MU-NLPC/Calc-aqua_rat huggingface dataset:
How many ways can 10 letters be posted in 5 post boxes, if each of the post boxes can take more than 10 letters ?	Options:	A) 5^10	B) 5^11	C) 5^18	D) 5^12	E) 5^16

Solution: Each of the 10 letters can be posted in any of the 5 boxes.   So, the first letter has 5 options, so does the second letter and so on and so forth for all of the 10 letters.   i.e. 5*5*5*….*5 (upto 10 times)   = 5 ^ 10.   5^10nswer: 5^10
Answer: A
The difference between C.I. and S.I. on an amount of $15,000 for 2 years is $54. What is the rate of interest per annum?
Choose the correct choice from the following
A) 5% B) 6% C) 7% D) 8% E) 9%

Solution: $54 is the interest on the first year of interest.   Let x be the interest rate.   The interest after the first year is 15000*x.   The interest on the first year's interest is 15000*x*x   15000*x^2 = 54   x = 0.06   The answer is 6%.
Answer: B
The difference in compound interest earned on a deposit (compounded annually) in year 1 and year 2 is $ 40. Had the interest rate been three times its present value, the difference z would have been how much?
Select
A) 40/3
B) 40
C) 120
D) 360
E) 420

Solution: CASE 1:   Deposit = $x;   Rate of increase = r.   Interest yearned in 1 year = xr. Deposit in 1 year = x + xr.   Interest yearned in 2 year = (x + xr)r.   The difference z= (x + xr)r - xr = xr^2 = 40.   CASE 2:   Deposit = $x;   Rate of increase = 3r.   Interest yearned in 1 year = x(3r). Deposit in 1 year = x + 3xr.   Interest yearned in 2 year = (x + 3xr)3r.   The difference = (x + 3xr)3r - 3xr = 9xr^2. Since from CASE 1 we know that xr^2 = 40, then 9xr^2 = 9*40= 
9*40 = 360
360.   Answer: 360.
Answer: D
Lagaan is levied on the 60 percent of the cultivated land. The revenue department collected total Rs. 3,84,000 through the lagaan from the village of Mettur. Mettur, a very rich farmer, paid only Rs.480 as lagaan. The percentage of total land of Mettur over the total taxable land of the village is:  Pick one:
A) 0.20833 B) 0.34667 C) 0.45788 D) 0.78452 E) 0.97343

Solution: Total land of Sukhiya = \inline \frac{480x}{0.6} = 800x   \therefore Cultivated land of village = 384000x   \therefore Required percentage = \inline \frac{800x}{384000}\times 100 = 0.20833   0.20833
Answer: A
Each light bulb at a hotel is either incandescent or fluorescent. At a certain moment, forty percent of the incandescent bulbs are switched on, and eighty percent of the fluorescent bulbs are switched on. If 75 percent of all the bulbs are switched on at this moment, what percent of the bulbs that are switched on are incandescent?  Choose the correct answer.
A) 6.7% B) 10.3% C) 14.5% D) 18.2% E) 23.6%

Solution: Let I be the number of incandescent bulbs.   Let F be the number of fluorescent bulbs.   0.4I + 0.8F = 0.75(I+F)   0.05F = 0.35I   F = 7I   This means that for every 1 incandescent bulb, there are 7 fluorescent bulbs.   The percent of bulbs that are switched on which are incandescent is:   0.4I / (0.4I + 0.8F) = 0.4I / (0.4I + 0.8*7I) = 0.4I / 6I = 1/15 which is about 6.7%.   The answer is 6.7%.
Answer: A
A man is standing on a railway bridge which is 165 m long. He finds that a train crosses the bridge in 20 seconds but himself in 8 seconds. Find the length of the train and its speed.	Choices:
A) 10 m/sec
B) 13.75 m/sec
C) 18 m/sec
D) 19 m/sec
E) 25 m/sec

