how many private independent schools are there in District A? Choose one.
A) 1 B) 3 C) 4 D) 5 E) 6

Solution: Total Private Schools = 8   Dist 1: High Schools = 18 ==> Private Schools = ?   Dist B: High Schools = 17 ==> Private Schools = 2   Dist C: High Schools = 15 ==> Private Schools = 5   Therefore, 8 - 2 - 5 ==> 1   1nswer 1)
Answer: A
25 children are going to a picnic. What is the smallest number of cakes that must be brought to the picnic so that each child receives the same number of cakes?	Choose the correct choice from the following answers:  A) 35  B) 40  C) 15  D) 75  E) 9

Solution: The number of children going to the picnic are 25   The answer will be 75 because only 75 is divisible by 25
Answer: D
The average mark of the students of a class in a particular exam is 80. If 5 students whose average mark in that exam is 40 are excluded, the average mark of the remaining will be 90. Find the number of students who wrote the exam. Choose the correct choice
A) 11	B) 23	C) 25	D) 77	E) 81

Solution: Let the number of students who wrote the exam be x.   Total marks of students = 80 x.   Total marks of (x - 5) students = 90(x - 5)   80x - (5 * 40) = 90(x - 5)   250 = 10x => x = 25   Answer: 25
Answer: C
The area of the square formed on the diagonal of a rectangle as its side is 108 1/3 % more than the area of the rectangle. If the perimeter of the rectangle is 28 units, find the difference between the sides of the rectangle?	Choose the most appropriate option:	A) 2	B) 6	C) 7	D) 9	E) 1

Solution: Let the sides of the rectangle be l and b respectively.   From the given data,   (√l2 + b2) = (1 + 108 1/3 %)lb   => l2 + b2 = (1 + 325/3 * 1/100)lb   = (1 + 13/12)lb   = 25/12 lb   => (l2 + b2)/lb = 25/12   12(l2 + b2) = 25lb   Adding 24lb on both sides   12l2 + 12b2 + 24lb = 49lb   12(l2 + b2 + 2lb) = 49lb   but 2(l + b) = 28 => l + b = 14   12(l + b)2 = 49lb   => 12(14)2 = 49lb   => lb = 48   Since l + b = 14, l = 8 and b = 6   l - b = 8 - 6= 
8 - 6 = 2
2m.   2nswer:2
Answer: A
Siddharth wants to borrow Rs.8000 at rate of interest 6% p.a. at S.I and lend the same amount at C.I at same rate of interest for two years. What would be his income in the above transaction?
Pick one: A) s.28.80 B) s.21.29 C) s.22.29 D) s.21.26 E) s.21.12

Solution: Amount of money Siddharth borrowed at S.I at 6% p.a. for two years = Rs.8,000   He lend the same amount for C.I at 6% p.a. for two years.   => Siddharth's income = C.I - S.I   = p[1 + r/ 100]n - p - pnr/100   = p{ [1 + r/ 100]2 - 1 - nr/100   = 8,000{ [1 + 6/100]2 - 1 - 12/100}   = 8,000 {(1.06)2- 1 - 0.12} = 8,000(1.1236 - 1 - 0.12)   = 8,000 (0.0036) = 8 * 3.6 = Rs.28.80   s.28.80nswer: s.28.80
Answer: A
A scale 6 ft. 8 inches long is divided into 4 equal parts. Find the length of each part.	Select:  A) 17 inches  B) 20 inches  C) 15 inches  D) 18 inches  E) None of these

Solution: Explanation:   Total length of scale in inches = (6*12) + 8= 
(6*12) + 8 = 80
80 inches   Length of each of the 4 parts= 80/4= 
80/4 = 20
20 inches   ANSWER 20 inches
Answer: B
A gambler began playing blackjack with $110 in chips. After exactly 12 hands, he left the table with $320 in chips, having won some hands and lost others. Each win earned $100 and each loss cost $10. How many possible outcomes were there for the first 5 hands he played? (For example, won the first hand, lost the second, etc.)  Pick:
A) 10
B) 18
C) 26
D) 32
E) 64

