MU-NLPC/Calc-aqua_rat huggingface dataset:
The probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact?
Choose the correct choice from the following answers:
A) 18/35 B) 19/35 C) 18/30 D) 78/35 E) 18/55

Solution: Explanation:   If both agree stating the same fact, either both of them speak truth of both speak false.   Probability = 3/5 * 4/7 + 2/5 * 3/7   = 12/35 + 6/35 = 18/35   18/35nswer: Option 18/35
Answer: A
A composer’s guild is planning its spring concert, and ten pieces have been submitted for consideration. The director of the guild knows that they will only have time to present four of them. If the pieces can be played in any order, how many combinations of pieces are possible? Select the correct option.
A) 40
B) 210
C) 1090
D) 5040
E) 10000

Solution: Combination question..   10C4 = 210..   ANS option 210 is correct..
Answer: B
Kathleen can paint a room in 2 hours, and Anthony can paint an identical room in 3 hours. How many hours would it take Kathleen and Anthony to paint both rooms if they work together at their respective rates? Choose one.
A) 8/15
B) 4/3
C) 12/5
D) 9/4
E) 15/4

Solution: (1/2 + 1/3)t=2   t=12/5   Answer: 12/5
Answer: C
5/4 of all married couples have more than one child. 2/5 of all married couples have more than 3 children. What fraction of all married couples have 2 or 3 children?  Choose the correct choice.
A) 1/5	B) 1/4	C) 17/20	D) 3/5	E) It cannot be determined from the given information.

Solution: Plug in simple numbers. Take 100 couples for example.   5/4 of 100 couples have more than one child = 125 couples.   2/5 of 100 couples have more than 3 kids = 40 couples.   This implies that 40 couples are a subset of 125 couples   We need to find couples that have 2 or 3 kids, so essentially, it is  125 - 40= 
 125 - 40 = 85
85. Fraction will be 85/100= 17/20.   Option 17/20
Answer: C
Tough and Tricky questions: Exponents.
If 2^m3^m3^m = 9^n, then m/n = Choose the correct choice from the following answers.
A) 1/3	B) 2/3	C) 1	D) 3/2	E) 3

Solution: I also soved it, but a bit differently. Thank you for reminding me of this much easier and logical way!   What I did was to test powers of 3 that would lead to 9.   So, we have 3 raised to the same power 3 times and 9 raised to another power one time: 3^m3^m3^m = 9^n   What I did was test 3 raised to the power of 2 like this:   3^2*3^2*3^2 = 9*9*9 = 9^3. This means that m=2 and n=3. So, m/n=3/2.   3/2
Answer: D
The sum of two numbers is 25 and their difference is 13. Find their product.
Choose the correct choice from the following choices:
A) 104 B) 114 C) 315 D) 325 E) 400

Solution: Explanation:   Let the numbers be x and y.   Then x + y = 25 and x - y = 13.   x = 19; y = 6   xy = 19 * 6= 
19 * 6 = 114
114   ANSWER IS 114
Answer: B
Find curved surface area of a cylinder with diameter of base 14 cm and height 60 cm.
Choices:
A) 2601cm2 B) 2610cm2 C) 2620cm2 D) 2630cm2 E) 2640cm2

Solution: Volume = πR2H= π x 72 x 60 = 9240	cm3   Curved surface area = 2πRH = (2 π x 7 x 60) cm2 =2640 cm2   answer :2640cm2
Answer: E
Raman travelled for 10 hours. He covered the first half of the distance at 20 kmph and remaining half of the distance at 15 kmph. Find the distance travelled by Raman?  Choose the correct option:  A) 161.42  B) 181.42  C) 178.42  D) 191.42  E) 171.42

Solution: Let the distance travelled be x km.   Total time = (x/2)/20 + (x/2)/15 = 10 => x/40 + x/30 = 10 => (3x + 4x)/120 = 10   => x = 171.42 km   Answer:171.42
Answer: E
A girl has to make pizza with different toppings. There are 8 different toppings. In how many ways can she make pizzas with 2 different toppings?  Choose the correct choice:	A) 16	B) 56	C) 112	D) 28	E) 38