Solution: If length of train is l and speed of train is s, then   l/s = 8   (l+165)/s = 20   (l+165)/l = 20/8 =5/2   2l+330 =5*l   3*l= 330   l=110 mtrs   s= l/8 = 110/8= 
110/8 = 55/4 = around 13.75
13.75 m/sec   ANSWER:13.75 m/sec
Answer: B
A grocer is storing soap boxes in cartons that measure 25 inches by 48 inches by 60 inches. If the measurement of each soap box is 8 inches by 6 inches by 5 inches, then what is the maximum number of soap boxes that can be placed in each carton? Choose the correct choice from the following:
A) 210	B) 252	C) 280	D) 320	E) 300

Solution: however the process of dividing the volume of box by the volume of a soap seems flawed but it does work in this case due to the numbers   Dimensions of the box =25*48*60   Dimensions of the soap = 5*6*8   we get = 5x6x10 = 300   so the question is why this particular arrangement, in order to maximize number of soaps we need to minimize the space wasted and this is the only config where we dont waste any space so we can expect the maximum number   the answer is (300)
Answer: E
A Book was sold at a loss of 10%. If it was sold for $140 more, there would have been a gain of 4%. What is the cost price?
Choices:
A) $1200
B) $1300
C) $1000
D) $1700
E) $1050

Solution: $1000   $1000   90%   104%   --------   14% ---- 140   100% ---- ? => $1000
Answer: C
A straight line is formed using two points A(3,3) and B(6,6). Another point P(x,y) lies between A and B such that AP/BP = 2. What are the coordinates of P?	Choose the correct choice from the following options
A) (7/2, 7/2)
B) (4, 4)
C) (21/5, 21/5)
D) (9/2, 9/2)
E) (5, 5)

Solution: The equation of the straight line is y = x, so the x- and y-coordinates of P are the same.   The x, y coordinates are 2/3 of the distance from 3 to 6.   x = 3 + (6-3)*(2/3) = 3 + 2= 
3 + 2 = 5
5= y   The answer is (5, 5).
Answer: E
John sells encyclopedias door-to-door. He earns $160 on every paycheck, regardless of how many sets he sells. In addition, he earns commission as follows:
Commission Sales
10% $0.00 - $10,000.00
5% $10,000.01 --->
He does not earn double commission.That is, if his sales are $12,000, he earns 10% on the first $10,000 and 5% on the remaining $2,000.
His largest paycheck of the year was $1,320. What were his sales for that pay period?  Choose the correct choice from the following choices.
A) A)13,000
B) B)13,200
C) C)16,400
D) D)15,800
E) E)19,600

Solution: His pay check was $1320.   Out of this, $160 was his fixed salary so the total commission he earned was $1320 - $160 = $1160   He earns 10% on the sales of first $10,000 which gives a commission of $1000.   He earns 5% on every subsequent dollar. Since he earns another $160, he must have had sales of another 160*(100/5)  1320 -  160= 
 1320 -  160 = 1_160
$1160   He earns 10% on the sales of first $10,000 which gives a commission of $1000.   He earns 5% on every subsequent dollar. Since he earns another $160, he must have had sales of another   160*(100/5)= 
  160*(100/5) = 3_200
3200   So his total sales must have been $10,000 + $3200= $13,200   13,200
Answer: B
The C.P of 16 books is equal to the S.P of 18 books. Find his gain% or loss%?	Choose one:
A) 16 2/3% loss  B) 11 1/9% loss  C) 16 3/3% loss  D) 36 2/3% loss  E) 56 2/3% loss

Solution: 16 CP = 18 SP   18 --- 2 CP loss   100 --- ? => 11 1/9% loss   Answer:11 1/9% loss
Answer: B
On multiplying a number A by 153, the result obtained was 102325. However, it is found that both the 2's are wrong. Find the correct result.  Choose the correct choice from the following answers.
A) 104345 B) 107375 C) 108385 D) 109395 E) 105355

