MU-NLPC/Calc-aqua_rat huggingface dataset:
Two electronic musical instruments were purchased for Rs. 8000. The first was sold at a profit of 40% and the second at a loss of 40%. If the sale price was the same in both the cases, what was the cost price of the electronic musical instruments?  Select the correct option.
A) 1400,5600
B) 3400,5600
C) 2400,5600
D) 2400,4600
E) 2400,3600

Solution: let cost prices be x and 8000-x   s.p1=s.p2   (140/100)*x=(60/100)*(8000-x)   x=2400   cost prices are 2400,5600   ANSWER:2400,5600
Answer: C
The sum of ages of 4 children born 1 years different each is 38 years. What is the age of the Elder child? Choose the correct choice:
A) 8  B) 11  C) 10  D) 16  E) 17

Solution: Let the ages of children be x, (x + 1), (x + 2), (x + 3) years.   Then, x + (x + 1) + (x + 2) + (x + 3) = 38   4x = 32   x = 8.   x+3= 8+3= 
8+3 = 11
11   Answer : 11
Answer: B
In how many ways a committee, Consisting of 4 men and 6 women can be formed from 8 men and 10 women?	Choose the correct option
A) 266  B) 86400  C) 11760  D) 14700  E) 15720

Solution: To choose Required number of ways to form a committee:   Select 4 men out of 8 men and 6 women out of 10 women.   That is 8C4 * 10C6.   8C4=8!/4!*4!   =70   10C6=10!/6!*4!   =210   The Required number of ways=210*70= 
210*70 = 14_700
14700   14700
Answer: D
Two pipes A and B can fill a tank in 2 and 6 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank? Choose the correct choice from the following answers.
A) 2.5 min	B) 1.8 min	C) 1.5 min	D) 3.5 min	E) 2 min

Solution: Part filled by the first pipe in 1 minute = 1/2   Part filled by the second pipe in 1 minute = 1/6   Net part filled by pipe A and pipe B in 1 minute = (1/2)+(1/6)=2/3   i.e, pipe A and B together can fill the tank in   3/2= 
  3/2 = 3/2 = around 1.5
1.5 minutes   Answer is 1.5 min
Answer: C
A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank? Choose the most appropriate option:
A) 65 hrs
B) 99 hrs
C) 35 hrs
D) 45 hrs
E) 32 hrs

Solution: Suppose pipe A alone takes x hours to fill the tank.   Then, pipes B and C will take x/2 and x/4 hours respectively to fill the tank.   1/x + 2/x + 4/x = 1/5   7/x = 1/5 => x = 35 hrs.Answer: 35 hrs
Answer: C
How many ways could three bottle caps can be used to close five bottles of which two of the bottles will remain opened?	Choose the correct choice.
A) 8 B) 12 C) 60 D) 118 E) 120

Solution: ways in which 3 bottles out of 5 can be selected = 5603   ways in which 3 caps can be used to close 3 bottles = 3!   Total ways of arrangement = 5603*3!   =5*4/2*6   =10*6= 
10*6 = 60
60   Ans= 60
Answer: C
If the simple interest on a sum of money for 4 years at 8% per annum is Rs. 560, what is the compound interest on the same sum at the rate and for the same time? Pick one: A) Rs. 640.86 B) Rs. 430.86 C) Rs. 330.86 D) Rs. 630.86 E) Rs. 130.86

Solution: Sum = (50 * 100) / (2 * 5) = Rs. 1,750.00   C.I. on Rs. 1,750.00 for 4 years at 8% = Rs. 2,380.86.   = Rs. 2,380.86 - 1,750.00 = Rs. 630.86   ANSWER:Rs. 630.86
Answer: D
A certain industrial loom weaves 0.128 meters of cloth every second. Approximately how many seconds will it take for the loom to weave 25 meters of cloth?
Choose the correct choice from the following answers:	A) 205	B) 200	C) 180	D) 195	E) 175

Solution: Explanation:   Let the required number of seconds be x   More cloth, More time, (direct proportion)   Hence we can write as   (cloth) 0.128 : 25 :: 1 : x   ⇒0.128x=25   ⇒x=25/0.128   =25000/128   =3125/16≈195   Answer: Option 195
Answer: D
How many 5 letter combinations can be made from the letters of the word VERMONT if the first letter has to be a vowel and the last letter has to be a consonant, and each letter can be used only once? Choose the most appropriate option.
A) 21 B) 42 C) 120 D) 600 E) 720

