MU-NLPC/Calc-aqua_rat huggingface dataset:
A class of 4 Gangs is to be chosen from five Gangs.Each Gang contains 2 people.What is the number of different Gangs that can be chosen if two people who are in same gang to each other cannot both serve on the class?
Choose the correct choice from the following options:
A) 840 B) 960 C) 60 D) 720 E) 1050

Solution: Each GANG can send only one representative to the class. Let's see in how many ways we can choose 3 gangs (as there should be 3 members) out of 4 to send only one representatives to the class: 5C4=60.   But each of these 3 gangs can send two persons : 2*2*2*2=2^4=16.   Total # of ways: 5C4*2^4=960.   Answer: 960.
Answer: B
The sum of all the integers k such that –23 < k < 24 is  Choose the most appropriate option:
A) 0
B) -43
C) -25
D) -49
E) -51

Solution: -22------------------0-----------------23   values upto+23 cancels outwe are left with only -22-21 sum of which is - 43. hence option D.   -43
Answer: B
If b does not equal zero, and ab = b/2, what is the value of a? Choose the correct option.
A) A)1/8
B) B)1/4
C) C)1/3
D) D)1/2
E) of the above

Solution: Explanation:   To solve for a, divide both sides of the equation by b: ab = b/2   (ab)/b = (b/2)/b   a = (b/2)*1/b   a = 1/2   Answer: (1/2).
Answer: D
If grapes are 92% water and raisins are 20% water, then how much did a quantity of raisins, which currently weighs 10 pounds, weigh when all the raisins were grapes? (Assume that the only difference between their raisin-weight and their grape-weight is water that evaporated during their transformation.)	Choices:  A) 25 pounds  B) 46 pounds  C) 92 pounds  D) 100 pounds  E) 146 pounds

Solution: Since only water evaporates, then the weight of pulp (non-water) in grapes and raisins is the same. Thus 0.08*{weight of grapes}=0.8*{weight of raisins} --> 0.08x = 0.8*10 --> x = 100.   Answer: 100 pounds.
Answer: D
Find large number from below question The difference of two no.'s is 1365. On dividing the larger no. by the smaller, we get 6 as quotient and the 15 as remainder? Choose one:  A) 1456  B) 1563  C) 1546  D) 1643  E) 1635

Solution: Let the smaller number be x. Then larger number = (x + 1365).   x + 1365 = 6x + 15   5x = 1350   x = 270   Large number = 270+1365= 
270+1365 = 1_635
1635   1635
Answer: E
Excluding stoppages, the speed of a bus is 40 kmph and including stoppages, it is 30 kmph. For how many minutes does the bus stop per hour?	Choose the correct choice from the following answers:
A) 10 min
B) 12 min
C) 18 min
D) 15 min
E) 20 min

Solution: Due to stoppages, it covers 10 km less.   Time taken to cover 10 km = (10/40 x 60) min = 15 min   Answer : 15 min
Answer: D
If the difference between compound interest (interest compounded yearly)and simple interest on a sum for 2 years at 10% p.a. is Rs.150 then sum is  Choose the correct choice from the following answers
A) Rs.12,000 B) Rs.15,000 C) Rs.13,000 D) Rs.10,000 E) Rs.14,000

Solution: compund interest = p[1+r/100]^t-p   CI = p[21/100]   simple interest = ptr/100   SI = p[20/100]   difference p[21/100]-p[20/100] = 150   p=15,000   ANSWER:Rs.15,000
Answer: B
Jessica can text 85 words per minute, while Maurice can text 25 words per minute. An abridged English translation of Tolstoy’s War and Peace contains 410,400 words. Working together, how many days will it take Jessica and Maurice to text the entire abridged translation of War and Peace?
Choose one:
A) 0.3 B) 1.3 C) 3 D) 2.6 E) 11.3

Solution: Since the answer choices are reasonably spaced out, we can approximate and save time   Combined words per day = 110*60*24   410400/158400 will be closest to only 2.6   So, Answer should be 2.6.
Answer: D
If the sides of a cube are in the ratio 5:3. What is the ratio of their diagonals? Select the correct option
A) 5:9 B) 9:3 C) 5:4 D) 3:5 E) 5:3

Solution: 5:3xplanation:   Diagonal of a Cube=a√3 where a is side   a1:a2 = 5:3   d1:d2 = 5:3 where√3 cancelled both side   ANSW5:3R:5:3
Answer: E
A and B can do a piece of work in 18 days; Band C can do it in 24 days A and C can do it in 36 days. In how many days will A, Band C finish it together?  Options:
A) 14 B) 16 C) 19 D) 18 E) 20