Solution: The only thing you actually know about the correct number A is that it is divisible by 153 and has 5 as a factor.   You should immediately try to find the factors of 153 and look for them in the options.   153 = 9*17   Divisibility by 9 is easy to check. Only (109395) satisfies.
Answer: D
From a group of 3 boys and 3 girls, 2 children are to be randomly selected. What is the probability that 1 boy and 1 girl will be selected?  Choose the correct option:
A) 1/10
B) 4/9
C) 1/2
D) 9/15
E) 2/3

Solution: The total number of ways to choose 2 children from 6 is 6C2 = 15   The number of ways to choose 1 boy and 1 girl is 3*3= 
3*3 = 9
9   P(1 boy and 1 girl)= 9/15   The answer is 9/15.
Answer: D
In what time will a train 110 m long cross an electric pole, it its speed be 128 km/hr?	Choose one.
A) 2.5 sec B) 2.9 sec C) 3.1 sec D) 8.7 sec E) 8.5 sec

Solution: Speed = 128 * 5/18 = 36 m/sec   Time taken = 110/36 = 3.1 sec.   Answer: 3.1 sec
Answer: C
In the following list of numerals, how many 3s are followed by 3, but NOT preceded by 3?
2463315 7833346233339723	Choose the correct choice from the following choices:  A) 1  B) 2  C) 3  D) 4  E) 5

Solution: total 3 are there   ANSWER:3
Answer: C
Two circular signs are to be painted. If the diameter of the larger sign is seven times that of the smaller sign, how many times more paint is needed to paint the larger sign? (We can assume that a given amount of paint covers the same area on both signs.)  Choose the correct choice from the following answers:
A) 7
B) 14
C) 42
D) 49
E) 98

Solution: Let R be the radius of the smaller sign.   Then the diameter of the smaller sign is 2R, the diameter of the larger sign is 14R, and the radius of the larger sign is 7R.   The area A of the smaller sign is A = piR^2.   The area of the larger sign is pi(7R)^2=49piR^2=49A.   Since the area is 49 times larger, we need 49 times more paint for the larger sign.   The answer is 49.
Answer: D
A,B and C engage in a business with a joint capital of Rs. 25000. If at the end of a year A gets Rs.5000, B Rs.2000 and C Rs.3000 out of profits, how much capital did B contribute? Pick one:
A) Rs.6000
B) Rs.5500
C) Rs.4500
D) Rs.4000
E) Rs.5000

Solution: Total profit = Rs.10000 B's profit share =2000/10000 =1/5 of the total profit B's capital =1/5*25000=Rs.5000 Answer : Rs.5000
Answer: E
A side of beef lost 20 percent of its weight in processing. If the side of beef weighed 640 pounds after processing, how many pounds did it weigh before processing?	Pick one:	A) 191	B) 355	C) 800	D) 840	E) 900

Solution: Let weight of side of beef before processing = x   (80/100)*x = 640   => x = (640 * 100)/80= 
(640 * 100)/80 = 800
800   Answer 800
Answer: C
Fox jeans regularly sell for $15 a pair and Pony jeans regularly sell for $18 a pair. During a sale these regular unit prices are discounted at different rates so that a total of $9 is saved by purchasing 5 pairs of jeans: 3 pairs of Fox jeans and 2 pairs of Pony jeans. If the sum of the two discounts rates is 33 percent, what is the discount rate on Pony jeans? Choose one
A) 9%  B) 10%  C) 11%  D) 12%  E) 65%

Solution: x discount on Pony jeans, (0.33-x) discount on Fox jeans.   Set the equation: 3*15(0.33-x)+2*18x=9 --> x=0.65=65%   Answer: 65%.
Answer: E
Murugan, Prasanna and Arun invested Rs.8000, Rs.4000 and Rs.8000 respectively in a business. Arun left after six months .If after eight months, there was a gain of Rs.4005, then what will be the share of Prasanna?	Choose the most appropriate option
A) Rs.890 B) Rs.1335 C) Rs.1602 D) Rs. 1780 E) None