Solution: VERMONT consists of 2 vowels and 5 consonants:   The number of way to choose a vowel for the first letter = C12==2.   The number of way to choose a consonant for the last letter= C15==5.   The number of ways to choose middle three letters out of 5 remaining letters = C35==10.   The number of arrangements of these three letters = 3! = 6.   Total = 2*5*10*6= 
2*5*10*6 = 600
600.   Answer: 600.
Answer: D
A and B can do a piece of work in 6 2/3 days and 5 days respectively. They work together for 2 days and then A leaves. In how many days after that B will complete the work alone.  Choose the correct choice from the following answers:
A) 2 days
B) 1 ½ days
C) 3 days
D) 3 ½ days
E) 4 days

Solution: Explanation:   3/20 * 2 + (2 + x)/5 = 1   x = 1 ½ days   Answer: Option 1 ½ days
Answer: B
10 people are assigned a library of audio clips to be transcribed in 100 days. If 2 people have to take 25 days leave in between, how many more people should be added on the last day to complete the task in 100 days itself?	Choose the correct choice from the following options.
A) 25  B) 50  C) 75  D) 100  E) 15

Solution: B   For 25 days, instead of 10, only 8 people were transcribing the audio clips.   If 1 person transcribes N number of audio clips in 1 day, additional backlog, 25 X N X 2   10 : M :: 10 X N : 25 X 2 X N = 10 : 50   Thus, M = 10 X 50 / 10 = 50
Answer: B
In a group of 120 people, 90 have an age of more 30 years, and the others have an age of less than 20 years. If a person is selected at random from this group, what is the probability the person's age is less than 20? Choose the correct choice from the following choices.
A) 0.25 B) 0.55 C) 0.65 D) 0.75 E) 0.85

Solution: Number of people whose age is less than 20 is given by   120 - 90= 
120 - 90 = 30
30   Probability P that a person selected at random from the group is less than 20 is gieven by    30 / 120= 
 30 / 120 = 1/4 = around 0.25
0.25   correct answer 0.25
Answer: A
A car travels first half distance between two places with a speed of 40 kmph and the rest half distance with a speed of 60 kmph. The average speed of the car is Answers
A) 48 kmph B) 37 kmph C) 44 kmph D) 45 kmph E) None of these

Solution: we know that speed = distance traveled/time taken   let the total distance traveled by the car is 2x km.   then time taken by it to cover first half is x/60 hour.   and for second half is x/40 hour.   then average speed= total distance traveled/ total time   taken.   =2x/[(x/60) + (x/40)]   =2x/[5x/120] (on simplification)   =48 kmph   48 kmphNSWER:48 kmph
Answer: A
Ron begins reading a book at 2: 30 p.m. and reads at a steady pace of 30 pages per hour. Michelle begins reading a copy of the same book at 4: 00 p.m. If Michelle started 5 pages behind the page that Ron started on and reads at an average pace of 50 pages per hour, at what time would Ron and Michelle be reading the same page?	Choose the correct choice from the following choices.
A) 5: 00 p.m. B) 6: 30 p.m. C) 7: 45 p.m. D) 8: 00 p.m. E) 8: 30 p.m.

Solution: M gains 50-30= 
50-30 = 20
20 pages per hour on R   at 4pm R has read 45 pages and M is  45+5= 
 45+5 = 50
50 pages behind him   time=50/20= 
50/20 = 5/2 = around 2.5
2.5 hours   they are on the same page at 6:30pm   6: 30 p.m.
Answer: B
In a class there are 20 boys and 21 girls. In how many ways can a boy and a girl be selected?	Answers: A) 508 B) 420 C) 800 D) 570 E) 503

Solution: We can select one boy from 20 boys in 20 ways.   We select one girl from 21 girls in 21 ways   We select a boy and girl in 20 * 21 ways i.e., = 420 ways.   Answer:420
Answer: B
In a class of 36 students 26 play football and play 20 long tennis, if 17 play above, many play neither?
Answers
A) 7  B) 8  C) 10  D) 12  E) 14

Solution: 26 + 20 - 17= 
26 + 20 - 17 = 29
29   36 - 29= 
36 - 29 = 7
7 play neither   7nswer is 7
Answer: A
if (p/q)-(q/p)=21/10
then what ia the value of(4p/q)+(4q/p) Pick one:  A) 58/5  B) 59/5  C) 121/105  D) 101/105  E) 1/2