Solution: In 8 different toppings, selecting 2 diff toppings = 8c2   formula is n!/(n-c)!   n = total number of toppings   C = number chosen in a grouping.   n=8 and c=2 so we get   8!/(8-2)! = (8*7*6*5*4*3*2*1)/(6*5*4*3*2*1)   = 8*7= 
8*7 = 56
56   ANSWER:56
Answer: B
A clock store sold a certain clock to a collector for 30 percent more than the store had originally paid for the clock. When the collector tried to resell the clock to the store, the store bought it back at 60 percent of what the collector had paid. The shop then sold the clock again at a profit of 90 percent on its buy-back price. If the difference between the clock's original cost to the shop and the clock's buy-back price was $150, for how much did the shop sell the clock the second time?
Options: A) $1010.46 B) $505.23 C) $2020.92 D) $800.46 E) $1515.69

Solution: Now, in the question above, lets say the original cost of the clock to store was C$ and then it sold the same to the collector at 30% profit.   This means the clocks' selling price was C (1.3) and this becomes cost price for the collector.   Now, when the collector tries to sell the same clock to the store, the store buys it for 60% the price at which the collector bought it.   Thus, you get = 1.3*0.6*C = 0.78 C   Furthermore, the store sells the clock for the second time for 90% profit and thus the selling price of the clock becomes = cost price of the clock for the store at buy-back * 1.9 = 1.9 * 0.78 C   Finally given that C - 0.78 C = 150 ----> C = 681.82$   Thus, the cost of the clock the second time around = 1.9*0.78 C = 1.9 * 0.78 * 681.82 = 1010.46$. Hence $1010.46 is the correct answer.
Answer: A
Which of the following is not a prime number ?  Select:
A) 2  B) 3  C) 11  D) 19  E) 20

Solution: Clearly, 20 is not a prime number.   Answer : 20
Answer: E
in a bus left side are 15 seats available,3 few seats in right side because in rear exit door .Each seat hold 3 people.In addition ,there is a seat back can sit 11 people all together .how many people can sit in a bus?
Choose the correct choice from the following.
A) 52  B) 92  C) 95  D) 88  E) 66

Solution: Right Side =15 seat   Left Side =15-3 (3 few seat in right side)= 12 seat   Total= 15+12= 
15+12 = 27
27   People can seat in 27 seat= 27*3= 
27*3 = 81
81   People can seat in Last Seat= 11   Total People can seat= 81+11= 
81+11 = 92
92   ANSWER:92
Answer: B
P is able to do a piece of work in 15 days and Q can do the same work in 20 days. If they can work together for 4 days, what is the fraction of work left?	Pick one:
A) 8/15
B) 7/15
C) 1/15
D) 3/15
E) None of these

Solution: Explanation:   P's 1-day work = 1/15   Q's 1-day work = 1/20   Work done by (P + Q) in 1 day = 1/15 + 1/20 = 7/60.   Work done by them in 4 days = (7/60) * 4 = 7/15.   Work left = 1 - (7/15) = 8/15.   8/15NSWER IS 8/15
Answer: A
The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is  Choose the correct answer
A) 30 kg
B) 31 kg
C) 37 kg
D) 39 kg
E) 41 kg

Solution: Let A, B, C represent their respective weights. Then, we have:   A + B + C = (45 x 3) = 135 .... (i)   A + B = (40 x 2) = 80 .... (ii)   B + C = (43 x 2) = 86 ....(iii)   Adding (ii) and (iii), we get: A + 2B + C = 166 .... (iv)   Subtracting (i) from (iv), we get : B = 31.   31 kg's weight = 31 kg   31 kg)
Answer: B
In how many different ways can the letters of the word MISSISSIPPI be arranged if the vowels must always be together? Choose the correct choice from the following answers
A) 48	B) 144	C) 210	D) 420	E) 840

