MU-NLPC/Calc-aqua_rat huggingface dataset:
Q-1) Of the 84 parents who attended a meeting at a
school, 35 volunteered to supervise children during
the school picnic and 11 volunteered both to supervise
children during the picnic and to bring refreshments to
the picnic. If the number of parents who volunteered
to bring refreshments was 2 times the number of
parents who neither volunteered to supervise children
during the picnic nor volunteered to bring
refreshments, how many of the parents volunteered to
bring refreshments?	Choose one.
A) 25 B) 40 C) 38 D) 42 E) 45

Solution: i used the following formula: total = group1 + group2 + neither - both   using the information from the question stem, we have:   84 total people   35 who supervise (group1)   x who neither supervise nor bring refreshments   2 x people who bring refreshments (group2)   11 who supervise AND bring refreshments (both)   therefore...   84 = 35 + 2x + x - 11   solving, we get x = 20   since we want the value of those who bring refreshments AND supervise:   2(20) = 40   answer is 40
Answer: B
A fruit seller had some mangoes. He sells 30% mangoes and still has 280 mangoes. Find the number of mangoes he had. Choose one
A) 588 mangoes
B) 400 mangoes
C) 672 mangoes
D) 700 mangoes
E) None of these

Solution: Explanation:   Suppose originally he had X mangoes.   Then, (100 – 30)% of X = 280   70/100 * X = 280   X = (280 * 100) / 70= 
(280 * 100) / 70 = 400
400   ANSWER: 400 mangoes
Answer: B
Rahul can finish one-fifth of hhis homework in one hour.Neha can finish three-seventh of her homework in one hout thirty minutes and riya can finish three fourth of her homework in three hours thirty minutes.If all of them start their homework at 12:00pm and can go to play as soon as they all finish their homework,when can they start to play,if they take a break at 3:30pm for thirty minutes? Choose the correct choice from the following choices.
A) 5.00pm	B) 5:30pm	C) 4.40pm	D) 6.30pm	E) 3.30pm

Solution: Let the work be 1   Then Rahul do 1/5 work in 60min   So Rahul do 1 work in 300 min   Then Neha do 3/7 work in 90min   So Neha do 1 work in 210min   Then Riya do 3/4 work in 210min   So Riya do 1 work in 280 min   5:30pmy 300min i.e 5hr all will complete their work so   12-1,1-2,2-3,3-3:30, 4-4:30,4:30-5:30   5:30pmy 5:30 they all go to play   ANSWER:5:30pm
Answer: B
Five kilograms of oranges contained 98% of water. If the next day the concentration of water decreased by 2%, what was the new weight of the oranges, in kilograms?	Choose the correct choice from the following options.
A) 4.9
B) 4.8
C) 2.5
D) 2
E) 0.2

Solution: If C is the answer, then the question means that the concentration of water the newt day became 96%.   Out of 5 kilograms 98%, or 4.9 kilograms was water and 0.1 kilograms was non-water.   The next day, after some water evaporated, oranges became 96% water and 4% of non-water, so the next day 0.1 kilograms of non-water composed 4% of oranges, which means that the new weight of the oranges was x*0.04=0.1 --> x=2.5 kilograms.   Answer: 2.5.
Answer: C
Aravind had $ 2100 left after spending 30 % of the money he took for shopping. How much money did he
take along with him?	Choose the correct answer.
A) $ 3500
B) $ 3600
C) $ 3800
D) $ 3000
E) $ 4000

Solution: Let the money he took for shopping be m.   Money he spent = 30 % of m   = 30/100 × m   = 3/10 m   Money left with him = m – 3/10 m = (10m – 3m)/10 = 7m/10   But money left with him = $ 2100   Therefore 7m/10 = $ 2100   m = $ 2100× 10/7   m = $ 21000/7= 
21000/7 = 3_000
$ 3000   Therefore, the money he took for shopping is $ 3000.   $ 3000)
Answer: D
A train 140 m long is running with a speed of 50 km/hr. In what time will it pass a man who is running at 4 km/hr in the direction opposite to that in which the train is going?	Choose one:
A) 8.1
B) 7.0
C) 9.33
D) 8
E) 9

