MU-NLPC/Calc-aqua_rat huggingface dataset:
A painting crew painted 80 houses. They painted the first y houses at a rate of x houses per week. Then more painters arrived and everyone worked together to paint the remaining houses at a rate of 6.25x houses per week. How many weeks did it take to paint all 80 houses, in terms of x and y?	Choices:	A) (320 - y)/(5x)	B) (y +190)/(5x)	C) 5(80 - y)/(4x)	D) (y + 400)/(4x)	E) (4y + 320)/(5x)

Solution: Ans (y +190)/(5x)   Plug some numbers   Let y = 40 houses and x = 20   then they painted 20 houses per week   as painters were added to the group , the rate of the group increased to 6.25 x => 6.25 * 20= 
6.25 * 20 = 125
125 houses per week   total time they took= (40/20) + (40/125) = 2.3 weeks   Putting the values of x and y in equation (y +190)/(5x)   (y +190)/(5x) = (40+190)/5*20 = 230/100= 
230/100 = 23/10 = around 2.3
2.3
Answer: B
What is the next number of the following sequence
2, 12, 4, 24, 8, 48, (...)  Choose the correct choice:
A) 10  B) 12  C) 16  D) 20  E) 22

Solution: The series is   2*6= 
2*6 = 12
12   12/3= 
12/3 = 4
4   4*6= 
4*6 = 24
24   24/3= 
24/3 = 8
8   8*6= 
8*6 = 48
48   48/3= 
48/3 = 16
16   ANSWER: 16
Answer: C
A committee has 5 men and 6 women. What are the number of ways of selecting 2 men and 3 women from the given committee?	Choose the correct choice from the following answers
A) 188  B) 200  C) 277  D) 266  E) 121

Solution: The number of ways to select two men and three women = ⁵C₂ * ⁶C₃   = (5 *4 )/(2 * 1) * (6 * 5 * 4)/(3 * 2)= 
(5 *4 )/(2 * 1) * (6 * 5 * 4)/(3 * 2) = 200
200   Answer: 200
Answer: B
15% of 75 is the same as vx% of 450.find x. Choose one
A) 1
B) 2.5
C) 3
D) 4
E) 5

Solution: 15%of 75=11.25   450*x/100=11.25   x=2.5   ANSWER:2.5
Answer: B
In a set of numbers from 100 to 1000 inclusive, how many integers are odd and do not contain the digit 9?  Choose the most appropriate option
A) 180  B) 196  C) 288  D) 286  E) 324

Solution: We have to find the total number of 3-digit odd numbers not having 9 as a digit.   Units digits will be among 1,3,7,5   Tenth digits will be among 0,1,2,3,4,6,7,8,5   Hundredth digits will be among 1,2,3,4,6,7,8,5   So total numbers = 4*9*8= 
4*9*8 = 288
288   Answer : 288
Answer: C
Can you deduce the pattern and find the next number in the series?
13, 24, 35, 46, __?	Choose the correct option:
A) 59
B) 65
C) 54
D) 25
E) 57

Solution: Solution:   57   57xplanation:     11+2= 
  11+2 = 13
13   22+2= 
22+2 = 24
24   33+2= 
33+2 = 35
35   44=2=46   55+2= 
55+2 = 57
57   Answer 57
Answer: E
What is the perimeter of a triangle with sides 7 and 5 that has the maximum possible area? Choose the correct answer:
A) 12 + √7 B) 12 + 4√7 C) 12 + √47 D) 12 + 4√47 E) 12 + √74

Solution: We can maximize the area of the triangle by making these two sides the base and the height of a right angle triangle. Then the third side is the hypotenuse with a length of √(49+25)= 
(49+25) = 74
√74   The perimeter is 12 + √74   The answer is 12 + √74.
Answer: E
A cistern is filled by a tap in 8 1/2 hours. Due to leak in the bottom of the cistern, it takes half an hour longer to fill the cistern. If the cistern is full how many hours will it take the leak to empty it?  Choices:  A) 133  B) 143  C) 153  D) 163  E) 173

Solution: filling rate - leak rate = net rate   1/8.5 - leak rate = 1/9   leak rate = 2/17 - 1/9 = 1/153   The answer is 153.
Answer: C
If x + y = 11 and x – y = 3, then x^2 - y^2 =  Choose the most appropriate option:  A) -4  B) 4  C) 10  D) 33  E) 40

