MU-NLPC/Calc-aqua_rat huggingface dataset:
In a bag containing 3balls, a white ball was placed and then 1ball was taken out at random. What is the probability that the extracted ball would turn on to be white, if all possible hypothesis concerning the color of theballs that initiallyin the bag were equally possible ?  Choose the correct answer.
A) 2/3
B) 5/8
C) 3/5
D) 4/7
E) 4/9

Solution: Since, all possible hypothesis regarding the colour of the balls are equally likely, therefore these could be 3 white balls, initially in the bag.   ∴ Required probability = 1/4 [1 + 3/4 + 1/2 + 1/4]   = 1/4 [(4 + 3 + 2 + 1)/4] = 5/8   5/8
Answer: B
The function f is defined by subtracting 25 from the square of a number and the function a is defined as the square root of one-half of a number. If a(f(x))=10, then which of the following is a possible value of x?
Choose the correct choice.
A) -15 B) -5 C) 0 D) 5 E) 25

Solution: f(x) = x^2-25   a(x) = sqrt(x/2) not sqrt(x)/2, because the question clearly says its square root of (half of the number).   a(f(x)) = 10   a(x^2-25) =10   sqrt((x^2-25)/2) = 10   => (x^2-25)/2 = 100   =>x^2 = 225   => x = 15 or -15   -15nswer is -15.
Answer: A
John weighs twice as much as Susan. Susan's weight is 60% of Sam's weight. Mark weighs 50% of Lynn's weight. Lynn weighs 170% of John's weight. Which of these 5 people weighs the least?  Choose the correct option.
A) John	B) Susan	C) Sam	D) Mark	E) Lynn

Solution: John weighs twice as much as Susan --> J=2S --> John cannot weigh the least;   Susan's weight is 60% of Sam's weight --> S=0.6*Sam --> Sam cannot weigh the least;   Mark weighs 50% of Lynn's weight --> M=0.5*L --> Lynn cannot weigh the least;   Lynn weighs 170% of John's weight --> L=1.9*J --> John cannot weigh the least (we already know that);   As you can see the answer is either Susan (S) or Mark (M). To compare their weights we should express their weights in regards of the same person: M=0.5*L=0.5*(1.7*J)=0.85*J and from J=2S, S=0.5*J --> Susan weights the least: Susan's weight is 50% of that of John and Mark's weight ismore than 50%of that of John.   Answer: Susan.
Answer: B
Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?	Choose the correct answer:
A) 210 B) 7200 C) 1890 D) 31970 E) 10984

Solution: Number of ways of selecting (3 consonants out of 7) and (2 vowels out of 4)   = (7C3 x 4C2)   = 210.   210NSWER 210 210
Answer: A
In a 1000 m race, A beats B by 200 meters or 25 seconds. Find the speed of B?  Choose the correct option:
A) 8	B) 9	C) 7	D) 6	E) 5

Solution: Since A beats B by 200 m or 25 seconds, i   t implies that B covers 200 m in 25 seconds.   Hence speed of B = 200/25= 
200/25 = 8
8 m/s.   8nswer:8
Answer: A
If each digit in the set of A = {0,1,2,3,4,5,6,7,8,9} is exactly used once, in how many ways can the digits be arranged such that the 2 and 5 are not adjacent?	Answers:	A) 10! / 2!	B) 10! - 9!	C) 9!	D) 10!	E) 8*9!

Solution: The answer should be the (total arrangements) - (arrangements when 2 and 5 are adjacent).   The number of ways to arrange 10 units is 10!   If we think of 2 and 5 as one single unit, the number of arrangements is 9!   Note that 2 and 5 can have two arrangements, so we multiply by 2 to get 2*9!   The total number of valid arrangements is 10! - 2*9! = 10*9! - 2*9! = 8*9!   The answer is 8*9!.
Answer: E
Three taps A, B and C can fill a tank in 12, 15 and 20 hours respectively. If A is open all the time and B and C are open for one hour each alternately, the tank will be full is?
Select the correct option.
A) 7  B) 8  C) 10  D) 5  E) 2

Solution: (A + B)'s 1 hour work = (1/12 + 1/15) = 3/20   (A + C)'s 1 hour work = (1/12 + 1/20) = 2/15   Part filled in 2 hrs = (3/20 + 2/15) = 17/60   Part filled in 6 hrs = 3 * 17/60 = 17/20   Remaining part = 1 - 17/20 = 3/20   Now, it is the turn of A and B and 3/20 part is filled by A and B in 1 hour.   Total time taken to fill the tank = (6 + 1)= 
(6 + 1) = 7
7 hrs   7NSWER 7
Answer: A
If Re.1 amounts to Rs.9 over a period of 10 years. What is the rate of simple interest?  Choose one:
A) 90%	B) 30%	C) 50%	D) 80%	E) 70%