Solution: p/q =a then q/p = 1/a   a+1/a=21/10   by solving this we get a=5/2   then 4*5/2+4*2/5 = 58/5   58/5NSWER:58/5
Answer: A
The owner of a furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8339 for a computer table, then what was the cost price of the computer table?	Choose the correct choice from the following choices.
A) 2299	B) 2699	C) 2670	D) 6725	E) 2601

Solution: CP = SP * (100/(100 + profit%))   = 8339(100/124) = Rs. 6725.   Answer:6725
Answer: D
Average weight of 10 people increased by 3 kg when one person of 45 kg is replaced by a new
man. Then weight of the new man is
Choose one
A) 50 B) 55 C) 60 D) 65 E) 75

Solution: Explanation:   Total weight increased is 3 * 10= 
3 * 10 = 30
30.   So weight of new person is 45+30= 
45+30 = 75
75   Answer: Option 75
Answer: E
The average age of 32 students in a group is 16 years. When teacher’s age is included to it, the average increases by one. What is the teacher’s age in years?	Choose the correct choice from the following.
A) cannot be determined
B) None of these
C) 48
D) 49
E) 50

Solution: Age of the teacher = (33 × 17 – 32 × 16) years   = 49 years.   Answer 49
Answer: D
Two bus tickets from city A to B and three tickets from city A to C cost Rs. 77 but three tickets from city A to B and two tickets from city A to C cost Rs. 73. What are the fares for cities B and C from A ? Choose the correct choice from the following choices:
A) 11  B) 13  C) 44  D) 55  E) 61

Solution: Explanation:   Let Rs. x be the fare of city B from city A and Rs. y be the fare of city C from city A. Then, 2x + 3y = 77 ...(i) and 3x + 2y = 73 ...(ii) Multiplying (i) by 3 and (ii) by 2 and subtracting, we get: 5y = 85 or y = 17. Putting y = 17 in (i), we get: x = 13.   Answer: 13
Answer: B
A shopkeeper sells two articles at Rs.1000 each, making a profit of 20% on the first article and a loss of 20% on the second article. Find the net profit or loss that he makes? Select.
A) 6% B) 7% C) 8% D) 4% E) 1%

Solution: SP of first article = 1000   Profit = 20%   CP = (SP)*[100/(100+P)] = 5000/6 = 2500/3   SP of second article = 1000   Loss = 20%   CP = (SP)*[100/(100-L)] = 5000/4= 
5000/4 = 1_250
1250   Total SP= 2000   Total CP = 2500/3 + 1250 = 6250/3   CP is more than SP, he makes a loss.   Loss = CP-SP = (6250/3)- 2000 = 250/3   Loss Percent = [(250/3)/(6250/3)]*100   =0.04 * 100= 
0.04 * 100 = 4
4%   Answer: 4%
Answer: D
Two trains 100 m and 60 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?  Choose the correct choice from the following answers:
A) 10.9 sec
B) 5.76 sec
C) 10.6 sec
D) 10.8 sec
E) 20.8 sec

Solution: Relative speed = 60 + 40= 
60 + 40 = 100
100 km/hr.= 100 * 5/18 = 250/9 m/sec.   Distance covered in crossing each other = 100 + 60= 
100 + 60 = 160
160 m.   Required time= 160 * 9/250= 
160 * 9/250 = 144/25 = around 5.76
5.76= 5.76 sec.   Answer: 5.76 sec
Answer: B
From a group of 25 astronauts that includes 13 people with previous experience in space flight, a 3-person crew is to be selected so that exactly 1 person in the crew has previous experience in space flight. How many different crews of this type are possible?  Choose the correct choice from the following choices.
A) 785 B) 858 C) 864 D) 964 E) 722

Solution: number of astronauts with previous experience = 13   Remaining =12   we need to pick exactly one from the first group   and 2 from the second group   (13C1)*(12C2)   =13*66= 
13*66 = 858
858   Answer : 858
Answer: B
A high school has 400 students 1/2 attend the airthmetic club, 5/8 attend the biology club and 3/4 attend the chemistry club. 1/4 attend all 3 clubs. If every student attends at least one club how many students attend exactly 2 clubs.  Choose the correct choice from the following options.
A) 100  B) 150  C) 140  D) 120  E) 110