Solution: The fastest approach has already been shown. Here's one more option.   Given:   x + y = 11   x – y = 3   Add the two equations to get: 2x = 14, which means x = 7   If x = 7, we can plug that value into either equation, to conclude that y = 4   If x = 7 and y = 4, then x² - y² = 33   Answer: 33
Answer: D
During a particular baseball game, the probability of a team's pitcher throwing a strike on each throw is 2/5. What is the least number of times that the pitcher should pitch the ball that will increase the probability of getting a strike at least once to more than 50%.
Choose the correct choice.
A) 3	B) 2	C) 1	D) 4	E) 5

Solution: Rule of Subtraction: P(A) = 1 - P(A')   Rule of Multiplication: P(A ∩ B) = P(A) P(B)   The probability that the pitcher throws a strike at least once in 2 guesses is 1- (3/5)^2 = 1 - 9/25 = 16/25 > 50%.   Answer: 2
Answer: B
In a box of 12 pens, a total of 6 are defective. If a customer buys 2 pens selected at random from the box, what is the probability that neither pen will be defective?	Choose the correct choice from the following options:
A) 1/6
B) 5/22
C) 6/11
D) 9/16
E) 3/4

Solution: Method- 1   There are 9 fine pieces of pen and 6 defective in a lot of 12 pens   i.e. Probability of first pen NOT being defective = (6/12)   i.e. Probability of Second pen NOT being defective = (5/11) [11 pen remaining with 5 defective remaining considering that first was defective]   Probability of 5/22oth pen being NON-defective = (6/12)*(5/11) = 5/22   Answer: option 5/22
Answer: B
A train 125 m long passes a man, running at 15 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?  Choices:
A) 60 B) 50 C) 28 D) 26 E) 29

Solution: Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 15) km/hr. x - 15 = 45 ==> x = 60 km/hr   60nswer: 60
Answer: A
What is the probability of rolling two normal six-sided dice and getting exactly one six?
Choose the correct answer:
A) 1/36
B) 1/6
C) 5/18
D) 11/36
E) 1/3

Solution: Possible pairs having exactly one six are (1,6), (2,6),(3,6),(4,6),(5,6),(6,1)...(6,5) = 10 pairs   Total number of possible pairs = 6*6= 
6*6 = 36
36   Therefore, probability of getting exactly one six= 1036=5181036=518   Answer: 5/18
Answer: C
A man walking at the rate of 5 km/hr crosses a bridge in 15 minutes. What is the length of the bridge (in metres)?
Choose the correct option
A) 1250	B) 1280	C) 1320	D) 1340	E) 1450

Solution: Explanation:   Speed = 5 km/hr   Time = 15 minutes = 1/4 hour   Length of the bridge = Distance Travelled by the man = Speed × Time = 5×1/4 km   = 5 × 1/4 × 1000 metre=1250 metre   1250nswer: Option 1250
Answer: A
How many positive integers, from 2 to 100, inclusive, are not divisible by even integers greater than 1? Choose one:
A) 5
B) 6
C) 8
D) 10
E) 50

Solution: The no will be of the form 2^n to achieve this. Since any other form will have odd no in the prime factorization.   Hence we need to find solution of n for equation - 1< 2^n < 101.   2^6 = 64, 2^7 - 128   Hence n can take values from 1 to 6.   Hence Ans- (6) 6
Answer: B
How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length?
Choose the correct choice from the following answers:  A) 12.9 sec  B) 12.1 sec  C) 17.9 sec  D) 37.9 sec  E) 12.8 sec

Solution: Speed = 72 * 5/18= 
72 * 5/18 = 20
20 m/sec   Total distance covered= 110 + 132= 
110 + 132 = 242
242 m.   Required time= 242/20= 
242/20 = 121/10 = around 12.1
12.1 sec.   Answer: 12.1 sec
Answer: B
Jerry, an electrician, worked 7 months out of the year. What percent
of the year did he work? (round answer to the nearest hundredth)
What percent 12 is 7? 12 months = 1 year
Choose the correct choice:
A) 58.33%  B) 68.33%  C) 78.33%  D) 88.33%  E) 98.33%

Solution: 1. Multiply the opposites   7 x 100 = 700   100=7/12   Divide by the remaining number   58.33   12)58.33/700.00   58.33% (rounded to hundredth)   correct answer 58.33%
Answer: A
For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum of all the even integers between 99 and 181? Select the correct option
A) 3820	B) 5740	C) 6580	D) 7360	E) 9200

Solution: 100 + 102 + ... + 180 =   100*41 + (2+4+...+80) =   100*41 + 2*(1+2+...+40) =   100*41 + 2(40)(41)/2 =   100*41 + 40*41 = 140(41) = 5740   The answer is 5740.
Answer: B
The value of a stock is X dollars. On Sunday the stock's value grew by third of its value, but on Monday its value dropped to a third of its new value. What is the stock's value at the end of Monday? Options:
A) X.
B) X/2.
C) 2X/3.
D) X/3.
E) 4X/9.