Solution: Solution   Murugan : Prasanna : Arun	=(8000×6):(4000×8):(8000×8)   = 48 : 32 : 64   = 3 : 2 : 4.   Kamal's share	= Rs.4005×2/9)   = Rs.890.   Rs.890nswer Rs.890
Answer: A
The present ages of three persons are in proportions 4:7:9. Eight years ago, the sum of their ages was 56. Find their present ages.
Choose the correct answer
A) 16, 28, 38  B) 16, 28, 36  C) 16, 28, 32  D) 16, 28, 30  E) 16, 28, 31

Solution: Let their present ages be 4x, 7x and 9x years respectively.   Then, (4x - 8) + (7x - 8) + (9x - 8) = 56   20x = 80 => x = 4   Their present ages are 16, 28 and 36 years respectively.   Answer: 16, 28, 36
Answer: B
If the price of a TV is first decreased by 20% and then increased by 50%, then the net change in the price will be :
Options:
A) 20% increase  B) 10% increase  C) 10% decrease  D) 6% increase  E) None of these

Solution: Explanation :   Solution: let the original price be Rs. 100.   New final price = 150% of(80% of 100) =Rs. 150/100 * 80/100 * 100 = Rs. 120.   .'. Increase = 20%   20% increasenswer : 20% increase
Answer: A
Weights of two friends Ram and Shyam are in the ratio of 4 : 5. Ram’s weight increases by 10% and the total weight of Ram and Shyam together becomes 82.8 kg, with an increase of 15%. By what per cent did the weight of Shyam increase?  Pick:	A) 12.5%	B) 17.5%	C) 19%	D) 21%	E) None of these

Solution: Let the weights of Ram and Shyam be 4x and 5x. Now,according to question,   4x×110/100+Shyam?snewwt4x×110100+Shyam?s new wt = 82.8........ (i)   and 4x + 5x = 9x+115/100 4  + 5= 
 4  + 5 = 9
9x+115/100= 82.8........ (ii)   From (ii), x = 8   Putting in (i),   we get Shyam’s new wt = (82.8 – 35.2) = 47.6   % increase in Shyam’s wt = (47.6−40/40×100) = 19   Answer 19%
Answer: C
nine baseball players each stand at different corners of a baseball diamond. The sides of the diamond are all of equal length. Two arrangements of baseball players are considered different only when the relative positions of the players differ. How many different ways can the baseball players arrange themselves around the diamond? Choose the correct choice from the following answers
A) 40320 B) 40213 C) 40311 D) 24089 E) 25608

Solution: it is like a circular arrangement.   total ways for n people to arrange in a circle is = factorial (n-1)   in this case n= 9   hence ans = 8 factorial = 40320   hence 40320
Answer: A
Two numbers are respectively 20% and 25% more than a third number. The percentage that is first of the second is? Choose the correct choice from the following.
A) 86%	B) 98%	C) 96%	D) 36%	E) 91%

Solution: I II III   120 125 100   125----------120   100-----------? => 96%   Answer: 96%
Answer: C
Two numbers are in the ratio of 1 : 2. If 10 be added to both, their ratio changes to 3 : 5. The greater number is	Choose the correct choice:
A) 20
B) 24
C) 28
D) 32
E) 40

Solution: Let the ratio be X : Y,   Given X/Y = 1/2 ,   (X + 10)/(Y + 10) = 3/5   => X = 20   And Y = 40   ANSW40R:40
Answer: E
If y exceeds x by 30%, then x is less than y by?	Choose the correct choice from the following options:
A) 1/7%	B) 1/9%	C) 1/11%	D) 1/13%	E) 1/17%

Solution: X=100	y=130   130------30   100-------? => 23 1/13%   Answer:1/13%
Answer: D
How many multiples of 10 are there between 10 and 1000, exclusive?	Choose the correct choice from the following:  A) 98  B) 99  C) 100  D) 101  E) 97