Solution: A-Club has 200 members (1/2 of 400)   B-Club has 250 members (5/8 of 400)   C-Club has 300 members (3/4 of 400)   We can create an equation to solve this:   200+250+300 = n + x + 2y   where n is the number of students, x is the number of students in two clubs, and y is the number of students in three clubs.   The question provides y for us (100).   750 = 400 + x + 200   x = 150   150
Answer: B
Tough and Tricky questions: Combinations.
Five contestants representing four different countries advance to the finals of a fencing championship. Assuming all competitors have an equal chance of winning, how many possibilities are there with respect to how a first-place and second-place medal can be awarded? Choose the correct choice from the following choices
A) 6
B) 7
C) 12
D) 15
E) 24

Solution: Four contestants representing four different countries advance to the finals of a fencing championship. Assuming all competitors have an equal chance of winning, how many possibilities are there with respect to how a first-place and second-place medal can be awarded?   We have 2 slots to be filled using 5 contestants:5 options for slot1*3 option for slot2   = 5* 3= 
5* 3 = 15
15   Ans. 15) 15
Answer: D
If -2 < h < 0, which of the following has the greatest value?
Choices
A) a) 1-h  B) b) 1+h  C) c) 1+h^2  D) d) 1-1/h  E) e) 1-1/(h^2)

Solution: easiest way of solving this would be to substitute a value.   lets say h= - 1/2   a) 3/2   b) 1/2   c) 5/4   d) 3   e) - 3   the value you chose is wrong . h cannot be 0.9 as -1<h<0. if you chose -0.9 answer will still be D.   Answer is e) 1-1/(h^2).
Answer: E
A local business made a $125,000 profit on its first $1 million in sales and a $80,000 profit on its next $2 million in sales. By approximately what percent did the ratio of profit to sales decrease from the first $1 million in sales to the next $2 million in sales?
Choose the correct choice from the following options.
A) 100%  B) 150%  C) 200%  D) 250%  E) 300%

Solution: Solution:   This is a percent decrease problem. We will use the formula: percent change = (new – old)/old x 100 to calculate the final answer.   We first set up the ratios of profits to sales. The first ratio will be for the first 1 million in sales, and the second ratio will be for the next 2 million in sales. Because all of the sales are in millions, we do not have to express all the trailing zeros in our ratios.   First 1 Million   profit/sales = 125/1000 = 1/8   Next 2 Million   profit/sales = 8/200 = 2/50   We can simplify each ratio by multiplying each by the LCM of the two denominators, which is 400. Keep in mind that we are able to do this only because our answer choices are expressed in percents.   First 1 Million   royalties/sales = (1/8) x 400 = 50   Next 2 Million   royalties/sales = (2/50) x 400 = 16   We can plug 5 and 6 into our percent change formula:   (new – old)/old x 100   [(16 – 50)/16] x 100   =-34/16 x 100 so approximately a 200% decrease.   Answer 200%.
Answer: C
A 6 litre sol is 20% alcohol .How many litres of pure alcohol must be added to produce a sol that is 50% alcohol ?  Options.
A) A.0.6 B) B.1 C) C.2.1 D) D.3.6 E) E.5.4

Solution: 20% of 6 = 1.2   50% of 6 = 3   shortage is 1.8   so we need to have 1.8/50% to get 50% alcohol content.   = 3.6 D.3.6
Answer: D
A college has raised 75% of the amount it needs for a new building by receiving an average donation of Rs. 600 from the people already solicited. The people already solicited represent 60% of the people the college will ask for donations. If the college is to raise exactly the amount needed for the new building, what should be the average donation from the remaining people to be solicited? Choose the correct choice from the following options.
A) Rs 300 B) Rs 250 C) Rs 400 D) Rs 500 E) None of these

Solution: Explanation :   Let x be the total no. of people the college will ask for donation.   The people already solicited 0.6x.   Amount raised from the people solicited 600 x 0.6x = 360x.   Now, 360 constitutes 75% of the amount.   Hence, the remaining 25% = 120x.   Hence, the average donation from remaining people   = 120x / 0.4x = 300.   Rs 300nswer : Rs 300120  / 0.4= 
120  / 0.4 = 300
300.   Rs 300nswer : Rs 300
Answer: A
For any two numbers X and Y , define X# Y=X+Y -XY . If X,Y>0.5, then X#X < Y#Y if
i. 1>X>Y
ii. 1>Y>X
iii. Y>X>1	Choose the correct choice from the following
A) i only	B) option ii only	C) i and ii only	D) ii and iii only	E) i and ii only

