MU-NLPC/Calc-aqua_rat huggingface dataset:
If the average (arithmetic mean) of a and b is 110, and the average of b and c is 160, what is the value of a − c?  Choose the most appropriate option.
A) −220 B) −100 C) 100 D) 135 E) It cannot be determined from the information given

Solution: (a + b)/ 2 =110 ===> a + b = 220   (b + c)/2 = 160 ===> b + c = 320   (a + b) - (b + c) = 220 - 320 ===> a + b - b - c = - 100 ===> a - c = - 100   Answer: −100
Answer: B
If the total distance of a journey is 120 km .If one goes by 60 kmph and comes back at 40kmph what is the average speed during the journey?
Pick:
A) 38km/hr
B) 58km/hr
C) 68km/hr
D) 48km/hr
E) 47km/hr

Solution: total distance=2*120   total time=120/60+120/40= 
120/60+120/40 = 5
5 hours   avg=120*2/5= 
120*2/5 = 48
48km/hr   ANSWER:48km/hr
Answer: D
Raj invested an amount of Rs.17400 for two years. Find the rate of compound interest that will fetch him an amount of Rs.1783.50 at the end of two years?
Choose the correct choice from the following:
A) 7 B) 6 C) 9 D) 5 E) 4

Solution: Let the rate of interest be R% p.a.   17400[1 + R/100]2 = 17400 + 1783.50   [1 + R/100]2 = (17400 + 1783.50)/17400   = 1 + 1025/10000 = 1 + 41/400   = 441/400 = [21/20]2   [1 + R/100] = 21/20   R/100 = 1/20   Therefore R = 5   Answer:5
Answer: D
For any integer k greater than 1, the symbol k* denotes the product of all integers between 1 and k, inclusive. If k* is a multiple of 315 what is the least possible value of k?	Pick one.
A) 5
B) 7
C) 9
D) 11
E) 13

Solution: 315 = 3*3*5*7   Thus k must include numbers at least up to the number 7.   The answer is 7.
Answer: B
A sum of Rs. 12500 amounts to Rs. 15000 in 4 years at the rate of simple interest. What is the rate of interest? Pick:  A) 4%  B) 5%  C) 6%  D) 8%  E) 14%

Solution: S.I. = (15000 - 12500) = Rs. 2500/-   Rate = (100 * 2500) / (12500 * 4)= 
(100 * 2500) / (12500 * 4) = 5
5%   ANSWER:5%
Answer: B
In how many ways can 9 people, A, B, C, D, E, F, G, H, I be seated in a row such that C and D are not seated next to each other as well as A and B are not seated next to each other?  Choose the correct choice from the following answers
A) 3841258 B) 39600 C) 576822 D) 362784 E) 69600

Solution: Number of total arrangements = 9!   Restriction 1= ABC362784 not next to each other --> let say AB and C362784 are considered as one unit, respectively   Restriction 2= AB is not the same as BA + C362784 is not the same as 362784C --> the number will increase by 2*2   Total number of arrangements - Number out of restrictions = Result   9! - (4!*2*2) = 362880 - (24*2*2)= 
362880 - (24*2*2) = 362_784
362784   Answer 362784
Answer: D
A 270 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train? Choose the correct choice from the following answers
A) 230
B) 240
C) 250
D) 260
E) 270

Solution: Relative speed = 120 + 80= 
120 + 80 = 200
200 km/hr.= 200 * 5/18 = 500/9 m/sec.   Let the length of the other train be x m.   Then, (x + 270)/9 = 500/9 => x = 230.   230nswer: Option 230
Answer: A
A pharmaceutical company received $3 million in royalties on the first $25 million in sales of and then $9 million in royalties on the next $130 million in sales. By approximately what percentage did the ratio of royalties to sales decrease from the first $25 million in sales to the next $130 million in sales?
Choose the correct choice from the following answers:
A) 8%  B) 15%  C) 35%  D) 42%  E) 56%

Solution: (9/130)/(3/25) = 15/26 = 57.7% it means that 9/130 represents only 57.7%. Therefore a decrease of 42%.   Answer 42%
Answer: D
A windmill is taking advantage of strong air currents in order to produce electrical energy. On a typical day the wind speed is around 20 mph and in that speed the windmill produces 300 kw/h (kilowatts per hour). On a stormy day a windmill produces 20% more energy. How much kw/h can three windmills produce in two hours on a stormy day?  Choose the correct answer.
A) 2880.  B) 2160.  C) 5780  D) 5760  E) 6380.

