MU-NLPC/Calc-aqua_rat huggingface dataset:
If a, b, c are consecutive positive integers and b<a<c, which of the following must be true?
I. c-b=2
II. abc is an even integer
III. (a+b+c)/3 is an integer  Select:
A) I	B) II	C) I and II	D) II and III	E) I, II and III

Solution: 1. c-b=2 --> b, a, c are consequitive positive integers and a<b<c then c=b+2 --> c-b=2. So this statement is always true;   2. abc is an even integer --> out of any 3 consecutive integers at least one must be even thus abc=even. So this statement is also always true;   3. (a+b+c)/4 is an integer --> the sum of odd number of consecutive integers is ALWAYS divisible by that odd number. Or: (a+b+c)/4=fraction.   Answer: I and II.
Answer: C
A tank has both an inlet pipe and an outlet pipe. Working alone, the inlet pipe can fill up the tank in 5 hours. Working alone, the outlet pipe can empty out the tank in 15 hours. If it is desired that the tank should be filled, from empty, exactly 7 hours after the inlet pipe is turned on at 9:30am, then at what time should the outlet pipe be opened ?  Select:
A) 9:30am
B) 10:30am
C) 11:30am
D) 10:40am
E) 10:50am

Solution: In 7 hours the inlet pipe will pump in water equal to 7*1/5 = 7/5 of the pool. So, 2/5 more than necessary, which should be compensated by the outlet pipe. To pump out 2/5 of the water the outlet pipe needs 30/5= 
30/5 = 6
6 hours.   Therefore, the outlet pipe should be opened at 9:30am + 7 hours - 6 hours= 10:30am.   Answer: 10:30am
Answer: B
The largest 4 digit number exactly divisible by 88 is? Choose the correct choice from the following
A) 9768 B) 9750 C) 9468 D) 9568 E) 9944

Solution: Largest 4-digit number = 9999   88) 9999 (113   88   ----   119   88   ----   319   264   ---   55   ---   Required number = (9999 - 55)= 
(9999 - 55) = 9_944
9944.   9944)
Answer: E
An entrance exam question paper consists of five problems, each problem having three choices. In how many ways can a student attempt one or more problems?
Choose the correct option:
A) 500
B) 1023
C) 1024
D) 1035
E) 1300

Solution: paper 5 problems and each 3 choices so no of ways = 4^5 -1   = 2^10 - 1 = 1024 - 1= 
1024 - 1 = 1_023
1023   ANSWER 1023
Answer: B
A man can hit a target once in 5 shots. If he fires 4 shots in succession, how many ways that he will hit his target? Choose the correct choice from the following answers.
A) 71/234 B) 81/133 C) 81/343 D) 34/83 E) 91/324

Solution: The man will hit the target if he hits it once or twice or thrice or all four times in the four shots that he takes.   So, the only possibility when the man will not hit the target is when he fails to hit the target in even one of the four shots that he takes.   The event of not hitting the target even once is the complement of the event of hitting the target at least once.   The probability that he will not hit the target in any given shot = 1 - 1/5 = 4/5   Therefore, the probability that he will not hit the target in any of the four shots = 4/5^4 = 34/83   34/83
Answer: D
One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in Select:
A) 144 mins  B) 140 mins  C) 136 mins  D) 132 mins  E) 130 mins

Solution: Explanation:   Let the slower pipe alone fill the tank in x minutes   then faster will fill in x/3 minutes.   Part filled by slower pipe in 1 minute = 1/x   Part filled by faster pipe in 1 minute = 3/x   Part filled by both in 1 minute =1/x+3/x=1/36   =>4/x=1/36   x=36âˆ—4=144mins   144 minsNSWER IS 144 mins
Answer: A
Average age of 9 members of a club is 29 years. If 2 more persons with the average age of 40 years have become the members of the club, find average age of all the 11 members. Choose the correct choice from the following options.
A) 15	B) 31	C) 77	D) 99	E) 22

Solution: Average age of 9 members = 29 years; Excess age of 2 new members = (40 - 29) × 2 = 22 years   Therefore, Increase in the average age on inclusion of 2 new members = 22112211 = 2 years   Therefore, Average age of 11 members = 29 + 2= 
29 + 2 = 31
31 years   Answer:31
Answer: B
A city had 600 migrants in the year 2000. Since then, The number of migrants in a countrythe city has doubled every 3 years. If there were 600 migrants in the country in the year 2000, What was the increase in the population of migrants during the period from 2009 to 2012?
Choose the correct choice from the following
A) 2400 B) 4800 C) 6600 D) 8200 E) 16400