Solution: 8 = (1*10*R)/100   R = 80%   ANSWER:80%
Answer: D
If a and b are the roots of the equation x2 - 7x + 7 = 0, then the value of a2 + b2 is:  Choose the correct choice from the following answers
A) 35	B) 24	C) 17	D) 6	E) 5

Solution: Sol.(b) The sum of roots = a+ b = 7   Product of roots = ab = 8   Now, a2 + b2 = (a + b)2 - 2ab = 49 - 14= 
49 - 14 = 35
35   35nswer 35
Answer: A
If the simple interest on a certain sum of money for 4 years is one–fifth of the sum, then the rate of interest per annum is  Choose the correct choice from the following answers:
A) 4%
B) 7%
C) 6%
D) 5%
E) 3%

Solution: Explanation:   Let the Principal(P) be x   Then, Simple Interest(SI) = x/5   Time(T) = 4 years   Rate of interest per annum(R) = (100×SI)/PT   = (100 × (x/5)/(x × 4) = 20/4= 
20/4 = 5
5%   Answer: Option 5%
Answer: D
A train 180 m long passed a pole in 10 sec. How long will it take to pass a platform 800 m long?
Pick:
A) 80
B) 89
C) 54
D) 67
E) 56

Solution: Speed = 180/10= 
180/10 = 18
18 m/sec.   Required time= (180+ 800)/18 = 54 sec.   Answer: Option 54
Answer: C
A basketball coach will select the members of a five-player team from among 10 players, including John and Peter. If the five players are chosen at random, what is the probability that the coach chooses a team that includes both John and Peter?	Choose the correct option
A) 1/9  B) 1/6  C) 2/9  D) 5/18  E) 1/3

Solution: straight forward way is to group J and P as always present on the team and as order does not matter so we just need to find the total number of ways to select rest three players = 8c3   total number of ways of selecting 5 players out of 10 = 10c5   probability = 8c3/10c5 =2/9   2/9
Answer: C
If two numbers are in the ratio 2:3. If 17 is added to both of the numbers then the ratio becomes 3:4 then find the smallest number?
Choose the correct choice from the following
A) A)10 B) B)20 C) C)34 D) D)30 E) E)35

Solution: 2:3   2x + 17 : 3x + 17 = 3 : 4   4[2x + 17] = 3[3x + 17]   8x + 68 = 9x + 51   9x - 8x = 68 - 51= 
68 - 51 = 17
17   Then smallest number is= 2   2x = 34   34orrect Option 34
Answer: C
The area of a square field is 900 km2. How long will it take for a horse to run around at the speed of 12 km/h ?	Choose the correct answer:
A) 12 h  B) 10 h  C) 8 h  D) 6 h  E) None of these

Solution: Explanation Area of field = 900 km2. Then, each side of field = √900=30km Distance covered by the horse = Perimeter of square field = 30 × 4 = 120 km ∴ Time taken by horse = distances/peed=120/12= 
120/12 = 10
10h Answer 10 h
Answer: B
If a and b are two different prime numbers, which of the following cannot be true? Choose the correct choice from the following choices: A) ab is odd. B) a/b is an integer C) a +b is odd. D) ab is even. E) a + b is even

Solution: A prime number is a positive integer with exactly two distinct positive divisors: 1 and itself. So, a prime number cannot be a multiple of another prime number. Which makes option C not possible (a/b=integer means that a is a multiple ofb).   Answer: C.   All other options are possible:   A. ab is odd --> a=3 and b=5;   B. a + b is even --> a=3 and b=5;   C. a + b is odd --> a=2 and b=3;   D. ab is even --> a=2 and b=3;   a +b is odd.
Answer: C
The sum of the ages of 5 children born at the intervals of 3 years each is 80 years. What is the age of the youngest child?
Answers.
A) 2 years
B) 4 years
C) 6 years
D) 8 years
E) 10 years

Solution: Let the ages of the children be x, (x + 3), (x + 6), (x + 9) and (x +12) years.   Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 80   5x = 50 => x = 10.   Age of youngest child = x = 10 years.   ANSW10 yearsR:10 years
Answer: E
The ratio between the number of sheep and the number of horses at the Stewart farm is 4 to 7, If each horse is fed 230 ounces of horse food per day and the farm needs a total 12,880 ounces of horse food per day, what is the number of sheep in the farm?
Select the correct option
A) 18	B) 28	C) 32	D) 56	E) 60

