MU-NLPC/Calc-aqua_rat huggingface dataset:
A GOLF BALL HAS DIAMETER EQUAL TO 4.1CM. ITS SURFACE HAS 150 DIMPLES EACH OF RADIUS 2MM (0.2 CM) .CALCULATE TOTAL SURFACE AREA WHICH IS EXPOSED TO SURROUNDINGS ASSUMING THAT THE DIMPLES ARE HEMISPHERCAL.  Choose the most appropriate option:	A) 81.62cm2	B) 71.62cm2	C) 61.62cm2	D) 51.62cm2	E) 41.62cm2

Solution: the total surface area of the golf ball without considering the dimples is 4*3.14*sqrt(4.1/2).   Due to 150 pits on the surface a there will be a reduction in surface area of ball which will be equal to opening area of the dimples which is 150*3.04*sqrt(0.2). again due to formation of the pits there will be an increase in surface area due to hemispherical concave surface of the pits which will be 150*2*3.14*sqrt(0.2) .So, the total surface area will be 4*3.4*sqrt(4.1)-150*3.14*sqrt(.2)+150*2*3.14*sqrt(.2)=71.62cm2   ANSWER:71.62cm2
Answer: B
A and B can do a work in 5 days and 10 days respectively. A starts the work and B joins him after 3 days. In how many days can they complete the remaining work?
Choose the correct choice from the following choices.
A) 4/3 days B) 2 days C) 8 days D) 3 days E) 9 days

Solution: Work done by A in 3 days = 3/5   Remaining work = 2/5   Work done by both A and B in one day = 1/5 + 1/10 = 3/10   Remaining work = 2/5 * 10/3 = 4/3 days.   4/3 daysnswer: 4/3 days
Answer: A
Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 36 kmph. Of how many minutes does the train stop per hour?	Choices:
A) 18	B) 77	C) 12	D) 99	E) 12

Solution: T = 9/45 * 60= 
9/45 * 60 = 12
12   Answer:12
Answer: C
How many different combinations of clothes can rahul make if he have 2 pairs of pants, 4 shirts, and 3 jackets?
Select
A) 10	B) 18	C) 24	D) 20	E) 15

Solution: number of ways rahul can make is 4*3*2= 
4*3*2 = 24
24   Answer:24
Answer: C
If x and y are odd integers, which of the following must always be a non-integer? Choose the correct choice from the following:
A) xy
B) x/y
C) y/x
D) xy/2
E) -xy

Solution: A) xy: (1)(1) = 1 and 1 is an integer. ELIMINATE   B. x/y: 1/1= 
1/1 = 1
1 and 1 is an integer. ELIMINATE   C. y/x: 1/1= 
1/1 = 1
1 and 1 is an integer. ELIMINATE   D. xy/2   E. -xy: -(1)(1)= -1 and -1 is an integer. ELIMINATE   As X and Y are odd, multiplication of x and y would result in odd integer   (Odd Integer)/2 will always be non integer   ANSWER:xy/2
Answer: D
A work can be finished in 11 days by forty women. The same work can be finished in eleven days by four men. The ratio between the capacity of a man and a woman is
Select
A) 4:1	B) 3:4	C) 2:3	D) 3:2	E) 4:5

Solution: Work done by 40 women in 1 day = 1/11   Work done by 1 woman in 1 day = 1/(40Ã—11)   Work done by 4 men in 1 day = 1/11   Work done by 1 man in 1 day = 1/(4Ã—11)   Ratio of the capacity of a man and woman =1/(4Ã—11) : 1/(40Ã—11) = 1/4 : 1/40   = 1/1:1/4 = 4:1   4:1nswer is 4:1.
Answer: A
Find the sum lend at C.I. at 5 p.c per annum will amount to Rs.441 in 2 years? Pick:	A) 200	B) 400	C) 378	D) 883	E) 732