Solution: The population will increase in the following order:   2000: 600   2003: 1200   2006: 2400   2009: 4800   2012: 9600   Difference between 2009 and 2012 = 4800   Option 4800
Answer: B
how many 3 digit numbers can be formed by using 2,4 and 5 such that product of the digits of numbers become even...	Choose the correct choice from the following options:
A) 27
B) 26
C) 25
D) 24
E) 23

Solution: A 3-digit no. is to be formed.   So no. of digits = 3*3*3 (with repetition ,as no condition is given)   But, the product of digits has to be even in each case..   hence, 125 (5*5*5) has to be excluded from those 27 no.s   Thus, answer is   27 - 1= 
  27 - 1 = 26
26   ANSWER:26
Answer: B
In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 4 boys when a boy gets any no. of prizes?  Pick
A) 45	B) 70	C) 64	D) 56	E) 67

Solution: Ans.(C)   Sol. In this case, repetitions are allowed, so all the three prizes can be given in 4 ways, i.e. (4 x 4 x 4) ways = 43 ways = 64 ways Or nr ways = 43 ways = 64 ways
Answer: C
Pipe A can fill a tank in 8 hours, pipe B in 16 hours and pipe C in 48 hours. If all the pipes are open,in how many hours will the tank be filled ?	Choose the most appropriate option
A) 4.7 B) 4.5 C) 4.6 D) 4.8 E) 5

Solution: 1/8+1/16+1/48=10/48=1/4.8. so 4.8 hrs   ANSWER:4.8
Answer: D
A certain amount earns simple interest of 1750 after 7 years Had the interest been 2% more, how much more interest would it have earned?
Choose the correct option:
A) 35
B) 245
C) 350
D) Cannot be determined
E) None of these

Solution: We need to know the S.I., principal and time to find the rate. Since the principal is not given, so data is inadequate.   Answer Cannot be determined
Answer: D
A car runs at the speed of 30 km per hour when not serviced and runs at 120 kmph when serviced. After servicing the car covers a certain distance in 8 hours. How much time will the car take to cover the same distance when not serviced?  Choose the correct option.
A) 18 hours 12 minutes  B) 32 hours  C) 28 hours 15 minutes  D) 17 hours 12 minutes  E) None

Solution: Explanation :   Time = 120*8 / 30= 
120*8 / 30 = 32
32 hours   Answer â€“ 32 hours
Answer: B
For any numbers a and b, a#b = ab(4 − b). If a and a#b both represent positive numbers, which of the following could be a value of b?  Pick
A) 3.2.1  B) 4  C) 5  D) 6  E) 7

Solution: a#b positive then b may be positive or negative. if positive then b< 4 may be 3,2 or 1 and if negative then it is more than or equal to -negative . ab will be -ve which is not possible as a and a#b should be positive.   ans 3,2 and 1   3.2.1
Answer: A
A can give B 100 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race?
Choices:
A) 111.12	B) 111.67	C) 111.64	D) 111.11	E) 101.12

Solution: A runs 1000 m while B runs 900 m and C runs 800 m.   The number of meters that C runs when B runs 1000 m,   = (1000 * 800)/900 = 8000/9 = 888.88 m.   B can give C = 1000 - 888.88= 
1000 - 888.88 = 111.12
111.12 m.   111.12nswer:111.12
Answer: A
10% of (50% of $500) is? Choose the most appropriate option
A) $15 B) $20 C) $25 D) $30 E) $22

Solution: 10% of (50% of $500) = 10/100 (50/100 * 500) = $25   Answer is $25
Answer: C
Let's say in a lottery John have a 4% chance of winning the jackpot.
All lined up and 1st four people on the line lose. John is 5th in the row.
What's the chance of John winning now?
Choose the correct choice from the following answers
A) 5%
B) 4%
C) 6%
D) 3%
E) 7%

Solution: 4%   The winning chance probability is still 4% as the outcome of Samuel winning the lottery is a separate event from the 1st four losing it.
Answer: B
A,B,C invested some money such that capital of C is half of B and capital of B is half of A. If they get a profit of Rs.7000 then profit share of B is Choose the correct choice:  A) Rs.3000  B) Rs.2000  C) Rs.2500  D) Rs.3500  E) Rs.3600