Solution: The word MISSISSIPPI has 4 I , 4S , 2P and M .   The only vowel present in the word is I and we have to consider 4 I's as a single group   Number of different ways = 8!/(4!*2!)   =(8*7*6*5)/2= 
(8*7*6*5)/2 = 840
840   Answer 840
Answer: E
Before 6 years, dog A’s age was 4 times of dog B’s age and after 4 years, dog A’s age will be 3 times of dog B’s age. What is the difference of dog A’s age and dog B’s now?
Choose the correct choice from the following answers.
A) 36 B) 42 C) 54 D) 60 E) 64

Solution: A - 6 = 4(B - 6) --> A - 4B = -18.............1   A + 4 = 3(B + 4) --> A - 3B = 8.............2   (2) - (1) --> B = 26 --> A = 3(30)=90   A - B = 90 - 26= 
90 - 26 = 64
64   Answer: 64
Answer: E
In the year 1990 there are 5000 men 3000 women 2000 boys. In 1994 men are increased by 20% women are increased by ratio of boys and women?  Options.
A) 11000 B) 12000 C) 13000 D) 14000 E) 15000

Solution: total population in year 1990 = 5000+3000+2000= 
5000+3000+2000 = 10_000
10000   total population in year 1994=((5000*120/100)+(3000+(3000*2/3))+(2000))= 
((5000*120/100)+(3000+(3000*2/3))+(2000)) = 13_000
13000   ANSWER:13000
Answer: C
A shirt goes on sale for 70% of its original price. One week later, the sale price is marked down 10%. The final price is what percent of the original price?	Pick one:
A) 63%
B) 70%
C) 62%
D) 50%
E) 28%

Solution: Just assume original price is 100.   Sale price = 70   Then it is marked down by 10% = 70-7= 
70-7 = 63
63.   Hence it is 63% od the original price. Hence answer is 63%.
Answer: A
A die is thrown twice and the sum of the numbers appearing is observed to be 6.
find the conditional probability that the number 4 has appeared at least once?  Choose the correct choice from the following answers
A) 1/5  B) 1/4  C) 2/5  D) 3/7  E) 3./11

Solution: Let E be the event that ‘number 4 appears at least once’ and F be   the event   that ‘the sum of the numbers appearing is 6’.   Then, E = {(4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (1,4), (2,4), (3,4),   (5,4), (6,4)}   and F = {(1,5), (2,4), (3,3), (4,2), (5,1)}   We have P(E) = 11/36   and P (F) = 5/36   Also EnF = {(2,4), (4,2)}   Therefore P(EnF) = 2/36   the required probability   P(E|F) = P(EnF)/P(F) = (2/36)/(5/36) = 2/5.   2/5
Answer: C
A book store bought copies of a new book by a popular author, in anticipation of robust sales. The store bought 400 copies from their supplier, each copy at wholesale price y. The store sold the first 150 copies in the first week at 80% more than y, and then over the next month, sold a 100 more at 20% more than y. Finally, to clear shelf space, the store sold the remaining copies to a bargain retailer at 40% less than y. What was the bookstore’s net percent profit or loss on the entire lot of 400 books?	Select the correct option:
A) 30% loss
B) 10% loss
C) 10% profit
D) 20% profit
E) 60% profit

Solution: [[y(150)(1.8)+y(100)(1.2)+y(150)(0.6)]/400y] - 1   [50[(3)(1.8) + (2)(1.2) + (3)(0.6)] / (50)(8)] - 1   [(5.4 + 2.4 + 1.8)/8] - [8/8]   +1.6/8   +20%   answer is 20% profit
Answer: D
A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length?  Answers: A) 15 B) 44 C) 40 D) 27 E) 12

Solution: Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec   Total distance = 360+140= 
360+140 = 500
500 meter   Time= Distance/speed   = 500 * (2/25)= 
500 * (2/25) = 40
40 seconds   Answer: 40
Answer: C
The sector of a circle has radius of 21 cm and central angle 135o. Find its perimeter?
Select the correct option.
A) 17.6 cm  B) 18.6 cm  C) 91.5 cm  D) 16.5 cm  E) 14.6 cm