Solution: (A + B)'s 1 day's work = (1/18) (B + C)'s 1 day's work = (1/24)   and (A + C)'s 1 day's work = (1/36)   Adding, we get: 2 (A + B + C)'s 1 day's work =¬(1/18 + 1/24 + 1/36)   =9/72 =1/8   (A +B + C)'s 1 day's work =1/16   Thus, A, Band C together can finish the work in 16 days.   ANSWER 16 16
Answer: B
How many common two-digit whole numbers are there which gives a remainder of 2 when divided by 9 and gives a remainder of 5 when divided by 8? Choose the correct choice from the following options:
A) Five
B) Three
C) One
D) Two
E) Four

Solution: Answer = One) One   Two digit numbers giving remainder 2 when divided by 9 = 11, 20, 29, 38, 47, 56, 65, 74, 83, 92   Two digit numbers giving remainder 5 when divided by 8 = 13, 21, 29, 37, 45, 53, 61, 69, 77, 85, 93   Oneommon Numbers = 29 = 1
Answer: C
As a treat for her two crying children, a mother runs to the freezer in which she has two cherry ice pops, four orange ice pops, and four lemon-lime ice pops. If she chooses two at random to bring outside to the children, but realizes as she runs out the door that she cannot bring them different flavors without one invariably being jealous of the other and getting even more upset, what is the probability that she has to return to the freezer to make sure that they each receive the same flavor?  Choose the correct option.
A) 1/9
B) 1/6
C) 5/18
D) 4/45
E) 5/6

Solution: Probability of not getting the same flavor ->   Favorable -> Cherry - orange [ 2C1 * 4C1 [or simply 2*4 ] or Cherry - lemon [ 2*4] or orange - lemon [4*4]   Prob = (2*4 + 2*4 + 4*4 ) / 9C2 = 32/360 = 4/45   Answer -> 4/45
Answer: D
Alex takes a loan of $6,000 to buy a used truck at the rate of 8 % simple Interest.Calculate the annual interest to be paid for the loan amount.  Choose the correct choice from the following answers
A) 680
B) 700
C) 720
D) 480
E) 420

Solution: From the details given in the problem Principle = P = $6,000 and R = 8% or 0.08 expressed as a decimal.   As the annual Interest is to be calculated, the time period T =1.   Plugging these values in the simple Interest formula,   I = P x T x R   = 6,000 x 1 x 0.08   = 480.00   Annual Interest to be paid = $480   answer :480
Answer: D
If the diameter of circle R is 60% of the diameter of circle S, the area of circle R is what percent of the area of circle S?
Select.
A) 50%	B) 46%	C) 36%	D) 26%	E) 38%

Solution: Let diameter of circle R , dr = 60   and diameter of circle S , ds = 100   Radius of circle R , Rr = 30   Radius of circle S , Rs = 50   Area of circle R/ Area of circle S = (pi * Rr ^2 ) /( pi * Rs^2 )   = (30/50)^2 = (6/10)^2   =36%   Answer :36%
Answer: C
Find the number of square tiles to cover the floor of a room measuring 6.5 m * 8.5 m leaving 0.25 m space around the room. A side of square tile is given to be 25 cms?
Select:
A) 768 B) 476 C) 429 D) 428 E) 413

Solution: Floor area to be covered by tiles = 6 * 8= 
6 * 8 = 48
48   tiles area= 0.25 * 0.25= 
0.25 * 0.25 = 0.0625
0.0625   No. of tiles= 48/0.0625= 
48/0.0625 = 768
768   768nswer : 768
Answer: A
k = 2^n + 6, where n is an integer greater than 1. If k is divisible by 9, which of the following MUST be divisible by 9?  Choose the correct choice from the following options.
A) 2^n - 8	B) 2^n - 2	C) 2^n-3	D) 2^n + 4	E) 2^n + 5

Solution: Given: k, M and N are integers   If k is a divisor of both N and M, then k is a divisor of N+M (and N–M and M–N)   We're told that 9 is a divisor of 2^n + 6   We also know that 9 is a divisor of9.   So, applying the abov erule, 9 is a divisor of 2^n + 6 +9, and 9 is a divisor of 2^n + 6 -9 =2^n-3   2^n-3
Answer: C
A train speeds past a pole in 15 seconds and a platfrom 100 m long in 25 seconds. Its length is :
Select the correct option:
A) 100 m	B) 125 m	C) 130 m	D) 150 m	E) None