Solution: X#X = 2X-X^2 and Y#Y=2Y-Y^2   X#X <Y#X   => 2X - X^2 < 2Y - Y^2   => 2(X-Y) < (X-Y)(X+Y)   => X+Y>2 and X-Y>0 or X+Y<2 and X-Y<0   => X+Y>2 and X>Y or X+Y<2 and X<y (i),="" 1="" if="" using="">X>Y, then the first case applies but X+Y>2 is not satisfied. False.   Using (ii), if 1>Y>X, then the second case applies and X+Y<2 is satisfied. True.   Using (iii), if Y>X>1, then the second case applies but X+Y<2 is not satisfied. False.   Therefore only (ii) is true, and choice (option ii only) is correct.</y>
Answer: B
Find the distance covered by a man walking for 24min at a speed of 10km/hr? Choose the correct answer:
A) 1km	B) 3km	C) 4km	D) 5km	E) 6km

Solution: Distance = 10*24/60= 
10*24/60 = 4
4 km   Answer is 4km
Answer: C
There are 5 locks and 5 keys and each of the 5 keys matches each of the 5 locks. What is the minimum and the maximum trial numbers of attempts F needed to confirm that each of the 5 keys matches each of the 5 locks?
Select the correct option:
A) 5,15
B) 4,15
C) 5,10
D) 4,10
E) 5,20

Solution: Assume you have locks 1-5 and keys A-E.   Minimum: assume you are lucky to find the correct key/combo on the first try. So, 1 -> A, 2 -> B, 3 ->C, and 4 -> D, then 5 must match with E. Therefore, you only need to try 4 combos at a minimum.   Maximum: assume that it takes as many guesses as possible. So, with the first key you try A, B, C, and D with no success, therefore E must be the match (so 4 attempts). For key 2 you no longer have E available so you try A, B, and C, with no success, therefore D must be the match (3 attempts). And so on for key 3 (2 attempts) and key 4 (1 attempt). Key 5 matches with the remaining lock for a total of F= 4 + 3 + 2 + 1= 
4 + 3 + 2 + 1 = 10
10 attempts.4,10
Answer: D
Each of three investments has a 20% of becoming worthless within a year of purchase, independently of what happens to the other two investments. If Simone invests an equal sum K in each of these three investments on January 1, the approximate chance that by the end of the year, she loses no more than 1/3 of her original investment is  Choose the correct answer.
A) 90% B) 80% C) 70% D) 60% E) 40%

Solution: The problem asks for the approximate chance that no more than 1/3 of the original investment is lost. We can apply the “1 – x” technique: what’s the chance that more than 1/3 of the original investment is lost? There are two outcomes we have to separately measure:   (a) All 3 investments become worthless.   (b) 2 of the 3 investments become worthless, while 1 doesn’t.   Outcome (a): The probability is (0.2)(0.2)(0.2) = 0.008, or a little less than 1%.   Outcome (b): Call the investments X, Y, and Z. The probability that X retains value, while Y and Z become worthless, is (0.8)(0.2)(0.2) = 0.032. Now, we have to do the same thing for the specific scenarios in which Y retains value (while X and Z don’t) and in which Z retains value (while X and Y don’t). Each of those scenarios results in the same math: 0.032. Thus, we can simply multiply 0.032 by 3 to get 0.096, or a little less than 10%.   The sum of these two probabilities is   0.008 + 0.096= 
  0.008 + 0.096 = 0.104
0.104, or a little more than 10%. Finally, subtracting from 100% and rounding, we find that the probability we were looking for is approximately 90%.   The correct answer is A.   This problem illustrates the power of diversification in financial investments. All else being equal, it’s less risky to hold a third of your money in three uncorrelated (independent) but otherwise equivalent investments than to put all your eggs in one of the baskets. That said, be wary of historical correlations! Housing price changes in different US cities were not so correlated—and then they became highly correlated during the recent housing crisis (they all fell together), fatally undermining spreadsheet models that assumed that these price changes were independent.
Answer: A
A man is walking at the rate of 6 km/hr crosses a bridge in 15 minutes. The length of the bridge is
Choices:
A) 1000 meters
B) 1050 meters
C) 1200 meters
D) 1500 meters
E) None of these

