MU-NLPC/Calc-aqua_rat huggingface dataset:
There are 200 female managers in a certain company. Find the total number Y of female employees in the company, if 2/5 of all the employees are managers and 2/5 of all male employees are managers.	Choose the correct answer: A) 300 B) Y=400 C) Y=500 D) Y=600 E) None of these

Solution: {Managers} = {Female Managers} + {Male Managers};   We are told that the total number of managers in the company is 2/5 of all the employees , thus{Managers} = 2/5 (M + F), where M and F are number of female and male employees, respectively.   Also, we know that 2/5 of all male employees are managers:{Male Managers} = 2/5 * Mas well as there are total of 200 female managers:{Female Managers} = 200;   Thus:2/5 (M + F) = 200 + 2/5 * M-->F = 500.   Answer: Y=500.
Answer: C
The number of meters in MB is equal to the square root of the number of centimeters in MB. What is the length of MB (1 meter=100 centimeters)?
Choose the most appropriate option:  A) 100 meters  B) 10 meters  C) 100 centimeters  D) 10 centimeter  E) 1 centimeter

Solution: I'd plug in the options for this question.   Check option A: if the number of meters in MB is 100, then the number of centimeters is 100*100. The square root of 100*100 is 100: 100 = 100.   100 metersnswer: 100 meters.
Answer: A
On a summer camp, 25% of the campers paid $100 each, 35% paid $80 each and the rest paid $65 each. What percentage of the total amount paid came from the campers who paid $80?
Choose the correct choice from the following options
A) 18%  B) 21%  C) 26%  D) 35.44%  E) 37.5%

Solution: let the total no of campers be 100   total amount = (25*100)+(35*80)+(40*65) = 2500+2800+2600= 
2500+2800+2600 = 7_900
$7900   required percentage= (28/79)*100 = 400/12 = 100/3 =35.44%   35.44%
Answer: D
The average of 6 no.'s is 4.60. The average of 2 of them is 3.4, while the average of the other 2 is 3.8. What is the average of the remaining 2 no's?
Choose the correct choice from the following answers.
A) 2.3	B) 6.6	C) 3.6	D) 4.5	E) 4.6

Solution: Sum of the remaining two numbers = (4.6 * 6) - [(3.4 * 2) + (3.8 * 2)]   = 27.60 - (6.8 + 7.6) = 27.60 - 14.40 = 13.20.   Required average = (13.2 / 2) = 6.6.   Answer : 6.6
Answer: B
A and B together can do a work in 6 days. If A alone can do it in 10 days. In how many days can B alone do it?
Choose the correct answer:	A) 10	B) 15	C) 77	D) 55	E) 21

Solution: 1/6 – 1/10 = 1/15   => 15   Answer: 15
Answer: B
A = {1, 2, 3} and B = {4, 5, 6}.Find A-B  Pick
A) {2,8,4}
B) {1,3,5}
C) {1,2,3}
D) {5,10,15}
E) {8,9,10}

Solution: A = {1, 2, 3}   B = {4, 5, 6}   correct answer :A - B = {1, 2, 3}   {1,2,3}
Answer: C
Every disk in a bag is either blue, yellow or green. The ratio of blue disks to yellow disks to green disks in this bag is 3 : 7 : 8. If the total number of disks in the bag is 108, how many more green disks than blue disks are in the bag? Choose the correct choice from the following options.
A) 25 B) 28 C) 30 D) 35 E) 40

Solution: Let B:Y:G = 3x:7x:8x.   3x + 7x + 8x = 18x 3  + 7  + 8= 
3  + 7  + 8 = 18
18x= 108 --> x= 6.   G - B = 8x - 3x = 5x 8  - 3= 
8  - 3 = 5
5x= 30.   The answer is 30.
Answer: C
How many meters are there in 220 centimeters?	Select:	A) 220 meters	B) 20 meters	C) 22 meters	D) 2.2 meters	E) 1 meter