Solution: Speed of train relative to man = 50 +4= 
50 +4 = 54
54 km/hr.= 54 * 5/18= 
54 * 5/18 = 15
15 m/sec.   Time taken to pass the men= 140 * 1/15 = 9.33 sec.   Answer: Option 9.33
Answer: C
A contractor agreeing to finish a work in 150 days, employed 75 men each working 8 hours daily. After 90 days, only 2/7 of the work was completed. Increasing the number of men by­­ ________ each working now for 10 hours daily, the work can be completed in time.
Choose the correct choice from the following answers:
A) 140 workers
B) 150 workers
C) 160 workers
D) 155 workers
E) 130 workers

Solution: total man work in 90 days is = 90*75*8==>54000 man work   remaining work =1-2/7=5/7   now, 2/7 work have 54000 man work   5/7 work will have (54000*7/2)*5/7 ==> 135000 man work   days left =60 and 10 hrs per day   so, no. of workers = 135000/(60*10)==>225   this is total workers.   so, workers needed ==>225-75= 
225-75 = 150
150 workers   ANSWER:150 workers
Answer: B
Steve Purchased a house for $15000 and he like to resell it with 20% profit. And what price he want to sell that? Choose the correct choice from the following answers
A) 16000  B) 17500  C) 18000  D) 19500  E) 21000

Solution: Explanation:   C.P= 15000   Profit% = 20% = (Profit*C.P) / 100   Profit= (Profit% * C.P) / 100 = (20*15000) / 100= 
(20*15000) / 100 = 3_000
3000   S.P= C.P + Profit = 15000+3000= 
15000+3000 = 18_000
18000 . Answer: 18000
Answer: C
The product of two numbers is 4107. If the H.C.F. of these numbers is 37, then the greater number is: Choose the correct choice from the following:
A) 101
B) 107
C) 111
D) 185
E) 192

Solution: Let the numbers be 37a and 37b.   Then, 37a x 37b = 4107   ab = 3.   Now, co-primes with product 3 are (1, 3).   So, the required numbers are (37 x 1, 37 x 3) i.e., (37, 111).   Greater number = 111.   Answer: Option 111
Answer: C
A certain company items price list has an average of 6 and a standard deviation of d (d is positive). Which of the following pairs of data when added to the list, must result in a list of 102 data with standard deviation less than d?	Choose the correct choice from the following choices:
A) (-6;0)
B) (0;0)
C) (0;6)
D) (0;12)
E) (6;6)

Solution: Standard deviation shows how much variation there is from the mean. A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.   So when we add numbers, which are far from the mean we are stretching the set making SD bigger and when we add numbers which are close to the mean we are shrinking the set making SD smaller.   According to the above adding two numbers which are closest to the mean will shrink the set most, thus decreasing SD by the greatest amount.   Closest to the mean are 6 and 6 (actually these numbers equal to the mean) thus adding them will definitely shrink the set, thus decreasing SD.   Answer: (6;6).
Answer: E
An article was sold after a discount of 20% and therewas a gain of 20%. If the profit madeon it was Rs.6 less thanthe discount offered on it, find its SP? Choose the correct choice from the following options: A) Rs. 60 B) Rs. 69 C) Rs. 72 D) Rs. 89 E) Rs. 92

Solution: Let CP = Rs. 100x   SP = Rs. 120x   MP = 120x/80 * 100 = Rs. 150x   D = Rs. 150x - Rs. 120x = Rs. 30x   D - P = 30x - 20x = Rs. 6, 10x = Rs. 6   120x = 120/10 * 6 = Rs. 72   Rs. 72
Answer: C
A bag contains 6 red, 5 blue and 2 green balls. If 2 ballsare picked at random, what is the probability that both are red?	Choose the correct choice from the following answers:
A) 1/15  B) 2/13  C) 5/26  D) 6/27  E) 6/13

Solution: P(Both are red),   =65/262135/262=65/262135/262   =5/26   5/26
Answer: C
In how many ways can the letters of the word JUPITER be arranged in a row so that the vowels appear in alphabetic order? Pick
A) 736 B) 768 C) 792 D) 840 E) 876

Solution: three letters can be arranged in 3! ways.   only one combination EIU is required.   7 letters can be arranged in 7! ways.   thus 7!/ 3! * 1 = 840.   840
Answer: D
Eight identical machines can produce 360 aluminum cans per hour. If all of the machines work at the same constant rate, how many cans could 5 such machines produce in 2 hours? Pick:
A) 450	B) 750	C) 1,800	D) 5,900	E) 7,500