Solution: Perimeter of the sector = length of the arc + 2(radius)   = (135/360 * 2 * 22/7 * 21) + 2(21)   = 49.5 + 42= 
49.5 + 42 = 91.5
91.5 cm   Answer:91.5 cm
Answer: C
A man buys a cycle for Rs. 2000 and sells it at a loss of 10%. What is the selling price of the cycle?	Select the correct option.
A) 1800 B) 1420 C) 1430 D) 1440 E) 1540

Solution: S.P. = 90% of Rs. 2000 = 90/100 x2000= Rs. 1800   answer : 1800
Answer: A
6 noun, 4 verbs and 3 adjectives are written on blackboard.we can form sentence by choosing 1 from each available set without caring it makes sense or not.what is the number of ways of doing this??  Select.
A) 412  B) 432  C) 472  D) 524  E) 554

Solution: we have to choose one from each set. 1 from 6 nouns and 1 from 4 verbs and 1 from 3 adjectives.   then we have to arrange 3 different set in 3! ways.   so,   6c1*4c1*3c1*3!=432   ANSWER:432
Answer: B
The average weight of 29 students is 28 kg. By the admission of a new student, the average weight is reduced to 27.4 kg. The weight of the new student is
Choose the correct option.
A) 22 kg
B) 21.6 kg
C) 22.4 kg
D) 10 kg
E) None of these

Solution: Exp . The total weight of 29 students = 29* 28   The total weight of 30 students = 30* 27.4   Weight of the new student = ( 30*27.4 – 29*28)   = 822 - 812= 
822 - 812 = 10
10   Answer:10 kg
Answer: D
A train 120m long is running at 60kmph. In how much time will it pass a platform 240m long?  Pick:	A) 15.6 seconds	B) 24.6 seconds	C) 21.6 seconds	D) 30.6 seconds	E) 35.6 seconds

Solution: Distance travelled = 120 + 240= 
120 + 240 = 360
360mSpeed= 60 * 5/8 = 50/3mTime = 360 * 3/50= 
360 * 3/50 = 108/5 = around 21.6
21.6 SecondsAnswer : 21.6 seconds.
Answer: C
Factory X's bulbs work for over 4000 hours in 59% of cases, whereas factory Y's bulbs work for over 4000 hours in 65% of cases. It is known that factory X supplies 60% of the total bulbs available. What is the chance that a purchased bulb will work for longer than 4000 hours? Choose the correct choice from the following
A) 66.4%  B) 61.4%  C) 77.4%  D) 65%  E) 53.9%

Solution: For X, 60% of 59% will work.   For Y, 40% of 65% will work. *40% is the rest of the bulb supply in the market.   So, the probability that a purchased bulb will work is:   0.60(0.59) = .354   0.40(0.65) = 0.26   The combined probability then is 35.4 + 26.00= 
35.4 + 26.00 = 61.4
61.4%   ANS 61.4%
Answer: B
The average age of a committee of 8 members is 40 years. A member aged 55 years
retired and his place was taken by another member aged 32 years . The average age of
present committee is; Choices
A) 39 years
B) 38 years
C) 36 years
D) 37.125 years
E) 34 years

Solution: Exp. Total age of the committee = 40*8= 
40*8 = 320
320,   Total age when a member is retired   and a new one was joined= 320-55 +32, =297   Average age of present committee = 297/8 = 37.125.   Answer: 37.125 years
Answer: D
Tim is now 16 years older than Donna. If in 4 years Tim will be twice as old as Donna, how old will Tim be in 11 years?  Choices.
A) 35
B) 37
C) 39
D) 41
E) 43