Solution: Stock value= X   AT sunday end= x+X/3= 4X/3=1.3X   On monday the value drop to 1/3rd of its value on sunday   1.3x/3= 4X/9   4X/9. is the answer
Answer: E
If a sum of money doubles itself in 15 years at simple interest, the ratepercent per annum is	Choose one.
A) 12
B) 12.5
C) 6.67
D) 13.5
E) 14

Solution: Explanation:   Let sum = x then Simple Interest = x   Rate = (100 * x) / (x * 15) = 6.67   Option 6.67
Answer: C
If the diagonal of a rectangle is 17cm long and its perimeter is 46 cm. Find the area of the rectangle.
Choose the correct choice:
A) 110	B) 120	C) 130	D) 140	E) 150

Solution: Explanation:   let length = x and breadth = y then   2(x+y) = 46 => x+y = 23   x²+y² = 17² = 289   now (x+y)² = 23²   =>x²+y²+2xy= 529   289+ 2xy = 529   => xy = 120   area =xy=120 sq. cm Answer: 120
Answer: B
A beekeeper has 100,000 bees living in five beehives. Among these beehives, the sizes of the beehives are proportional to the numbers of bees living in them. No beehive has less than 80% the number of bees of any other beehive. What is the maximum possible number of bees that the greatest beehive could have?	Choose the most appropriate option:
A) 2381
B) 24000
C) 34000
D) 26000
E) 37000

Solution: x be the # of bees in the hive with the max # of bees. Let other hives have same # of bees. So, x+4*(0.8)*x = 100,000 => 4.2x = 100,000 => x = 2381.   2381 is the answer.
Answer: A
A bullet train 140 m long is running at 60 kmph. In how much time will it pass a platform 410 m long?	Choose the correct choice from the following
A) 33 Seconds	B) 22 Seconds	C) 41 Seconds	D) 24 Seconds	E) 29 Seconds

Solution: Distance travelled = 140 + 410= 
140 + 410 = 550
550m   Speed= 60 * 5/8 = 50/3m   Time = 550 * 3/50= 
550 * 3/50 = 33
33 Seconds   33 SecondsNSWER 33 Seconds
Answer: A
Suzie’s Discount Footwear sells all pairs of shoes for one price and all pairs of boots for another price. On Monday the store sold 22 pairs of shoes and 16 pairs of boots for $460. On Tuesday the store sold 8 pairs of shoes and 32 pairs of boots for $560. How much more do pairs of boots cost than pairs of shoes at Suzie’s Discount Footwear?  Choose the correct choice:
A) 12  B) 14  C) 16  D) 15  E) 18

Solution: Let X be pair of shoes and Y be pair of boots.   22x+16y = 460 ... eq1   8x +32y = 560....eq 2.   Now multiply eq 1 by 2 and sub eq 2.   44x = 920   8x = 560.   36x = 360 => x = 10.   Sub x in eq 2.... we get 80 + 32y = 560... then we get 32y = 480 then y = 15   15ifferenece between X and Y is 5   Answer : 15
Answer: D
If x/y=4 and y is not '0' what % of x is 2x-y	Choices:
A) 100%
B) 125%
C) 175%
D) 185%
E) 195%

Solution: x/y=4   or,x=4y....(1)   "what % of x is 2x-y" means   what % of (4y)x is (2*4y-y)2x-y.   or,(7y/4y)*100=175%   ANSWER:175%
Answer: C
It takes Megan 7 minutes to run a mile, and it takes Mike 8 minutes. If Megan and Mike both begin running at exactly 8:00 a.m. without pausing, when is the first time at which they will finish running a mile simultaneously?
Choices:
A) 8:28 am
B) 8:35 am
C) 8:42 am
D) 8:49 am
E) 8:56 am