Solution: 8 machines/ 360 cans = 5 machines/ x cans   8x= 1800   x=225   (225)(2 hours)= 450 cans. The answer is 450.
Answer: A
If s and t are positive integers such that s/t = 64.28, which of the following could be the remainder when s is divided by t?  Choose the correct choice from the following answers:
A) 12
B) 15
C) 18
D) 21
E) 24

Solution: 0.28 = 28/100 = 7/25   The remainder must be divisible by 7.   The answer is 21.
Answer: D
At what rate percent on simple interest will Rs.750 amount to Rs.900 in 5 years? Choose the correct choice from the following:
A) 7%
B) 9%
C) 4%
D) 2%
E) 4%

Solution: 150 = (750*5*R)/100   R = 4%   Answer: 4%
Answer: C
If Bill can buy 3 pairs of jeans and 2 shirts for $69 or 2 pairs of jeans and 3 shirts for $81, how much does one shirt cost?  Pick one
A) $10 B) $12 C) $13.20 D) $21 E) $16.80

Solution: 3J + 2S = 69   2J + 3S = 81   ----------------   5J + 5S = 150 ----(divide by 5)---> J + S = 30   3J + 2S = J + 2(J + S) = J + 60 = 69 ---> J = 9   3*9 + 2S = 69   27 + 2S = 69   2S = 42   S = 21   Answer: $21
Answer: D
In May, the grounds keeper at Spring Lake Golf Club built a circular green with an area of 49π square feet. In August, he doubled the distance from the center of the green to the edge of the green. What is the total area of the renovated green?	Choose the correct choice from the following options: A) 100PI B) 144PI C) 196 PI D) 80 E) 90

Solution: AREA OF 196 PIIR196 PILE 49PI SQ FEET =PI R^2 THEREFORE R =7   NOW GREEN RADI DOUBLED I.E R =14 AREA =196 PI   196 PI
Answer: C
A wheel makes 1200 revolutions in covering a distance of 60 km. Find the radius of the wheel.	Answers: A) 10.5m B) 11m C) 11.25m D) 11.45m E) None of these

Solution: Explanation: Distance covered in one revolution =((60X 1200)/1000)= 72m.   2πR = 72 => 2 x (22/7) x R = 72 => R = 72 x (7/44) = 11.45 m.   Answer: Option 11.45m
Answer: D
Pipe A can fill a tank in 4 hours, pipe B in 8 hours, and pipe C in 24 hours. If all the pipes are open, in how many hours will the tank be filled?
Choose the correct answer: A) 2.4 hours B) 2.8 hours C) 3.2 hours D) 4.8 hours E) 5.2 hours

Solution: The part filled by A + B + C in 1 hour   = 1/4 + 1/8 + 1/24   = 10/24   All the three pipes together will fill the tank in 24/10= 
24/10 = 12/5 = around 2.4
2.4 hours.   The answer is 2.4 hours.
Answer: A
The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 24 years. The present age of the husband is  Choose the correct choice from the following choices:  A) 40  B) 32  C) 45  D) 55  E) 65

Solution: Explanation:   Sum of the present ages of husband, wife and child = (27 * 3 + 3 * 3)= 
(27 * 3 + 3 * 3) = 90
90 years.   Sum of the present ages of wife and child= (24 * 2 + 5 * 2)= 
(24 * 2 + 5 * 2) = 58
58 years.   Husband's present age= (90 - 58)= 
(90 - 58) = 32
32 years   Option 32
Answer: B
In a hostel there were 100 students. To accommodate 20 more students the average is decreased by rupees 5. But total expenditure increased by Rs.400. Find the total expenditure of the hostel now?	Answers.
A) Rs.5800	B) Rs.5480	C) Rs.5400	D) Rs.5900	E) Rs.5430

Solution: 100x + 400   = 12(x – 5)   x = 50   100 * 50 + 400= 
100 * 50 + 400 = 5_400
5400   Answer:Rs.5400
Answer: C
From a group of 6boys&4girls a Committee of 4 persons is to be formed. In how many different ways can it be done, so that the committee has at least 2 boys?
Choose the most appropriate option.
A) 126
B) 138
C) 185
D) 198
E) 200

Solution: The committee of 4 persons is to be so formed that it has at least 2 men. The different ways that we can choose to form such a committee are:   (i) 2m. 2w in 6C2 x 4 C1=6X5 - 2X1 X 3X3 2X1 =n an (ii) 3m. 1w in 6C3 x 4C1 =6X5X4 3X2X1 X4 _n - a ''''   (iii) 4m in 6C4 -2x1 = 15 Total no. of different ways in which a committee of 4 persons can be formed so that it has at least 2 men. = 90 + 18 + 15 = 185   185
Answer: C
I bought two books; for Rs.480. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss?	Select:
A) 167  B) 280  C) 187  D) 178  E) 170