Solution: T=D+16 so D=T-16.   T+4=2(D+4).   T+4=2(T-16+4).   T+4=2T-24.   T=28.   In 11 years, Tim will be 39 years old.   The answer is 39.
Answer: C
Which of the following inequalities is equivalent to −8 < x < 4?	Choose the correct choice from the following options: A) |x - 1| < 7 B) |x + 2| < 6 C) |x + 3| < 5 D) |x - 2| < 6 E) None of the above

Solution: We know that |x| < a means -a < x < a, where Sum of lower limit of x (i.e -a) and the upper limit of x (i.e a), is 0   Given is, -8 < x < 4, let's say by adding y to this inequality we will get into the above format   -8+y < x+y < 4+y   Now, to move this into the mod format, we need to have (-8+y) + (4+y) = 0 => y = -2   Thus, -6< x+2 < 6 => |x+2| < 6.   Hence, answer is |x + 2| < 6
Answer: B
The average speed of a car is 1 4/5 times the avg speed of a bike. A tractor covers 575km in 23hrs. How much distance will the car cover in 4hrs if the speed of the bike is twice speed of the tractor?	Options:
A) 300 km
B) 320 km
C) 360 km
D) 390 km
E) 400 km

Solution: Sol. Average speed of a tractor = 25 km / h   The speed of a bus in an hour = 25 × 2 = 50 km   The speed of a car in an hour = 9/5 * 50= 
9/5 * 50 = 90
90 km   So, the distance covered by car in 4 h is   90 × 4= 360 km   Ans.(360 km)
Answer: C
Two vessels having volumes in the ratio 3:5 are filled with water and milk solutions. The ratio of milk and water in the two vessels are 5:1 and 6:4 respectively. If the contents of both the vessel are empties into a larger vessel, find the ratio of milk and water in the larger vessel.  Choose the most appropriate option:
A) 12:5	B) 11:5	C) 13:5	D) 14:5	E) 9:5

Solution: Vessel A = 300 gallons --> milk = 250, water = 50;   Vessel 11:5 = 500 gallons --> milk = 300, water = 200;   Vessel A + 11:5 = 800 gallons --> milk = 550, water 250   The ratio =550/250-->11:5   Answer: 11:5
Answer: B
How many different arrangements of letters are possible if three letters are chosen from the letters A through I and the letters E and A must be among the letters selected? Pick
A) 36 B) 38 C) 40 D) 42 E) 44

Solution: Besides A and E, there are 7 letters and we can choose one of them.   7C1 = 7   Three letters can be arranged in 3! ways.   The number of arrangements is 7*3! = 42   The answer is 42.
Answer: D
Two trains 135 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet?  Pick one:
A) 7.18  B) 7.12  C) 7.3  D) 7.45  E) 7.51

Solution: T = (135 + 165)/ (80 + 65) * 18/5   T = 7.45   Answer:7.45
Answer: D
Of the 200 stamps in a collection, 90 are foreign and 80 are more than 10 years old. If 20 stamps are both foreign and more than 10 years old, how many stamps are neither foreign nor more than 10 years old? Choices:  A) 50  B) 80  C) 100  D) 130  E) 150

Solution: 20 stamps are both foreign and more than 10 years old.   70 stamps are foreign only.   60 stamps are 10 years old only.   The number of remaining stamps is  200 - (20+70+60)= 
 200 - (20+70+60) = 50
50   The answer is 50.
Answer: A
What percent of a day is 6 hours? Pick.
A) 6.25% B) 20% C) 25% D) 12.5% E) None of these

Solution: Explanation :   Total hours in a day = 24   Required percentage = (6/24) × 100 = 25%   Answer : Option 25%
Answer: C
Vijay sells a cupboard at 12% below cost price. Had he got Rs.1500 more, he would have made a profit of 12%. What is the cost price of the cupboard? Choose the most appropriate option:
A) 7450	B) 14900	C) 6250	D) 6000	E) None of these

Solution: Explanation:   6250ost price = 1500/(0.12 + 0.12) = 1500/0.24   = Rs.6250   ANSWER 6250
Answer: C
A cistern is normally filled in 8 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?	Answers.
A) 27 B) 20 C) 40 D) 73 E) 72