Solution: 441 = P(21/20)2   P = 400   Answer: 400
Answer: B
A train passes a station platform in 40 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?	Choose the correct choice from the following choices.
A) 328  B) 279  C) 240  D) 288  E) 300

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 / 40= 15   x + 300 = 600   x = 300 m. Answer:300
Answer: E
A crate of mangoes contains one bruised mango for every thirty mango in the crate. If three out of every four bruised mango are considerably unsalable and there are 12 unsaleable mangoes in the crate then how many mango are there in the crate?  Choices.
A) 180
B) 280
C) 380
D) 480
E) 580

Solution: Let the total no of mangoes in the crate be x   Then the no of bruised mango = 1/30 x   Let the no of unsalable mangoes =3/4 (1/30 x)   1/40 x =12   x=480   ANSWER 480
Answer: D
The ratio of radius of a circle and the side of a square is 2 : 7. Find the ratio of their areas:
Choose the correct option.
A) 2 : 1	B) 4 : 7	C) 8 : 77	D) 4 : 49	E) None

Solution: radius/side = 2/7   â‡’ area of circle/area of square= 4/49   Answer: 4 : 49
Answer: D
How many members are there between 1 to 100 which are divisible by 9 and the sum of two digits is 9?
Answers.
A) 13 B) 11 C) 7 D) 9 E) 10

Solution: 9,18,27,36,45,54,63,72,81,90,99   9 is not a two digit number   99 sum is 18;   ans=9   ANSWER:9
Answer: D
A patient is given exactly 750 milliliters of a mixture of two medications daily. Medication A contains 40% pain killer and medication B contains 20% pain killer. If the patient receives exactly 215 milliliters of pain killer daily, how many milliliters of medication B are in the mixture? Choose the most appropriate option:
A) 150
B) 225
C) 325
D) 425
E) 550

Solution: Let there be A milliliters of Medication A   and B milliliters of Medication B   A+B = 750 -- 1   Medication A contains 40% pain killer and medication B contains 20% pain killer.   (40/100)*A + (20/100)*B = 215   => (2/5)*A + (1/5)*B = 215   Multiplying by 5 , we get   2A + B = 1075 -- 2   Equation 2- Equation 1 , we get   A = 325   B = 425   Answer 425
Answer: D
The volumes of two cubes are in the ratio 27: 125, what shall be the ratio of their surface areas?
Choices:
A) 6:25 B) 3:5 C) 9:25 D) 16:25 E) 19:25

Solution: a13 : a23 = 27 : 125   a1 : a2 = 3 : 5   6 a12 : 6 a22   a12 : a22 = 9 : 25   ANSWER:9:25
Answer: C
Fifteen participants are participating in a competition. In how many ways can the first three prizes be won?  Pick one.
A) 920  B) 680  C) 2730  D) 720  E) 620

Solution: Out of 15 participants, the first three prizes can be won in,   15P3 = 15! / (15 - 3)!   = 15 x 14 x 13   = 2730 ways   ANSWER:2730
Answer: C
If x is equal to the sum of the integers from 20 to 40, inclusive, and y is the number of even integers from 20 to 40, inclusive, what is the value of x + y?	Choose the correct choice
A) 601  B) 611  C) 621  D) 631  E) 641

Solution: x = 20 + 21 +...+ 40 = 21(30) = 630   y = 11   x+y = 641   The answer is 641.
Answer: E
A man spend 1/5 of his salary on food , 1/10 of his salary on house rent and 3/5 salary on clothes. he still has $16000 left with him. find salary..
Select the correct option
A) $10800 B) $18000 C) $160000 D) $1800 E) None

Solution: [1/(x1 / y1 + x2/y2 + x3/y3)] * Total amount= Balance amount   [1-(1/5 + 1/10 + 3/5)} * total salary= $16000, = [1-9/10] * Total salary = $16000, Total salary = $16000*10= 
16000*10 = 160_000
$160000, correct answer ($160000)
Answer: C
Katie has 9 employees that she must assign to 3 different projects. If 3 employees are assigned to each project and no one is assigned to multiple projects, how many different combinations S of project assignments are possible? Choose the correct option.
A) 252	B) 1,680	C) 2,340	D) 362,880	E) 592,704

