MU-NLPC/Calc-aqua_rat huggingface dataset:
Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?  Pick one
A) 457 km	B) 444 km	C) 547 km	D) 645 km	E) 453 km

Solution: 1h ----- 5   ? ------ 60   12 h   RS = 16 + 21= 
16 + 21 = 37
37   T= 12   D = 37 * 12= 
37 * 12 = 444
444   Answer:444 km
Answer: B
5 nouns, 5 verbs and 3 adjectives are written on blackboard.we can form sentence by choosing 1 from each available set without caring it makes sense or not.what is the number of ways of doing this??	Choose the correct choice from the following answers.
A) 360	B) 390	C) 420	D) 450	E) 540

Solution: we have to choose one from each set. 1 from 5 nouns and 1 from 5 verbs and 1 from 3 adjectives.   then we have to arrange 3 different sets in 3! ways.   so,   5c1*5c1*3c1*3!=450   ANSWER:450
Answer: D
The factorial expression 25!/15! is not divisible by which of the following integers?	Choose the correct choice from the following options
A) 31 B) 12 C) 16 D) 17 E) 19

Solution: 25!/15! => 25 x 24 x 23 x 22 x 21 x 20 x 19 x 18 x 17 x 16   (31) 31 None of the Multiplicands present   (B) 12 Can divide 24   (C) 16 Can divide 16   (D) 17 Can divide 17   (E) 19 Can divide 19   Hence answer will be (31)
Answer: A
0.002 x 0.6 = ?  Options:
A) 0.0012	B) 0.001	C) 0.01	D) 0.1	E) NONE OF THESE

Solution: Explanation:   2 x 6 = 12.   Sum of decimal places = 4   0.002 x 0.6 = 0.0012   0.0012nswer- 0.0012
Answer: A
Kate and her boyfriend Ben, completed the painting of their new apartment together in 6 days.If they were to work separately, how long will it take each of them to complete it, if Ben can complete the painting 5 days earlier than Kate.
Answers: A) 6 and 11 B) 5 and 10 C) 10 and 15 D) 8 and 13 E) 6 and 10

Solution: Work = (A)(B)/(A+B) where A and B are the individual times of each entity.   Here, we're told that (working together) the two workers would complete a job in 12 days. This means that (individually) each of them would take MORE than 10 days to do the job.   Answers E, A and C are illogical, since the individual times must both be greater than 10 days.   so we can TEST the values for Answers B and D.   Using the values for Answers C and D...   Answer 10 and 15: (10)(15)/(10+15) = 150/25= 
150/25 = 6
6 This is a match   Final Answer:   10 and 15
Answer: C
A man walks at a speed of 3 km/hr and runs at a speed of 6 km/hr. How much time will the man require to cover a distance of 12 km, if he completes half of the distance, i.e., (6) km on foot and the other half by running?  Select the correct option:  A) 2.6  B) 2.2  C) 2.5  D) 2  E) 3

Solution: Required time = (6)/3 + (6)/6= 
(6)/3 + (6)/6 = 3
3 hours.   Answer:3
Answer: E
Josh spends a total of $5.00 buying N items in the convenience store. If each of the items is either a 5 cents single bubblegum, or a 50 cents bubblegum pack, then N may be which of the following? Choose the most appropriate option.
A) 91  B) 100  C) 101  D) 109  E) 140

Solution: Let x be 0.05$ single bubblegum and y be the total 0.5$ packs ---> 0.05x+0.5y=5.0 ---> x+10y=100 ...(1)   Also, x+y=N ...(2)   Solving 1 and 2 , we get, N = 110-9y ---> only value satisfied is when y = 1---> N = 100-9= 
100-9 = 91
91.   A is the correct answer. Other options are not equal to multiples of 9 removed from 100.
Answer: A
If a certain number is divided by 11, the quotient, dividend, and divisor, added together, will amount to 71. What is the number?	Choose the correct choice from the following answers:	A) 18	B) 28	C) 48	D) 38	E) 55

Solution: Let x = the number sought.   Then x/11 + x + 11 = 71   And x = 55.   55
Answer: E
Three small cruise ships, each carrying 6 passengers, will dock tomorrow. One ship will dock at Port A, another at Port B, and the third at Port C. At Port A, two passengers will be selected at random and each winner will receive one gift certificate worth $50. At Port B, one passenger will be selected at random to receive a gift certificate worth $35, and at Port C, one passenger will be selected at random to receive a gift certificate worth $25. How many different ways can the gift certificates be given out?
Choose the correct choice from the following answers.
A) 1520 B) 2260 C) 2870 D) 3240 E) 4590