Solution: Since Megan will run s miles after s × 7 minutes and Mike will run c miles after c × 8 minutes, they both will finish running a mile at the same time when s × 7 = c × 8. Since s and c must be integers (they represent the number of miles finished) this question is asking you to find a common multiple of 7 and 8. The question asks for the first time they will finish running a mile simultaneously, so you must find the least common multiple. The least common multiple of 7 and 8 is 56, so in the context of the question, this would be 56 minutes. Therefore, the first time they will finish running a mile at the same time is 8:00 + 56 minutes, or 8:56 a.m. The answer is (8:56 am).
Answer: E
There r 4 prime numbers in ascending order. The multiplication of first 3 is 385 and that of last 3is 1001. what is the last number is
Pick.
A) 12  B) 15  C) 16  D) 13  E) 18

Solution: Explanation:   abcbcd=3851001=>ad=513   abcbcd=3851001=>ad=513   So d = 13   13
Answer: D
A batsman hits a score of 78 runs in the 16th inning and thus increases his average by 4. Find his average after 16th inning. Select
A) 13
B) 18
C) 27
D) 39
E) 40

Solution: Explanation :   Let the average after 16th inning = x.   Average after 15th inning =(x-4).   => 15(x-4)+78 = 16x   => x = 18.   Answer : 18
Answer: B
The two trains of lengths 400 m, 600 m respectively, running at same directions. The faster train can cross the slower train in 180 sec, the speed of the slower train is 48 km. then find the speed of the faster train?	Choose one:	A) 29	B) 68	C) 92	D) 23	E) 23

Solution: Length of the two trains = 600m + 400m   Speed of the first train = X   Speed of the second train= 48 Kmph   1000/X - 48 = 180   1000/x - 48 * 5/18 = 180   50 = 9X - 120   X = 68 Kmph   Answer:68
Answer: B
A person borrows Rs.5000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 8% p.a for 2 years. Find his gain in the transaction per year.  Choose the correct choice from the following answers
A) 167.5	B) 150	C) 200	D) 112.5	E) 212.5

Solution: Explanation :   The person borrows Rs. 5000 for 2 years at 4% p.a. simple interest   Simple interest that he needs to pay = PRT/100=5000×4×2/100=400   He also lends it at 8% p.a for 2 years   Simple interest that he gets = PRT/100=5000×8×2/100=800   His overall gain in 2 years = Rs.800 - Rs.400 = Rs.400   His overall gain in 1 year = 400/2 = Rs.200   Answer : Option 200
Answer: C
If a is a positive integer, and if the units digit of a^2 is 9 and the units digit of (a+1)^2 is 4, what is the units D digit of (a+2)^2?
Pick:
A) 1  B) 3  C) 5  D) 6  E) C. 14

Solution: I also got A. By punching in numers:   D...7^2=...9   ...8^2=...4   ...9^2=...1.1
Answer: A
The H.C.F. of two numbers is 28 and the other two factors of their L.C.M. are 12 and 15. The larger of the two numbers is	Options.
A) 420 B) 430 C) 312 D) 322 E) None

Solution: Solution   Clearly, the numbers are (28 x 12) and (28 x 15).   Larger number = (28 x 15)	= 420.   420nswer 420
Answer: A
If n is a positive integer and n^2 is divisible by 36, then the largest positive integer that must divide n is
Options.
A) 6  B) 12  C) 24  D) 36  E) 48

