MU-NLPC/Calc-aqua_rat huggingface dataset:
In a simultaneous throw of pair of dice. Find the probability of getting
the total more than 7
Select
A) 1/2
B) 1/4
C) 5/12
D) 7/12
E) 1/6

Solution: Here n(S)=(6*6)= 
(6*6) = 36
36   let E=event of getting a total more than 7   ={(2,6),(3,5),(3,6),(4,4),(4,5),(4,6),(5,3),(5,4),(5,5),(5,6),(6,2),(6,3),(6,4),(6,5),(6,6)}   P(E)=n(E)/n(S)=15/36=5/12.   Answer 5/12) 5/12.
Answer: C
A circle graph shows how the MegaTech corporation allocates its Research and Development budget: 13% microphotonics; 24% home electronics; 15% food additives; 29% genetically modified microorganisms; 8% industrial lubricants; and the remainder for basic astrophysics. If the arc of each sector of the graph is proportional to the percentage of the budget it represents, how many degrees of the circle are used to represent basic astrophysics research?  Choose the correct option:  A) 8°  B) 40°  C) 18°  D) 36°  E) 52°

Solution: Here all percentage when summed we need to get 100% . As per data  13+24+15+29+8= 
 13+24+15+29+8 = 89
89%.   So remaining 11% is the balance for the astrophysics.   Since this is a circle all percentage must be equal to 360 degrees.   100% ---- 360 degrees   Then 11% will be 40 degrees..   IMO option 40°.
Answer: B
A train crosses a bridge of length 800 m in 45 seconds and a lamp post on the bridge in 15 seconds. What is the length of the train in metres?	Pick:
A) 375 m	B) 750 m	C) 400 m	D) 800 m	E) 300 m

Solution: Let Length of Train = L   Case-1: Distance = 800+L (While crossing the bridge)   Time = 45 Seconds   i.e. Speed = Distance / Time = (800+L)/45   Case-2: Distance = L (While passing the lamp post)   Time = 15 Seconds   i.e. Speed = Distance / Time = (L)/15   But Since speed has to be same in both cases so   (800+L)/45 = (L)/15   i.e. 800 + L = 3L   i.e. 2L = 800   i.e. L = 400   Answer: option 400 m
Answer: C
The owner of a furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 7967 for a computer table, then what was the cost price of the computer table?
Choose the correct choice from the following answers:
A) 6425  B) 6887  C) 6728  D) 6725  E) 2871

Solution: :   CP = SP * (100/(100 + profit%))   = 7967(100/124) = Rs. 6425.   6425nswer: 6425
Answer: A
A rectangle has width a and length b.If the width is decreased by 20% and the length is increased by 10%,then what is the area of the new rectangle in percentage compared to 'ab' ? Options:
A) 77%  B) 88%  C) 92%  D) 75%  E) 68%

Solution: New area =(80/100*a*110/100*b)=(4/5*11/10*ab)=(22/25*ab).   Required percentage =(22/25*ab*1/ab*100)%=88%.   Answer is 88%
Answer: B
If a & b are the root of the equation 4x^2+3x+7=0, then 1/a+1/b=  Pick one
A) -3/7	B) 3/7	C) -3/5	D) 3/5	E) -3/4

Solution: we know that a+b=-3/4 and ab=7/4   so 1/a+1/b=(a+b)/ab   =(-3/7)   -3/7NSWER:-3/7
Answer: A
A, B and C started a business by investing certain amount in the ratio 3 : 4 : 5 for two years, in the second year they earn 10% more profit than earned in the first year. If total profit for two years is Rs.44100. then what is the share of A in the second year ?
Select the correct option: A) Rs.5775 B) Rs.6050 C) Rs.5500 D) Rs.3200 E) Rs.8800

Solution: Let first year profit be 100.   Then second year profit = 100 + 100 × 10 / 100 = 110   First year + second year = 100 + 110= 
100 + 110 = 210
210 or 210%   Second year profit= 44100 / 210 × 110 = 23100   Rs.5775 share in second year = 23100 × 3 / 12 = 5775   Option Rs.5775
Answer: A
Train A leaves the station traveling at 30 miles per hour. Two hours later train В leaves the same station traveling in the same direction at 35 miles per hour. How many miles from the station was train A overtaken by train B?	Pick:
A) 420	B) 450	C) 480	D) 510	E) 540