Solution: Solution:   1 meter = 100 centimeters   Just divide 220 by 100   550 Ã· 100 = 2.2, so there are 2.2 meters in 220 centimeters   Option 2.2 meters
Answer: D
Frances can complete a job in 16 hours, and Joan can complete the same job in 8 hours. Frances starts the job at 9 a.m., and stops working at 3 p.m. If Joan starts working at 4 p.m. to complete the job, at what time is the job finished?
Choose the correct choice:
A) 9 p.m.
B) 7 p.m.
C) 8 p.m.
D) 10 p.m.
E) 12 p.m.

Solution: Let the total work be 24 units.   Frances can complete 1.5 units/hr   Joan can complete 3 units/hr   Work done by Frances in 6 hours is 9 units ; work left for Joan is 15 units ( 24 - 9)   Time required by Jones to complete the remaining work will be   15/3= 
  15/3 = 5
> 5 hours   Given Jones starts at 4PM , so she would complete the work at 9 PM   9 p.m.nswer will be (9 p.m.)
Answer: A
A owes B Rs.50. He agrees to pay B over a number of consecutive days on a Monday, paying single note or Rs.10 or Rs.20 on each day. In how many different ways can A repay B.
Pick one
A) 2  B) 8  C) 9  D) 6  E) 5

Solution: He can pay by all 10 rupee notes = 1 way   3 Ten rupee + 1 twenty rupee = 4!3!×1!4!3!×1! = 4 ways   1 Ten rupee + 2 twenty rupee notes = 3!2!×1!3!2!×1! = 3 ways   Total ways = 1 + 4 + 3= 
1 + 4 + 3 = 8
8   Answer:8
Answer: B
Private Benjamin is a member of a squad of 10 soldiers, which must volunteer 4 of its members for latrine duty. If the members of the latrine patrol are chosen randomly, what is the probability Q that private Benjamin will be chosen for latrine duty? Choose the correct choice from the following:
A) 1/10	B) 1/5	C) 2/5	D) 3/5	E) 4/5

Solution: Easier way : Desired probability = 1- 'excluded' probability   In this case, Excluded probability = probability of Benjamin not being a part of the 4 volunteers. We can choose 4 out of 9 remaining soldiers in 9C4 ways. total ways possible = 10C4.   Thus excluded probability = 9C4/10C4 = 3/5   Thus, the desired probability Q= 1- 3/5 = 2/5. Thus 2/5 is the correct answer.
Answer: C
A shopkeeper sells 20% of his stock at 10% profit ans sells the remaining at a loss of 5%. He incurred an overall loss of Rs. 400. Find the total worth of the stock?	Choose the correct choice from the following options:
A) 30000	B) 20000	C) 23000	D) 21020	E) 28211

Solution: Explanation:   Let the total worth of the stock be Rs. x.   The SP of 20% of the stock = 1/5 * x * 1.1 = 11x/50   The SP of 80% of the stock = 4/5 * x * 0.95 = 19x/25 = 38x/50   Total SP = 11x/50 + 38x/50 = 49x/50   Overall loss = x - 49x/50 = x/50   x/50 = 400 => x = 20000   Answer: 20000
Answer: B
In a certain brick wall, each row of bricks above the bottom row contains one less brick than the row just below it. If there are 5 rows in all and a total of 200 bricks in the wall, how many bricks does the bottom row contain ?	Options:
A) 42
B) 35
C) 40
D) 33
E) 38

Solution: The bottom row has x bricks   x+x-1+x-2+x-3+x-4 = 200   5x-10=200   5x=190   x=38   Answer:38
Answer: E
For a certain set, the value range of its members is 108.4. A new set is created from the members of the old set as follows: 12 is subtracted from a member of the old set, and the result is divided by 4. The resulting value is a member of the new set. If this operation is done for each member of the old set, what is the range of values of the members of the new set?	Choose the correct choice from the following answers
A) 24.1
B) 27.1
C) 54.4
D) 98.4
E) 108.4