Solution: The number of ways for the ships to go to the ports is 3! = 6.   At Port A, the number of ways to choose two winners is 6C2 = 15.   At Port B, the number of ways to choose one winner is 6.   At Port C, the number of ways to choose one winner is 6.   The total number of ways to give out gift certificates is  6*15*6*6= 
 6*15*6*6 = 3_240
3240   The answer is 3240.
Answer: D
The average salary of a person for the months of January, February, March and April is Rs.8000 and that for the months February, March, April and May is Rs.8500. If his salary for the month of May is Rs.6500, find his salary for the month of January?	Choose the correct choice from the following answers.
A) Rs.4580
B) Rs.4570
C) Rs.4500
D) Rs.4550
E) Rs.2500

Solution: Sum of the salaries of the person for the months of January, February, March and April   = 4 * 8000= 
4 * 8000 = 32_000
32000 ----(1)   Sum of the salaries of the person for the months of February, March, April and May= 4 * 8500= 
4 * 8500 = 34_000
34000 ----(2)   (2)-(1) i.e. May - Jan= 2000   Salary of May is Rs.6500   Salary of January = Rs.4500   Answer:Rs.4500
Answer: C
Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is?
Select the correct option:
A) 18 sec	B) 17 sec	C) 48 sec	D) 19 sec	E) 12 sec

Solution: Relative speed = 60 + 90= 
60 + 90 = 150
150 km/hr.= 150 * 5/18 = 125/3 m/sec.   Distance covered = 1.10 + 0.9= 
1.10 + 0.9 = 2
2 km= 2000 m.   Required time = 2000 * 3/125= 
2000 * 3/125 = 48
48 sec.   Answer: 48 sec
Answer: C
A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio of revenue from car sales in 1996 to revenue from truck sales in 1996?
Pick one:
A) 1:2 B) 4:5 C) 1:1 D) 3:2 E) 5:3

Solution: A.. I have probably solved this question 3-4 times by now.. Remember the answer.. 1:2
Answer: A
How many numbers between 200 and 600 are divisible by 4,5 and 6?  Select:
A) 5
B) 6
C) 7
D) 8
E) 9

Solution: Solution   Every such number must be divisible by L.C.M of 4,5,6 i.e, 60.   Such numbers are 240,300,360,420,480,540.   Clearly, there are 6 such numbers.   Answer 6
Answer: B
David bought 4 toys with the average cost of $8. If David also buys the fifth toy with the price of $ 10, what is the average (arithmetic mean) price of those 5 toys?	Choose one:
A) $5	B) $6	C) $8.4	D) $10	E) $11

Solution: 4 toys -> Total cost = 4 * Avg cost = 4*8= 
4*8 = 32
32   Fifth toy cost= 10   Total cost for 5 toys= 32+10= 
32+10 = 42
42   AM= 42/5= 
42/5 = 42/5 = around 8.4
8.4   Hence $8.4
Answer: C
Wanda baked 168 cookies, packaged them in boxes of 12, and sold each box for
$1.20.How many boxes of 12 can be packaged if there are 168 cookies?What was
the total amount of money that Wanda made for all of the boxes sold?	Choose the correct choice:
A) $26.80  B) $36.80  C) $46.80  D) $76.80  E) $16.80

Solution: Divide 168 ÷ 12 = 14   Multiply $1.20 x 14 = $16.80   correct answer $16.80
Answer: E
A work can be finished in 16 days by twenty women. The same work can be finished in fifteen days by sixteen men. The ratio between the capacity of a man and a woman is Choose the correct choice from the following.
A) 4:3	B) 3:4	C) 2:3	D) 3:2	E) 4:5

Solution: Work done by 20 women in 1 day = 1/16   Work done by 1 woman in 1 day = 1/(16×20)   Work done by 16 men in 1 day = 1/15   Work done by 1 man in 1 day = 1/(15×16)   Ratio of the capacity of a man and woman =1/(15×16) : 1/(16×20) = 1/15 : 1/20   = 1/3 :1/4 = 4:3   4:3nswer is 4:3.
Answer: A
The diagonal of a rhombus are 40 m and 30 m. Its area is:	Answers:	A) 600	B) 450	C) 350	D) 500	E) 620