Solution: Ratio of their capital ie c:b:a=1:2:4   Hence b's share of profit =2/(7) *7000= 
2/(7) *7000 = 2_000
2000   ANSWER:Rs.2000
Answer: B
The average monthly salary of 24 employees in an organisation is Rs. 1500. If the manager's salary is added, then the average salary increases by Rs. 400. What is the manager's monthly salary ?	Answers:
A) Rs. 11,522
B) Rs. 11,500
C) Rs. 11,128
D) Rs. 11,228
E) Rs. 11,129

Solution: Manager's monthly salary   = Rs. (1900 x 25 - 1500 x 24)   = Rs. 11,500   Answer: Rs. 11,500
Answer: B
If x is a positive integer such that x3 + 8x2 + 12x-385 = 0, then x is  Choices:
A) less than 6 B) between 7 and 11 C) between 12 and 20 D) between 22 and 34 E) larger than 50

Solution: Let f(x) = x3 +8x2 +12x􀀀385. Since   f(6) = 63 +862 + 126-385 = 62(6 +8 +2)-385 = 36 16 - 385 > 0   and f(0) = -385 < 0, there must be some t 2 (0; 6) for which f(t) = 0. Therefore, f(x)   has a positive real root between 0 and 6. Descartes' Rule of Signs implies that there is   only one positive real root, so the answer must be (a). Or one can observe that f(5) = 0   to obtain the answer.   correct answer less than 6
Answer: A
A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are drawn what is the probability that one is yellow and two are red? Choose one.
A) 12/458 B) 12/456 C) 12/455 D) 12/453 E) 12/451

Solution: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.   When three marbles are drawn, the probability that one is yellow and two are red   = (²12/455₁)(⁴12/455₂)/¹⁵12/455₃   = (2 * 4 * 3 * 3 * 2)/(1 * 2 * 15 * 14 * 13)   = 12/455   Answer:12/455
Answer: C
A bicycle wheel has a diameter of 0.81m. How many complete revolutions does it make in 1km?  Select.
A) 246
B) 448
C) 393
D) 710
E) 223

Solution: 1 revolution = 3.14 * diameter.   Number of revolutions in 1km = 1000m / ( 3.14 * 0.81m ) = 393.2. Hence 393 complete revolutions.   Answer 393
Answer: C
We have 8 people and 5 chairs. In how many ways chairs can be occupy?
Choose the correct choice from the following options.
A) 1200
B) 1450
C) 1680
D) 1912
E) 900

Solution: no. of ways they can be occupy = 8*7*6*5= 
8*7*6*5 = 1_680
1680   Answer is 1680
Answer: C
there r 5 papers Ratio of marks obtained in each subject is 6:7:8:9:10. Total marks obtained is 60%. 50% is pass marks. In how many subjects did he get above 50%.  Choose one: A) 1 B) 2 C) 3 D) 4 E) 5

Solution: Total marks in 5 papers = 60% (i.e., 60*5 = 300)   6x+ 7x+ 8x+ 9x+ 10x =60/100(500)   Put x= 8 for solving,   6x= 48; 7x = 56; 8x = 64 ; 9x = 72; 10x = 80   Marks are 6:7:8:9:10 = 48+56+64+72+80   = 300   So, 4 subjects he got 50% above   ANSWER:4
Answer: D
Anand and Deepak started a business investing Rs. 22,500 and Rs. 35,000 respectively. Out of a total profit of Rs. 13,800, Deepak's share is:
Select
A) Rs. 5400	B) Rs. 7200	C) Rs. 8400	D) Rs. 9600	E) None of these

Solution: Explanation:   Ratio of their shares = 22500 : 35000 = 9:14   Deepak's share = 13800 * 14/23 = Rs. 8400.   ANSWER IS Rs. 8400
Answer: C
Dara ran on a treadmill that had a readout indicating the time remaining in her exercise session. When the readout indicated 24 min 18 sec, she had completed 10% of her exercise session. The readout indicated which of the following when she had completed 40% of her exercise session?
Choose the correct choice from the following answers:
A) 10 min 48 sec
B) 14 min 52 sec
C) 14 min 58 sec
D) 16 min 6 sec
E) 16 min 12 sec