Solution: Actual number of horses = 12,880/230 (hold it since it is a harder calculation)   Ratio multiplier = 1288/(23*7)   Actual number of sheep = 1288/(23*7) * 4.   First divide 1288 by 7 to get: 184*4/23   Use the last digit to figure out that 23 will go 8 times into 184. Confirm. 8*4 = 32   Answer (32)
Answer: C
A cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 9 hours. If both the taps are opened simultaneously, then after how much time cistern will get filled ? Choices.
A) 7 hours
B) 7.1 hours
C) 7.2 hours
D) 7.3 hours
E) 7.4 hours

Solution: Explanation:   When we have question like one is filling the tank and other is empting it, then we subtraction as,   Filled in 1 hour = 1/4   Empties in 1 hour = 1/9   Net filled in 1 hour = 1/4 - 1/9   = 5/36   So cistern will be filled in 36/5 hours i.e. 7.2 hours   ANSWER IS 7.2 hours
Answer: C
At a certain diner, Joe ordered 3 doughnuts and a cup of coffee and was charged $ 2.25. Stella ordered 2 doughnuts and a cup of coffee and was charged $ 1.60. What is the price of 2 doughnuts? Options
A) $ 0.55
B) $ 1.00
C) $ 1.10
D) $ 1.30
E) $ 1.80

Solution: 3$ 1.30 + C = 2.25......(1)   2$ 1.30 + C = 1.6........(2)   (1) - (2) --> $ 1.30 = 0.65 --> 2$ 1.30 = 1.3   Answer: $ 1.30
Answer: D
An aeroplane covers a certain distance of 480 Kmph in 4 hours. to cover the same distance in 4 1/3 hours, it Must travel at a speed of  Choose the correct choice from the following answers
A) 440	B) 540	C) 443	D) 740	E) 250

Solution: Speed of aeroplane = 480 Kmph   Distance travelled in 4 hours   = 480 * 4= 
480 * 4 = 1_920
1920 Km   Speed of aeroplane to acver 1920 Km in 13/3= 1920*3/13 = 443 Km   Answer 443.
Answer: C
The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?
Select the correct option:	A) 6%	B) 3%	C) 8%	D) 1%	E) 4%

Solution: 65*(90/100)*((100-x)/100) = 56.16   x = 4%   Answer: 4%
Answer: E
Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is  Choose the correct choice from the following:
A) 5/18
B) 5/12
C) 5/19
D) 5/15
E) 5/11

Solution: Using question number 11 and 12, we get the probability as   1 - (1/36 + 5/9) = 5/12   Answer: 5/12
Answer: B
Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 sec. What is the length of the fast train?  Choose the most appropriate option.
A) 27 7/5  B) 27 7/09  C) 27 7/2  D) 27 7/9  E) 24 7/2

Solution: Relative speed = (40 - 20)= 
(40 - 20) = 20
20 km/hr.= 20 * 5/ 18 = 50/9 m/sec.   Length of faster train = 50/9 * 5 = 250/9 = 27 7/9 m.   Answer: 27 7/9
Answer: D
Both Robert and Alice leave from the same location at 7:00 a.m. driving in the same direction, but in separate cars. Robert drives 30 miles per hour while Alice drives 50 miles per hour. After 6 hours, Alice’s car stops. At what time will Robert’s car reach Alice’s car?  Choose the correct choice from the following options.
A) 1 p.m. B) 3 p.m. C) 4 p.m. D) 7 p.m. E) 9 p.m.

Solution: 7:00 am so 6 hours later is 1:00 pm   In six hours, Robert will have driven  6*30= 
 6*30 = 180
180 miles   In six hours, Alive will have driven 6*50= 
6*50 = 300
300 miles   So Robert needs  300-180= 
 300-180 = 120
120 miles do catch Alice up.   So at 30 mph, he will need 2 hours   1:00 pm + 6 hours= 7:00 pm   ANS : 7 p.m.
Answer: D
If the diameter of circle R is 40% of the diameter of circle S, the area of circle R is what percent of the area of circle S? Choose the most appropriate option.
A) 16%
B) 18%
C) 20%
D) 22%
E) 24%