Solution: The ways to select three employees out of 9 for first project = 9C3   The ways to select three employees out of Remaining 6 for Second project = 6C3   Third Project already has the group of three to be assigned to it so need to select that   So total ways to assign 3 employees to each of 3 projects S= 9C3 * 6C3 * 1 = 1,680   Answer: Option 1,680
Answer: B
A car travels the first 1/3 of certain distance with a speed of 10km/hr the next 1/3 distance with a speed of 20 km/hr, and the last 1/3 distance with a speed of 10 km/hr. the average speed of the car for the whole journey is?  Answers
A) 12km/hr  B) 18km/hr  C) 89km/hr  D) 52km/hr  E) 79km/hr

Solution: Let the whole distance travelled be x km   and the average speed of the car for he whole journey be y km/hr   then (x/3)/10+(x/3)/20+(x/3)/10=x/y   x/30+x/60+x/30=x/y   1/12y=1   y=12km/hr   12km/hrnswer(12km/hr)
Answer: A
Of the goose eggs laid at a certain pond, 2/3 hatched and 3/4 of the geese that hatched from those eggs survived the first month. Of the geese that survived the first month, 3/5 did not survive the first year. If 125 geese survived the first year and if no more than one goose hatched from each egg, how many goose eggs were laid at the pond?
Choices:
A) 280
B) 400
C) 540
D) 625
E) 840

Solution: Of the goose eggs laid at a certain pond, 2/3 hatched and 3/4 of the geese that hatched from those eggs survived the first month:   2/3*3/4 = 1/2 survived the first month.   Of the geese that survived the first month, 3/5 did not survive the first year:   (1-3/5)*1/2 = 1/5 survived the first year.   120 geese survived the first year:   1/5*(total) = 125 --> (total) = 625.   Answer: 625.
Answer: D
y =2x^2 +2bx + 512 cuts the x axis at (h, 0) and (k, 0). If h and k are integers, what is the least value of b?
Choose the correct choice from the following answers.
A) 256	B) -256	C) -128	D) -64	E) -257

Solution: As the curve cuts the x-axis at (h,0) and (k,0). Therefore h,k are the roots of the quadratic equation.   For the quadratic equation is in the form ofax^2+bx+c=0,   The product of the roots =c/a= 512/2= 
512/2 = 256
256 and the sum of the roots=-b/a=-b   256 can be expressed as product of two numbers in the following ways:   1 * 256   2 * 128   4 * 64   8 * 32   16 * 16   The sum of the roots is maximum when the roots are 1 and 256 and the maximum sum is 1 + 256= 
1 + 256 = 257
257.   The least value possible for b is therefore -257.   -257
Answer: E
Calculate the share of profit made by 2 business partners, who invested $800 and $1200 respectively in a business if the profit made is $600.	Choose the correct option
A) $241,$360 B) $240,$2260 C) $240,$360 D) $230,$360 E) $220,$360

Solution: A:B = 800:1200   A:B = 2 : 3   A's share = 600*2/5= 
600*2/5 = 240
$240   B's share= 600*3/5= 
600*3/5 = 360
$360   Answer is $240,$360
Answer: C
What is the average of xx, 2x2x, and 66? Choose the correct choice:
A) x+2 B) x+3 C) x+2x+2 D) x+4 E) 2x+5

Solution: By the definition of an average, we get:   x+2x+63=3x+63x+2x+63=3x+63   =3(x+2)3=x+2.=3(x+2)3=x+2.   Hence, the answer is x+2x+2 or Option x+2x+2
Answer: C
If the average (arithmetic mean) of x, x + 2, and x + 4 is 73, what is the value of x? Choose the correct choice from the following answers.
A) 71	B) 75	C) 85	D) 83	E) 82