Solution: 90% of the exercise should be completed in 24min 18 sec (1458 sec)   When she completes 40% of her exercise timer should show the time remaining for 60% of her exercise.   If 90% requires 1458 sec then 60% requires --> (60 * 1458)/90 = (2/3)*(1458) = 2 * 486= 
2 * 486 = 972
972 secs   Required answer= 972/60 = 16 min 12 sec   Answer: 16 min 12 sec
Answer: E
Mike weighs twice as much as Mary. Mike's weight is 150% of Michelle's weight. Alan weighs 20% more than Charlie. Charlie weighs 170% of Mary's weight. Which of these 5 people weighs the highest?  Choose the correct choice from the following options:
A) Mary
B) Mike
C) Michelle
D) Alan
E) Charlie

Solution: Mary < Michelle < Mike   Charlie < Alan   Let x be Mary's weight.   Mike's weight is 2x and Alan's weight is   1.2*1.7= 
  1.2*1.7 = 2.04
2.04x.   The answer is Alan.
Answer: D
Rahim bought 65 books for Rs.1150 from one shop and 50 books for Rs.920 from another. What is the average price he paid per book ?  Choices.
A) 11	B) 18	C) 99	D) 787	E) 12

Solution: Average price per book = (1150 + 920) / (65 + 50)   = 2070 / 115   = Rs.18   Answer:18
Answer: B
At what price must an article costing Rs.66.5 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 25% on the cost price?  Select: A) 87.5 B) 89.5 C) 82.3 D) 82.1 E) 92.4

Solution: CP = 66.5   SP = 66.5*(125/100)= 
66.5*(125/100) = 83.125
83.125   MP*(95/100)= 59.375   MP = 87.5   87.5nswer:87.5
Answer: A
What is the CP of Rs 100 stock at 5 discount, with 1/5% brokerage?	Select the correct option:
A) 96.9 B) 96.3 C) 95.2 D) 96.7 E) 96.21

Solution: Explanation:   Use the formula,   CP= 100 â€“ discount + brokerage%   CP= 100-5+1/5   95.2   Thus the CP is Rs 95.2.   ANSWER: 95.2
Answer: C
A take twice as much time as B or thrice as much time to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in?  Choose the correct choice from the following answers.
A) 19
B) 12
C) 11
D) 19
E) 114

Solution: Suppose A, B and C take x, x/2 and x/3 respectively to finish the work.   Then, (1/x + 2/x + 3/x) = 1/2   6/x = 1/2 => x = 12   So, B takes 6 hours to finish the work.   Answer: 12
Answer: B
Of the 40 animals at the shelter, 20 percent are cats. How many dogs must be adopted in order to bring the number of cats up to 50 percent of the animals in the shelter?	Choose the correct choice from the following choices:
A) 22 B) 24 C) 26 D) 32 E) 34

Solution: Now, there are 8 cats (20% of 40) and   40-8= 
  40-8 = 32
32 dogs at the shelter. We need there to be 8 cats and dogs, in this case there will be 50% cats and 50% dogs.   Therefore  32-8= 
 32-8 = 24
24 dogs must be adopted.   Answer: 24.
Answer: B
A bus covers a certain distance at a speed of 54 kmph excluding stoppages and 45 kmph including stoppages.for how many minutes does the bus stop per hour?  Answers.
A) 5 min.
B) 10 min.
C) 15 min.
D) 20 min.
E) 30 min.

Solution: Due to stoppages, it covers 9 km less.   Time taken to cover 9 km =	9/54	x 60	min	= 10 min.   ANSWER:10 min.
Answer: B
In a lottery, there are 11 prizes and 55 blanks. A lottery is drawn at random. What is the probability of getting a prize?  Choose the correct choice from the following choices
A) 1/2 B) 1/4 C) 1/6 D) 1/8 E) 1/10

Solution: P(winning a prize) = 11 / (11+55) = 11/66 = 1/6   The answer is 1/6.
Answer: C
Nitin's age was equal to square of some number last year and the following year it would be cube of a number. If again Nitin's age has to be equal to the cube of some number, then for how long he will have to wait?	Pick
A) 10 years
B) 38 years
C) 39 years
D) 64 years
E) 52 years

Solution: Explanation:   Clearly, we have to first find two numbers whose difference is 2 and of which the smaller one is a perfect square and the bigger one a perfect cube.   Such numbers are 25 and 27.   Thus, Nitin is now 26 years old. Since the next perfect cube after 27 is 64,   so required time period = (64 - 26)= 
(64 - 26) = 38
38 years.   Answer: 38 years
Answer: B
The probability of a team winning a match given Matt is playing the match is 0.75. The probability of the team winning a match given Matt is not playing the match is 0.5. The probability of Matt playing any match is 0.8.
If it is known that the team has won the last match, what is the probability that Matt played the match?	Select.
A) 0.8321  B) 0.7  C) 0.8571  D) 0.7531  E) 0.8213