Solution: Let diameter of circle R , dr = 40   and diameter of circle S , ds = 100   Radius of circle R , Rr = 20   Radius of circle S , Rs = 50   16%rea of circle R/ 16%rea of circle S = (pi * Rr ^2 ) /( pi * Rs^2 )   = (20/50)^2 = (4/10)^2   =16%   16%nswer :16%
Answer: A
What is the area of square field whose side of length 13 m?	Select the correct option: A) 225 B) 662 C) 169 D) 882 E) 21

Solution: 13 * 13= 
13 * 13 = 169
169 sq m   Answer:169
Answer: C
Look at this series: 53, 53, 40, 40, 27, 27, ... What number should come next?	Pick one:  A) 14  B) 15  C) 17  D) 19  E) 11

Solution: 14   14   In this series, each number is repeated, then 13 is subtracted to arrive at the next number.
Answer: A
Each student is given a five-character identification code. The first two characters are selected from the numbers 0 to 9 inclusive, and the last three characters are selected from the 26 letters of the alphabet. If characters may be repeated and the same characters used in a different order constitute a different code, how many different identification codes can be generated following these rules?
Choose the correct choice from the following.
A) 1,491,000
B) 1,527,200
C) 1,638,400
D) 1,757,600
E) 1,841,800

Solution: The number of possible codes is 10*10*26*26*26=1,757,600.   The answer is 1,757,600.
Answer: D
A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that all the four bulbs are defective?
Choose the correct choice from the following answers
A) 1/127 B) 1/129 C) 1/128 D) 1/198 E) 1/126

Solution: Out of nine, five are good and four are defective. Required probability   = ⁴C₄/⁹C₄   = 1/126   Answer: 1/126
Answer: E
find S.P when CP=Rs 80.40,loss=5% Options:
A) Rs 66.34  B) Rs 69.34  C) Rs 58.34  D) Rs 68.34  E) Rs 60.34

Solution: CP=Rs 80.40,loss=5%   sol: sp=85% of Rs 80.40   =Rs {(85/100)*80.40}=Rs 68.34.   Answer is Rs 68.34.
Answer: D
How many words can be formed by using all letters of the word â€˜DAUGHTERâ€™ so that the vowels always come together?  Answers:
A) 42
B) 420
C) 470
D) 5400
E) 4320

Solution: Sol. Given word contains 8 different letters. When the vowels AUE are always together, we may suppose them to form an entity, treated as one letter.   Then, the letters to be arranged are DGNTR (AUE).   Then 6 letters to be arranged in 6p6 = 6! = 720 ways.   The vowels in the group (AUE) may be arranged in 3! = 6 ways.   Required number of words = (720x6) = 4320.   ANSW4320R 4320
Answer: E
A man gets a simple interest of Rs.500 on a certain principal at the rate of 5% p.a in two years. Find the compound interest the man will get on twice the principal in two years at the same rate.
Choose the correct choice from the following answers:  A) Rs.500  B) Rs.250  C) Rs.5012.50  D) Rs.5062.50  E) None of these.

Solution: Let the principal be Rs.P   S.I at 5% p.a in 8 years on Rs.P = Rs.500   (P)(8)(5)/100 = 500   P = 1250   C.I on Rs.2P i.e., Rs.2500 at 5% p.a in two years   =2500{ [1 + 5/100]2 - 1} = 2500{ 212 - 202 /202}   = 2500/400(441 - 400)   = 25/4(41) = 1025/4 = Rs.256.25   ANSWNone of these.R:None of these.
Answer: E
Jacob is 18years old. He is 2 times as old as his brother. How old will Jacob be when he is twice as old?
Answers
A) 36	B) 38	C) 33	D) 32	E) 38

Solution: j=18;   j=2b;   b=18/2= 
18/2 = 9
9;   twice as old so b=9(now)+(9)=18;   jacob is  18+18= 
 18+18 = 36
36   36NSWER:36
Answer: A
The price for a loaf of bread in April was $1.23, in May the price was $1.22, and in June the price was $1.08. If 2/3 as much bread was sold in April as in May, and twice as much was sold in June as in April, what was the average price for a loaf of bread sold during the three-month period?	Choose the correct choice from the following answers.
A) $1.16
B) $1.15
C) $1.14
D) $1.13
E) $1.12

Solution: Let x be the number of loaves sold in May.   Then 2x/3 loaves were sold in April and 4x/3 loaves were sold in June.   The average price was (2x/3)(123) + 122x + (4x/3)(108) / (2x/3 + x + 4x/3) =   (82 + 122 + 144) / (3) = 348/3 = $1.16   The answer is $1.16.
Answer: A
The total price of a basic computer and printer are $2,500. If the same printer had been purchased with an enhanced computer whose price was $500 more than the price of the basic computer, then the price of the printer would have been 1/4 of that total. What was the price of the basic computer? Answers:  A) 1500  B) 1600  C) 1750  D) 1900  E) 2000