Solution: After two hours, Train A is ahead by 60 miles.   Train B can catch up at a rate of 5 miles per hour.   The time to catch up is 60/5= 
60/5 = 12
12 hours.   In 12 hours, train A travels another  30*12= 
 30*12 = 360
360 miles for a total of 420 miles.   The answer is 420.
Answer: A
Mary deposited $7,000 to open a new savings account that earned 14 percent annual interest, compounded semi-annually. If there were no other transactions in the account, what the amount of money in Mary account one year after the account was opened?
Choose the correct answer:
A) $7,201
B) $7,205
C) $7,300
D) $7,454
E) $7,294

Solution: Approach #1:   14 percent annual interest compounded semi-annually --> 7% in 6 moths.   For the first 6 moths interest was 7% of $7,000, so $140;   For the next 6 moths interest was 7% of $7,000,plus 7% earned on previous interest of $140, so $140+$14=$154;   Total interest for one year was $140+$154  140+ 14= 
  140+ 14 = 154
$154;   Total interest for one year was $140+$154=$294, hence balance after one year was $7,000+ $294 140+ 154= 
 140+ 154 = 294
$294, hence balance after one year was $7,000+ $294=$7,294.   Answer: $7,294.
Answer: E
Together, Andrea and Brian weigh p pounds; Brian weighs 18 pounds more than Andrea. Brian and Andrea's dog, Cubby, weighs p/4 pounds more than Andrea. In terms of p, what is Cubby's weight in pounds?  Choose one.
A) p/2 - 10  B) 3p/4 - 9  C) 3p/2 - 9  D) 5p/4 - 10  E) 5p - 5

Solution: Together, Andrea and Brian weigh p pounds --> A + B = p.   Brian weighs 10 pounds more than Andrea --> B = A + 18 --> A + (A + 18) = p --> A = (p - 18)/2 = p/2 - 9.   Brian and Andrea's dog, Cubby, weighs p/4 pounds more than Andrea --> C = A + p/4 = (p/2 - 9) + p/4 = 3p/4 -9.   Answer: 3p/4 - 9.
Answer: B
12.1212+17.0005 - 9.1101 = ? Select:
A) 20.0116 B) 20.0105 C) 20.0115 D) 20.1015 E) None

Solution: Solution   Given expression   =(12.1212+17.0005)-9.1101   = (29.1217 - 9.1101)   =20.0116.   20.0116nswer 20.0116
Answer: A
The food in a camp lasts for 30 men for 40 days. If ten more men join, how many days will the food last?	Pick:  A) 11  B) 30  C) 99  D) 88  E) 61

Solution: one man can consume the same food in 30*40= 
30*40 = 1_200
1200 days.   10 more men join, the total number of men= 40   The number of days the food will last = 1200/40= 
1200/40 = 30
30 days.   Answer: 30
Answer: B
For how many integers n is 2^y = y^2 ?
Choose one
A) None of these	B) One	C) Four	D) Three	E) More than four

Solution: draw a graph with y^2 and 2^y, you'll see 3 intercepts between the 2 curves, but one is in the 2nd quadrant, so it can't be an integer (for integer values of x, 2^x can be an integer only for x>0). Thus 2 are valid, and the answer is None of these
Answer: A
A man took loan from a bank at the rate of 12% p.a. S.I. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was?
Choose one
A) 15028
B) 15029
C) 15000
D) 13029
E) 15921

Solution: Principal = (100 * 5400) / (12 * 3)   = Rs.15000   Answer: 15000
Answer: C
Excluding stoppages, the speed of a train is 48 kmph and including stoppages it is 36 kmph. Of how many minutes does the train stop per hour?	Choose the correct choice from the following choices:
A) 16  B) 17  C) 15  D) 18  E) 12