Solution: If X is number of wins and Y num of losses then   100X - 10Y = 210   10X-Y = 21......only when Y = 9 and X = 3 it satisfies....so we have 3 wins and 9 losses.   for first 5, we can have the following:   0 wins 5 losses = 1 way   1 win and 4 losses = 5261 = 5   2 wins and 3 losses = 5262 = 10   3 wins and 2 losses = 5263 = 10   Add total ways = 26 ways   ANSWER:26
Answer: C
. For the FIFA world cup, Paul the octopus has been predicting the winner of each match with amazing success. It is rumored that in a match between 2 teams A and B, Paul picks A with the same probability as A’s chances of winning. Let’s assume such rumors to be true and that in a match between Ghana and Bolivia; Ghana the stronger team has a probability of 2/3 of winning the game. What is the probability that Paul will correctly pick the winner of the Ghana-Bolivia game?  Choose the correct choice from the following.
A) 59  B) 88  C) 77  D) 26  E) 18

Solution: The probability that Paul correctly picks the winner = (59's Chances of winning)x(Pauls picking the winner corectly) + (59's chances of loosing) x (Paul picks wrongly) = 23×23+13×13=59   59nswer:	59
Answer: A
A certain quantity is measured on two different scales, the P-scale and the S-scale, that are related linearly. Measurements on the P-scale of 6 and 24 correspond to measurements on the S-scale of 30 and 60, respectively. What measurement on the P-scale corresponds to a measurement of 100 on the S-scale?	Choose the correct choice from the following choices.
A) 20
B) 36
C) 48
D) 60
E) 84

Solution: First, we have to understand what linearly means. It's not a straight ratio (since 6:30 does NOT equal 24:60). We need to look at the increases in each measurement to see what the scalar actually is.   From 6 to 24 we have an increase of 18. From 30 to 60 we have an increase of 30. Therefore, the increase ratio is 18:30 or 3:5. In other words, for every 3 that P increases, S increases by 5.   We know that S is 100. To get from 60 to 100, we went up by 40, or 8 jumps of 5; therefore, P will go up by 8 jumps of 3.   24 + 8(3) = 24 + 24= 
24 + 24 = 48
48=48
Answer: C
Goods were bought for Rs. 600 and sold the same for Rs. 688.50 at a credit of 9 months and thus gaining 2% The rate of interest per annum is: Select.
A) 6 2/3% B) 6 2/8% C) 6 4/3% D) 8 2/3% E) 2 2/3%

Solution: S.P. = 102% of Rs. 600 = 102	x 600 = Rs. 612.   100   Now, P.W. = Rs. 612 and sum = Rs. 688.50.   T.D. = Rs. (688.50 - 612) = Rs. 76.50.   Thus, S.I. on Rs. 612 for 9 months is Rs. 76.50.   Rate = 100 x 76.50	%	= 16%   612 x	3   4   6 2/3%nswer: 6 2/3%
Answer: A
A man can row at 5 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place?
Choose the correct choice from the following
A) 2.4 km	B) 2.5 km	C) 3 km	D) 3.6 km	E) None

Solution: Solution   Speed downstream = (5 + 1)= 
(5 + 1) = 6
6kmph.   Speed upstream= (5 -1)= 
(5 -1) = 4
4 kmph.   Let the required distance be x km.   Then, x/6 + x/4= 1   = 2x + 3x = 12   ‹=›5x = 12   ‹=›x = 2.4.   2.4 kmnswer 2.4 km
Answer: A
Set A contains three different positive odd integers and four different positive even integers. Set B contains two different positive odd integers and three different positive even integers. If one integer from set A and one integer from set B are chosen at random, what is the probability that the product of the chosen integers is even?
Options:
A) 3/5
B) 7/15
C) 11/15
D) 23/35
E) 29/35

Solution: There can be an odd product only if both integers are odd.   P(odd product) = 3/7*2/5 = 6/35   P(even product) = 1 - 6/35 = 29/35   The answer is 29/35.
Answer: E
For each positive integer,the quantitySn is defined such thatSn+2=(Sn)^2 -S(n+2).in addition ,S2=1.then which of the following must be true.
Pick: A) a)S4 +S3 +1=0 B) b)(S1)^2 +S4 +2=0 C) c) ifS1=-1thenS4 is also equal to-1. D) d) ifS4 =-7thenS1=-2. E) e) ifS1 =-3thenS4=-7