Solution: 600rea of the rhombus = 1/2 d1d2 = ( 1/2 Ã— 40 Ã— 30) Cm(power)2   = 40 Ã— 15 = 600 Cm(power)2   600nswer is 600.
Answer: A
If C.P. of 27 books is equal to S.P of 30 books , then your gain or loss is ? Pick:
A) 23 1/3 gain %	B) 30 10/23 loss %	C) 10% loss %	D) 30 1/3 loss %	E) 40 1/3 loss %

Solution: Say the cost price of 27 books is $27 so $1 for a book.   The cost of 30 books would be $30, and the selling price of 30 books would be 27$, hence the loss = ($30 - $27)/$30 = 10%.   Answer: 10% loss %.
Answer: C
Of the five numbers in a sequence, the first term is 20,000, and each of the following terms is 20% of the previous term. What is the value range of the five numbers?
Choose the correct answer:  A) 9,375  B) 9,750  C) 9,975  D) 9,984  E) 19,968

Solution: 1st number= 20,000   2nd number = 20% of 20,000= 4000   3rd number= 20% of 4000= 800   4th number = 20% of 800= 160   5th number= 20% of 160= 32   Range = 20,000-32= 19968   19,968 is the answer
Answer: E
What quantity of water should taken out to concentrate 24 liters of 40% acidic liquid to 60% acidic liquid?	Choose the correct choice from the following answers
A) 5liters
B) 10liters
C) 15liters
D) 8liters
E) 6liters

Solution: Required answer is = 24(60-40)/60 = 8 liters   Answer is 8liters
Answer: D
Jane makes toy bears. When she works with an assistant, she makes 90 percent more bears per week and works 10 percent fewer hours each week. Having an assistant increases Jane’s output of toy bears per hour by what percent?
Choose one.
A) 20% B) 80% C) 100% D) 120% E) 200%

Solution: We can use fractional equivalents here to solve the problem   80% = 4/5; this means that in 1st case if she prepares 5 bears, in 2nd case she prepares 9 bears   10% = 1/10; this means that in 1st case if she needs 10 hours, in 2nd case she needs 9 hours   Now we come to productivity   Based on above fractional values the productivity in 1st case is 0.5 bears / hour and in the 2nd case it is 1 bear / hour   Hence the productivity is double with the assistant i.e. the increase in productivity is 120%   120%
Answer: D
If r = 199,999 and s = 991,999, which of the following is the units digit of r^4 + s^3?
Pick.
A) 0  B) 1  C) 2  D) 8  E) 9

Solution: The exponents of 9 cycle between 9 (odd exponents) and 1 (even exponents).   Then the sum of r^4+s^3 will have the units digit of 1+9= 
1+9 = 10
10 as a units digit.   The answer is 0.
Answer: A
If a boat goes 4km upstream in 12 minutes and the speed of the stream is 8 kmph, then the speed of the boat in still water is ?
Choose the correct answer.
A) 28  B) 29  C) 30  D) 31  E) 32

Solution: Rate upsteram =(4/12*60)= 
(4/12*60) = 20
20kmph.   speed of the stream=8kmph let speed in still water be xkm/hr. then speed upstream=(x-8)km/hr. x-8=20==>x=28km/hr 28nswer(28)
Answer: A
A candidate got 35% of the votes polled and he lost to his rival by 2460 votes. How many votes were cast?
Choose the most appropriate option:
A) 7500	B) 3388	C) 2665	D) 8200	E) 2661

Solution: 35%-----------L   65%-----------W   ------------------   30%----------2460   100%---------? => 8200   Answer: 8200
Answer: D
19 people are there, they are shaking hands together, how many hand shakes possible,if they are in pair of cyclic sequence.  Choose the correct choice from the following answers:  A) 19  B) 20  C) 21  D) 22  E) 23

Solution: in case of cycle no of handshakes = no of persons   hence ans = 19   19NSWER:19
Answer: A
Last year Sandy saved 6% of her annual salary. This year, she made 10% more money than last year, and she saved 10% of her salary. The amount saved this year was what percent of the amount she saved last year?
Options
A) 133%  B) 145%  C) 158%  D) 170%  E) 183%

Solution: Let last year's salary be x.   Last year, Sandy save 0.06x   This year, Sandy saved  0.1*1.1= 
 0.1*1.1 = 0.11
0.11x   0.11x / 0.06x= 11/6 = 1.83 = 183%   The answer is 183%.
Answer: E
The probability that a number selected at random from the first 50 natural numbers is a composite number is ? Answers:
A) 17/29
B) 17/25
C) 17/265
D) 17/252
E) 17/21