Solution: Out of 100 matches:   Matt is plays in 80 and not plays in 20.   Out of 80 matches Matt plays in, team wins   0.75*80= 
  0.75*80 = 60
60.   Out of 20 matches Matt does not play in, team wins   0.5*20= 
  0.5*20 = 10
10.   So, out of 100 matches 60 + 10= 
60 + 10 = 70
70 are won.   It is known that the team has won the last match. Out of 70 matches won, Matt is in 60: 60/70= 0.8571...   Answer: 0.8571.
Answer: C
A trader marked the price of a car 20% above the cost price and allowed the purchaser 5% discount on the marked price there by gained $8400. Find the cost price of the Bike?  Select the correct option
A) 70000  B) 60500  C) 85000  D) 60000  E) 55000

Solution: 60000   $60000
Answer: D
A solution of 66 litres contains milk and water in the ratio 7:x. If four litres of water is added to the solution, the ratio becomes 3:2, find the value of x?  Pick.
A) 8	B) 5	C) 3	D) 4	E) 2

Solution: Exp. Total new quantity = original sol + water =66+4= 
66+4 = 70
70   New ratio= 3:2, New quantity of milk =3/5*70= 
3/5*70 = 42
42 Lit,   New quantity of water= 2/5*70= 
2/5*70 = 28
28 Lit   Water present initially= (28-4)= 
(28-4) = 24
24 Lit   Ratio= 42/24 =7/4 There for x = 4   Answer: 4
Answer: D
Unit size cubes are stacked inside a big rectangular box having dimensions corresponding to three consecutive multiples of 5. Choose exact number of cubes that can completely fill the box.
Choices:
A) 750	B) 850	C) 950	D) 1050	E) None of the above

Solution: Let the dimensions of the box be, length=5*a, breadth=5*(a+1), height=5*(a+2)   Hence, volume=5*5*5*a*(a+1)*(a+2)   Among any 3 consecutive positive integers, we will either have (a number that is divisible by both 23) or (a number divisible by 2 and another number divisible by 3).   Volume= multiple of (125*2*3)   750=125*2*3   750nswer:750
Answer: A
The value of a machine depreciates at 20% per annum. If its present value is Rs. 1,50,000, at what price should it be sold after two years such that a profit of Rs. 28,000 is made?	Choose the correct answer.
A) 328897 B) 120000 C) 877888 D) 124000 E) 188871

Solution: The value of the machine after two years = 0.8 * 0.8 * 1,50,000 = Rs. 96,000   SP such that a profit of Rs. 28,000 is made = 96,000 + 28,000 = Rs. 1,24,000   Answer: 124000
Answer: D
The difference between the two digit number and the number obtained by interchanging its digits is 54. The difference between the digits is? Choose the correct choice from the following choices:  A) 4  B) 6  C) 1  D) 7  E) 8

Solution: (10x + y) – (10y + x) = 54   x – y = 6   ANSWER:6
Answer: B
Thirty percent of the women in a college class are science majors, and the non-science majors make up 60% of the class. What percentage of the men are science majors if 40% of the class are men?	Choose the correct choice from the following answers.
A) 35%	B) 45%	C) 55%	D) 65%	E) 75%

Solution: Science majors make up 0.4 of the class.   60% of the class are women and   0.3*0.6= 
  0.3*0.6 = 0.18
0.18 of the class are female science majors.   Then 0.22 of the class are male science majors.   0.4x= 0.22   x = 0.55 = 55%   The answer is 55%.
Answer: C
Two trains start simultaneously from opposite ends of a 150-km route and travel toward each other on parallel tracks. Train X, traveling at a constant rate, completes the 150-km trip in 4 hours. Train Y, travelling at a constant rate, completes the 150-km trip in 3.5 hours. How many kilometers had Train X traveled when it met Train Y?
Choose the correct choice from the following options
A) 68 B) 70 C) 72 D) 74 E) 76

