MU-NLPC/Calc-aqua_rat huggingface dataset:
Three years ago , the average age of A, B and C was 27 years and that of B and C 5 years ago was 20 years. A’s present age is :	Select the correct option:
A) 22
B) 88
C) 40
D) 87
E) 17

Solution: Explanation:   Sum of the present ages of A, B and C = (27× 3 + 3 × 3) years = 90 years.   Sum of the present ages of B and C = (20 × 2 + 5 × 2) years = 50 years.   A's present age = 90 – 50 = 40 years.   Answer: 40
Answer: C
Pipes A and B can fill a tank in 4 and 6 hours. Pipe C can empty it in 8 hours. If all pipes are opened together, then the tank will be filled in? Select:	A) 60/17 hr	B) 22/7 hr	C) 52/11 hr	D) 6 hr	E) 63/19 hr

Solution: Net part filled in 1 hour = 1/4 + 1/6 - 1/8= 7/22   The tank will be full in 22/7 hr   Answer is 22/7 hr
Answer: B
There are 4 boys and 2 girls. In how many ways can they be seated in a row so that all the two girls do not sit together?
Choose the correct choice from the following options:
A) 630
B) 716
C) 564
D) 846
E) 478

Solution: The required number of ways = (4+2)! - (4-2)!*2! = 6!-2!*2! = 720-4= 
720-4 = 716
716   Answer is 716
Answer: B
What is the remainder when 4990990900032 is divided by 32 ?	Select
A) 16 B) 0 C) 4 D) 2 E) 5

Solution: Though i was unaware of the divisibility test for 32 but i guessed the pattern!!   divisibility rule for 4- last two digits must be divisible by 4   divisibility rule for 8- last three digits must be divisible by 8   similarly, divisibility rule for 32 - last five digits must be divisible by 32   Hence, Ans 0
Answer: B
Four car rental agencies A, B, C and D rented a plot for parking their cars during the night. A parked 15 cars for 12 days, B parked 12 cars for 20 days, C parked 18 cars for 18 days and D parked 16 cars for 15 days. If A paid Rs. 1125 as rent for parking his cars, what is the total rent paid by all the four agencies?
Choose the correct option
A) 6157	B) 6187	C) 6128	D) 6150	E) 6113

Solution: The ratio in which the four agencies will be paying the rents = 15 * 12 : 12 * 20 : 18 * 18 : 16 * 15   = 180 : 240 : 324 : 240 = 45 : 60 : 81 : 60   Let us consider the four amounts to be 45k, 60k, 81k and 60k respectively.   The total rent paid by the four agencies = 45k + 60k + 81k + 60k= 246k   It is given that A paid Rs. 1125   45k 45  + 60  + 81  + 60= 
45  + 60  + 81  + 60 = 246
246k   It is given that A paid Rs. 1125   45k= 1125 => k = 25   246k = 246(25) = Rs. 6150   Thus the total rent paid by all the four agencies is Rs. 6150.   Answer: 6150
Answer: D
The base and height of a parallelogram are 12m and 6m respectively. Then its area is ======?  Choose the correct option:  A) 27Sq.m  B) 126Sq.m  C) 84Sq.m  D) 18Sq.m  E) 72Sq.m

Solution: A= b*h => A= 12*6= 
12*6 = 72
72Sq.m. Answer: (72Sq.m)
Answer: E
The length T of a rectangle is decreased by 15% and its width is increased by 40%. Does the area of the rectangle decrease or increase and by what percent?
Choose the correct choice:  A) Decreases by 19%  B) Decreases by 25%  C) Increases by 6%  D) Increases by 19%  E) Increases by 25%

Solution: Let the length T of the rectangle be 100x, and width be 100y. Area = 100x * 100y = 10000xy   Now after the change Length 100  * 100= 
100  * 100 = 10_000
10000xy   Now after the change Length= 85x, and width = 140 y. Area = 11900xy   % Change = (11900xy - 10000xy)/(10000xy) = 19 % Increase. Hence Increases by 19%.
Answer: D
The floor of a rectangular room is 20 m long and 12 m wide. The room is surrounded by a veranda of width 2 m on all its sides. The area of the veranda is : Choose the correct choice from the following options
A) 144 m2  B) 120 m2  C) 108 m2  D) 158 m2  E) None of these