Solution: T = 12/48 * 60= 
12/48 * 60 = 15
15   Answer: 15
Answer: C
The least number which should be added to 2497 so that the sum is exactly divisible by 5, 6, 4 and 3 is:	Choose the most appropriate option:  A) 13  B) 33  C) 23  D) 43  E) 53

Solution: L.C.M. of 5, 6, 4 and 3 = 60.   On dividing 2497 by 60, the remainder is 37.   Number to be added = (60 - 37)= 
(60 - 37) = 23
23. Answer: Option '23'
Answer: C
A shopkeeper forced to sell at cost price, uses a 900 grams weight for a kilogram. What is his gain percent?  Choose the correct choice from the following choices.
A) 10%  B) 9%  C) 11.11%  D) 12 %  E) None of these

Solution: Shopkeeper sells 900g instead of 1000g.   So, his gain = 1000 - 900= 
1000 - 900 = 100
100g.   Thus, %Gain= (100 *100)/900 = 11.11%.   answer : OPTION 11.11%
Answer: C
A train passes a station platform in 36 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:	A) 120 m	B) 240 m	C) 300 m	D) 120 m	E) None of these

Solution: Speed = 54 x	5/18	m/sec = 15 m/sec.   Length of the train = (15 x 20)m = 300 m.Let the length of the platform be x metres.   Then,	9x + 3000/36	= 15   x + 300 = 540   x = 240 m. Answer: Option 240 m
Answer: B
If A is a negative integer, which of the following must be a negative integer?  Choose the correct answer.
A) A + 1
B) A/2+3
C) A^4
D) A – y
E) A^11

Solution: We need to check each option here:   A. A + 1   This will depend on the value of A. Nothing can be said   B. A/2+3   This will depend on the value of A. Nothing can be said   C. A^4   This will always be positive. Even powers of negative numbers are positive and odd powers are negative   D. A – y   This will depend on the value of A. Nothing can be said   E. A^11   This will always be negative. A^11ven powers of negative numbers are positive and odd powers are negative   Correct Option: A^11
Answer: E
If a coin is tossed 4 times what is the probability that it will land either heads 4 times or tails 4 times?
Choose the correct choice from the following answers:
A) 1/4 B) 1/8 C) 1/16 D) 1/2 E) 1/32

Solution: The probability of 4 heads is (1/2)^4 = 1/16   The probability of 4 tails is (1/2)^4 = 1/16   The probability of 4 heads or 4 tails is 1/16 + 1/16 = 1/8   The answer is 1/8.
Answer: B
K-numbers are positive integers with only 2's as their digits. For example, 2, 22, and 222 are K-numbers. The K-weight of a number n is the minimum number of K-numbers that must be added together to equal n. For example, the K-weight of 50 is 5, because 50 = 22 + 22 + 2 + 2 + 2. What is the K-weight of 450?	Choose one:	A) 5	B) 11	C) 12	D) 13	E) 14

Solution: 450 = 2*222 + 3*2   K weight of 600 = 2 +3= 
2 +3 = 5
5   5nswer5
Answer: A
69 laboratories raise the bacterium, the laboratory have 48 culture dishes on average, which has about 25,075 bacteria each. How many bacteria are there approximately?	Pick.
A) 10^7  B) 10^8  C) 10^9  D) 10^10  E) 10^11

Solution: 69 laboratories raise the bacterium, the laboratory have 48 culture dishes on average, which has about 25,075 bacteria each. How many bacteria are there approximately?   A. 10^7   B. 10^8   C. 10^9   D. 10^10   E. 10^11   -> Due to approximately, 69=70, 48=50, 25,075=25,000 are derived, which makes (69)(48)(25,075)=(70)(50)(25,000)=10^7. The answer is 10^7.
Answer: A
A vending machine randomly dispenses four different types of fruit candy. There are twice as many apple candies as orange candies, twice as many strawberry candies as grape candies, and twice as many apple candies as strawberry candies. If each candy cost $0.5, and there are exactly 90 candies, what is the minimum amount of money required to guarantee that you would buy at least three of each type of candy?  Choose the correct choice from the following answers.
A) $3.00 B) $20.75 C) $22.50 D) $41.50 E) $45.00