Solution: 1/8 - 1/x = 1/10   x = 40   Answer: 40
Answer: C
If w,x,y,z are consecutive positive integers ; then which of the following is always odd?
[1] w*x+(y+2)^2*z
[2] w^x + z^y
[3] 51y
Pick
A) 1	B) 2	C) 3 and 2	D) 1 and 2	E) 2 and 3

Solution: Plug in some numbers   w = 1   x = 2   y = 3   z = 4   3 and 2heck the options -   [1] w*x+(y+2)^2*z = 1*2 + (3+2)^2 * 4 => 2 + 25*4= 
2 + 25*4 = 102
102{ Not an odd Number }   [2] w^x + z^y= 1^2 + 4^3 => 1 + 64= 
1 + 64 = 65
65{ Odd number }   [3] 51y= 51*3= 
51*3 = 153
153 odd   [2] and [3]   3 and 2
Answer: C
The avg weight of A,B & C is 84 kg. If D joins the group, the avg weight of the group becomes 80 kg.If another man E who weights is 4 kg more than D Replaces A, Then the avgof B,C,D&E becomes 79 kg. What is the weight of A? Choose the correct choice from the following
A) 76
B) 65
C) 75
D) 89
E) 90

Solution: A + B + C = 3 *84= 
3 *84 = 252
252   A + B + C + D= 4 * 80= 
4 * 80 = 320
320 ---- (i)   So, D= 68& E = 68 + 4= 
68 + 4 = 72
72   B + C + D +E= 79 * 4= 
79 * 4 = 316
316 --- (ii)   From Eq. (i) & (ii)   76-E= 320 – 316 = 4   76 = E +4 = 72 + 4= 
72 + 4 = 76
76   76
Answer: A
If x,y ,and z are positive real numbers such that x(y+z) = 62, y(z+x) =82 , and z(x+y) = 100, then xyz is	Choose the correct option:
A) 120 B) 50 C) 60 D) 70 E) 90

Solution: xy+xz = 62 --------------------------------------1)   yz+yx = 82---------------------------------------2)   xz+zy = 100---------------------------------------3)   Re-writing equation 3 as follows:   xz+zy = 82+ 18   xz+zy = yz+yx + 18   xz = yx + 18 ............... (4)   120dding (1)(4)   2xz = 80   xz = 40   xyz has to be multiple of 40, only 120 fits in   120nswer = 120
Answer: A
If a function f is defined by f(x)= -1/x for all non zero numbers x. If f(a) = -1/3 and f(ab) = 1/9 then b= ?	Pick one:
A) 1/6.	B) -1/3.	C) 1/3.	D) -3.	E) 12.

Solution: f(a) = -1/3 = -1/a, and thus a = 3   f(ab) = 1/9, and thus ab = -9   3b = -9   b = -3   The answer is -3..
Answer: D
Nicole cycles at a constant rate of 20 kilometers per hour, and is passed by Jessica, who cycles at a constant rate of 40 kilometers per hour. If Jessica cycles at her constant rate for x minutes after passing Nicole, then stops to wait for her, how many minutes will Jessica have to wait for Nicole to catch up to her?  Select:
A) a) x minutes B) b) x/2 minutes C) c) 2x/3 minutes D) d) 3x/2 minutes E) e) 2x minutes

Solution: Speed of nicole = 20km/h or 20/60 km/min = 1/3 km/min.   Once jessica passed the nicole, the distance between the nicole and jessica will increase at the rate of   (30-20)= 
  (30-20) = 10
10km/h or 1/6 km/min   now jessica is cycling for x minutes after passing the nicole, so in those x minutes distance between jessica and nicole would be (1/6)*x= x/6 km.   So, the time taken by nicole to travel x/6 km = (x/6)/(1/3) = 3x/2. hence answer should be d) 3x/2 minutes.
Answer: D
For the symbol, m”n=n^2−m for all values of m and n. What is the value of 5”3? Options
A) 5  B) 3  C) 2  D) 4  E) 0