Solution: The question asks aboutthe largest positive integer that MUST divide n, not COULD divide n. Since the least value of n for which n^2 is a multiple of 72 is 12 then the largest positive integer that MUST divide n is 12.   Complete solution of this question is given above. Please ask if anything remains unclear.   I spent a few hours on this one alone and I'm still not clear. I chose 12 at first, but then changed to 48.   I'm not a native speaker, so here is how I interpreted this question:the largest positive integer that must divide n=the largest positive factor of n. Since n is a variable (i.e. n is moving), so is its largest factor. Please correct if I'm wrong here.   I know that if n = 12, n^2 = 144 = 2 * 72 (satisfy the condition). When n = 12, the largest factor of n is n itself, which is 12. Check: 12 is the largest positive number that must divide 12 --> true   However if n = 48, n^2 = 48 * 48 = 32 * 72 (satisfy the condition too). When n = 48, the largest factor of n is n itself, which is 48. Check: 48 is the largest positive number that must divide 48 --> true   So, I also notice that the keyword isMUST, notCOULD. The question is, why is 48 notMUST divide 48, but instead onlyCOULD divide 48? I'm not clear right here. Why is 12MUST divide 12? What's the difference between them?   Only restriction we have on positive integer n is that n^2 is divisible by 72. The least value of n for which n^2 is divisible by 72 is 12, thus nmustbe divisible by 12 (n is in any case divisible by 12). For all other values of n, for which n^2 is divisible by 72, n will still be divisible by 12. This means that n is always divisible by 12 if n^2 is divisible by 72.   Now, ask yourself: if n=6, is n divisible by 48? No. So, n is not always divisible by 48.   6
Answer: A
As a bicycle salesperson, Norman earns a fixed salary of $20 per week plus $6 per bicycle for the first six bicycles he sells, $12 per bicycle for the next six bicycles he sells, and $18 per bicycle for every bicycle sold after the first 12. This week, Norman earned more than twice as much as he did last week. If he sold a bicycles last week and y bicycles this week, which of the following statements must be true?
I. y > 2a
II. y > a
III. y > 3 Choose the most appropriate option: A) I only B) II only C) I and II D) II and III E) I, II, and III

Solution: This is kind of like doing your taxes, lets summarize the data in terms of bike sales and salary -   0 Bikes - $20   6 Bikes - $56   12 Bikes - $128   More than 12 bikes - 128 + 18*(a-12) where x is the total number of bikes sold (when a>12).   A = cycles sold last week   AS = Salary last week.   Y = cycles sole this week   YS = Salary this week.   given YS>2AS   lets test all statements with A=0;   AS = 20   YS >40   True when Y = 4   satisfies all the statements but we can only be sure of iii as Y will only increase from here. So iii must be true. Eliminate A,B,C   lets test all statements with A=1;   AS = 26   YS>52   True when Y=6   Still satisfies all the statements - Nothing achieved   lets test all statements with A=6;   AS = 56   YS>112   True when Y = 11   This proves statement i wrong, hence eliminate E so we are left with   Answer II and III
Answer: D
Find the number of ways of arranging the boy and 3 guests at a circular table so that the boy always sits in a particular seat?
Choose the most appropriate option
A) 3!  B) 8!  C) 11!  D) 12!  E) 14!

Solution: Ans.(A)   Sol. Total number of persons = 4 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 3 places => 3! Ways ... The number of required arrangements = 3! x 1= 3! = 3! ways
Answer: A
In the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30. In the sport formulation, the ratio of flavoring to corn syrup is three times as great as in the standard formulation, and the ratio of flavoring to water is half that of the standard formulation. If a large bottle of the sport formulation contains 2 ounces of corn syrup, how many ounces of water does it contain?	Pick one
A) 15  B) 30  C) 45  D) 60  E) 90

Solution: Standard:   Fl: Corn S: Water = 1:12:30   Sport:   Fl: Corn S: Water = 3:12:180   This simplifies to 1:4:60   If the large bottle has a capacity of x ounces, then   4x / 65 = 2.   So, x = 32.5 ounces.   Water = (60 / 65) * (65/2) = = 30 ounces.   Ans 30
Answer: B
The incomes of two persons A and B are in the ratio 3:4. If each saves Rs.100 per month, the ratio of their expenditures is 1:2 . Find their incomes?  Select.
A) 150,222	B) 150,209	C) 150,200	D) 150,202	E) 150,201

Solution: The incomes of A and B be 3P and 4P.   Expenditures = Income - Savings   (3P - 100) and (4P - 100)   The ratio of their expenditure = 1:2   (3P - 100):(4P - 100) = 1:2   2P = 100 => P = 50   Their incomes = 150, 200   Answer: 150,200
Answer: C
In a card game, a combination of three aces beats all others. If Jose is the first to draw from a standard deck of 52 cards, what is the probability that he wins the game with the best possible combination?  Choose the correct answer
A) 1/5000
B) 1/5520
C) 1/5525
D) 1/5545
E) 1/5600

Solution: he best possible combination is the case when he wins in his first two draws   There are 52 cards in a deck of cards with 4 aces in it.   Probability of first card to be ace = 4/52   Probability of Second card to be ace = 3/51   Probability of third card to be ace = 2/50   Probability of Best possible case = (4/52)*(3/51)*(2/50) = 1/5525   1/5525
Answer: C
At a certain health club, 30 percent of the members use both the pool and sauna, but 50 percent of the members who use the pool do not use the sauna. What percent of the members of the health club use the pool?  Choose the correct choice from the following choices: A) 33 1/3% B) 46 2/3% C) 50% D) 62 1/2% E) 75%