Solution: Normal Day = 300 kw/h   Stormy Day = 300*1.2= 
300*1.2 = 360
360 kw/h   3 windmills for 2 hours on stormy day     360*3*2= 
  360*3*2 = 2_160
2160   Answer: 2160.
Answer: B
A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is  Select: A) 20 years B) 21 years C) 22 years D) 24 years E) None of these

Solution: Explanation:   Let the son's present age be x years. Then, man's present age = (x + 24) years   => (x + 24) + 2 = 2(x + 2)   => x + 26 = 2x + 4   So, x = 22   Option 22 years
Answer: C
In how many ways can 5 boysand 2 girls be arranged at a table if 2 girls are never together?
Choices.
A) 320 B) 350 C) 365 D) 420 E) 480

Solution: Total ways of arranging 7 person in a circle = 6! = 720 ways   If we consider two women as one, then we have   5+1= 
  5+1 = 6
6 persons. Arranging these six persons in circle will take= 5! = 120 ways   And two women can arrange themselves in 2! ways   Total ways in which two women sit together in circle = 5!*2! = 240 ways   Total ways in which two women doesn’t sit together in circle = 6! - 5!*2! = 720 - 240= 
720 - 240 = 480
480 ways   480
Answer: E
A CAN FINISH A WORK IN 12 DAYS AND B CAN DO THE SAME WORK IN15 DAYS. B WORKED FOR 10 DAYS AND LEFT THE JOB. IN HOW MANY DAYS, A ALONE CAN FINISH THE REMAINING WORK?	Choose one
A) 4  B) 5 1/2  C) 6  D) 8  E) NONE OF THESE

Solution: B'S 10 DAY'S WORK=(1/15*10)=2/3 REMAINING WORK = (1-2/3)=1/3   NOW, 1/18 WORK IS DONE BY A IN 1 DAY   1/3 WORK IS DONE BY A IN  (12*1/3)= 
 (12*1/3) = 4
4 DAYS.   CORRECT OPTION:4
Answer: A
On a sum of money, simple interest for 2 years is Rs 660 and compound interest is Rs 696.30, the rate of interest being the same in both cases.  Pick one
A) 8%  B) 9%  C) 10%  D) 11%  E) 12%

Solution: Explanation:   Difference between C.I and S.I for 2 years = 36.30   S.I. for one year = 330.   S.I. on Rs 330 for one year = 36.30   So R% = \frac{100*36.30}{330*1} = 11%   Option 11%
Answer: D
In a group of 800 people, 1/5 play at least one instrument, 64 play two or more. What is the probability that one student play exactly one instrument?	Choose the correct choice from the following answers:
A) 3/25
B) 3/125
C) C)2/25
D) 3/25
E) 1/5

Solution: P(playing 2 or more instruments) = 64/800 = 2/25.   Then, the probability of playing exactly one instrument is given by:   P(playing 1 or more instruments) - P(playing 2 or more instruments) = 1/5 - 2/25 = 3/25.   3/25nswer 3/25.
Answer: A
Dhoni can read m pages in 2 minutes. At this rate, how long will it take him to read n pages? Select
A) (2/m)*n B) (3/m)*n C) (4m)*n D) (6/m)*n E) (8/m)*n

Solution: m page in 2 mins   i.e. 1 page in 2/m mins   i.e. n pages in (2/m)*n   (2/m)*nnswer: option (2/m)*n
Answer: A
If the perimeter of a rectangular garden is 600 m, its length when its breadth is 100 m is?  Choose the most appropriate option
A) 650 m
B) 600 m
C) 200 m
D) 300 m
E) 350 m