Solution: Sol.   Let the length of the train be x metres and its speed be y m/sec.   They, x / y = 15 ⇒ y = x/15   ∴ x + 100 / 25 = x / 15 ⇔ x = 150 m.   Answer 150 m
Answer: D
A bag contains five white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color? Choose the correct answer:  A) 5/1  B) 5/9  C) 5/5  D) 5/3  E) 5/2

Solution: Two balls can be picked from nine balls in ⁹C₂ ways.   We select one white ball and one red ball from five white balls and four red balls. This can be done ⁵C₁ . ⁴C₁ ways.   The required probability   = (5 * 4)/⁹C₂   = 20/36   = 5/9   Answer:5/9
Answer: B
Raju, Rahim, Rajesh together can do a work in 5 days. Raju alone can do the work in 10 days and Rahim alone can do the same work in 20 days. Find in what time Rajesh alone can do that work?
Options: A) 10days B) 15days C) 20days D) 30days E) 18days

Solution: The required answer is = 5*10*20 / 10*20-5(10+20)   = 1000/50= 
1000/50 = 20
20days   Answer is 20days
Answer: C
A certain list consists of 21 different numbers. If n is in the list and n is 4 times the average(arithmetic mean) of the other 20 numbers in the list, then n is what fraction E of the sum of the 21 numbers in the list?	Choose the correct option
A) 1/20
B) 1/6
C) 1/5
D) 4/21
E) 5/21

Solution: This is how I used to calculate which I think works pretty well:   if you let the average of the 20 other numbers equal a, can you write this equation for sum of the list (S)   n + 20a = S   the question tells us that   n = 4a   plug this back into the first equation and you get that the sum is 24a   4a + 20a = 24a   therefore fraction E of n to the total would be   4a/24a or 1/6   answer 1/6 4  + 20= 
 4  + 20 = 24
24a   therefore fraction E of n to the total would be   4a/24a or 1/6   answer 1/6
Answer: B
The wages earned by Robin is 50% more than that earned by Erica. The wages earned by Charles is 60% more than that earned by Erica. How much percent is the wages earned by Charles more than that earned by Robin?
Choose the correct answer:
A) 18.75%	B) 23%	C) 30%	D) 50%	E) 7%

Solution: Let wage of 7%rica = 10   Wage of Robin = 1.5*10= 
1.5*10 = 15
15   Wage of Charles= 1.6 *10= 
1.6 *10 = 16
16   Percentage by which wage earned by Charles is more than that earned by Robin= (16-15)/15 * 100%   = 1/15 * 100%   =7%   Answer 7%
Answer: E
What is 92% of 3/5?	Select the correct option
A) 0.552  B) 69.0  C) 0.6845  D) 0.6859  E) 0.69

Solution: 92%*(3/5)=0.92*0.6= 
0.92*0.6 = 0.552
0.552   0.552nswer :0.552
Answer: A
The area of a rectangular plot is 460 square metres. If the length is 15% more than the breadth, what is the breadth of the plot?	Select:
A) 14 metres	B) 20 metres	C) 18 metres	D) 16 metres	E) 17 metres

Solution: Explanation:   length =115% of breadth.   length×breadth =460 m2   ⇒ 115% of breadth×breadth =460 m2   ⇒ 115/100× breadth×breadth =460 m2   ⇒ breadth×breadth =400 m2   ⇒ breadth =20 m   Answer: Option 20 metres
Answer: B
There are 13 South American countries, Anncy has won a ticket to fly from Denver to one South American country and then directly to another South American Country before returning home to Denver again. Assuming there are four airports in each country, how many flights paths can Anncy choose from? Choices
A) 13.12.11.10.4.4.
B) 13.12.11.10.4
C) 13.12.4.4.
D) 13.12.4
E) 13.13.13.13

Solution: flights paths can Anncy choose from There are 13 ways to chose the first destination,   then, 12 ways to chose next destination, with option of 4 airports (13x4)   then, to return he has 4 options to chose the airports   Thus, 13*12*4*4 ways.   Using permutations:   If the solution had written 13P1 instead of 13C1 it won't matter. As per the definition - making arrangements of the combinations gives permutations.   Since there are no arrangement for 1 item, permutationscombinations are equal.13.12.4.4.
Answer: C
Starting with 0, a mathematician labels every non-negative integer as one of five types: alpha, beta, gamma, delta, or epsilon, in that repeating order as the integers increase. For instance, the integer 8 is labeled delta. What is the label on an integer that is the sum of an alpha raised to the seventh power and an epsilon raised to the seventh power?  Choose one:
A) alpha
B) beta
C) gamma
D) delta
E) epsilon