Solution: 144 m2rea of the outer rectangle = 24 Ã— 16 = 384 m2   144 m2rea of the inner rectangle = 20 Ã— 12 = 240 m2   Required area = (304 â€“ 180) = 144 m2   144 m2nswer 144 m2
Answer: A
Pumping alone at their respective constant rates, one inlet pipe fills an empty tank to 1/2 of capacity in 6 hours and a second inlet pipe fills the same empty tank to 2/3 of capacity in 6 hours. How many hours will it take both pipes, pumping simultaneously at their respective constant rates, to fill the empty tank to capacity?  Choose the correct choice:
A) 3.25 B) 3.6 C) 4.2 D) 4.4 E) 5.14

Solution: Time taken by First tank Fill 1/2 the tank = 6 hours   i.e. Time taken by First tank to Fill 1 complete the tank =12 hours   Time taken by Second tank Fill 2/3 the tank = 6 hours   i.e. Time taken by First tank to Fill 1 complete the tank = (3/2)*6= 
(3/2)*6 = 9
9 hours   in 1 Hour, Both tanks together Fill the tank= (1/12)+(1/9) = 7/36 tank   i.e. Time taken by Both tank to Fill 1 complete the tank = 36/7 hours = 5.14 hours   Answer: option 5.14
Answer: E
Anup start a bike at 6am. and rides it at 60kmph. Raghu started at 7pm with his car at 70kmph. When will Raghu overtake Anup?  Choose the correct option
A) 8:30am B) 9:40am C) 10:00am D) 01:00pm E) 11:10am

Solution: Suppose bike is overtaken by car xhrs after 6am   01:00pmistance covered by the bike in x hrs = distance covered by the car in x-1 hr   60x = 70(x-1)   10x = 70   x = 7 hrs   Required time = 6+7 = 01:00Pm   Answer is 01:00pm
Answer: D
The average of first thirteen prime numbers which are odd is?	Choose the correct choice
A) 20.15
B) 21.15
C) 22.15
D) 23.15
E) 24.15

Solution: Explanation:   Sum of first 13 prime no. which are odd = 275   Average = 275/13 = 21.15   Answer:21.15
Answer: B
A train passes a station platform in 48 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?	Pick one:
A) 123 B) 166 C) 420 D) 157 E) 198

Solution: Speed = [54 * 5/18] m/sec = 15 m/sec.   Length of the train = (15 * 20)= 
(15 * 20) = 300
300 m.   Let the length of the platform be x meters.   Then, (x + 300) / 48= 15   x + 300 = 720   x = 420 m.   Answer: 420
Answer: C
What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 20%?	Select:	A) 20%	B) 28%	C) 27%	D) 40%	E) 70%

Solution: SP2 = 2/3 SP1   CP = 100   SP2 = 80   2/3 SP1 = 80   SP1 = 120   100 --- 20 => 20%   20%nswer:20%
Answer: A
A Car comes with 7 different possible exterior colors and 6 different interior colors. How many different color combinations are there? Choose the correct choice from the following answers:
A) 26
B) 42
C) 7!6!/2!
D) 7!6!
E) 13!/2!

Solution: For each exterior color out of 7 there are 6 different interior colors possible, so there are total of   7*6= 
  7*6 = 42
42 color combinations. This is basically the same as Principle of Multiplication: if one event can occur in mm ways and a second can occur independently of the first in nn ways, then the two events can occur in mnmn ways.   Answer: 42.
Answer: B
Two goods trains each 750 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?	Choose the correct option: A) 72 B) 45 C) 48 D) 51 E) 44

Solution: Relative speed = 45 + 30= 
45 + 30 = 75
75 km/hr.   75 * 5/18= 125/6 m/sec.   Distance covered = 750 + 750= 
750 + 750 = 1_500
1500 m.   Required time= 1500 * 6/125= 
1500 * 6/125 = 72
72 sec.   72nswer: Option 72
Answer: A
Tough and Tricky questions: Combinations.
seven 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 one.
A) 6 B) 7 C) 12 D) 16 E) 21

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 7 contestants:7 options for slot1*3 option for slot2   = 7* 3= 
7* 3 = 21
21   Ans. 21) 21
Answer: E
Average of five numbers is -10, and the sum of three of the numbers is 16, wat is the average of the other 2 no's?  Choose the correct choice:	A) -33	B) 23	C) -34	D) -39	E) 32