Solution: Let x and z be the smallest and largest of the original set, respectively.   z - x = 108.4   The smallest and largest members of the new set will be (x-12) / 4 and (z-12) / 4.   Then the range is (z-12) / 4 - (x-12) / 4 = (z-x) / 4 = 108.4 / 4= 
108.4 / 4 = 27.1
27.1   The answer is 27.1.
Answer: B
A present value of a machine is $1000. Its value depletiation rate is 10% per annum then find the machine value after 2 years?	Choose the correct choice:
A) $900 B) $810 C) $915 D) $715 E) $795

Solution: P= $1000   R = 10%   T = 2 years   Machine value after 2 years = P[(1-R/100)^T]   =1000*9/10 * 9/10= 
1000*9/10 * 9/10 = 810
$810   Answer is $810
Answer: B
Month Noah Landing Bellaville
1 3 2
2 2 0
3 0 4
4 2 X
5 1 1
Monthly rainfall was recorded for two towns over a five-month period using the chart above. If the median rainfall in Noah’s Landing was equal to the average (arithmetic mean) rainfall in Bellaville, what is the value of x?	Choose one.
A) 1 B) 8/5 C) 2 D) 3 E) 10

Solution: Arrange Noah's landing rainfall in order which is 0,1,2,2,3 and hence median is 2   Given median of Noah's landing = AM of Bellaville   So 5 * 2 is the sum of all values,   to find x , 10 = 1 + 2+ 4 + x   gives x = 3 ,   Answer is 3
Answer: D
If a natural number p has 8 factors, then which of the following cannot be the difference between the number of factors of p^3 and p?
Choose the correct choice from the following answers
A) 14
B) 30
C) 32
D) 56
E) None of these

Solution: p has 8 factors. That gives following possibilities:   a) p has one prime factor with power 7   => p^3 will have 22 factors. Difference with number of factors of p = 22-8= 
22-8 = 14
14: A is ok   b) p has two prime factors with powers 3 and 1=> p^3 will have 40 factors. Difference with number of factors of p =40-8= 
40-8 = 32
32 : C is ok   c) p has three prime factors with powers 1 each=> p^3 will have 64 factors. Difference with number of factors of p=64-8= 
64-8 = 56
56 : D is ok   There are no other possibilities. Hence remaining answer choice B is not possible.   Answer 30
Answer: B
If t is an even integer and q is an odd integer, which of the following must be an odd integer?	Choose the correct choice from the following answers: A) t/q B) tq C) 2t+q D) 2(t+q) E) 3t/q

Solution: this is a must question:   A. t/q   can be a non-integer   B. tq   always even   C. 2t+q   2t = even -> even+odd = odd   D. 2(t+q)   always even - t+q = odd *2 -> even   E. 3t/q   might be a non integer.   2t+q
Answer: C
On a game show, a contestant spins three different wheels; each wheel is numbered 1 to 12. What is the probability that the contestant will spin all tens?  Choose the correct choice:
A) 52 B) 1/1728 C) 67 D) 2/58 E) 9/7

Solution: All 12s:   1st wheel = 12= 1/12   2nd wheel = 12 = 1/12   3rd wheel = 12 = 1/12   (1/12)(1/12)(1/12) = 1/1728   Answer: 1/1728
Answer: B
Find the value of * in the following
(1 5/3) ÷ 3/11 × */11 = (2 2/3 × 7/5 × 6/7)	Choose the most appropriate option.
A) 1 B) 1.5 C) 3.6 D) 4 E) 4.1

Solution: Option '3.6'
Answer: C
The H.C.F. of two numbers is 11 and their L.C.M. is 7700. If one of the numbers is 275, then the other is: Choose the correct choice from the following answers:	A) 306	B) 308	C) 310	D) 311	E) 315