Solution: Explanation:   We need to get the answer in meters. So we will first of change distance from km/hour to meter/sec by multiplying it with 5/18 and also change 15 minutes to seconds by multiplying it with 60.   Speed=6âˆ—5/18=5/3m/sec   Time=15âˆ—60seconds=900seconds   1500 metersistance=Timeâˆ—Speed/1500 metersistance=5/3âˆ—900=1500meter   Option 1500 meters
Answer: D
if a three-digit number is selected at random from the integers 100 to 999, inclusive, what is the probability that the first digit and the last digit of the integer will both be exactly two less than the middle digit?
Choose the correct choice from the following:
A) 1:900 B) 7:900 C) 1:1,000 D) 1:100 E) 7:100

Solution: There are 900 numbers between 100 and 999 (inclusive).   Numbers of the form A7:900A are: 131, 242,353,464,575,686,797 = total 7   Thus the probability asked = 7/900   7:900 is the correct answer.
Answer: B
Anil purchased 30 kg of wheat at the rate of Rs. 22 per kg and 20 kg of wheat at the rate of Rs. 24 per kg. He mixed the two. Approximately at what rate per kg should he sell the mixture to make 25% profit?	Answers
A) Rs. 25  B) Rs. 28.5  C) Rs. 30  D) Rs. 32.5  E) None of these

Solution: Explanation:   Total quantity of mixture = 30 + 20= 
30 + 20 = 50
50 kg.   By earning a profit of 25% on the total cost, the selling price of the mixture is   125/100 * (660 + 480= 1140) = Rs. 1425   Selling price per kg = Total selling price / Total of mixture   = 1425 / 50   = Rs. 28.5   ANSWER Rs. 28.5
Answer: B
A pipe can empty 2/3rd of a cistern in 12mins. In 5 mins, what part of the cistern will be empty?
Choose the correct choice from the following answers:
A) 2/3
B) 5/18
C) 4/9
D) 3/8
E) 4/7

Solution: 2/3 ---- 12   ? ----- 5 ==> 5/18   5/18
Answer: B
The radius of the two circular fields is in the ratio 3: 5 the area of the first field is what percent less than the area of the second? Choose the correct choice from the following choices:
A) 69%  B) 79%  C) 60%  D) 64%  E) 24%

Solution: r = 3 πr2 = 9   r = 5 πr2 = 25   25 π – 16 π   100 ---- ? => 64%   Answer: 64%
Answer: D
If a < b < c , which of the following must be true?
(I) a < b^2
(II) b − a > c
(III) a^2 < b^2 < c^2  Options:
A) II only
B) I only
C) None
D) III only
E) II and III

Solution: (I) a < b^2. Not necessarily true fractions: try a=1/3 and b=1/2.   (II) b − a < c. Not necessarily true: try a=-1/2, b=-1/3, and c=-1/4.   (III) a^2 < b^2 < c^2. Not necessarily true: try a=-1, b=0, and c=1.   None of the options must be true.   Answer: None.
Answer: C
According to a survey, at least 50% of people like apples, at least 75% like bananas and at least 80% like cherries. What is the minimum percentage of people who like all three?  Choose the correct choice
A) 5%
B) 10%
C) 15%
D) 20%
E) 25%

Solution: To minimize the percentage who like all three, let's maximize the percentage who like 2 out of 3.   80% like cherries and 20% don't like cherries.   Let's combine this with the people who like bananas.   20% don't like cherries but do like bananas.   55% like cherries and bananas.   25% like cherries but not bananas.   Now let's distribute the people who like apples.   20% like bananas and apples, but not cherries.   25% like cherries and apples, but not bananas.   5% like all three.   50% like cherries and bananas, but not apples.   The answer is 5%.
Answer: A
A pen factory stores its toys in either a big box or a small box. The big box can store 27 pens while the small box can store 18 pens. If the factory is to store 112 newly manufactured pens, what is the least number of pens that will be left unboxed?	Choose the correct choice from the following: A) 6 B) 2 C) 4 D) 3 E) 1

Solution: Total pens to be stored 112   The big box can store 27   small box can store 18   storing 112 pens in big box 112/27 =4 r 4   least number of pens that will be left unboxed=4   Answer: 4
Answer: C