Solution: Let the five numbers be a, b, c, d, e. Then their average is (a+b+c+d+e5)=10.(a+b+c+d+e5)=10.   Now three of the numbers have a sum of 16, say, a+b+c=16a+b+c=16.   So substitute 16 for a+b+ca+b+c in the average above: (16+d+e5)=10.(16+d+e5)=10.   Solving this equation for d+ed+e gives d+e=−66d+e=−66.   Finally, dividing by 2 (to form the average) gives (d+e2)=−33.(d+e2)=−33.   Hence, the answer is -33: -33
Answer: A
A, B and C enter into a partnership. A initially invests Rs. 25 lakhs and adds another Rs. 10 lakhs after one year. B initially invests Rs. 35 lakhs and withdraws Rs. 10 lakhs after 2 years and C invests Rs. 30 lakhs. In what ratio should the profits be divided at the end of 3 years ?  Choose the correct choice from the following choices
A) 11:10:15 B) 20:17:23 C) 19:19:18 D) 5:4:9 E) None of these

Solution: Explanation:   A:B:CA:B:C =(25 lakhsÃ—Ã—1)+(35 lakhsÃ—Ã—2) :(35 lakhsÃ—Ã—2+25 lakhsÃ—Ã—1) :(30 lakhsÃ—Ã—3)   = 95 lakhs : 95 lakhs : 90 lakhs =19:19:18=19:19:18.   ANSWER IS 19:19:18
Answer: C
A bag contains 7 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is ? Choose the correct choice from the following choices.
A) 7/14 B) 7/18 C) 7/12 D) 7/11 E) 7/15

Solution: Drawing two balls of same color from seven green balls can be done in ⁷C₂ ways.   Similarly from eight white balls two can be drawn in ⁸C₂ ways.   P = ⁷C₂/¹⁵C₂ + ⁸C₂/¹⁵C₂ = 7/15   Answer:7/15
Answer: E
If k^3 is divisible by 84, what is the least possible value of integer k?  Select.
A) 36
B) 42
C) 48
D) 56
E) 60

Solution: k^3 = 84*x = 2^2*3*7= 
2*3*7 = 42
42.   The answer is 42.
Answer: B
The seating chart of an airplane shows 30 rows of seats. Each row has 3 seats on each side of the center aisle, and one of the seats on each side is a window saet. The view from the window seats in 20 of the rows is obscured by the wings of the airplane. If the first person to be assigned a seat is assigned a window seat and thw window seat is assigned randomly, what is the probability that the person will get a seat with an unobscured view?	Choose the correct option:
A) 1/6
B) 1/3
C) 2/3
D) 5/6
E) 17/18

Solution: priyalr   6 seats per row, think of a boeing 737. We have 30 rows, therefore window 30 seats one one side and 30 window seats on the other, totaling 60 window seats on the whole plane.   the view of the window of 20 rows is blocked. two wings, therefore 40 window seats are blocked.   Total window seats = 60   Total blocked window seats = 40   Total unblocked seats = 20   We know that a window seat was given, therefore probability for not window seat is 20/60 =1/3   ANS 1/3
Answer: B
A pool which was 1/5 full to begin with, was filled at a constant rate for 6/5 hours until it was until it was 8/9 full. At this rate, how much time would it take to completely fill this pool if it was empty to begin with?  Options:	A) 8 hrs 45 mins.	B) 9 hrs.	C) 9 hrs 30 mins.	D) 1 hrs 45 mins.	E) 15 hrs 30 mins

Solution: The pool was 1/5 full initially.   In 6/5 hrs, it was filled to 8/9 of its capacity.   Therefore, in 6/5 hrs, 8/9 - 1/5 was the amount of volume filled.   So, 6/5 hrs = 8/9 - 1/5 = 31/45   Therefore, for filling the vessel from empty to full, you would require 6/5 * 45/31 = 1 Hrs 45 Mins.   Hence 1 hrs 45 mins.
Answer: D
The difference between the number and its three fifth is 40, what is the number?
Choose the correct choice from the following choices.
A) 80	B) 100	C) 90	D) 120	E) 130

Solution: Explanation:   Let the number be x. Then,   x - (3/5)x = 40   (2/5)x = 40   x = (40 x 5)/2 = 100   Answer: Option 100
Answer: B
The three digits of a number add up to 26. The number is divisible by 5. The leftmost digit is double the middle digit. What is the product of the three digits?	Choose the correct answer:
A) 450	B) 460	C) 500	D) 520	E) 490