Solution: The number of exhaustive events = ⁵⁰C₁ = 50.   We have 15 primes from 1 to 50.   Number of favourable cases are 34.   Required probability = 34/50 = 17/25.   Answer: 17/25
Answer: B
A woman put $580 into a savings account for one year. The rate of interest on the account was 6½%. How much was the interest for the year in dollars and cents? (Round to the nearest cent)	Choose the most appropriate option.
A) $37.70
B) $47.70
C) $57.70
D) $67.70
E) $77.70

Solution: we have   6 1/2/100=x/580   Multiply the opposites:   6 ½ x 580 = 3770   we take   37.70/3770 .00   100   $37.70   correct answer $37.70
Answer: A
If x/y = 3 and (2a - x)/(5b - y) = 3, then the value of a/b is?
Choose the correct choice from the following answers:  A) 15/2  B) -2  C) 1  D) 2  E) 3

Solution: x = 3y   2a - 3y = 3(5b - y)   2a - 3y = 15b - 3y   2a = 15b   a/b = 15/2   15/2nswer: 15/2
Answer: A
The labeled price of a table is Rs. 7,000. The shopkeeper sold it by giving 5% discount on the labeled price and earned a profit of 15%. What approximately is the cost price of the table? Choose the correct choice.
A) Rs. 5782
B) Rs. 6195
C) Rs. 6650
D) Rs. 7200
E) None of these

Solution: Explanation:   Labeled price = Rs. 7,000   By giving 5% discount on labeled price, the selling price is   = 95 / 100 * 7000 = Rs. 6650   By earning 15% profit on the selling of price Rs. 6650 the cost price is   = 100 / 115 * 6650 = Rs. 5782   Therefore, approximate cost is 5782   Rs. 5782NSWER Rs. 5782
Answer: A
There are 18 students in a class. On the day the test was given, Alice was absent. The other 17 students took the test and their average was 78. The next day, Alice took the test, and with this grade included, the new average was 79. What was Alice's grade on the test?	Choose the correct choice from the following answers:
A) 96  B) 95  C) 94  D) 93  E) 92

Solution: 17*78+Alice's grade=18*79   Alice's grade is   18*79-17*78= 
  18*79-17*78 = 96
96.   The answer is 96.
Answer: A
The difference of two numbers is 1097. On dividing the larger number by the smaller, we get 10 as quotient and the 17 as remainder. What is the smaller number ?  Choose one.
A) 230
B) 120
C) 95
D) 310
E) 320

Solution: Solution: Let the smaller number be x. Then larger number = (x + 1097) x + 1097 = 10x + 17 9x = 1080 x = 120   Answer 120
Answer: B
If 0.3 of a number is equal to 0.06 of another number, the ratio of the numbers i
Options:
A) 3 : 15  B) 1 : 2  C) 3 : 20  D) 20 : 3  E) None

Solution: Sol.   0.3A = 0.06 B â‡” A / B = 0.06 / 0.30 = 6/30 = 3/15.   âˆ´ A : B = 3 : 15.   3 : 15nswer 3 : 15
Answer: A
Y can do a work in 2/3 the time it takes X. Z can do the same work in ¾ the time it takes Y.When all three are typing at the same time what fraction of their total work does Y do	Choose the correct choice from the following answers
A) 1/3	B) 4/13	C) 9/23	D) 8/29	E) 9/29

Solution: given the ratio of the time of y and x is 2/3 : 1   therefore the ratio of speed of the x and y becomes 2 : 3.   similarly the ratio of the speed of the z and y given as 4 : 3   therefore the speed of the y and z becomes 3 : 4.   now , comparing the ratio of the x,y and z   it becomes 2: 3 :: 3 : 4   hence the y is doing 3/9 hence it is doing 1/3 work.   1/3NSWER:1/3
Answer: A
An amusement park charges $8 for an adults' ticket, and $6 for a children's ticket. On a certain day, a total of 150 tickets were sold for a total cost of $1020. How many more children's tickets were sold than adults' tickets?  Pick one.
A) 30
B) 50
C) 80
D) 90
E) 120