Solution: 71M of x, x + 2, and x + 4 = x + (x + 2) + (x + 4) / 3 = 3x + 6 /3 = x + 2   Given that x + 2 = 73   x = 71   71nswer : 71
Answer: A
The ratio of number of students studying Arts, Commerce and Science in a College is 3 : 5 :4. What is the new ratio of the number of students studying Arts, Commerce and Science respectively if there is an increase of 20%, 40% and 25% in the number of students studying Arts, Commerce and Science? Choose one:
A) 18 : 35 : 50	B) 3 : 10 : 10	C) 4 : 8 : 5	D) 8 : 35 : 25	E) None of these

Solution: Suppose the number of students studying Arts, Commerce and Science be 3x, 5x and 4x respectively.   When their numbers are increased by 20%, 40% and 25% respectively the new ratio becomes   3x × 120% : 5x × 140% :   4x × 125% = 36 : 70 : 50   = 18 : 35 : 25   Answer 8 : 35 : 25
Answer: D
The ratio of money with Ram and Gopal is 7 : 17 and that with Gopal and Krishan is 7: 17. If Ram has Rs. 539, Krishan has ?	Select the correct option:	A) s. 2890	B) s. 2330	C) s. 1190	D) s. 1620	E) s. 3179

Solution: Ram : Gopal = 7 : 17 = 49 : 119   Gopal : Krishan = 7 : 17 = 119 : 289   Ram : Gopal : Krishan = 49 : 119 : 289   Ram : Krishan = 49 : 289   Thus, 49 : 289 = 539 : N   &there N = 289 x 539 / 49   = Rs. 3179   Answer :s. 3179
Answer: E
Lucy deposited $62500 in an investment fund that provided 22 percent annual return compounded quarterly. If she made no other transactions with the fund, in how much time, in years, did her investment earn a total interest of $5100?  Choose the correct choice from the following:
A) 1/2
B) 1/7
C) 3
D) 6
E) 6.1

Solution: A = P + I = 62500 + 5100= 
62500 + 5100 = 67_600
67600   67600= 62500(1 + 22/4*100)^(4t)   t = 1/7 yrs   Answer: 1/7
Answer: B
What is the greatest prime factor of 5^6 - 1? Choose the correct option:
A) 29
B) 31
C) 37
D) 41
E) 43

Solution: 5^6-1 = (5^3-1)(5^3+1) = 124*126 = 4*31*3*42   The answer is 31.
Answer: B
Which of the following inequalities has a solution set, when graphed on the number line, is a single line segment of finite length?
Choose the correct choice from the following options:
A) 2 <= 8x+10 <= 6  B) 2 <= 34x+4 <= 6  C) 2 <= 3x+4 <= 6  D) 2 <= 3465x+4 <= 6  E) 2 <= 346x+4 <= 6

Solution: The key words in the stem are:a singleline segment offinite length   Now, answer choices A, B, and C can not be correct answers as solutions sets for these exponential functions are not limited at all (>= for even powers and <= for odd power) and thus can not be finite (x can go to + or -infinity for A and C and x can got to -infinity for B). As for D: we have thatabsolute valueof x is between two positive values, thus the solution set for x (because of absolute value) will be two line segments which will be mirror images of each other.   Answer: 2 <= 3x+4 <= 6.
Answer: C
In a series of eight football matches between Germany and Argentina , the probability of Germany winning a match is 1/3 and the probability that the match ends in a draw is 1/4. If a win gets the team 2 points, a draw 1 point and a loss 0 Points, What is the probability that Germany will end up in 8 draws in the series?
Choose the correct answer:
A) 24/576  B) 125/864  C) 1/25  D) 1/65536  E) 1/5