Solution: LCM X HCF = First No. X Second No.   LCM=7700   HCF=11   First No.=275   7700 X 11 = 275 X Second No.   Second No.= 308   answer :308
Answer: B
Two trains 200m and 250m long run at the speed of 72kmph and 18kmph in opposite directions in parallel tracks. The time which they take to cross each other is?	Choose the correct choice from the following answers:
A) 5.6sec B) 8.9sec C) 10.8sec D) 12.6sec E) 18 sec

Solution: Relative speed = 72+18= 
72+18 = 90
90 kmph * 5/18= 25 m/s   Distance covered in crossing each other = 200+250= 
200+250 = 450
450m   Required time= 450*1/25= 
450*1/25 = 18
18 sec   Answer is 18 sec
Answer: E
An urn contains 10 black and 5 white balls. Two balls are drawn from the urn one after the other
without replacement. What is the probability that both drawn balls are black?  Choose the most appropriate option:	A) 1/5	B) 2/7	C) 3/7	D) 4/5	E) 5/4

Solution: Let E and F denote respectively the events that first and second ball drawn   are black. We have to find P(E n F) or P (EF).   Now P(E) = P (black ball in first draw) = 10/15   Also given that the first ball drawn is black, i.e., event E has occurred, now there are 9 black balls and five white balls left in the urn. Therefore, the probability that the second ball drawn is black, given that the ball in the first draw is black, is nothing but the conditional probability of F given that E has occurred.   That is P(F|E) = 9/14   By multiplication rule of probability, we have   P (E n F) = P(E) P(F|E)   = 10/15 × 9/14 = 3/7   3/7
Answer: C
The simple interest on Rs.12000 at a certain rate of interest in five years is Rs.7200. Find the compound interest on the same amount for five years at the same rate of interest.  Choose the correct option.
A) Rs.3502.80 B) Rs.3052.40 C) Rs.3054.8 D) Rs.3052.80 E) None of these

Solution: R = 100 I / PT   => R = (100 * 7200)/ (12000 * 5)= 
(100 * 7200)/ (12000 * 5) = 12
12%   CI= P{ [1 + R /100]n - 1}   = 12000 { [ 1 + 12 / 100]2 - 1} = Rs.3052.80   ANSWER:Rs.3052.80
Answer: D
a, b, c, and d are positive consecutive even integers and a < b < c < d.
If the product of the highest and lowest numbers is six more than the sum of the middle numbers, what is the product of the smallest two numbers?
Choose the correct choice from the following choices
A) 2  B) 4  C) 8  D) 12  E) 20

Solution: We know the numbers must be consecutive even numbers, from the list 2, 4, 6, 8, 10, 12, 14, 16, and so on.   The product ad is 6 more than the sum bc. By testing some possible ad products (even numbers separated by two other even numbers), we can quickly see that the numbers have to be quite small: 6x12 is 72, much higher than any of the possible sums, and the products will go up much faster than the sums will.   However, the lowest possible sequence gives an ad product of 2x8, or 16. And summing the middle numbers gives 10, exactly six less than the product. We have found the sequence: 2-4-6-8.   The answer, then, is the product of the smallest two numbers, or 2x4, which is 8 (option 8).
Answer: C
A radio station has to choose a week of the four in a month to broadcast a certain program, and that set will repeat each month. The program can be broadcast equally on any of the four week —- 1st week vs. last week don’t matter at all —- nor does it matter whether the week the program airs are adjacent or not. Absolutely any week of the 4 weeks can be chosen. How many different week combinations of the 4 weeks can be constructed?  Pick one
A) 4  B) 15  C) 21  D) 35  E) 56

Solution: Pick 1 week out of 4.. 4C1 =4   4nswer : 4
Answer: A
A TV is bought for Rs.6000/- and sold at a loss of 25% find its selling price? Choose the correct choice from the following:
A) s.4000/-	B) s.5560/-	C) s.3580/-	D) s.4500/-	E) s.5600/-