Solution: Since all the answers include S4, let's start from there.   S4=S2^2-S3   S3=S1^2-S2   Substituting S3 into the first equation we get:   S4=S2^2-(S1^2-S2)   Since S2=1   S4=1-(S1^2-1)   S4=2-S1^2   We need S1^2 in order to calculate S4.   E) provides S1 and from there we can calculate S4:   S4=2-(-3)^2   S4=-7   Correct.   As a side note, I would be very careful with answers in the formif S4=x then S1=y(such as option D ), as we are dealing with S1^2 (not S1), S1 can have two different values and it can not be determined for sure which root is the right answer.   For example:   If S4=-7 then S1=3 :   if we substitute S4 with - 7 we get:   -7=2-S1^2   S1^2=9   now S1 can be +/-3 !!   e) ifS1 =-3thenS4=-7
Answer: E
Half the people on a bus get off at each stop after the first, and no one gets on after the first stop. If only one person gets off at stop number 8, how many people got on at the first stop?
Select:  A) 128  B) 64  C) 32  D) 16  E) 8

Solution: 7 - > 1   6 - > 2   5 - > 4   4 - > 8   3 - > 16   2 - > 32   1 - > 64   because people get off after the first stop   => the formula will be : 2^(n-1) where n is the stop number   in this case n = 5   => 2^(8-1) = 2^7 = 128   => answer is 128
Answer: A
Set A contains all the even numbers between 2 and 50 inclusive. Set B contains all the even numbers between 102 and 150 inclusive. What is the difference between the sum of elements of set B and the sum of the elements of set A?  Choose the most appropriate option:
A) 2500 B) 5050 C) 11325 D) 6275 E) 2550

Solution: SET A: {2, 4, 6, 8,...., 50}. Set of first 25 consecutive positive even numbers.   SET B: {102, 104, 106,....., 150}. Another set of 25 consecutive even numbers starting from 102.   Difference between 1st term of set A and that of set B is 100. Difference between 2nd term of set A and that of set B is 100.   Each term in set B is 100 more than the corresponding term in set A.   So sum of the differences of all the terms is (100 + 100 + 100 + ....) = 25 * 100= 
25 * 100 = 2_500
2500.
Answer: A
A and B start a business jointly. A invests Rs.16000 for 8 months and B remains in the business for 4 months. Out of the total profit B claims 2/7th share. How much money is contributed by B?
Choose the correct choice from the following answers
A) 27778
B) 12800
C) 27888
D) 29778
E) 17781

Solution: 16*8: x*4 = 5:2   x = 12.8 => Rs.12800   Answer: 12800
Answer: B
200 hundred multiples of seven are chosen at random, and 500 multiples of eight are chosen at random. Approximately what percentage of the 700 selected numbers are odd?
Choose the correct choice:  A) 14.29%  B) 15.29%  C) 16.29%  D) 17.29%  E) 18.29%

Solution: --> Multiples of 7 are 7, 14, 21, 28, 35, 42....   Out of first 4 multiples, 2 are odd; out of first 6 multiples, 3 are odd.   So approx. 50 % of the 200 multiples are odd i.e 100 multiples.   --> Similalrly, for 8 multiples are:8,16,24...   All are even so 0 % are odd.   Total odd= (100+0)/(200+500)= 100/700=1/7 = 14.29%   14.29%nswer 14.29%
Answer: A
A man can row his boat with the stream at 8 km/h and against the stream in 4 km/h. The man's rate is? Answers
A) 1 kmph	B) 2 kmph	C) 8 kmph	D) 7 kmph	E) 5 kmph

Solution: DS = 8   US = 4   S = ?   S = (8 - 4)/2= 
(8 - 4)/2 = 2
2 kmph   Answer: 2 kmph
Answer: B
A, B and C rents a pasture for Rs.480. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should C pay? Pick:
A) 270 B) 199 C) 676 D) 149 E) 122

Solution: 12*8 :16*9 = 18*6   8: 12: 9   9/29 * 480= 149   Answer: 149
Answer: D
What is the median from the below series 92, 93, 88, 95, 88, 97, 87, and 98
Select.
A) 80
B) 82
C) 92.25
D) 98
E) 100

Solution: Ordering the data from least to greatest, we get:   87, 88, 88,92, 93, 95, 96, 98   The median quiz score was 92.25 (Four quiz scores were higher than 92.25 and four were lower.)   92.25
Answer: C
What is the prime factors’ number of 18?
Select the correct option
A) 2
B) 3
C) 4
D) 5
E) 6