Solution: Since the probability of a draw is 1/4, then the probability of 8 draws in 8 matches is (1/4)^8=1/65536.   Answer: 1/65536.
Answer: D
The perimeter of a rectangle is equal to the perimeter of aright-angled triangle of height 12 cm. If the base of the triangle is equal to the breadth of the rectangle, what is the length of the rectangle”  Choose the correct choice
A) 18 cm B) 24 cm C) 22 cm D) Data inadequate E) None of these

Solution: P = 2(l + b) = L + B + h = L + b + 12.   Data inadequate.   Answer Data inadequate
Answer: D
At a meeting, 25 attendants used a pencil and 15 attendants used a pen. If exactly 20 attendants used only one of the two types of writing tools, how many attendants wrote with both types of writing tools?
Choose the correct option:	A) 10	B) 6	C) 7	D) 4	E) 14

Solution: Say x attendants wrote with both writing tools.   (25 - x) + (15 - x) = 20 --> x = 10.   10nswer: 10.
Answer: A
A numberais squared and then multiplied by negative 3. The result of this operation E is equal to three times the sum of three timesaand two. What is one possible value ofa?  Pick one
A) -3  B) -2  C) 1  D) 2  E) 3

Solution: E=-3*a^2=3(3a+2)   a= -2 or -1   a=-2=-2
Answer: B
There are 10person among whom 2are brother. The total no.of ways in which these persons can be seated around a round table so that exactly 1person sit between the brothers, is equal to?  Select
A) 7!*3!	B) 7!*2!	C) 6!*3!	D) 5!*2!	E) 8!*3!

Solution: Total number of ways = 7!*2!.   7!*2!
Answer: B
A person can row at 9 kmph and still water. He takes 4 1/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph?	Choices
A) 28  B) 26  C) 25  D) 21  E) 20

Solution: Let the distance between A and B be x km.   Total time = x/(9 + 1) + x/(9 - 1) = 4.5   => x/10 + x/8 = 9/2 => (4x + 5x)/40 = 9/2 => x = 20 km.   Answer:20
Answer: E
Two stations A and B are 65 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?	Choose the correct choice from the following options:	A) 9	B) 10	C) 11	D) 12	E) 8

Solution: Suppose they meet x hours after 7 a.m.   Distance covered by A in x hours = 20x km.   Distance covered by B in (x - 1) hours = 25(x - 1) km.   Therefore 20x + 25(x - 1) = 65   45x = 90   x = 2.   So, they meet at 9 a.m.   9nswer: Option 9
Answer: A
A completes a work in 6 days and B complete the same work in 12 days. If both of them work together, then the number of days required to complete the work will be	Choose the correct choice from the following options:
A) 8 days
B) 9 days
C) 10 days
D) 12 days
E) 4 days

Solution: If A can complete a work in x days and B can complete the same work in y days, then, both   of them together can complete the work in x y/ x+ y days   Therefore, here, the required number of days = 6 × 12/ 18 = 4days.   Answer : 4 days
Answer: E
If the population of a certain country increases at the rate of Two person every 60 seconds, by how many persons does the population increase in 100 minutes?  Select the correct option:
A) 120  B) 150  C) 240  D) 220  E) 200

Solution: Answer = 2 * 100= 
2 * 100 = 200
200   Answer= 200
Answer: E
A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions mad by the larger wheel is:
Select the correct option: A) 49 B) 4 C) 12 D) 9 E) 27

Solution: Let the required number of revolutions made by larger wheel be x.   Then, More cogs, Less revolutions (Indirect Proportion)   14 : 6 :: 21 : x 14 * x = 6 x 21   x =	(6 x 21)/14   x = 9.   Answer is 9.
Answer: D
The average age of a husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is: Choices:
A) 10 B) 19 C) 20 D) 25 E) 17