Solution: 5”3= 9 - 5= 
9 - 5 = 4
4   Answer: 4
Answer: D
5 books consisting of 2 financial management, 2 marketing management and 1 system management are placed on a shelf at random order. What is the probability that the books of each kind are all together.  Pick:
A) 1/120  B) 1/64  C) 1/32  D) 1/48  E) 1/56

Solution: Since the denominator will be 5! . And there is no way to divide 5 from numerator and denominator. Use a multiple of 5 in the denominator only answer .   1/120
Answer: A
There r 4 prime numbers in ascending order. The multiplication of first 3 is 385 and that of last 3is 1001. what is the last number is	Choose the correct answer.
A) 11 B) 12 C) 15 D) 13 E) 17

Solution: Explanation:   abcbcd=3851001=>ad=513   abcbcd=3851001=>ad=513   So d = 13   13
Answer: D
A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?  Choose the correct choice from the following options.
A) 120 m	B) 240 m	C) 300 m	D) 400 m	E) None of these

Solution: Speed = 54 * 5/18= 
54 * 5/18 = 15
15 m/sec.   Length of the train= 15 * 20= 
15 * 20 = 300
300 m.   Let the length of the platform be x m . Then,   (x + 300)/36= 15 => x = 240 m.   ANSWER:240 m
Answer: B
The Guests at a football banquet consumed a total of 406 pounds of food. if no individual guest consumed more than 2.5 pounds of food, What is the minimum number of guests that could have attended the banquet?
Choose the most appropriate option
A) 160 B) 161 C) 162 D) 163 E) 164

Solution: To minimize one quantity maximize other.   162*2.5 (max possible amount of food a guest could consume) = 405 pounds, so there must be more than 162 guests, next integer is 163.   Answer: 163.
Answer: D
A man invests some money partly in 12% stock at 108 and partly in 10% stock at 60.To obtain equal dividends from both,he must invest the money in the ratio :	Options:
A) 3 : 4
B) 3 : 2
C) 4 : 5
D) 16 : 15
E) None

Solution: Solution   For an income of Rs. 1 in 12% stock at 108, investment = Rs. (108/12)= Rs. 9 .   For an income of Rs. 1 in 10% stock at 60, investment = Rs.(60/10) = Rs. 6.   ∴ Ratio of investments = 9 :6 =3:2   Answer 3 : 2
Answer: B
John want to buy a $100 Trouser at the store, but he think itâ€™s too expensive. Finally, it goes on sale for $75. What is the percent decrease?	Choose the correct choice from the following options
A) 20% B) 30% C) 40% D) 25% E) 60%

Solution: The is always the difference between our starting and ending points. In this case, itâ€™s 100 â€“ 75 = 25. The â€œoriginalâ€ is our starting point; in this case, itâ€™s 100. (25/100)*100 = (0.25)*100= 
(0.25)*100 = 25
25%.   25%
Answer: D
A train 120 m long passed a pole in 12 sec. How long will it take to pass a platform 380 m long? Pick one.
A) 25 sec  B) 50 sec  C) 75 sec  D) 100 sec  E) 125 sec

Solution: Speed = 120/12= 
120/12 = 10
10 m/sec.   Required time= (120 + 380)/10= 
(120 + 380)/10 = 50
50 sec   Answer:50 sec
Answer: B
If 2 + 2/x = 3 - 3/x, then x =	Choose the correct choice.
A) -5  B) 2/3  C) 1  D) 3/2  E) 5

Solution: We're given the equation 2 + 2/X = 3 - 3/X. We're asked for the value of X.   The common-denominator of these 4 numbers is X, so we have to multiple 2 of the numbers to give them that denominator...   2X/X + 2/X = 3X/X - 3/X   We can then eliminate that denominator, which gives us....   2X + 2 = 3X - 3   5 = X   Final Answer:5
Answer: E