Solution: 100 % ------> 6000 (100 * 60 = 600)   75 % ------> 4500 (75 * 60 = 4500)   Selling price = Rs.4500/-   Option 's.4500/-'
Answer: D
Of the 720 students at a certain university, 25 percent are seniors. If x seniors were to graduate early and leave the university and no additional students entered or left the university, what value of x would reduce the number of seniors at the university to 20 percent? Choose the correct option.
A) 30	B) 36	C) 42	D) 45	E) 48

Solution: Sol:   180-x= 20% of (720-x)   4x=180   x=45   ANSWER:45
Answer: D
Find the value of x. (47% of 1442 - 36% of 1412) + 66 = x? Pick one.
A) 1
B) 2
C) 3
D) 6
E) 5

Solution: 6) 6
Answer: D
You forgot the three digit code of your safe. But you have written some hints to calculate the code if you forgot the code.
Below are the hints that you have written
Hint-1 : One of the numbers is correct and is placed in its correct position
5 4 7
Hint-2: Nothing is correct
5 3 0
Hint-3: Two numbers are correct but not placed at its correct position.
2 5 9
Hint-4: One number is correct but not placed at its correct position.
7 0 6
Hint-5: One number is correct but not placed at its correct position.
6 4 9
What's is the code.
Choose the correct choice from the following choices:
A) 927  B) 937  C) 947  D) 957  E) 967

Solution: Solution:   927   1) 5 4 7 : 7 is placed correctly   2) 5 3 0 : None of the numbers is in the code   3) 2 5 9 : 2 & 9 are correct number of code but placed at wrong position   4) 7 0 6: Number 7 is there but placed at wrong position   5) 6 4 9: Number 9 is there but placed at wrong position   927nswer 927
Answer: A
A box contains 30 mangoes out of which 7 are spoilt. If seven mangoes are chosen at random, find the probability that A number is selected at random from first ninty natural numbers. What is the chance that it is a multiple of either 9 or 11?
Choices.
A) 1/5	B) 3/5	C) 2/5	D) 4/15	E) 7/5

Solution: The probability that the number is a multiple of 9 is 10/90. (Since 9*10= 
9*10 = 90
90).   Similarly the probability that the number is a multiple of 11 is 8/90. {Since   11*8= 
  11*8 = 88
88).   Neither 9 nor 11 has common multiple from 1 to 90. Hence these events are mutually exclusive events. Therefore chance that the selected number is a multiple of 9 or 11 is (10+8)/90= 1/5.   1/5NSWER:1/5
Answer: A
A motorist travels for 6 hours, the first half at 60 Kmph and the rest at 48 Kmph. Find the distance Traveled by him. Answers: A) 234 B) 124 C) 324 D) 452 E) 352

Solution: Distance = 3 * 60 + 3 * 48   = 180 + 144= 
180 + 144 = 324
324 Km   Answer 324.
Answer: C
A person want to give his money of $1000 to his 3 children A,B,C in the ratio 6:4:5 What is the A+B share?	Choose one:
A) $660.67
B) $646.67
C) $666.67
D) $500.56
E) $600.24

Solution: A's share = 1000*6/15= 
1000*6/15 = 400
$400   B's share= 1000*4/15= $266.67   A+B = $666.67   Answer is $666.67
Answer: C
Tough and Tricky questions: Combinations.
Seven students - 4 boys and 3 girls - are to sit side by side for a makeup exam. How many ways could they arrange themselves given that no two boys and no two girls can sit next to one another?
Choose the correct choice from the following
A) 12	B) 36	C) 72	D) 288	E) 720