Solution: x*(85/100)   = (480 - x)119/100   x =280   Answer:280
Answer: B
Jar Y has 10% more marbles than Jar X . What percent of marbles from Jar Y need to be moved into X so that both jars have equal marbles
Options:	A) 4.54%	B) 9.09%	C) 10%	D) 11%	E) 12.25 %

Solution: No; the choices will be approximated only when GMAT question explicitly mentions that;   Here the answer is very close 4.54, not 5.   Jar Y has 10% more marbles than X   Y = 1.1X   If k marbles are taken out of Y. The remaining marbles in Jar Y= 1.1X-k   If k marbles are added to X. The new marbles' count in Jar X= X+k   And we know they are equal;   X+k = 1.1X-k   2k = 0.1X   k= 0.05X   The marbles taken out of Y = 0.05X   Question is: 0.05X is what percent of marbles that was originally there in Y i.e. 1.1X   0.05X1.1X∗1000.05X1.1X∗100   0.05X1.1X∗1000.05X1.1X∗100   5011=4.54¯≈4.545011=4.54¯≈4.54   4.54%NSWER:4.54%
Answer: A
During the first week of performances of a certain play, 5,400 tickets were sold, all at reduced price. During the remaining weeks of performances, 5 times as many tickets were sold at full price as were sold at reduced price. If the total number of tickets E sold was 25,200, how many of them were sold at full price?  Select the correct option: A) 21,000 B) 19,800 C) 16,500 D) 15,800 E) 8,700

Solution: Given:   The question tells us about the number of tickets sold in the first week at reduced price = 5,400. It also tells us that during the remaining weeks, the number of tickets sold at full price was 5 times the no. of tickets sold at reduced price. The total tickets sold was 25,200, and we are asked to find the number of tickets that where sold at full price.   Approach:   The question asks us to find the number of ticket sold at full price. We know that the number of tickets sold at full price was 5 times the no. of tickets sold at reduced price in remaining weeks. Hence, assuming tickets sold at reduced price in remaining weeks to be x would give us the no. of tickets sold at full price to be 5x.   Tickets sold in first week + Tickets sold in remaining weeks = Total no. of tickets soldi.e.   Tickets sold in first week + Tickets sold at full price in remaining weeks + Tickets sold at reduced price in remaining weeks = Total no. of tickets sold   We know the no. of tickets sold during first week and the total no. of tickets sold. We will use this relation to get to our answer.   Working Out:   Tickets sold in first week + Tickets sold at full price in remaining weeks + Tickets sold at reduced price in remaining weeks = Total no. of tickets sold   Substituting values in the equation, we get   5,400 + 5x + x = 25,200   x= 3,300   Tickets sold at full price = 5x = 16,500   Answer: Option 16,500
Answer: C
In an interview , the probability of appointing Husband is 1/5 while that of wife is
¼.find probability that only one of them get selected in interview.  Choices:
A) 3/20 B) 4/20 C) 5/20 D) 6/20 E) 7/20

Solution: p(H)=1/5   p(w)=1/4   P(H bar)=1-1/5=4/5   p(w bar)=1-1/4=3/4   Required probability=p(H)*p(w bar)+p(w)*p(H bar)   1/5*3/4+1/4*4/5   7/20   ANSW7/20R:7/20
Answer: E
What is the sum which earned interest?
I. The total simple interest was Rs. 7000 after 7 years.
II. The total of sum and simple interest was double of the sum after 5 years.
Choose the most appropriate option.
A) I alone sufficient while II alone not sufficient to answer
B) II alone sufficient while I alone not sufficient to answer
C) Either I or II alone sufficient to answer
D) Both I and II are necessary to answer
E) None of these

Solution: Explanation:   Let the sum be Rs. x.   I gives, S.I. = Rs. 7000 and T = 7 years.   II gives, Sum + S.I. for 5 years = 2 x Sum Sum = S.I. for 5 years.   Now, S.I. for 7 years = Rs. 7000.   therefore, S.I. for 1 year = Rs. 1000.   Thus, I and II both are needed to get the answer.   Answer: Both I and II are necessary to answer
Answer: D
A is thrice as good a workman as B and therefore is able to finish a job in 40 days less than B. working together, they can do it in
Choose the correct choice from the following answers:
A) days B) ½ days C) days D) days E) days