Solution: 98   multiples of 5 between 1 and 36 exclusive.   from 10 * 2 upto 10*99, (2,3,4,...,99). Hence, 98 multiples !   correct option is 98
Answer: A
In a competitive examination in State A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 79 more candidates got selected than A. What was the number of candidates appeared from each State?	Choose the correct choice from the following options.
A) 7000  B) 7900  C) 6000  D) 5000  E) 4000

Solution: State A and State B had an equal number of candidates appeared.   In state A, 6% candidates got selected from the total appeared candidates   In state 7900, 7% candidates got selected from the total appeared candidates   7900ut in State 7900, 79 more candidates got selected than State A   From these, it is clear that 1% of the total appeared candidates in State 7900 = 79   => total appeared candidates in State 7900 = 79 x 100 = 7900   => total appeared candidates in State A = total appeared candidates in State 7900 = 7900
Answer: B
Which of the following describes all values of x for which 1–x^2 <= 0?
Choose the correct choice
A) x >= 1	B) x <= –1	C) 0 <= x <= 1	D) x <= –1 or x >= 1	E) –1 <= x <= 1

Solution: Which of the following describes all values of x for which 1–x^2 >= 0?   (A) x >= 1   Plugged in 2. 1–(2)^2 >= 0 -3>=0? yes. But are these all the values? No. Wrong   (B) x <= –1   Plugged in -2. 1–(-2)^2 >= 0 -3>=0? yes. But are these all the values? No. Wrong.   (C) 0 <= x <= 1   Start with 0. 1-0 = 1. Wrong. All the other values wrong as well.   (D) x <= –1 or x >= 1   This is the Correct Answer as it captures both A and B. Answer is D.   (E) –1 <= x <= 1   Plug in 0. Value is greater than 0. Wrong.   Correct answer is x <= –1 or x >= 1.
Answer: D
Three years ago, John’s age was half of the age he will be in 8 years. How old is he now?  Choose the correct choice from the following options.
A) 14years	B) 15years	C) 16years	D) 17years	E) 18years

Solution: Let John=j,j-3=(j+8)/2,then j=14years   14yearsNSWER:14years
Answer: A
Ten years ago, the age of Anand was one-third the age of Bala at that time. The present age of Bala is 14 years more than the present age of Anand. Find the present age of Anand?  Choose the correct option:
A) 13 B) 14 C) 15 D) 16 E) 17

Solution: Let the present ages of Anand and Bala be 'a' and 'b' respectively.   a - 10 = 1/3 (b - 10) --- (1)   b = a + 14   Substituting b = a + 12 in first equation,   a - 10 = 1/3 (a + 4) => 3a - 30 = a + 4   => 2a = 26 => a = 13.   13NSWER:13
Answer: A
In covering a distance of 30 km, Arun takes 22 hours more than Anil. If Arun doubles his speed, then he would take 1 hour less than Anil. What is Arun's speed?  Pick
A) 8kmph
B) 5kmph
C) 4kmph
D) 7kmph
E) 9kmph

Solution: Explanation:   If Arun doubles his speed, he needs 3 hour less. Double speed means half time. Hence, half of the time required by Arun to cover 30 km =3 hour   i.e., Time required by Arun to cover 30 km =6 hour   Arun's speed =30/6= 
30/6 = 5
5 kmph   ANSWER IS 5kmph
Answer: B
Income and expenditure of a person are in the ratio 15 : 8. If the income of the person is Rs. 15000, then find his savings?
Select the correct option:
A) 6999
B) 7000
C) 7001
D) 7002
E) 7003

Solution: Let the income and the expenditure of the person be Rs. 15x and Rs. 8x respectively.   Income, 15x = 15000 => x = 1000   Savings = Income - expenditure = 15x - 8x = 7x 15  - 8= 
15  - 8 = 7
7x= 7(1000)   So, savings = Rs. 7000.   Answer:7000
Answer: B
There are 5,290 feet in 1 mile and 12 inches in one foot. How many inches are in a mile?
Choose one.
A) 5,280 - 12  B) 5,280/12  C) 12(5,280)  D) 12^2(5,280)  E) 12*5,290