Solution: Explanation:   2(l + 100) = 600 => l = 200 m   ANSWER IS 200 m
Answer: C
How many different pairs of positive integers (a, b) satisfy the equation 1/a+1/b=32/51 ?  Choose the most appropriate option:
A) 6
B) 3
C) 2
D) 1
E) 0

Solution: There is no certain way to solve 2 unknown with 1 equation. The best way is to look at the question and retrospect the most efficient way. In this question, a and b are only positive integers. So that is a big relief. Now, we can start with putting a=1,2,.. and so on till the time we are confident about one of the options.   So, we start with   a=1, we get b as -ve. out   a=2, we get b as 6. Yes (Now (a,b) = (2,6). We can directly see that (a,b)=(6,2) will also satisfy. So we have 2 possible solutions)   a=3, we get b as 3. Yes (Now we have 3 possible solutions)   a=4, we get b as fraction. Out   a=5, we get b again as some fraction. Out   a=6 already taken.   We have A,B options left. C,D,E are out.   A is 6. To have 6 as the answer, we will need one more pair like2,6and one more solution where a=b.   When a=b, we have only 1 solution = 2. So, one more solution, where a=b is not possible.   So, answer will be 2.
Answer: C
How many positive integers W between 200 and 300 (both inclusive) are not divisible by 2, 3 or 5? Choose the correct choice from the following choices
A) 3	B) 16	C) 75	D) 24	E) 26

Solution: 1) I figured there are 101 integers (300 - 200 + 1 = 101). Since the set begins with an even and ends with an even, there are 51 evens.   2) Question says integers are not divisible by 2, leaving all of the odds (101 - 51 = 50 integers).   3) Question says integers are not divisible by 5, removing all the integers ending in 5 (already took out those ending in 0). Take out 10 integers (2?5, ? = 0 to 9), leaving us with 40 integers.   4) Now the painstaking part. We have to remove the remaining numbers that are multiples of 3. Those are 201, 207, 213, 219, 231, 237, 243, 249, 261, 267, 273, 279, 291, and 297...a total of 14 numbers. 26 numbers left!   6) Answer choice 26.
Answer: E
If x is negative, which of the following must be positive ?
I. x^2
II. (-1) x
III. 1/x
Choose the correct answer
A) I only
B) I and II only
C) I and III only
D) II and III only
E) I, II, and III

Solution: x=-ve   I. x^2   will be positive   II. (-1) x   =-ve*-ve= +ve   will be positive   III. 1/x   =1/-ve =-ve   will be negative   Answer I and II only
Answer: B
The mean of 50 observations was 36. It was found later that an observation 47 was wrongly taken as 23. The corrected new mean is
Select the correct option
A) 35.24 B) 36.16 C) 36.22 D) 36.48 E) None

Solution: Solution   Correct sum = (36x50+47-23)   = 1824.   âˆ´ Correct mean = 1824 / 50   = 36.48.   Answer 36.48
Answer: D
The ratio of red boxes to blue boxes in a certain warehouse is 10 to 25. If the number of the red boxes were doubled and the number of blue boxes were increased by 150 the ratio would be halved. How many total boxes are in the warehouse?  Choose the correct choice:
A) 37
B) 74
C) 70
D) 148
E) 244

Solution: Ratio = R/B = 10/25 or R = 10/25 B -----------(1)   2R/B+150 = 10/25*1/2 = 1/5 or we can say that 10R=B+150 -------------(2)   solving (1) and (2) we get   B=50 and R = 20   so total boxes is B + R = 50+20= 
50+20 = 70
70   Hence C. 70 is the correct answer
Answer: C
A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is? Choose the correct option
A) 152 m  B) 726 m  C) 688 m  D) 150 m  E) 176 m