Solution: Let the alpha be 5k and let the epsilon be 5j+4.   (5k)^7 + (5j+4)^7 which has the form 5k+4, which is an epsilon.   The answer is epsilon.
Answer: E
A man opens a shop. He buys water bottles for 50 cents each, fruit for 25 cents each, and snacks for a dollar each. He wants to start a bundle of selling a bottle a water, 3 snacks and 2 fruits for D dollars. Every 5th bundle sold will be sold for 2 dollars and a complimentary snack at the owner's expense. What should he charge at least to not lose any money?
Choose the correct option
A) 4.6	B) 3.0	C) 4.1	D) 3.2	E) 2.9

Solution: W=0.50   F = 0.25   S = 1.00   B= W+2F+3S = 4.00 they pay, he pays 4, net loss 0   fifth bundle = 2 they pay, he pays 5, net loss 3 dollars   3/5 = 60 cents.   Charging 60 more cents on each bundle will be safe.   answer: 4.6
Answer: A
The marked price of a book is 20% more than the cost price. After the book is sold, the vendor realizes that he had wrongly raised the cost price by a margin of 25%. If the marked price of the book is Rs.30, what is the original cost price of the book?  Options:
A) Rs.30
B) Rs.25
C) Rs.45
D) Rs.20
E) Rs.10

Solution: Let the incorrect cost price be C1 and let the original cost price be C2.   Marked price of book is Rs.30. It is 20% more than C1.   Therefore, (120/100) X C1 = 30   Or C1 = 25.   C1 is more than C2 margin of 25%.   Or C1 = (125/100)C2   Therefore, C2 = (100/125) x 25 = Rs 20   ANSWER:Rs.20
Answer: D
A bat is bought for Rs.400 and sold at a gain of 10% find its selling price?	Choose the correct choice from the following options.
A) s.460/-
B) s.480/-
C) s.500/-
D) s.520/-
E) s.440/-

Solution: 100 % ------> 400 (100 * 4 = 400)   110 % ------> 440 (120 * 4 = 440)   Selling price = Rs.440/-   Option 's.440/-'
Answer: E
Two water pumps, working simultaneously at their respective constant rates, took exactly 5 hours to fill a swimming pool. If the constant rate of one pump was 1.5 times the constant rate of the other, how many hours would it have taken the faster pump to fill the pool if it had worked alone at its constant rate? Choose the correct choice from the following.
A) 5/3	B) 16/3	C) 17/3	D) 22/3	E) 25/3

Solution: Let the rate of the slow pump be x. Then the rate of the fast pump is 1.5x.   (x+1.5x)*5 = 2.5x*5 = 12.5x, which is the capacity of the whole pool.   Working alone:   1.5x*Time 2.5 *5= 
2.5 *5 = 12.5
12.5x, which is the capacity of the whole pool.   Working alone:   1.5x*Time= 12.5x   Time = 12.5/1.5 = 125/15 = 25/3 hours   The answer is 25/3.
Answer: E
The population of bacteria culture doubles every 2 minutes.approximately how many minutes will it take for the population to grow from 1000 to 500,000 bacteria?  Pick.
A) 10
B) 12
C) 14
D) 18
E) 20

Solution: 2000^1,2000^2,2000^3,2000^4.......2000^9   population increases in this sequence   taking   9*2= 
  9*2 = 18
18   ANSWER:18
Answer: D
Using all the letters of the word "SATURDAY", how many different words can be formed?  Select
A) A)7	B) B)8	C) C)8!	D) D)7!	E) E)3

Solution: Explanation:   Total number of letters = 8   Using these letters the number of 8 letters words formed is ⁸P₈ = 8!.   Answer: Option 8!
Answer: C
The true discount on a bill due 9 months hence at 16% per annum is Rs. 270. The amount of the bill is  Choose the correct choice
A) 2200
B) 2520
C) 2600
D) 3354
E) None of these