Solution: prime factors’ number, as I assume, for a number X=a^n*b^m*c^o*d^p... is = n+m+o+p...   So, 24 = 2^1*3^2   prime factors’ number will be 1+2= 
1+2 = 3
3.   Hence, answer is 3.
Answer: B
A 30% solution of barium chloride is mixed with 10 grams of water to form a 20% solution. How many grams of original solution did we start with ?
I am trained to complete above problem as per following technique. Is it possible to solve in following manner.
30%_________100%
______20%
ratio is 100-20 : 20-30, which is wrong. There should not be 20. Instead, value in the middle should be in between 30% to 100%. Answers
A) 10	B) 15	C) 20	D) 25	E) 30

Solution: We're told that 10g of water are mixed with an unknown amount of 30% barium mixture to form a 20% barium final mixture. We're asked to figure out how much barium mixture we have....   Logically, if we had 10g of water mixed with 10g of barium mixture, we'd end up with a 15% overall mixture, so 10 is NOT the answer. We need MORE barium mixture to raise the final mixture up to 20%. Since the numbers in the prompt are allroundnumbers, it's highly likely that the correct answer will ALSO be a round number....   Let's TEST Answer C = 20g   (20g of barium mixture)(30% barium) = 6g barium   + 10g water.....   (6g barium)/(30g total liquid) = .2 = 20% final barium mixture.   So, the initial barium mixture MUST be 20g   ANSWER 20
Answer: C
Find the greatest number that will divide 205, 626 and 588 leaving 5, 6 and 8 as remainders respectively	Choices.
A) 19
B) 17
C) 13
D) 9
E) 20

Solution: 20xplanation:   Answer will be HCF of (205-5, 626-6, 588-8)   HCF of (200, 626, 580) = 20   Option 20
Answer: E
30 binders can bind 1400 books in 21 days. How many binders will be required to bind 1600 books in 20 days?
Choose the correct choice:  A) 87  B) 18  C) 17  D) 36  E) 10

Solution: Binders Books 36ays   30 1400 21   x 1600 20   x/30 = (1600/1400) * (21/20) => x = 36   Answer:36
Answer: D
A person purchased a TV set for Rs. 2000 and a DVD player for Rs. 1500. He sold both the items together for Rs. 4000. What percentage of profit did he make?
Choose the correct choice from the following choices.
A) 14.28% B) 1.20% C) 15.21% D) 14.20% E) 10.32%

Solution: The total CP = Rs. 2000 + Rs. 1500   = Rs. 3500 and SP = Rs. 31150   Profit(%) = (4000 - 3500)/3500 * 100   = 14.28%   14.28%nswer: 14.28%
Answer: A
A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 20%? Choose the correct choice from the following options.
A) 600
B) 299
C) 797
D) 179
E) 642

Solution: Cost price = Rs.500   profit = 20% of 500 = Rs.100   Selling price = Cost price + Profit   = 500 + 100= 
500 + 100 = 600
600   600nswer:600
Answer: A
A city with a population of 97,500 is to be divided into 6 voting districts, and no district is to have a population that is more than 10 percent greater than the population of any other district. What is the minimum possible population that the least populated district could have?	Choose one:
A) 15,000
B) 15,500
C) 16,000
D) 16,500
E) 17,000

Solution: The minimum possible population occurs when all the other districts have a population that is 10% greater than the least populated district.   Let p be the population of the least populated district.   Then 97,500 = p + 5(1.1)p   6.5p=97,5000   p = 15,000   The answer is 15,000.
Answer: A
Hillary and Tenzing are climbing to the summit of Mt. Everest from a base camp 4,800 ft from the summit. When they depart for the summit at 06:00, Hillary climbs at a rate of 800 ft/hr with Tenzing lagging behind at a slower rate of 500 ft/hr. If Hillary stops 800 ft short of the summit and then descends at a rate of 1,000 ft/hr, at what time do Hillary and Tenzing pass each other on her return trip? Select the correct option:
A) 12.0
B) 11.0
C) 10.0
D) 13.0
E) 14.0

Solution: Solution:H stopped 800 ft before reaching the final point, time taken to reach 4000 ft= 4000/800= 
4000/800 = 5
5hrs.   this means she reached there at 11:00.   speed difference between them is 800-500= 
800-500 = 300
300 ft/hr   so by the time H stops they have 1500 ft of distance   so now here we use relative speed formula they both are travelling toward each other with speed of 1000 and 500 total 1500 ft/hr and distance between them is 1500 ft so time taken to meet= 1 hr from 11:00   means 12:00 is the answer.   12.0
Answer: A
In a BCCI meeting there are 12 people. All shake hands with each other once. How many handshakes will be there altogether?	Options:
A) 28 B) 11 C) 12 D) 19 E) 18