Solution: Sum of the present ages of husband, wife and child = (23 * 2 + 5 * 2) = 57 years.   Required average = 57/3= 
57/3 = 19
19 years.   ANSWER 19
Answer: B
Rectangle ABCD is constructed in the coordinate plane parallel to the x- and y-axes. If the x- and y-coordinates of each of the points are integers which satisfy 2 ≤ x ≤ 11 and -5 ≤ y ≤ 5, how many possible ways are there to construct rectangle ABCD?
Select: A) 396 B) 1260 C) 2475 D) 7920 E) 15840

Solution: As the rectangle is parallel to coordinate axes, the coordinates of the points of the rectangle would be   (X1, Y1), (X2, Y1), (X2, Y2), (X1,Y2)   given that X1, X2 lie between 2 and 11..ie., 10 possible numbers   Possible combinations for X1,X2 would be 10C2 = 45   Similarly, Possible combinations for Y1, Y2 would be 11C2 = 55   Possible ways of constructing rectangle is by selecting any of the combination of X1,X2 and Y1,Y2   = 45 * 55= 
45 * 55 = 2_475
2475   Ans. 2475
Answer: C
The average monthly income of P and Q is Rs. 2050. The average monthly income of Q and R is Rs. 5250 and the average monthly income of P and R is Rs. 6200. The monthly income of P is:  Pick one
A) 3050	B) 3000	C) 4000	D) 4050	E) 3100

Solution: Explanation:   Let P, Q and R represent their respective monthly incomes. Then, we have:   P + Q = (2050 x 2) = 4100 .... (i)   Q + R = (5250 x 2) = 10500 .... (ii)   P + R = (6200 x 2) = 12400 .... (iii)   Adding (i), (ii) and (iii), we get: 2(P + Q + R) = 27000 or P + Q + R = 13500 .... (iv)   Subtracting (ii) from (iv), we get P = 3000.   P's monthly income = Rs. 3000.   Answer: 3000
Answer: B
The number which exceeds 16% of it by 42 is?
Pick one
A) 50
B) 25
C) 52
D) 58
E) 60

Solution: Let the number be x.   Then, x - 16% of x = 42.   x - 16/100 x = 42   x = (42 * 25)/21= 
(42 * 25)/21 = 50
50   50NSWER:50
Answer: A
Rs.1430 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share?	Choices:
A) s.528
B) s.542
C) s.528
D) s.540
E) s.660

Solution: A+B+C = 1430   4A = 3B = 2C = x   A:B:C = 1/4:1/3:1/2 = 3:4:6   6/13 * 1430 = Rs.660   Answer: s.660
Answer: E
There are 5 more women than there are men on a local co-ed softball team. If there are a total of 15 players on the team, what is the ratio of men to women?  Choose the correct answer:
A) 10/16
B) 6/16
C) 5/10
D) 6/10
E) 4/10

Solution: w = m+5   w+m = 15   m+5+m = 15   2m = 10   m = 5   w = 10   ratio:5:10   Ans: 5/10
Answer: C
In how many ways 8 different tickets R can be distributed between Jane and Bill if each is to receive any even number of tickets and all 8 tickets to be distributed.	Options:
A) From 2 to 6 inclusive.  B) From 98 to 102 inclusive.  C) From 122 to 126 inclusive.  D) From 128 to 132 inclusive.  E) From 196 to 200 inclusive.

Solution: Possibilities   J 8 6 4 2 0   B 0 2 4 6 8   # of ways 8C8 8C6 8C4 8C2 8C0   R=1+28+70+28+1= 
1+28+70+28+1 = 128
128 Answer is From 128 to 132 inclusive..
Answer: D
Three numbers are in the ratio 3:4:5 and their L.C.M. is 1200. Their H.C.F is? Pick
A) 20  B) 30  C) 40  D) 50  E) 60