Solution: Explanation:   B = 3A   3A – A =40 days   A = 20days   Then, B = 90 days   (A + B) = 20 × 90/ 120 = 20 days .   daysnswer: Option days
Answer: A
The sum of 36 hours 45 minutes and 12 hours 15 minutes is approximately what percent of a week? Choose the most appropriate option
A) 24%
B) approx 29%
C) approx 24%
D) approx 18%
E) approx 12%

Solution: Since the question is asking for an approximate percentage   36:45+12:15 ~ 49 hours   % of day = (49*100)/(24*7) ~ 29%   Answer is approx 29%
Answer: B
Positive integer p has n factors; 3p has 3 factors; Which of the following values can n take?
I. 1
II. 2
III. 3  Choices
A) I or II  B) II or III  C) only I is true  D) only II is true  E) I or III

Solution: Squares have odd number of factors.The square which is a multiple of 3 is 9.   3 has factors 1,3 .   Therefore 2 factors   Answer only II is true
Answer: D
Sum of the numbers from 1 to 29 is
Choose the correct choice from the following options
A) 400	B) 430	C) 435	D) 405	E) None of these

Solution: Explanation: Sum of first n natural numbers = 1 + 2 + 3 + ..... n = n(n+1)/2   Substitute n = 29.   So S20=29Ã—30/2=435   435orrect Option: 435
Answer: C
If p is a positive integer and 10p/96 is an integer, then the minimum number of unique prime factors p could have is T:  Options.
A) T=1	B) T=2	C) T=3	D) T=4	E) T=5

Solution: 10p/96 should resolve to a integer => 5p/48 should resolve to an integer.   Hence p/48 should resolve to a integer.   48 -- > 2^4 * 3.   Hence p should have atleast 2^4*3 for p/48 to resolve to a int.   The unique prime factors in 2^4 * 3 is 2, 3 and hence the answer is T=2(2).
Answer: B
When 81 is divided by the cube of positive integer z, the remainder is 17. Which of the following could be the value of z?
I.	2
II.	4
III.	8 Choose the correct choice:
A) I only B) II only C) III only D) I and II only E) I, II and III

Solution: 81 divided by z^3 leaves a remainder of 17.   81 = q * 2^3 + 17   64 = q+z^3   Then I tried answer possibilities of 2, 4 and 8.   Only 2^3 = 64 fulfills the equation and yields a remainder of 17.   ANSWER:II only
Answer: B
Magnabulk Corp sells boxes holding d magnets each. The boxes are shipped in crates, each holding c boxes. What is the price charged per magnet, if Magnabulk charges m dollars for each crate?
Choices: A) 100cd/m B) 100m/(cd) C) cd/(100m) D) m/(cd) E) cd/m

Solution: crate has = cd magnates   each magnate cost for each crate = m / cd   Ans; m/(cd)
Answer: D
In a group of ducks and cows, the total number of legs are 32 more than twice the number of heads. Find the total number of cows.
Choices:	A) A)14	B) B)12	C) C)16	D) D)8	E) E)6

Solution: Explanation :   Let the number of ducks be d   and number of cows be c   Then, total number of legs = 2d + 4c = 2(d + 2c)   total number of heads = c + d   Given that total number of legs are 32 more than twice the number of heads   => 2(d + 2c) = 32 + 2(c + d)   => d + 2c = 16 + c + d   => 2c = 16 + c   => c = 14   i.e., total number of cows = 16   Answer : 16
Answer: C
If the sum of six numbers is between 135 and 164, then the average (arithmetic mean) of the six numbers could be which of the following? Choose the correct choice from the following answers
A) 15.4. B) 20.5 C) 25.5 D) 31.25 E) 32.5.