Solution: If the two trains cover a total distance D, then Train X travels (7/15)*D while Train Y travels (8/15)*D. If the trains travel 150 km to the meeting point, then Train X travels  (7/15)*150= 
 (7/15)*150 = 70
70 km. The answer is 70.
Answer: B
Some items were bought at 6 items for Rs. 5 and sold at 5 items for Rs. 6. What is the gain percentage? Select the correct option
A) 44%	B) 42%	C) 46%	D) 48%	E) 41%

Solution: gain percentage =(6*6/5*5-1)100   =11/25*100= 
11/25*100 = 44
44%   44%nswer : 44%
Answer: A
In how many different ways can the letters of the word 'DANCING' be arranged in such a way that the vowels always come together? Choose the correct option.
A) A)360  B) B)480  C) C)720  D) D)1440  E) of these

Solution: The word 'DANCING' has 7 different letters.   When the vowels AI are always together, they can be supposed to form one letter.   Then, we have to arrange the letters DNCNG (AI).   Now, 6 (5 + 1 = 6) letters can be arranged in 6! = 720 ways.   The vowels (EAI) can be arranged among themselves in 2! = 2 ways.   Required number of ways = (720 x 2) = 1440.   ANSWER:1440
Answer: D
How many even number in the range between 20 to 100 inclusive are not divisible by 3	Choices:  A) 28  B) 30  C) 31  D) 33  E) 46

Solution: We have to find the number of terms that are divisible by 2 but not by 6( as the question asks for the even numbers only which are not divisible by 3)   For 2,   20,22,24...100   using AP formula, we can say 100 = 20 + (n-1) *2   or n=41.   For 6,   24,36...96   using AP formu24la, we can say 96 = 24 + (n-1) *6   or n=13.   Hence, only divisible by 2 but not 3 = 41-13= 
41-13 = 28
28. hence, 28nswer 28
Answer: A
The area of a square field is 64816 sq m. How long will a lady take to cross the field diagonally at the rate of 7.2 km/hr? Choose the most appropriate option
A) 2 min
B) 4 min
C) 5 min
D) 3 min
E) 3.5 min

Solution: Area of a square field = 64816 sq m   Let the side of square = a   a^2 = 64816   => a = 254.59   3 miniagonal = (2)^(1/2) * a   = 1.414 * 254.59   =360   Speed of lady = 7.2 km / hour   = 7200 m / hour   = 120 m / min   Time taken by lady to cross the field diagonally = 360/120= 
360/120 = 3
3 min   Answer 3 min
Answer: D
What is the lowest possible common multiple of 2 distinct integers, each greater than 150? Choose the correct choice from the following options:	A) 151	B) 152	C) 302	D) 151*151	E) 151*152

Solution: The least common multiple of two numbers greater than 150 is 2(151) = 302, where the two distinct integers are 151 and 302.   The answer is 302.
Answer: C
From a group of 6boys&4girls a Committee of 4 persons is to be formed. In how many different ways can it be done, so that the committee has at least 2 boys? Choose the correct choice from the following options:
A) 120  B) 130  C) 185  D) 195  E) 210

Solution: The committee of 4 persons is to be so formed that it has at least 2 men. The different ways that we can choose to form such a committee are:   (i) 2m. 2w in 6C2 x 4 C1=6X5 - 2X1 X 3X3 2X1 =n an (ii) 3m. 1w in 6C3 x 4C1 =6X5X4 3X2X1 X4 _n - a ''''   (iii) 4m in 6C4 -2x1 = 15 Total no. of different ways in which a committee of 4 persons can be formed so that it has at least 2 men. = 90 + 18 + 15 = 185   185
Answer: C
A man sells an article at 5% profit. If he had bought it at 5% less and sold it for 1 less, he would have gained 10%. The cost price of the article is :  Choose the correct choice from the following choices.
A) 200
B) 150
C) 240
D) 280
E) None of these

Solution: Let the CP of the article be x.   Then, SP = 105x⁄100   Now, new CP = 95x⁄100 and new SP = 105x⁄100 - 1   200ccording to the question   105x/100−1−95/100=10×95x/100×100   ∴ x = 200   200nswer 200
Answer: A
A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are drawn what is the probability that one is yellow and two are red? Choose the correct answer:
A) 12/457
B) 12/456
C) 12/455
D) 12/454
E) 12/451

Solution: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.   When three marbles are drawn, the probability that one is yellow and two are red   = (2 * 4 * 3 * 3 * 2)/(1 * 2 * 15 * 14 * 13) = 12/455   Answer: 12/455
Answer: C