Solution: Let the price of basic computer be C and the price of the printer be P: C+P=$2,500.   The price of the enhanced computer will be C+500 and total price for that computer and the printer will be 2,500+500=$3,000. Now, we are told that the price of the printer is 1/4 of that new total price: P=1/4*$3,000=$750.   Plug this value in the first equation: 1750+750=$2,500 --> 1750=$1,750   Answer: 1750.
Answer: C
To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to 3/10 of its present?  Choose the correct choice from the following options:
A) 61.5	B) 60.5	C) 63.5	D) 83.333	E) 64.5

Solution: Let capacity of 1 bucket = x   Capacity of the tank = 25x   New capacity of the bucket = 3x/10   Hence, number of buckets needed = 25x/(3x/10)=(25×10)/3=83.33333   Answer is 83.333.
Answer: D
207,200,...,186,179,172
Insert the missing number	Answers:
A) 190 B) 191 C) 192 D) 189 E) 193

Solution: Missing number : 193   Answer : 193
Answer: E
In 1998 the profits of company N were 10 percent of revenues. In 1999, the revenues of company N fell by 30 percent, but profits were 14 percent of revenues. The profits in 1999 were what percent of the profits in 1998?  Choices: A) 80% B) 105% C) 120% D) 124.2% E) 98%

Solution: 0,098R = x/100*0.1R   Answer 98%
Answer: E
A certain store sells small, medium, and large toy trucks in each of the colors red, blue, green, and yellow. The store has an equal number of trucks of each possible color-size combination. If Paul wants a medium, red truck and his mother will randomly select one the trucks in the store, what is the probability that the truck she selects will have at least one of the two features Paul wants? Choices
A) 1/4
B) 1/3
C) 1/2
D) 7/12
E) 2/3

Solution: No. of colors=4   no. of sizes=3   Total outcomes=12   Remaining outcomes=6   hence probability that truck is neither red nor of medium size is 6/126/12.   hence probability that the truck she selects will have at least one of the two features Paul wants will be 1−6/121−6/12 or 1/2   ANSWER:1/2
Answer: C
How many days will there be from 26th January,1996 to 15th May,1996(both days included)?	Choose the correct choice from the following answers.
A) 102
B) 103
C) 111
D) 120
E) None of these

Solution: Explanation :   Number of days from 26-Jan-1996 to 15-May-1996 (both days included)   = 6(Jan) + 29(Feb) + 31 (Mar) + 30(Apr)+ 15(May) = 111.. Answer : Option 111
Answer: C
The present age of a father is 3 years more than three times the age of his son.Three years hence,father as age will be 8 years more than twice the age of the son.Find the present age of the father.  Choose the correct option
A) 88	B) 77	C) 33	D) 44	E) 27

Solution: Explanation:   Let the present age be 'x' years. Then father's present age is 3x+3 years. Three years hence (3x+3)+3=2(x+3)+8 x=8 Hence father's present age = 3x+3 =[ (3 x 8) + 3] = 27 years.   Answer: 27
Answer: E
If both 5^2 and 3^4 are factors of the number a*4^3*6^2*13^11, then what is the smallest possible value of a?
Answers:
A) 80
B) 120
C) 150
D) 225
E) 300

Solution: The number a must include at least 3^2*5^2 = 225   The answer is 225.
Answer: D
The ratio, by volume, of bleach to detergent to water in a certain solution is 2 : 40 : 100. The solution will be altered so that the ratio of bleach(B) to detergent is tripled while the ratio of detergent to water is halved. If the altered solution will contain 300 liters of water, how many liters of detergent will it contain?
Choices:  A) 40  B) 60  C) 50  D) 30  E) 70

Solution: 60:D:W = 2:40:100   60new / Dnew = (1/3)*(2/40) = (1/60)   Dnew / Wnew = (1/2)*(40/100) = (1/5)   Wnew = 300   Dnew = Wnew/5 = 300/5= 
300/5 = 60
60   So, answer will be 60   60
Answer: B
How long will it take a sum of money invested at 5% p.a. S.I. to increase its value by 50%?	Pick one
A) 10 years.  B) 4 years.  C) 8 years.  D) 12 years.  E) 14 years.