Solution: Let the numbers be 3x,4x and 5x   their L.C.M. = 60x   60x = 1200   x = 20   The numbers are 3*20 , 4*20 , 5*20   Hence required H.C.F. = 20   20nswer is 20
Answer: A
A is a working partner and B is a sleeping partner in the business. A puts in Rs.15000 and B Rs.25000, A receives 10% of the profit for managing the business the rest being divided in proportion of their capitals. Out of a total profit of Rs.9600, money received by A is?  Choose the correct choice from the following answers.
A) 4208
B) 4202
C) 4209
D) 4200
E) 42012

Solution: 15:25 => 3:5   9600*10/100= 
9600*10/100 = 960
960   9600 - 960= 
9600 - 960 = 8_640
8640   8640*3/8= 
8640*3/8 = 3_240
3240 + 960= 
3240 + 960 = 4_200
4200   Answer: 4200
Answer: D
Running at their respective constant rate, machine X takes 2 days longer to produce w widgets than machines Y. AT these rates, if the two machines together produce 5w/4 widgets in 3 days, how many days would it take machine X alone to produce 3w widgets.	Answers:  A) 4  B) 6  C) 18  D) 10  E) 12

Solution: I am getting 12. E. Hope havent done any calculation errors..   approach..   let y=no. of days taken by Y to do w widgets. Then X will take y+2 days.   1/(y+2) +1/y = 5/12(5/12 is because (5/4)w widgets are done in 3 days. So, x widgets will be done in 12/5 days or 5/12 th of a widget in a day)   Solving, we have y = 4   =>X takes 6 days to doing x widgets. So, he will take 18 days to doing 3w widgets.   Answer : 18
Answer: C
Two trains are running in opposite directions with the same speed. If the length of each train is 120 m and they cross each other in 12 sec, then the speed of each train is?
Options.
A) 17 km/hr
B) 88 km/hr
C) 36 km/hr
D) 99 km/hr
E) 45 km/hr

Solution: Let the speed of each train be x m/sec.   Then, relative speed of the two trains = 2x m/sec.   So, 2x = (120 + 120)/12 => x = 10   Speed of each train = 10 m/sec.   = 10 * 18/5 =- 36 km/hr.   Answer: 36 km/hr
Answer: C
An event manager has ten patterns of chairs and eight patterns of tables. In how many chairs can he make a pair of table and chair?
Pick.
A) 100 B) 120 C) 60 D) 80 E) 90

Solution: He has 10 patterns of chairs and 8 patterns of tables.   Hence,A chair can be arranged in 10 ways   A table can be arranged in 8 ways   Hence one chair and one table can be arranged=10*8= 
10*8 = 80
80 ways   Option 80
Answer: D
In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 60 questions and secures 120 marks, the no of questions he attempts correctly is :	Choose the correct choice from the following choices.
A) 35  B) 36  C) 40  D) 42  E) 44

Solution: Explanation:   Let the number of correct answers be X.   Number of incorrect answers = (60 – X).   4x – (60 – x) = 120   => 5x = 180   => x = 36   Answer: 36
Answer: B
There are 5 locks and 5 keys and each of the 5 keys matches each of the 5 locks. What is the minimum and the maximum trial numbers of attempts W needed to confirm that each of the 5 keys matches each of the 5 locks?	Choose the most appropriate option
A) 5,15 B) 4,15 C) 5,10 D) 4,10 E) 5,20

Solution: Assume you have locks 1-5 and keys A-E.   Minimum: assume you are lucky to find the correct key/combo on the first try. So, 1 -> A, 2 -> B, 3 ->C, and 4 -> D, then 5 must match with E. Therefore, you only need to try 4 combos at a minimum.   Maximum: assume that it takes as many guesses as possible. So, with the first key you try A, B, C, and D with no success, therefore E must be the match (so 4 attempts). For key 2 you no longer have E available so you try A, B, and C, with no success, therefore D must be the match (3 attempts). And so on for key 3 (2 attempts) and key 4 (1 attempt). Key 5 matches with the remaining lock for a total of W= 4 + 3 + 2 + 1= 
4 + 3 + 2 + 1 = 10
10 attempts.4,10
Answer: D