Solution: Explanation:   Let P.W. be Rs.x.   Then, S.I. on Rs. x at 16% for 9 months = Rs. 270.   x Ã— 16 Ã— (9/12) Ã— (1/100) = 270 or x = 2250.   P.W. = Rs. 2250   Sum due = P.W. + T.D. = Rs.(2250   270) = Rs. 2520   Answer: 2520
Answer: B
1/3 of certain journey is covered at the rate of 25kmph,one-fourth at the rate of 30kmph and the rest at 50 kmph.Find the avg speed for the whole journey.
Choose the correct answer.
A) 45 kmph
B) 44.35 kmph
C) 33.333 kmph
D) 39.57 kmph
E) 43.766 kmph

Solution: Average speed = total distance / total time   L33.333 kmphM = 3, 4 = 12   Average speed = 12 / (1/3*12*1/25 + ¼ * 12*1/30 +5/50)   = 12/ (4/25 + 3/30+ 5/30   = 150*12/54 = 33.333 kmph   33.333 kmph
Answer: C
Thomas's salary and Matt's salary are in the ratio 1:2. If both get an increment of Rs. 4000 their salaries would be in the ratio of 7:12. Find Thomas's salary as of now?	Choose the correct choice from the following choices:	A) 5000	B) 10000	C) 15000	D) 20000	E) 25000

Solution: Let salaries of Thomas and Matt be x and y respectively.   x/y = 1/2 => x = 1/2 y   (x+4000)/(y+4000) = 7/12   => 12x + 48000 = 7y+28000=> 12x = 7y-20000   10000ut x = 1/2 y   6y = 7y-20000   y = 20000   x = 10000   Thomas salary is Rs.10000   Answer:10000
Answer: B
In how many different ways can the letters of the word VALUES be arranged in such a way that the vowels occupy only the odd positions?	Choose the correct choice from the following answers:
A) 120	B) 36	C) 48	D) 32	E) 72

Solution: The 3 vowels can be arranged in three odd places in 3! ways.   Similarly, the 3 consonants can be arranged in three even places in 3! ways.   The total number of arrangements in which vowels occupy odd positions = 3! Ã— 3! = 6 Ã— 6 = 36   The answer is 36.
Answer: B
2, 3, 5, 16, 231, ?  Select
A) 62005
B) 52120
C) 422
D) 53105
E) 56200

Solution: Explanation :   2   3   32 - 22 = 5   52 - 32 = 16   162 - 52 = 231   2312 - 162 = 53105   Answer : Option 53105
Answer: D
In a certain city each of 28 primary schools is represented by a colored flag. Each flag consists of either a single color or a pair of two different colors. If each school has a different flag, what is the minimum number of colors needed for the flags. (Assume that the order of colors in a pair on a flag does not matter.)
Options
A) 7  B) 9  C) 8  D) 10  E) 5

Solution: A.7:   if we have 7 colors we can choose pairs in 7C2 ways = 21 and single color flags are 7. Therefore total number of flags = 28.   7NS 7.
Answer: A
The sides of a square region, measured to the nearest centimeter, are 7 centimeters long. The least possible value of the actual area of the square region is	Pick one
A) 42.25 sq cm	B) 45.25 sq cm	C) 43.25 sq cm	D) 50.25 sq cm	E) 52.25 sq cm

Solution: Though there might be some technicalities concerning the termnearest(as 6.5 is equidistant from both 6 and 7) the answer still should be A: 6.5^2=42.25.   42.25 sq cmnswer: 42.25 sq cm
Answer: A
An ant walks an average of 500 meters in 12 minutes. A beetle walks 15% less distance at the same time on the average. Assuming the beetle walks at her regular rate, what is its speed in km/h?  Choose the correct choice from the following options.
A) 2.215  B) 2.5.  C) 2.775  D) 3.2  E) 3.5

Solution: the ant walks an average of 500 meters in 12 minutes   or,   500 meters in 1/5 hours   the beetle walks 15% less distance = 500-75= 
500-75 = 425
425 meters in 12 minutes   or,   0.425 km in 12/60= 1/5 hours   speed = 0.425*5= 
0.425*5 = 2.125
2.125 km/h   2.215ns should be 2.125   2.215NSWER:2.215
Answer: A
Father John forms a choir from the church attendants. 30 people attend John's church, and the choir has 28 spots available, with one person as the lead singer. How many different combinations does John have? Select the correct option
A) 3005 B) 4412 C) 6544 D) 12180 E) 24366