Solution: 4!*3!*2 = 24*6*2 4 *3 *2= 
4 *3 *2 = 24
24*6*2= 
24*6*2 = 288
288 ways.   Ans. 288) 288
Answer: D
Which of the following is the ninth to the right of the twentieth element from the right end of the above arrangement? Choose the correct choice from the following: A) I only B) II only C) I and II D) WEWW E) II and III

Solution: Answer: Option WEWW
Answer: D
he L.C.M. of two numbers is 48. The numbers are in the ratio 2 : 3. Then sum of the number is:
Choose one.
A) 30 B) 40 C) 38 D) 36 E) 39

Solution: Let the numbers be 2x and 3x.   Then, their L.C.M. = 6x.   So, 6x = 48 or x = 8   The numbers are 16 and 24.   Hence, required sum = (16 + 24)= 
(16 + 24) = 40
40. Answer: Option 40
Answer: B
A University library checks out books for a 5-week period, but allows them to be renewed up to 6 times. What is the Maximum no.of Weeks the library will allow a book to be checked out?	Answers:
A) 33	B) 35	C) 37	D) 39	E) 41

Solution: Library checkout is 5 week period and can be renewed 6 times. So he can keep for a maximum of 8 weeks.   when he is allotted the book   0-5 weeks (1st renew)   5-10 weeks (2nd renew)   10-15 weeks (3rd renew)   15-20 weeks (4th renew)   20-25 weeks (5th renew)   25-30 weeks (6th renew)- maximum renew   after that,   30-35 (submission)   So 35 weeks is maximum.   ANSWER:35
Answer: B
X is a positive number which when increased by 17 is equal to 60 times the reciprocal of the number. Find value of X?	Options
A) 3
B) 4
C) 6
D) 7
E) 8

Solution: Let the number be x.   Then, x + 17 =	60   x   x2 + 17x - 60 = 0   (x + 20)(x - 3) = 0   x = 3   3
Answer: A
A train 120 m long is running with a speed of 66 km/hr. In what time will it pass a man who is roller skating at 12 km/hr in the direction opposite to that in which the train is going?  Pick.
A) 4.92
B) 6.92
C) 7.92
D) 4.92
E) 2.92

Solution: Speed of train relative to man = 66 + 12= 
66 + 12 = 78
78 km/hr.= 78 * 5/18 = 65/3 m/sec.   Time taken to pass the man = 150 * 3/65   = 6.92 sec.   Answer: 6.92
Answer: B
A train 300 m long can cross an electric pole in 10 sec and then find the speed of the train?  Choices:
A) 88 Kmph B) 89 Kmph C) 72 Kmph D) 16 Kmph E) 108 Kmph

Solution: Length = Speed * time   Speed = L/T   S = 300/10= 
300/10 = 30
30 M/Sec   Speed= 30*18/5 (To convert M/Sec in to Kmph multiply by 18/5)   Speed = 108 Kmph   Answer: 108 Kmph
Answer: E
In a class of 20 students in an examination in Mathematics 2 students scored 100 Marks each, 3 get
zero each and the average of the rest was 40. What is the average Of the whole class?
Select the correct option:	A) 46	B) 49	C) 40	D) 38	E) 35

Solution: Total marks obtained by a class of 20 students   = 2 * 100 + 3 * 0 + 15 * 40   = 200 + 600= 
200 + 600 = 800
800   : Average marks of whole class= 800/20= 
800/20 = 40
40   Answer is 40.
Answer: C
In how many ways can A, B, C, D and E be seated in a row such that A and B are not seated next to each other? Answers:
A) 24
B) 72
C) 56
D) 76
E) 96