Solution: Let the length of the train be x meters and its speed be y m/sec.   They, x / y = 15 => y = x/15   x + 100 / 25 = x / 15   x = 150 m.   Answer:150 m
Answer: D
A train 900 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?  Pick one
A) 400  B) 540  C) 500  D) 520  E) 589

Solution: Speed = 78 * 5/18 = 65/3 m/sec.   Time = 1 min = 60 sec.   Let the length of the train be x meters.   Then, (900 + x)/60 = 65/3   x = 400 m.   400nswer: Option 400
Answer: A
Solution X is 10 percent alcohol by volume, and solution Y is 30 percent alcohol by volume. How many milliliters of solution Y must be added to 100 milliliters of solution X to create a solution that is 25 percent alcohol by volume? Select
A) 250/3
B) 500/3
C) 300
D) 480
E) 600

Solution: we know that X is 10% , Y is 30% and W.Avg = 25% . what does this mean with respect to W.Avg technique ?   W.Avg is 1 portion away from Y and 3 portion away from X so for every 1 portion of X we will have to add 3 portions of Y.   If X = 100 then Y = 300   ANSWER:300
Answer: C
There is a sequence A(n) such that A(n+1)=2A(n)-1 and A(1)=3, where n is a positive integer. What is the value of A(34)-A(33)?  Choose one: A) 2^22+1 B) 2^23 C) 2^23+1 D) 2^33 E) 2^23+1

Solution: A1= 3   A2= 2*3-1= 
2*3-1 = 5
5   A3= 2*5-1= 
2*5-1 = 9
9   A4= 2*9-1= 
2*9-1 = 17
17   We can notice that there is a squence   A2-A1= 2^1   A3-A2= 2^2   A4-A3= 2^3   Hence A34-A33= 2^33   answer : 2^33
Answer: D
Tom and Linda stand at point A. Linda begins to walk in a straight line away from Tom at a constant rate of 4 miles per hour. One hour later, Tom begins to jog in a straight line in the exact opposite direction at a constant rate of 9 miles per hour. If both Tom and Linda travel indefinitely, what is the positive difference, in minutes, between the amount of time it takes Tom to cover half of the distance that Linda has covered and the amount of time it takes Tom to cover twice the distance that Linda has covered? Choose the correct choice from the following answers:
A) 60	B) 72	C) 84	D) 90	E) 216

Solution: E is the answer....   D = TS where D=distance, T=Time and S=Speed   To travel half distance, (2+4T) = 9T ==> T = 2/5 ==> 24 minutes   To travel double distance, 2(2+4T) = 9T ==> 4 ==> 240 minutes   Difference, 216 minutes   216
Answer: E
If x < 12, then it must be true that...  Choose one:
A) -x < -12 B) -x - 2 < 14 C) -x + 2 < -10 D) x + 2 < 10 E) x - 6 < 17

Solution: A. -x < -12 --> x>12. Not true.   B. -x - 2 < 14 --> x>-16. Not true, consider x=-20.   C. -x + 2 < -10 --> x>12. Not true.   D. x + 2 < 10 --> x<8. Not true, consider x=10.   E. x - 6 < 17 --> x<23. Since given that x<12, then x is for sure less than 13. Thus this statement must be true.   Answer: x - 6 < 17.
Answer: E
Find the slope of the line perpendicular to the line y = (1/3)x - 7
Choose the correct answer.
A) -1	B) -4	C) -3	D) 0	E) -5

Solution: Two lines are perpendicular if the product of their slopes is equal to -1. The slope of the given line is equal to 1 / 3. If m is the slope of the line perpendicular to the given line, then   m × (1/3) = -1   Solve for m   m = - 3   correct answer -3)-3
Answer: C
A train passes a man standing on the platform. If the train is 240 meters long and its speed is 72 kmph, how much time it took in doing so? Choose one.
A) 16 sec  B) 14 sec  C) 9 ½ sec  D) 8 ½ sec  E) 12 sec