Solution: Say the three-digit number is abc.   The leftmost digit is double the middle digit --> a=2b;   The number is divisible by 5 --> c is either 0 or 5;   The three digits of a number add up to 26 --> a+b+c=26   So, either a+b+c=2b+b+0=26 or a+b+c=2b+b+5=26. The first equation does not give an integer value of b, so it's not the case. From the second we get that b=7 --> a=14 and c=5 --> a*b*c=490.   Answer: 490.
Answer: E
A trader sells 40 metres of cloth for Rs.8200 at a profit of Rs.25 per metre of cloth. How much profit will the trder earn on 40 metres of cloth? Choose the correct choice
A) Rs.950  B) Rs.1500  C) Rs.1000  D) Rs.1200  E) None of these

Solution: Explanation:   SP of 1 metre cloth = 8200/40 = Rs.205.   CP of 1 metre cloth = Rs.205 – 25 = Rs.180   CP on 40 metres = 180 x 40 = Rs.7200   Profit earned on 40 metres cloth = Rs.8200 – Rs.7200 = Rs.1000.   Answer: Option Rs.1000
Answer: C
Three 6 faced dice are thrown together. The probability that all the three show the same number on them is	Pick one.
A) 1/87	B) 1/36	C) 1/18	D) 1/76	E) 1/10

Solution: It all 3 numbers have to be same basically we want triplets. 111, 222, 333, 444, 555 and 666. Those are six in number. Further the three dice can fall in 6 * 6 * 6= 
6 * 6 * 6 = 216
216 ways.   Hence the probability is 6/216= 1/36   Answer: 1/36
Answer: B
If the seventh day of a month is three days earlier than Friday, What day will it be on the nineteenth day of the month?  Choose the correct choice from the following answers:  A) Saturday  B) Monday  C) Sunday  D) Wednesday  E) Friday

Solution: Explanation:   Given that seventh day of a month is three days earlier than Friday   => Seventh day is Tuesday   => 14th is Tuesday   => 19th is Sunday   Answer: Option Sunday
Answer: C
A man buys two articles for Rs.1980 each and he gains 10% on the first and loses 10% on the next. Find his total gain or loss percent?	Choose the correct choice from the following: A) 9 B) 7 C) 4 D) 8 E) 3

Solution: (30*30)/100= 
(30*30)/100 = 9
9%loss   9nswer:9
Answer: A
How many 4 digit even numbers do not use any digit more than once
Choose the correct choice from the following.
A) 1720	B) 2160	C) 2240	D) 2460	E) 2520

Solution: A B 2240 D ( thousand , hundreds, tens, units)   D can be 0 2 4 6 8 ( any of the 5 digits )   A can be anything except (D or 0) so 8 possibilities   2240 can be anything except A and B so 8 possibilities   B can be anything except ( A D 2240 ) so 7 possibilities   total ways are   8 * 7 * 8 * 5= 
  8 * 7 * 8 * 5 = 2_240
2240   ANS:2240
Answer: C
242 students represent x percent of the boys at a school. If the boys at the school make up 50% of the total school population of x students, what is x?	Answers:  A) 120  B) 150  C) 180  D) 200  E) 220

Solution: Let B be the number of boys in the school.   242 = xB/100   B = 0.5x   24200=0.5x^2   x^2 = 48400   x = 220   The answer is 220.
Answer: E
A water tank is two-fifth full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?
Choose the correct choice from the following.
A) 6 min. to empty  B) 6 min. to full  C) 9 min. to empty  D) 9 min. to full  E) 8 min. to full

Solution: Clearly, pipe B is faster than pipe A and so, the tank will be emptied.   Part to be emptied = 2/5   Part emptied by (A + B) in 1 minute = (1/6 - 1/10) = 1/15   1/15 : 2/5 :: 1 : x   x = (2/5 * 1 * 15)= 
(2/5 * 1 * 15) = 6
6 min.   So, the tank will be emptied in 6 min.   6 min. to emptyNSWER:6 min. to empty
Answer: A
The positive number a is w percent greater than the positive number b, which is p percent less than a itself. If a is increased by p percent, and the result is then decreased by w percent to produce a positive number c, which of the following could be true?
I. c > a
II. c = a
III. c < a
Choose the correct choice from the following choices:
A) I only	B) II only	C) III only	D) I and II only	E) II and III only