Solution: 1 feet = 12 inches   1 mile = 5290 feet   1 mile = 5290*12 inches   Ans: 12*5,290
Answer: E
When two dice are rolled, what is the probability that the sum of the two numbers is 5?
Choices:
A) 1/9
B) 2/9
C) 1/3
D) 2/3
E) None of the above

Solution: We have 4 outcomes that satisfy the question:   1-4   2-3   3-2   4-1   the probability is (1/6*1/6)*4= 4/36= 1/9   I think the answer is 1/9
Answer: A
The average age of 50 students in a class is 10years. If teacher's age is also included then average increases 1year then find the teacher's age?	Choose the correct choice from the following answers:
A) 59
B) 55
C) 61
D) 45
E) 36

Solution: Total age of 50 students = 50*10= 
50*10 = 500
500   Total age of 51 persons= 51*11= 
51*11 = 561
561   Age of teacher= 561-500= 
561-500 = 61
61years   Answer is 61
Answer: C
A theater charges $12 for seats in the orchestra and $8 for seats in the balcony. On a certain night, a total of 380 tickets were sold for a total cost of $3,320. How many more tickets were sold that night for seats in the balcony than for seats in the orchestra? Pick:
A) 90
B) 110
C) 120
D) 130
E) 240

Solution: Orchestra Seats - a   Balcony Seats - b   a+b = 380   and 12a + 8b = 3320   Solving equations simultaneously (Multiply Equation 1 with 8 and subtract from second equation)   4a = 3320 - 8*380 = 3320 - 3040= 
3320 - 3040 = 280
280   i.e. a= 70   and b = 380-70= 
380-70 = 310
310   More seats in balcony than orchestra= b-a = 310 - 70= 
310 - 70 = 240
240   Answer: option 240
Answer: E
Two horses start trotting towards each other, one from A to B and another from B to A. They cross each other after one hour and the first horse reaches B, 5/6 hour before the second horse reaches A. If the distance between A and B is 50 km. what is the speed of the slower horse?
Choose the correct choice from the following answers.
A) 30 km/h
B) 15 km/h
C) 25 km/h
D) 20 km/h
E) 27 km/h

Solution: Explanation:   If the speed of the faster horse be \inline f_{s} and that of slower horse be Ss.then   Now, you can go through options.   The speed of slower horse is 20km/h   Since, 20+30=50 and 50/20=50/30=5/6   ANSWER IS 20 km/h
Answer: D
If a tank A can be filled within 10 hrs and 1/4th of tank B is filled in 19 hrs. Then what is the duration of the tank B to fill completely?
Choose the correct option:
A) 74 B) 75 C) 76 D) 77 E) 78

Solution: 1/4th of tank B takes 19hrs then   to fill completely it takes 19*4= 
19*4 = 76
76hrs   ANSWER:76
Answer: C
Amit and Ian paint a wall in alternating shifts. First Amit paints alone, then Ian paints alone, then Amit paints alone, etc. During each of his shifts, Amit paints 1/2 of the remaining unpainted area of the wall, while Ian paints 1/3 of the remaining unpainted area of the wall during each of his shifts. If Amit goes first, what fraction of the wall's area will remain unpainted after Amit has completed his 6th shift?	Choose the correct choice
A) 1/27  B) 1/54  C) 1/81  D) 1/162  E) 1/486