Solution: D = 240   S = 72 * 5/18= 
72 * 5/18 = 20
20 mps   T= 240/20= 
240/20 = 12
12 sec   Answer: 12 sec
Answer: E
A’s speed is 21/19 times that of B. If A and B run a race, what part of the length of the race should A give B as a head start, so that the race ends in a dead heat?	Choose the correct choice from the following answers: A) 2/21 B) 2/19 C) 1/11 D) 1/7 E) 1/5

Solution: Let D be the full distance.   Let x be the fraction of the distance that B runs.   Let v be the speed at which B runs.   The time should be the same for both runners.   Time = D / (21v/19) = xD/v   (19/21)*D/v = x*D/v   x = 19/21   B should have a head start of 2/21 of the full distance.   The answer is 2/21.
Answer: A
Find the area of the quadrilateral of one of its diagonals is 28 cm and its off sets 9 cm and 6 cm?	Choose the correct choice from the following choices
A) 210 cm2  B) 150 cm2  C) 168 cm2  D) 198 cm2  E) 987 cm2

Solution: 1/2 * 28(9 + 6)   = 210 cm2   210 cm2nswer: 210 cm2
Answer: A
In how many different ways can the letters of the word 'PROFILE' be arranged in such a way that the vowels occupy only the odd positions ?	Answers
A) 720  B) 550  C) 670  D) 625  E) 576

Solution: Number of ways of arranging the vowels =4P3=4!=24.   Also, the 4 consonants can be arranged at the remaining 4 positions.   Number of ways of these arrangements =4P4=4!=24.   Total number of ways =(24*24)= 
(24*24) = 576
576.   Answer is 576
Answer: E
The probability that A speaks truth is 4/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact?  Options:
A) 18/35
B) 19/35
C) 19/36
D) 18/33
E) 18/32

Solution: If both agree stating the same fact, either both of them speak truth of both speak false.   Probability = 4/5 * 4/7 + 1/5 * 3/7   = 16/35 + 3/35 = 19/35   Answer: 19/35
Answer: B
Ragav took a bus from home to market, that travels at 40 kmph. While walking back at 4 kmph,
halfway through, he suddenly realized he was getting late and he cycled back the remaining distance in 30 kmph. Find the average speed. Choose the most appropriate option:
A) 6.5 kmph  B) 12.0 kmph  C) 28.5 kmph  D) 18.5 kmph  E) none of these

Solution: Let the distance be 2x(one way)   Time taken by bus = 2x/40, by walking =x/4, by cycling = x/30 hours   :. Average speed = Total Distance/Total time   = 4x / x/20 + x/4 + x/30   = 4 *60 / 3+15+2   = 12.0   ANSWER:12.0 kmph
Answer: B
The cricket team of 11members is 27yrs old & the wicket keeper is 3 yrs older. If the ages ofthese 2are excluded, the average age of theremaining players is 1 year less than the average age of the whole team. What is the average age of the team ?
Choose the correct choice from the following answers:
A) 21 B) 22 C) 23 D) 25 E) 24

Solution: Let the average age of the whole team be x years.   11x - (27 + 30) = 9 (x - 1)   => 11x - 9x = 48   => 2x = 48   => x = 24.   So, average age of the team is 24 years.   24
Answer: E
The largest 4 digit number exactly divisible by 88 is: Choose the correct option.
A) 9944	B) 9955	C) 9966	D) 6677	E) 9958

Solution: Largest 4-digit number = 9999   88) 9999 (113   88   ----   119   88   ----   319   264   ---   55   ---   Required number = (9999 - 55)= 
(9999 - 55) = 9_944
9944.   9944nswer:9944
Answer: A
Ravi invested certain amount for two rates of simple interests at 6% p.a. and 7% p.a. What is the ratio of Ravi's investments if the interests from those investments are equal?
Choose the correct answer:
A) 4 : 3 B) 3 : 2 C) 6 : 5 D) 7 : 6 E) None of these