Solution: Let w = 10% then p = 100/11 %   let b = 100 then a = 110   after increasing a by p and decreasing by w we get c= 108   therefore c<a   III only it is answer
Answer: C
How many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?  Choose the correct answer: A) 879 meters B) 678 meters C) 500 meters D) 126 meters E) 107 meters

Solution: Let length of tunnel is x meter   Distance = 800+x meter   Time = 1 minute = 60 seconds   Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s   Distance = Speed*Time   800+x = (65/3) * 60   800+x = 20 * 65= 
20 * 65 = 1_300
1300   x= 1300 - 800= 
1300 - 800 = 500
500 meters   Answer:500 meters
Answer: C
The banker's discount on a bill due 4 months hence at 15% is Rs. 420. The true discount is:	Pick.
A) 400
B) 276
C) 129
D) 176
E) 186

Solution: T.D.   =	B.D. x 100   100 + (R x T)   = Rs. 420 x 100   100 + 15 x	1   3   = Rs. 420 x 100   105   = Rs. 400.   400nswer: 400
Answer: A
Tom drives from town W to town B, driving at a constant speed of 60 miles per hour. From town B Tom immediately continues to town C. The distance between W and B is twice the distance between B and C. If the average speed of the whole journey was 36 mph, then what is Tom's speed driving from B to C in miles per hour?	Choices
A) 12	B) 20	C) 24	D) 30	E) 36

Solution: Let's assume that it takes 4 hours to go from point W to B. Then the distance between them becomes 240 which makes distance between B and C 120. (240+120)/(4+x) gives us the average speed which is 36. You find x=6. So the question simplifies itself to   120/6= 
  120/6 = 20
20   Hence the answer is 20.
Answer: B
If a card is drawn from a well shuffled pack of cards, the probability of drawing a spade or a king is ?
Choose the correct answer:
A) 4/17
B) 4/18
C) 4/76
D) 4/13
E) 4/29

Solution: P(SᴜK)   = P(S) + P(K) - P(S∩K), where S denotes spade and K denotes king.   P(SᴜK)   = 13/52 + 4/52 - 1/52   = 4/13   Answer: 4/13
Answer: D
If 36 men can do a piece of work in 25 hours, in how many hours will 10 men
do it ?
Pick:
A) 65 hours B) 90 hours C) 30 hours D) 62 hours E) 66 hours

Solution: Let the required number of hours be x. Then,   Less men, More hours	(Indirect Proportion)   10 : 36 : : 25 : x	(10 x x) = (36 x 25)	(36 x 25)/10 = 90   Hence, 15 men can do it in 60 hours.   Answer is 90 hours.
Answer: B
A box contains 100 balls, numbered from 1 to 100. If 3 balls are selected at random and with replacement from the box. If the 3 numbers on the balls selected contain two odd and one even. What is the probability R that the first ball picked up is odd numbered?	Choose the correct choice from the following choices:
A) 0 B) 1/3 C) 1/2 D) 2/3 E) 1

Solution: Answer-D   Selecting the balls either Even or Odd is having probability 50/100=1/2   We have already selected 3 balls with 2 odd numbers and 1 even number.   So we have 3 combinations OOE, OEO, EOO. We have 3 outcomes and 2 are favourable as in 2 cases 1st number is odd. So probability R is 2/3.2/3
Answer: D
Find the odd man out? 3, 7, 15, 17, 22, 27, 29
Choose the correct answer.
A) 15 B) 17 C) 22 D) 27 E) 0

Solution: Each of the numbers is odd number except 22. The number 22 is the only even number.   ANSWER: 22
Answer: C
To fill a tank, 20 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to one-fifth of its present ?
Choose the correct choice:
A) 100	B) 200	C) 300	D) 400	E) 500

Solution: Let the capacity of 1 bucket = x.   Then, the capacity of tank = 20x.   New capacity of bucket = 1/5 x   Therefore, Required number of buckets = (20x)/(1x/5)   = (20x) x 5/1x   = 100/1= 
100/1 = 100
100   100nswer is 100.
Answer: A
Priya and Ishita start a business with Rs.15000 each, and after 3 months, Ishita withdraws half of her capital . How should they share the profits at the end of the 15 months?
Choose the correct choice from the following answers.
A) 14:9	B) 12:7	C) 4:3	D) 3:2	E) 12:5