Solution: P = pool S = sauna   given P+S = 30 then let only S be x and only P will be 100 - (30+x) = 70 -x   50% of (70-x) = x => 35 - 0.5x = x => x = 23 1/3% so only P = 70 -23 1/3 = 46 2/3%   Answer 46 2/3%
Answer: B
The number of bacteria in a petri dish increased by 50 percent every 2 hours. If there were 108 million bacteria in the dish at 1: 00 p.m., at what time were there 32 million bacteria in the dish?
Choose the correct choice from the following options: A) 7: 00 p.m. B) 8: 00 p.m. C) 6: 00 a.m. D) 8: 00 a.m. E) 10: 00 a.m.

Solution: Given:   The number of bacteria in a petri dish increased by 50 percent every 2 hours   There were 108 million bacteria in the dish at 2: 00 p.m   Since the bacteria is increasing by 50% every 2 hours, this means that the number is multiplied by 1.5 every 2 hours.   Required: At what time were there 32 million bacteria in the dish?   Assume that there were n intervals of 2 hours between 32 million and 108 million.   32 * (1.5)^n = 108   (3/2)^n = 108/32 = 27/8 = (3/2)^3   Hence n = 3 intervals.   Each interval was of 2 hours. Therefore, the number of hours = 6   Subtracting 6 hours from 1 PM, we get 7 AM as the answer.   Option 7: 00 p.m.
Answer: A
Ram's salary is 25% more than Raja's. How much percent is Raja's salary less than Ram's?  Choose the correct option:	A) 10%	B) 15%	C) 20%	D) 25%	E) 50%

Solution: Raja's salary less than Ram's by 25/(100+25) * 100= 
25/(100+25) * 100 = 20
20%   Answer is 20%
Answer: C
A box contains 7 pairs of shoes (14 shoes in total). If two shoes are selected at random, what it is the probability that they are matching shoes?  Select the correct option.
A) 1/190
B) 1/20
C) 1/19
D) 1/13
E) 1/9

Solution: The problem with your solution is that we don't choose 1 shoe from 14, but rather choose the needed one AFTER we just took one and need the second to be the pair of it. So, the probability would simply be: 1/1*1/13(as after taking one at random there are 13 shoes left and only one is the pair of the first one)=1/13   Answer: 1/13.
Answer: D
In a certain game, you perform three tasks. You flip a coin, and success would be heads. You roll a single die, and success would be a two. You pick a card from a full playing-card deck, and success would be picking a spades card. If exactly one of these three tasks is successful, then you win the game. What is the probability of winning? Choose the correct option
A) 11/16  B) 15/32  C) 14/36  D) 23/48  E) 17/56

Solution: The answer is 23/48   Probability of just one enent will be happining   So, Probability heads=1/2   Probability number 2 =1/6   Probability picking a spades card =1/4   so, Probability win by getting tails= 1/2*5/6*3/4 = 15/48   Probability win by getting number 6 = 1/2*1/6*3/4 = 3/48   Probability win by picking a spades card =1/2*5/6*1/4=5/48   Probability wining= 15/48+3/48+5/48 =23/48
Answer: D
In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr?  Choose the correct choice.
A) 2.5 sec B) 2.7 sec C) 3.5 sec D) 2.9 sec E) 9.5 sec

Solution: Speed = 144 * 5/18= 
144 * 5/18 = 40
40 m/sec   Time taken= 100/40= 
100/40 = 5/2 = around 2.5
2.5 sec.   2.5 secnswer: 2.5 sec
Answer: A
A survey of n people in the town of Eros found that 50% of them preferred Brand A. Another survey of 100 people in the town of Angie found that 60% preferred Brand A. In total, 55% of all the people surveyed together preferred Brand A. What is the total number of people surveyed?	Choose the correct choice from the following answers
A) 50  B) 100  C) 150  D) 200  E) 250

Solution: It is simply a weighted average question. Since the given average of 50% and 60% is 55% (right in the middle), it means the number of people surveyed in Eros (n) is same as the number of people surveyed in Angie.   So n = 100   Total = 100 + 100= 
100 + 100 = 200
200   Answer (200)
Answer: D