Solution: Let x be the investment of Ravi in 6% and y be in 7%   x(6)(n)/100 = y(7)(n)/100   => x/y = 7/6   x : y = 7 : 6   ANSWER:7 : 6
Answer: D
|x+3| – |2-x| = |8+x| How many solutions will this equation have? Select:
A) 0 B) 1 C) 2 D) 3 E) 4

Solution: You have |x+3| - |4-x| = |8+x|   First, look at the three values independently of their absolute value sign, in other words:   |x+3| - |4-x| = |8+x|   (x+3) - (4-x) = (8+x)   Now, you're looking at x < - 8, so x is a number less than -8. Let's pretend x = -10 here to make things a bit easier to understand.   when x=-10   I.) (x+3)   (-10+3)   (-7)   II.) (4-x)   (4-[-10]) (double negative, so it becomes positive)   (4+10)   (14)   III.) (8+x)   (8+-10)   (-2)   In other words, when x < -8, (x+3) and (8+x) are NEGATIVE. To solve problems like this, we need to check for the sign change.   Here is how I do it step by step.   I.) |x+3| - |4-x| = |8+x|   II.) IGNORE absolute value signs (for now) and find the values of x which make (x+3), (4-x) and (8+x) = to zero as follows:   (x+3)   x=-3   (-3+3)= 
(-3+3) = 0
0   (4-x)   x=4   (4-4)= 
(4-4) = 0
0   (8+x)   x=-8   (8+-8) = 2   2
Answer: C
Which natural number is nearest to 8485, which is completely divisible by 75 ?  Pick: A) 7845 B) 8475 C) 2540 D) 3520 E) 6540

Solution: 75) 8485 (113   75   ---   98   75   ----   235   225   ---   10   Required number = (8485 - 10) // Because 10 < (75 - 10)   = 8475.   ANSWER 8475
Answer: B
For a race a distance of 224 meters can be covered by P in 28 seconds and Q in 32 seconds. By what distance does P defeat Q eventually? Pick one:
A) 26m	B) 32m	C) 24m	D) 28m	E) None of these

Solution: Explanation:   This is a simple speed time problem. Given conditions:   =>Speed of P= 224/28= 
224/28 = 8
8m/s=>Speed of Q=224/32= 
224/32 = 7
7m/s=>Difference in time taken = 4 seconds   Therefore, Distance covered by P in that time= 8m/s x 4 seconds = 32 metres   ANSWER: 32m
Answer: B
A and B entered into a partnership investing Rs.25000 and Rs.30000 respectively. After 4 months C also joined the business with an investment of Rs.35000. What is the share of C in an annual profit of Rs.47000?
Choices:
A) 14000
B) 18000
C) 19000
D) 20000
E) 25000

Solution: 25*12: 30*12: 35*8   15:18:14   14/47 * 47000= 
14/47 * 47000 = 14_000
14000   14000NSWER 14000
Answer: A
The average of 1st 3 of 4 numbers is 6 and of the last 3 are 3. If the sum of the first and the last number is 13. What is the last numbers?	Choose the correct answer: A) 4 B) 2 C) 6 D) 7 E) 8

Solution: A + 2 + C = 18   2 + C + D = 9   A + D = 13   A – D = 9   A + D = 13   2D = 4   D = 2   ANSWER:2
Answer: B
How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 1 m x 2 m x 20 cm? Pick one
A) 5600
B) 6000
C) 237
D) 7200
E) 8600

Solution: Number of bricks =Volume of the wall/Volume of 1 brick =	(100 x 200 x 20)/(25 x 11.25 x 6) = 237.   Answer: Option 237
Answer: C
A garrison of 2000 men has provisions for 65 days. At the end of 15 days, a reinforcement arrives, and it is now found that the provisions will last only for 20 days more. What is the reinforcement? Options:
A) 1977
B) 1893
C) 1979
D) 3000
E) 1278

Solution: 2000 ---- 65   2000 ---- 50   x ----- 20   x*20 = 2000*50   x = 5000   2000   -------   3000   Answer: 3000
Answer: D
If -3x+5y=48 and 3x-2y=6, what is the product of x and y?	Pick one
A) 252 B) 428 C) 464. D) 200 E) 642