Solution: There will be n-1 handshakes as A person will shake hands with all the other members.   =12-1= 
12-1 = 11
11   Answer:11
Answer: B
If a and b are positive integers, and a=4b+16, the greatest common divisor of a and b CANNOT be Select.
A) 2 B) 9 C) 4 D) 8 E) 16

Solution: If b is 2, 4, 8, or 16, then GCD of a and b is 2, 4, 8, and 16 respectively. So, by POE the answer must be B.   Still: if b is a multiple of 9, then a is 16 greater than a multiple of 9, so not a multiple of 9, so both of them cannot be divisive by 9.   Answer: 9.
Answer: B
Find the 21th term of an arithmetic progression whose first term is 3 and the common difference is 5.  Choices:  A) 100  B) 102  C) 103  D) 150  E) 46

Solution: n th term of A.P = a +(n-1) *d   = 3+(21-1)*5 , = 3 + 100= 
3 + 100 = 103
103.   ANSWER:103
Answer: C
What is the next number of the following sequence
7,0,1,8,5,12,9,2,6,3,2,?	Choose the correct option:
A) 4
B) 5
C) 6
D) 7
E) 8

Solution: sum of alternate terms is same i.e:   ( 7,0,1,8)= 7+1= 
7+1 = 8
8 & 0+8= 
0+8 = 8
8   (5,12,9,2)=5+9= 
5+9 = 14
14 & 12+2= 
12+2 = 14
14   likewise ( 6,3,2,x)= since 6+2= 
6+2 = 8
8 , so 3+x=8,   hence x=5   ANSWER:5
Answer: B
Complete the numerical sequence by replacing the question mark with the correct numbers.
5+3+2 = 151022
9+2+4 = 183652
8+6+3 = 482466
5+4+5 = 202541
9+5+5 = ?????? Options.
A) 3	B) 588447	C) 845668	D) 454585	E) 544586

Solution: Series if formed as (a*b)(b*c)(c*a)   (9*5)(9*5)(9*5+9*5-5) => 454585   the number we take is 454585   Correct answer is: 454585)454585
Answer: D
One man selling a lottery there are 10 prizes and 25 no prizes. if a lottery is drawn randomly, What is the probability of getting a prize?
Choices:	A) 1/5	B) 2/7	C) 2/9	D) 3/11	E) 4/11

Solution: P (getting a prize) =	10	=	10	=	2/7   (10 + 25)	35   2/7
Answer: B
What least number should be subtracted from 642 so that the remainder when divided by 5, 7, and 9 will leave in each case the same remainder 4 ?  Pick:
A) 5  B) 6  C) 8  D) 9  E) 10

Solution: The LCM of 5, 7, and 9 is 315. The next multiple is  2*315= 
 2*315 = 630
630.   630 + {remainder}= 630 + 4= 
630 + 4 = 634
634, which is 8 less than 642.   Answer: 8.
Answer: C
If in a certain code "RANGE" is coded as 12345 and "RANDOM" is coded as 123678. Then the code for the word
"RAM" would be
Options:  A) 312  B) 128  C) 632  D) 122  E) 156

Solution: R-1   A-2   M-8   so for mango the code is 128   ANSWER:128
Answer: B
If 123xy is divisible by 40, then the value in place of x+y is :  Choose the correct choice from the following answers:
A) 1  B) 7  C) 4  D) 3  E) 9

Solution: 123xy     1 + 0= 
  1 + 0 = 1
1/4 ≠ 40   7 + 0= 70/4 ≠ 40   4 + 0 = 40/4= 
40/4 = 10
10   Answer: 4
Answer: C
In a sample of associates at a law firm, 25 percent are second-year associates, and 75 percent are not first-year associates. What percentage of the associates at the law firm have been there for more than two years?	Choose the correct choice from the following answers
A) 0  B) 25  C) 50  D) 75  E) 100

Solution: 75 percent are not first-year associates --> This means 75 percent associates are either two or more than two years   Already, we know % of second-year associates = 25 %   So, % of associates there for more than two years = 75 % - 25 % = 50 % .. => (C).. Is it correct ?
Answer: C