Solution: The problem is actually testing the concept of average and Maxima/Minima....   Let all the values be 135 , so the average will be 135/6= 
135/6 = 45/2 = around 22.5
> 22.5 ( Minima )   Let all the values be 164, so the average will be 164/6=> 27.3 ( Minima )   Hence answer will be (C) { any number between the maximum and minimum value.... }
Answer: C
Indu gave Bindu Rs.6250 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest? Select.
A) 5 B) 2 C) 10 D) 5 E) 1

Solution: 6250   = D(100/4)2   D = 10   Answer: 10
Answer: C
For what value of â€œkâ€ will the equation (2kx2 + 5kx +1)=0 have equal roots?
Select the correct option:
A) 2/7
B) 9/4
C) 8/25
D) 7/1
E) 7/2

Solution: for a 2nd degree equation ax2+bx_c=0 has equal roots the condition is b2-4ac =0   in the given equation   (5k)^2-4*2k*1=0   by solving this equation   we get k=0, k=8/25   ANSWER:8/25
Answer: C
In a college, 95 percent of students Passed in math, 97 percent of students Passed in English, 99 percent Passed in French and 92 percent Passed in German.
Can you find out the percentage of students who Passed in all 4 subjects ?
Choose the correct choice from the following options:
A) 92% B) 90% C) 96% D) 83% E) 89%

Solution: 83%   83% of student Passed in all four subjects.
Answer: D
A car gets 20 kilometers per gallon of gasoline. How many gallons of gasoline would the car need to travel 120 kilometers? Choose the correct choice from the following answers:	A) 8.5 gallons	B) 5 gallons	C) 7 gallons	D) 5.5 gallons	E) 6 gallons

Solution: Each 20 kilometers, 1 gallon is needed. We need to know how many 20 kilometers are there in 120 kilometers?   120 / 20 = 4.5 * 1 gallon = 6 gallons correct answer 6 gallons
Answer: E
Three candidates contested an election and received 1130, 7530 and 11620 votes respectively. What percentage of the total votes did the winning candidate get?
Pick one:	A) 57%	B) 57.3%	C) 65%	D) 90%	E) 80%

Solution: total votes are 20280 ( sum of votes obtained by 3 candidates)   percentage of the total votes recd by the winning candidate = 100*11620/20280 = 57.3%   ANSWER:57.3%
Answer: B
A and B can do a piece of work in 10 days, B and C in 15 days, C and A in 12 days. How long will C take to do it?	Choose the correct choice from the following choices:	A) 70 days	B) 55 days	C) 24 days	D) 40 days	E) 11 days

Solution: 2c = 1/15+ 1/12– 1/10 = 1/20   c = 1/40 => 40 days   Answer: 40 days
Answer: D
C, D and E invested Rs.4500, Rs.9500 and Rs.11000 respectively, in a partnership business. Find the share of E in profit of Rs.25000 after a year? Select.
A) 10000
B) 11000
C) 12000
D) 13000
E) 14000

Solution: Explanation:   4500:9500:11000   9:19:22   22/50 * 25000= 
22/50 * 25000 = 11_000
11000   11000)
Answer: B
If 0 < a < b and k = (2a + 9b)/b , which of the following must be true?	Choose the correct choice from the following options:
A) k < 2
B) k < 7
C) k < 9
D) k > 9
E) k > 11

Solution: Please follow posting guidelines (link in my signature) especially writing the correct topic title. Also do mention the source of the question if you select the tag:Source-Other Please Specify.   As for your question, it is very simple and straightforward with number plug in.   Assume a=1 and b=2 as a<b, you get k = (2+14)/2 = 10. This eliminates all but option k > 9 , making it the correct answer.
Answer: D
There are A girls in a class, and their average height is M inches. In the same class, there are B boys with an average height of N inches. What is the average height of all the students in the class?	Choose the correct choice from the following answers.
A) (X + Y)/(M + N)  B) (M + N)/(X + Y)  C) (AM + BN)/(A + B)  D) (XM + YN)/(X + Y)  E) MN/XY

Solution: Total height = AM+BN   No of students = A+B   Avg = (AM+BN)/(A+B)   Answer is (AM + BN)/(A + B)
Answer: C
In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?  Select the correct option.
A) 80  B) 90  C) 15  D) 209  E) 105

Solution: We may have (1 boy and 3 girls) or (2 boys and 2 girls) or (3 boys and 1 girl) or (4 boys).   Required number   of ways	= (6C1 x 4C3) + (6C2 x 4C2) + (6C3 x 4C1) + (6C4)   = (6C1 x 4C1) + (6C2 x 4C2) + (6C3 x 4C1) + (6C2)   = (24 + 90 + 80 + 15)= 
(24 + 90 + 80 + 15) = 209
209.   ANSWER 209 209
Answer: D
85% of a number is added to 24, the result is the same number. Find the number?  Choose the correct choice:
A) 228
B) 267
C) 277
D) 160
E) 882

Solution: (85/100) * X + 24 = X   3X = 480   X = 160   Answer: 160
Answer: D