Solution: Sol.   Let the sum be x. Then, S.I. = 50% of x = x/2; Rate =5%.   âˆ´ Time = [100 * x/2 * 1/x*5] = 10 years.   10 years.nswer 10 years.
Answer: A
Find the difference between the average of first n even numbers and the average of all the even numbers up to n (n is an even number).	Choices
A) n
B) (n-1)/2
C) n/2
D) cannot be determined
E) None of these

Solution: Explanation :   (n+1)-((n/2)+1)   Answer : n/2
Answer: C
Which is next
KUZ, MOX, OIV, QET  Choose the most appropriate option:
A) SUR
B) SAQ
C) RAR
D) SPZ
E) SAR

Solution: First letter in each word increases by 2   K+2=M, M+2=O, O+2=Q, Q+2=S   2nd letter decreases by 6 FOR 1ST 2 WORDS ND DSARC BY 4 FOR NSARXT 2 WORDS   U-6=O, O-6=I, I-4=SAR, SAR-4=A   3rd letter decreases by 2   Z-2=X, X-2=V, V-2=T, T-2=R   So the next word is SAR   ANSWSARR:SAR
Answer: E
Which of the following is closest to 10^180 – 10^20 ?	Answers.
A) 10^210
B) 10^180
C) 10^150
D) 10^90
E) 10^6

Solution: 10^180 – 10^20   10^20 * (10^160 – 1)   as we know 10^2 - 1 means 100-1 and we get 99, which is approximately 100. hence (10^160 – 1) would remain as 10^160.   and 10^20 * 10^160 = 10^180. Answer is 10^180.
Answer: B
The maitre 'd at an expensive Manhattan restaurant has noticed that 60% of the couples order dessert and coffee. However, 20% of the couples who order dessert don't order coffee. What is the probability Y that the next couple the maitre 'd seats will not order dessert?  Choose the correct answer:
A) 20%
B) 25%
C) 40%
D) 60%
E) 75%

Solution: could you use a venn diagram and just go with the number 100.   60 people order dessert and coffee... which is the union of D and C.   Y=2/10 of D aren't in D U C = so 8/10 of D are in DUC which means =60 =8/10D. So D in total=75, and 15 D's aren't in D union C. which means 25 people are in C only + Neither.   25% 25%
Answer: B
A train passes a station platform in 36 seconds and a man standing on the platform in 10 seconds. If the speed of the train is 72 km/hr, what is the length of the platform?	Select:
A) 338
B) 240
C) 520
D) 267
E) 191

Solution: Speed = (72 * 5/18) m/sec = 20 m/sec. Length of the train = (20 x 10)m = 200 m. Let the length of the platform be x meters. Then, (x + 200)/36 = 20 ==> x + 200 = 720 ==> x = 520 m.   Answer: 520
Answer: C
A grocer stacked oranges in a pile. The bottom layer was rectangular with 3 rows of 7 oranges each. In the second layer from the bottom, each orange rested on 4 oranges from the bottom layer, and in the third layer, each orange rested on 4 oranges from the second layer. Which of the following is the maximum number of oranges that could have been in the third layer?  Choose the correct choice from the following answers: A) 5 B) 4 C) 3 D) 2 E) 1

Solution: Bottom Layer = 7 x 3 = 21   IInd Layer = (7-1) x (3-1) = 12   IIIrd Layer = (6-1) x (2-1) = 5   5nswer = 5 = 5
Answer: A
Best friends Sprite and Icey have are playing a game of marbles. They invite 2 of their friends to play with them. There are 36 marbles in the bag. If all 4 people are playing, how many marbles does each person get?  Answers.
A) 3	B) 9	C) 5	D) 6	E) 7

Solution: Answer= 9   36 / 4= 
36 / 4 = 9
9   Answer= 9
Answer: B
If 5^r is a factor of 30!, which of the following is the maximum possible value of r?
Answers:
A) 4  B) 5  C) 6  D) 7  E) 8

Solution: 5^r is a factor of 30! We need the maximum value of r   Or in other words, we need the maximum power of 5 in 30!   Powers of 5 in 30! = [30/5] + [30/25] = 7, where [x] is the integral part of x   Other way is to calculate the number of 5's in 30!   In the multiplication upto 30, we will encounter: 5, 10, 15, 20,25, 30   Each of 5, 10, 15, 20, 30 contain one power of 5   25 contains 2 powers of 5.   Hence total powers of 5 in 30!= 5 + 2= 
5 + 2 = 7
7   Correct option: 7
Answer: D