Solution: When the constraint on an arrangement says,Two people should not be seated together,we do just the opposite. We make them sit together! Kind of tie them with a thread and assume they are one unit!   Let's see why....   These 5 people can be arranged in 5! ways. These are the total number of ways you get.   Now, when we tie 2 people together, we have only 4 entities to arrange. We can do this in 4! ways. But in each of these entities, the two people can sit in two different ways (AB and BA). So number of ways in which these two people sit together is 4!*2!.   Now, the ways in which these two people will not be together will be 5!- 4!*2! = 4!(5 - 2) = 72   Answer :72
Answer: B
A bowl was filled with 10 ounces of water, and 0.006 ounce of the water evaporated each day during a 50-day period. What percent of the original amount of water evaporated during this period?
Choose the correct answer
A) 0.004%
B) 0.04%
C) 0.40%
D) 3%
E) 40%

Solution: Total amount of water evaporated each day during a 50-day period = .006 * 50   =.006 * 100/2   = .6/2= 
.6/2 = 0.3
.3   percent of the original amount of water evaporated during this period= (.3/10) * 100= 
(.3/10) * 100 = 3
3 %   Answer 3%
Answer: D
Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 90 kmph and 72 kmph. In how much time will the trains cross each other?
Select:
A) 80/6	B) 80/7	C) 80/9	D) 80/2	E) 80/1

Solution: Relative speed = (90 + 72)* 5/18= 
(90 + 72)* 5/18 = 45
45 mps.   The time required= d/s = (100 + 100 + 200)/45   = 400/45 = 80/9 sec.   Answer:80/9
Answer: C
If x > 3000, then the value of (1.2x)/(0.5x-406) is closest to?	Choose the most appropriate option
A) 1/6  B) 1/3  C) 10/21  D) 1/2  E) 3/1

Solution: assume x = 3002   (1.2 x)/(0.5 x-406) = 3602.4 / (3002*0.5-406)   =3602.4 / 1095   = = 3 /1   3/1
Answer: E
A, B and C can do a piece of work in 9 days, 14 days and 28 days respectively. How long will they taken, if all the three work together?
Select the correct option:	A) 4.12 days	B) 4.52 days	C) 3.52 days	D) 2.52 days	E) 4.92 days

Solution: 1/9 + 1/14 + 1/28 = 55/252   => 252/55 days   =>4.52 days   ANSWER:4.52 days
Answer: B
Two kinds of Vodka are mixed in the ratio 1:2 and 2:1 and they are sold fetching the profit 10% and 40% respectively. If the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4/3 and 5/3 times respectively, then the mixture will fetch the profit of
Choose the correct choice from the following answers:	A) 18%	B) 20%	C) 21%	D) 40%	E) Cannot be determined

Solution: Answer: 40%.
Answer: D
The table below shows the enrollment in various classes at a certain college.
Class | Number of Students
Biology | 55
Physics | 35
Calculus | 40
Although no student is enrolled in all three classes, 15 are enrolled in both Biology and Physics, 10 are enrolled in both Biology and Calculus, and 12 are enrolled in both Physics and Calculus. How many different students are in the three classes?
Choose the correct choice from the following options
A) 51
B) 88
C) 93
D) 125
E) 162

Solution: No. of total students = no of students of biology + no of students of physics but not biology + no of students of calculus but not biology and physics   No. of total students = 55 + (35-15) + (40-10-12) = 55+20+18= 
55+20+18 = 93
93   Hence, Answer will be 93.
Answer: C
Set A contains three different positive odd integers and six 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?
Choose the most appropriate option.
A) 3/5 B) 7/10 C) 13/15 D) 23/30 E) 37/45

Solution: There can be an odd product only if both integers are odd.   P(odd product) = 3/9*2/5 = 2/15   P(even product) = 1 - 2/15 = 13/15   The answer is 13/15.
Answer: C
Last year a certain bond yielded 15 percent of its face value in interest. If that interest was approximately 4 percent of the bonds selling price of $7,500, what is the bonds face value? Options:
A) $2,000 B) $6,750 C) $7,425 D) $7,500 E) $9,375

Solution: Interest = 0.15*face value = 0.04*7,500 --> face value = 0.04*7,500/0.15 = 2,000.   $2,000nswer: $2,000.
Answer: A