Solution: Pick the lead first - there are 30 choices. Now John has to pick 27 more choir members out of the 29 still available. The order of picking the other members does not matter, since they are not assigned different roles in the choir. Since John can't pick the same person twice, there is no repetition. Use the combinations formula for selecting 27 out of 29, no repetition, not ordered.   Now, there are 30 choices for the lead vocal - multiply the number of choices for the choir by 30, because you need a lead AND 27 other members: 30×29×14 choices   Hmmm. This is painful to calculate, but the solution is a number that ends with 0 (why? look at the unit's digit for each of the numbers that are multiplied: 0×9×4 = something that ends with 0).   12180 is the only answer that ends with 0. Hallelujah John!
Answer: D
A department store perceived a run on a lower priced garment and raised the price by 20% to keep stock available until another shipment arrived. Customers fumed and the department store manager allowed them to purchase the garments at 80% of the new price to save face. What was the difference in the new retail price and the price the customers were allowed to pay instead?  Choose the correct answer:	A) 4.0%	B) 5.0%	C) 6.0%	D) 7.0%	E) 8.0%

Solution: Quantity X Rate = Price   1 X 1 = 1   0.8 X 1.20 = 0.960   Decrease in price = (0.040/1) Ã— 100 = 4.0%   4.0%nswer = Option 4.0%
Answer: A
Find the least number must be subtracted from 427398 so that remaining no.is divisible by 15?
Choose one.
A) 3	B) 4	C) 6	D) 9	E) 8

Solution: On dividing 427398 by 15 we get the remainder 3, so 3 should be subtracted   3
Answer: A
The least number which should be added to 4298 so that the sum is exactly divisible by 5, 6, 4 and 3 is?  Choose the correct choice from the following choices:	A) 12	B) 22	C) 32	D) 42	E) 52

Solution: L.C.M. of 5, 6, 4 and 3 = 60.   On dividing 4298 by 60, the remainder is 38.   Number to be added = (60 - 38)= 
(60 - 38) = 22
22   22)
Answer: B
A cistern is normally filled in 6 hours but takes two hours longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in?  Choose the correct choice:	A) 33	B) 88	C) 24	D) 99	E) 11

Solution: 1/6 - 1/x = 1/8   x = 24   Answer: 24
Answer: C
Find the 37.5% of 976 ?
Pick:
A) 368
B) 655
C) 366
D) 437
E) 545

Solution: 37.5 % of 976   = 37.5/100 * 976 = 375/1000 * 976 = 3/8 * 976   = 3 * 122= 
3 * 122 = 366
366.   Answer:366
Answer: C
It takes a boat 3 hours to travel down a river from point A to point B, and 5 hours to travel up the river from B to A. How long would it take the same boat to go from A to B in still water? Choose one:	A) 9 hours and 45 minutes	B) 3 hours and 45 minutes	C) 1 hours and 45 minutes	D) 6 hours and 45 minutes	E) 8 hours and 45 minutes

Solution: Let: S be the speed of the boat in still water, r be the rate of the water current and d the distance between A and B.   d = 3(S + r) : boat traveling down river   d = 5(S - r) : boat traveling up river   3(S + r) = 5(S - r)   r = S / 4 : solve above equation for r   d = 3(S + S/4) : substitute r by S/4 in equation B   d / S = 3.75 hours = Let: S be the speed of the boat in still water, r be the rate of the water current and d the distance between A and B.   d = 3(S + r) : boat traveling down river   d = 5(S - r) : boat traveling up river   3(S + r) = 5(S - r)   r = S / 4 : solve above equation for r   d = 3(S + S/4) : substitute r by S/4 in equation B   d / S = 3.75 hours = 3 hours and 45 minutes.   correct answer 3 hours and 45 minutes
Answer: B
At the faculty of Aerospace Engineering, 312 students study Random-processing methods, 232 students study Scramjet rocket engines and 112 students study them both. If every student in the faculty has to study one of the two subjects, how many students are there in the faculty of Aerospace Engineering?  Choose the correct choice from the following answers
A) 424.  B) 428.  C) 430.  D) 432.  E) 436

Solution: Students studying Random-processing methods = 312   Students studying Scramjet rocket engines = 232   Students studying them both = 112   Therefore ;   Students studying Only Random processing methods = 312 - 112= 
312 - 112 = 200
200   Students Studying Only Scramjet Rocket engines= 232 - 112= 
232 - 112 = 120
120   Students Studying Both= 112   Students Studying None = 0 (As mentioned in question that every student in the faculty has to study one of the two subjects)   Total Students in faculty of Aerospace Engineering = Students of Only Random processing methods + Students of Only Scramjet Rocket engines + Both + None   Total number of Students = 200 + 120 + 112 + 0= 
200 + 120 + 112 + 0 = 432
432 ....   Answer 432.
Answer: D