Solution: Given -3x+5y=48 ---Eq 1   3x -2y =6 -- Eq 2   Sum both eqns we get 3Y = 54 => Y = 18   Sub 2Y in eq 2 => 3X - 36 = 6.   => X = 14   Now XY = 14 * 18= 
14 * 18 = 252
252   Option 252 is correct answer.
Answer: A
A train passes a man standing on the platform. If the train is 170 meters long and its speed is 72 kmph, how much time it took in doing so? Choose the correct option:	A) 8 1/2 sec	B) 8 1/9 sec	C) 8 5/2 sec	D) 4 1/2 sec	E) 5 1/2 sec

Solution: D = 170   S = 72 * 5/18= 
72 * 5/18 = 20
20 mps   T= 170/20 = 8 1/2 sec   8 1/2 secnswer:8 1/2 sec
Answer: A
There are 10 women and 3 men in Room A. One person is picked at random from Room A and moved to room B, where there are already 3 women and 5 men. If a single person is then to be picked from room B, what is the probability that a woman will be picked?	Choose the most appropriate option:
A) 13/21 B) 49/117 C) 40/117 D) 15/52 E) 5/18

Solution: If M picked from room A, room 49/117 probability of picking W is 4/9   If W picked from room A, room 49/117 probability of picking W is 3/9   Conditional Probability   P(W in 49/117 and M picked in A) = P(W given M picked in A)*P(M picked in A) = 10/13*4/9   P(W in 49/117 and W picked in A) = P(W given W picked in A)*P(W picked in A) = 3/13*3/9   Sum 49/117   Ans.49/117
Answer: B
If 20 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, then in how many points do they intersect? Choose the correct option:
A) 110
B) 130
C) 150
D) 170
E) 190

Solution: If two lines are not parallel, then they will intersect in exactly one point. Lines can be extended infinitely on both ends so somewhere they will intersect with each other if they are not parallel. We are also given that no three lines are concurrent. This means that no three lines intersect at the same point. So every pair of two lines we select will have a unique point of intersection which they will not share with any third line.   The number of ways to select 2 lines from 20 lines is 20C2 = 190   The answer is 190.
Answer: E
How many seconds will a 500 m 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 choice from the following answers
A) 22  B) 30  C) 99  D) 77  E) 12

Solution: Speed of train relative to man = 63 - 3= 
63 - 3 = 60
60 km/hr.= 60 * 5/18 = 50/3 m/sec.   Time taken to pass the man = 500 * 3/50= 
500 * 3/50 = 30
30 sec.   Answer: 30
Answer: B
In a friendship gang Angel has 3 gang, in how many ways can he invite one or more of the gang to his house?
Answers:  A) 58  B) 5  C) 12  D) 9  E) 7

Solution: Angel can select one or more than one of his 8 gang.   => Required number of ways = 2^3 – 1= 7.   7
Answer: E
Solution X is 10% chemical A and 90% chemical B by volume. Solution Y is 20% chemical A and 80% chemical B by volume. If a mixture of X and Y is 12% chemical A, what percent of the mixture is Solution X?
Pick one
A) 80%	B) 75%	C) 70%	D) 65%	E) 60%

Solution: The volume of the mixture be X+Y.   0.1X +0.2Y=0.12(X+Y)   X=4Y   X/(X+Y)=4/5=80%.   The answer is 80%.
Answer: A
If xy is an integer, which of the following must also be an integer?
I. x/y
II. y/x
III. y	Choose the correct choice from the following
A) I alone
B) II alone
C) III alone
D) None of the above
E) I and II

Solution: Lets take X = 8/3 and Y = 3/2   Then XY = 4 which is an integer.   But X/Y = 8/3 divided by 3/2 = 16/9 --> Not an integer.   Y/X = 3/2 divided by 8/3 = 9/16 --> Not an integer.   Y alone is 3/2. Not an integer.   Hence D. None of the above.
Answer: D