Solution: ChildCount = ?   AdultCount = ?   TotalCount = 150   ChildAdmission = $6   AdultAdmission = $8   TotalAdmission = $1020   a) TotalCount = AdultCount + ChildCount   b) TotalAdmission = ( ChildAdmission * ChildCount) + (AdultAdmission * AdultCount)   Solve for a) for ChildCount = TotalCount - AdultCount   Substitute into b) :   TotalAdmission = (ChildAdmission * (TotalCount - AdultCount)) + (AdultAdmission * AdultCount)   => AdultCount = (TotalAdmission - (ChildAdmission * TotalCount)) / (AdultAdmission - ChildAdmission)   So, AdultCount = 60   and ChildCount = 90   So the difference is 30 more children then adults   A. 30
Answer: A
40 percent of the members of a study group are women, and 20 percent of those women are lawyers. If one member of the study group is to be selected at random, what is the probability that the member selected is a woman lawyer? Choose the correct choice from the following choices.
A) 0.2 B) 0.08 C) 0.16 D) 0.14 E) 0.15

Solution: Say there are 100 people in that group, then there would be 0.4*0.20*100= 
0.4*0.20*100 = 8
8 women lawyers, which means that the probability that the member selected is a woman lawyer is favorable/total=8/100.   Answer: 0.08
Answer: B
The C.P of 15 books is equal to the S.P of 18 books. Find his gain% or loss%?  Choose the correct choice from the following answers.
A) 16 2/3%
B) 16 2/7%
C) 16 0/3%
D) 18 2/3%
E) 26 2/3%

Solution: 15 CP = 18 SP   18 --- 3 CP loss   100 --- ? => 16 2/3% loss   16 2/3%nswer: 16 2/3%
Answer: A
Six 6 faced dice are thrown together. The probability that all the three show the same number on them is? Pick:
A) 1/32 B) 1/7776 C) 1/33 D) 1/38 E) 1/34

Solution: The three dice can fall in 6 * 6 * 6 * 6 * 6 * 6= 
6 * 6 * 6 * 6 * 6 * 6 = 46_656
46656 ways.   Hence the probability is 6/46656= 1/7776   Answer: 1/7776
Answer: B
power windows: 60%
anti-lock brakes: 25%
CD player: 50%
The table above shows the number of vehicles at Bill's car dealership that have certain features. No vehicle has all three features, but 10% have power windows and anti-lock brakes, 15% have anti-lock brakes and a CD player, and 22% have power windows and a CD player. What percent of the vehicles at Bill's car dealership have a CD player but no power windows or anti-lock brakes?
Choose one:	A) 25	B) 18	C) 11	D) 13	E) 0

Solution: Answer: D   Were looking for the number of cars with a CD player but no other features. We know that 40% of the cars have a CD player, 15% have a CD player and anti-lock brakes, while 22% have a CD player and power windows. Since no car has all three features, those account for all of the possibilities except for what were looking for.   If a car has a CD player, it must either have anti-lock brakes, power windows, or no other features. Since the total of cars with a C13 player is 50%, we can set up the following equation:   50=15+22+x   x=13, choice13.
Answer: D
If x^4 + y^4 = 300, then the greatest possible value of x is between:	Choose the correct choice from the following answers: A) 2 to 3 B) 5 to 7 C) 3 to 5 D) 6 to 8 E) 10 to 12

Solution: The answers to this question provide a great 'hint' as to how to go about solving it; since they're all essentially 'ranges', you can use them to figure out which solution contains the maximum value of X.   We're told that X^4 + Y^4 = 300. To maximize the value of X, we need to minimize the value of Y^4. The smallest that Y^4 could be is 0 (when Y = 0), so we'll have....   4^4 = 256   Looking at the answers, it makes sense to see what 4^4 equals....   4^4 = 256   Since that is BELOW 300, and 6^4 will clearly be MORE than 300, we have the correct answer.   Final Answer:   3 to 5
Answer: C
Series T is a sequence of numbers where each term after the first term is x greater than the term that precedes it. If the sum of the first and last terms of series T is 14, then what is the sum of the first three terms of series T and the last three terms of series T?	Options.
A) -7	B) 7	C) 14	D) 42	E) 84

Solution: Since no information is given about the first term, x, and anything else,   assume first term = 1; hence last term = 13,   so, 1 3 5 7 9 11 13 will suffice the series in which x = 2, from here answer is 42   also, 1 2 3 4 5 6 7 8 9 10 11 12 13 also suffices, where x = 1, from which the answer is again 42   ANSWER:42
Answer: D
A train with a length of 100 meters, is traveling at a speed of 72 km/hr. The train enters a tunnel 1.7 km long. How many minutes does it take the train to pass through the tunnel from the moment the front enters to the moment the rear emerges? Pick one
A) 0.9
B) 1.2
C) 1.5
D) 1.8
E) 2.1