Solution: Fraction of area unpainted after FIRST shift of Amit = 1-(1/2) = 1/2   Fraction of area unpainted after FIRST shift of Ian = (1/2)-(1/3)(1/2) = (2/3)(1/2)   Fraction of area unpainted after S1/486COND shift of Amit = (1/2)(2/3)(1/2)   Fraction of area unpainted after S1/486COND shift of Ian = (2/3)(1/2)(2/3)(1/2)   Fraction of area unpainted after THIRD shift of Amit = (1/2)(2/3)(1/2)(2/3)(1/2)   Fraction of area unpainted after THIRD shift of Ian = (2/3)(1/2)(2/3)(1/2)(2/3)(1/2)   Fraction of area unpainted after FORTH shift of Amit = (1/2)(2/3)(1/2)(2/3)(1/2)(2/3)(1/2)   Fraction of area unpainted after FORTH shift of Ian = (2/3)(1/2)(2/3)(1/2)(2/3)(1/2)(2/3)(1/2)   Fraction of area unpainted after FIFTH shift of Amit = (1/2)(2/3)(1/2)(2/3)(1/2)(2/3)(1/2)(2/3)(1/2)   Fraction of area unpainted after FIFTH shift of Ian = (2/3)(1/2)(2/3)(1/2)(2/3)(1/2)(2/3)(1/2)(2/3)(1/2)   Fraction of area unpainted after SIXTH shift of Amit = (1/2)(2/3)(1/2)(2/3)(1/2)(2/3)(1/2)(2/3)(1/2)(2/3)(1/2)=486   Answer: option 1/486
Answer: E
Find the area of the quadrilateral of one of its diagonals is 28 cm and its off sets 8 cm and 2 cm? Pick one
A) 140 cm2
B) 150 cm2
C) 168 cm2
D) 182 cm2
E) 200 cm2

Solution: 1/2 * 28(8 + 2)   = 140 cm2   140 cm2nswer: 140 cm2
Answer: A
Two representatives must be selected from each of two groups of students. One group consists of four men and one woman, and the other group consists of two women and one man. What is the probability that 2 men and 2 women will be selected ?	Choose the correct option
A) 1/6	B) 1/4	C) 2/7	D) 7/15	E) 1/2

Solution: Group 1: 4 Men and 1 Woman   Group 2: 1 Men and 2 Woman   Need: 2 Men and 2 women   Case 1: 2 Men from Group 1 and 2 women from group 2 - 4C2*2C2 = 6 ways   Case 2: 1 Men and 1 Woman from Group 1 and 1 Man and 1 women from group 2 - 4*1*1*2 = 8 ways   Total Favorable cases = 6+8= 
6+8 = 14
14   Total Possible ways of selecting students 2 from each group= 5C2*3C2 = 10*3= 
10*3 = 30
30   Probability= 14/30 = 7/15   Answer : Option 7/15
Answer: D
A can do a piece of work in 40 days; B can do the same in 30 days. A started alone but left the work after 10 days, then B worked at it for 10 days. C finished the remaining work in 10 days. C alone can do the whole work in?	Choose the correct choice
A) 24 days  B) 30 days  C) 44 days  D) 17 1/2 days  E) 60 days

Solution: Explanation:   10/40 + 10/30 + 10/x = 1   x = 24 days   24 daysnswer: 24 days
Answer: A
P is a prime number. If 6p is between 15 and 95, which of the following E can be a value of 7p + 2?  Choose the correct choice
A) E.15  B) E.79  C) 121  D) 65  E) 21

Solution: [3,5,7,11,13] are prime numbers that fits this equation 15< 6X <95. Afterwards subtract 2 from all the answer n see if it's divisible by 7. Therefore A and E are out. Leaves out with B C D.   B =11   C =17   D = 9   Only 11 is the set of prime numbers that fit between 15 and 95. Therefore 79 is the answer.E.79
Answer: B
here are 6 periods in each working day of a school. In how many ways can one organize 5 subjects such that each subject is allowed at least one period? Choose the correct option
A) 4561 B) 3564 C) 1542 D) 1800 E) 2451

Solution: 5 subjects can be arranged in 6 periods in 6P5 ways.   Any of the 5 subjects can be organized in the remaining period (5C1 ways).   Two subjects are alike in each of the arrangement. So we need to divide by 2! to avoid overcounting.   Total number of arrangements   = 6P5× 5C1 /2!=1800   Ans: 1800
Answer: D