Solution: Priya invests Rs.15000 for 18 months, but Ishita invests Rs.15000 for the first 3 months and then withdraws Rs.7500. So, the investment of Ishita for remaining 15 months is Rs.7500 only.   Priya:Ishita   15000*18 : (15000*3) + (7500*15)   270000 : 157500   Priya:Ishita = 12:7   Answer: 12:7
Answer: B
When a certain shoe store reduces the price of its best-selling style of shoe by 10 percent, the weekly sales of this style increase by 10 percent. Which of the following best describes the resulting change in the store's weekly revenue from sales of this style of shoe?	Choices:
A) Revenue decreases by 10% B) Revenue decreases by 1% C) There is no change in revenue D) Revenue increases by 1% E) Revenue increases by 10%

Solution: Old price = 10, old sales = 10 --> old revenue = 100;   New price = 9, new sales = 11 --> new revenue = 99.   Revenue decreased by 1%.   Answer: Revenue decreases by 1%.
Answer: B
Taylor is making a bracelet. He Starts with 4 blue knots, 6 red knots, and 1 yellow knots, in that order, and repeats the pattern until there is no more string. If the last Knot is yellow which of the following could be the total number of knots on the bracelet.
Choose the most appropriate option:
A) 89
B) 90
C) 95
D) 87
E) 102

Solution: Repeating sequence = 4 + 6 + 1= 
4 + 6 + 1 = 11
11.   As the pattern ends in Y this could be the 10th thread or 11 thread (both are yellow)   Out of the answer choices, correct on should be a multiple of 11(since 11 threads are repeating) and if not, multiple of 11 + 10 (since 11 threads are repeating and last sequence end at first yellow)   none of the options is a direct multiple of 11 and only option that is multiple of 11; + 10 is 87 (11*7) + 10   Hence, answer is 87
Answer: D
A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 700 m long? Pick:
A) 388	B) 190	C) 277	D) 288	E) 261

Solution: L = S*T   S= 1200/120= 
1200/120 = 10
10 m/Sec.   Total length (D)= 1900 m   T = D/S   T = 1900/10= 
1900/10 = 190
190 Sec .Answer:190
Answer: B
A cement mixture is composed of 3 elements. By weight, 1/3 of the mixture is sand, 1/2 of the mixture is water, and the remaining 8 pounds of the mixture is gravel. What is the weight of the entire mixture in pounds?  Choose the most appropriate option:	A) 30	B) 36	C) 42	D) 46	E) 48

Solution: Let the total weight be x.   Sand content= (1/3)x   Water content= (1/2)x   Gravel=x-(1/3)x-(1/2)x=(1/6)x=8   x=48   Then answer will be 48=48
Answer: E
Out of 10 persons working on a project, 5 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them?
Choose the correct choice from the following answers:
A) 5/7	B) 5/3	C) 5/1	D) 5/6	E) 11/12

Solution: P(at least one graduate) = 1 - P(no graduates)   = 1 - 5C₃/¹⁰C₃ = 1 - ( 5 * 4 * 3)/(10 * 9 * 8)   = 11/12   Answer: 11/12
Answer: E
A train of 24 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.5 km long?  Choose the most appropriate option.
A) 8 mins  B) 3 mins  C) 7 mins  D) 9 mins  E) 4 mins

Solution: D = 25 * 60 + 1500= 
25 * 60 + 1500 = 3_000
3000 m   T= 3000/60 * 18/5= 
3000/60 * 18/5 = 180
180 sec= 3 mins   Answer:3 mins
Answer: B
A fruit seller had some oranges. He sells 20% oranges and still has 380 oranges. How many oranges he had originally?	Choose the most appropriate option
A) 475 B) 700 C) 220 D) 400 E) None of these

Solution: Explanation :   He sells 20% of oranges and still there are 380 oranges remaining   => 80% of oranges = 380   ⇒ (80 × Total Oranges)/100 = 380   ⇒ Total Oranges/100 = 4.75   ⇒ Total Oranges = 4.75 × 100 = 475   475nswer : Option 475
Answer: A
Working at their respective constant rates, machine A makes 100 copies in 15 minutes and machine B makes 150 copies in 10 minutes. If these machines work simultaneously at their respective rates for 30 minutes, what is the total number of copies that they will produce?
Choose the correct choice from the following options:
A) 250 B) 425 C) 650 D) 700 E) 750

Solution: Machine A can produce 100 *30/15= 
100 *30/15 = 200
200 copies   And, Machine B can produce   150* 30/10= 
  150* 30/10 = 450
450 Copies   Total producing 650 Copies.   650 is the answer
Answer: C