Solution: 72 km/hr = 1.2 km/min   The total distance is 1.8 km.   1.8 / 1.2= 
1.8 / 1.2 = 1.5
1.5 minutes   The answer is 1.5.
Answer: C
If in a race of 130m, A covers the distance in 20 seconds and B in 25 seconds, then A beats B by:
Choose the correct choice from the following options:
A) 20m
B) 26m
C) 11m
D) 10m
E) 15m

Solution: Explanation:   The difference in the timing of A and B is 5 seconds. Hence, A beats B by 5 seconds.   The distance covered by B in 5 seconds = (130 * 5) / 25= 
(130 * 5) / 25 = 26
26m   Hence, A beats B by 26m.   ANSWER 26m
Answer: B
There are between 130 and 140 cards in a collection of cards. If they are counted out 3 at a time, there are 2 left over, but if they are counted out 4 at a time, there is 1 left over. How many cards are in the collection?	Select the correct option:  A) 131  B) 133  C) 135  D) 137  E) 139

Solution: The numbers with the form 4n+1 are 133 and 137.   Only 137 has the form 3k+2.   The answer is 137.
Answer: D
The incomes of two persons A and B are in the ratio 3:4. If each saves Rs.100 per month, the ratio of their expenditures is 1:2 . Find their incomes?
Choose one:
A) 827,988  B) 146,788  C) 150,200  D) 154,863  E) 154,983

Solution: The incomes of A and B be 3P and 4P.   Expenditures = Income - Savings   (3P - 100) and (4P - 100)   The ratio of their expenditure = 1:2   (3P - 100):(4P - 100) = 1:2   2P = 100 => P = 50   Their incomes = 150, 200   Answer:150,200
Answer: C
A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 48 years now, the son's age five years back was: Pick
A) 14 B) 17 C) 19 D) 22 E) 24

Solution: Let the son's present age be x years. Then, (48 - x) = x   2x = 48.   x = 24.   Son's age 5 years back (24 - 5)= 
(24 - 5) = 19
19 years.   answer :19
Answer: C
A can give B 100 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race?  Choices: A) 111.12 m B) 119.12 m C) 111.13 m D) 121.12 m E) 111.52 m

Solution: A runs 1000 m while B runs 900 m and C runs 800 m.   The number of meters that C runs when B runs 1000 m,   = (1000 * 800)/900 = 8000/9 = 888.88 m.   B can give C = 1000 - 888.88= 
1000 - 888.88 = 111.12
111.12 m.   111.12 mnswer:111.12 m
Answer: A
If x is equal to the sum of the even integers from 40 to 60 inclusive, and y is the number of even integers from 40 to 60 inclusive, what is the value of x+y?	Select:
A) 550
B) 551
C) 560
D) x+y=561
E) 572

Solution: sum of even integers = even number ( x is even)   number of even integers =11 ( y is odd )   so x+y = odd   A, C, E out ( all even)   Left with B and x+y=561 :551, 561   If you have ever added even numbers you see that the pattern is 0,2,4,6,8 and   2+4+6+8= 
  2+4+6+8 = 20
20   { there are 11 integers 5 in the 40's , 5 in the 50's and 60 , so when u add the u get  200+250+20+20+60= 
 200+250+20+20+60 = 550
550}   hence the sum is 550 ( x=550) or x+y cannot be 551 since x =550   hence answer is x+y=561
Answer: D
In a bag there are coins of 50 paisa, 25 paisa and one rupee in the proportion 2:3:5. If there are in all Rs.40.50, the number of 50 paisa coins is?
Options:  A) 18  B) 16  C) 12  D) 24  E) 36

Solution: 2x 3x 5x   50 25 100   100x + 75x + 500x = 4050   675x = 4050   x = 6 => 2x = 12   Answer: 12
Answer: C
If each participant of a chess tournament plays exactly one game with each of the remaining participants, then 105 games will be played during the tournament. Find the number of participants. Choose the correct option.
A) 15
B) 16
C) 17
D) 18
E) 19

Solution: Let P be the number of participants.   PC2 = 105   (P)(P-1) = 210 = 15*14   P = 15   The answer is 15.
Answer: A