Solution: Let number of Apple , Orange , strawberry and grape candies be A, O ,S and G respectively .   A= 2O   S= 2G   A= 2S   A= 4G   A+O+S+G = 90   =>A + A/2 + A/2 +A/4 = 90   => 9A/4 = 90   => A = 40   O = 20   S = 20   G = 10   Cost of each candy = .5 $   Mininum amount of money required to guarantee that you would buy at least three of each type of candy   We can buy 40 Apple candies , 20 orange candies , 20 strawberry candies and 3 grape candies to ensure atleast 3 of each type of candies .   Total = 83 candies   Amount required = 83 * .5= 
83 * .5 = 41.5
41.50 $   Answer $41.50
Answer: D
If Aug 15th,2012 falls on Thursday then June 11th,2013 falls on which day ?	Answers:
A) Wednesday
B) Monday
C) SaturdaY
D) Tuesday
E) MONDAY

Solution: Explanation:   First,we count the number of odd days for the left over days in the given period.   Here,given period is 15.8.2012 to 11.6.2013   Aug Sept Oct Nov Dec Jan Feb Mar Apr May Jun   16 30 31 30 31 31 28 31 30 31 11(left days)   2 + 2 + 3 + 2 + 3 + 3 + 0 + 3 + 2 + 3 + 4 (odd days) = 6 odd days   So,given day Thursday + 6 = Wednesday is the required result.   Wednesdaynswer: Wednesday) Wednesday
Answer: A
There is food for 760 men for 22 days. How many more men should join after two days so that the same food may last for 17 days more?	Choose the correct choice from the following:
A) 89 men
B) 120 men
C) 90 men
D) 60 men
E) 134 men

Solution: 760 ---- 22   760 ---- 20   x ----- 17   x*17 = 760*20   x = 894   760   -------   134   ANSW134 menR:134 men
Answer: E
At a certain committee meeting only associate professors and assistant professors are present. Each associate professor has brought 2 pencils and 1 chart to the meeting, while each assistant professor has brought 1 pencil and 2 charts. If a total of 10 pencils and 8 charts have been brought to the meeting, how many people are present?  Answers:
A) 6
B) 7
C) 8
D) 9
E) 10

Solution: Say there are 'A' associate professors. So we have 2A pencils and A charts.   Say there are 'B' assistant professors. So we have B pencils and 2B charts.   Total pencils are 10 so 26 + B = 10   Total charts are 11 so  6 + 2= 
 6 + 2 = 8
8   6dd both: 36 + 3B= 18 so 6 + B = 6   Total number of people = 6   6
Answer: A
What is the average (arithmetic mean) of all the multiples of ten from 10 to 210 inclusive?	Choose the correct choice
A) 90	B) 95	C) 100	D) 105	E) 110

Solution: The multiples of ten from 10 to 190 inclusive would be an evenly spaced set with 21 terms - 10, 20, 30,.......210   So average = (First term + Last Term)/2 = (10 + 210)/2 = 220/2= 
220/2 = 110
110   Hence, the correct answer is 110.
Answer: E
When x is divided by y, the quotient is z with remainder r. Which of the following is y in terms of r, x, and z? (Assume both y and z are nonzero.) Choose the correct choice from the following options
A) x – r – z B) (x+r)/z C) x/z−r D) (x−r)/z E) xr – z

Solution: When x is divided by y, the quotient is z with remainder r. Which of the following is y in terms of r, x, and z? (Assume both y and z are nonzero.)   A. x – r – z   B. (x+r)/z   C. x/z−r   D. (x−r)/z   E. xr – z   Given that when x is divided y, the quotient is z and remainder is r. This implies x-r is divisible by y and yz=(x-r) or y = (x-r)/z.   Answer (x−r)/z.
Answer: D
A bullet train leaves Kyoto for Tokyo traveling 240 miles per hour at 12 noon. Ten minutes later, a train leaves Tokyo for Kyoto traveling 160 miles per hour. If Tokyo and Kyoto are 320 miles apart, at what time will the trains pass each other? Choose the correct choice: A) 12:40pm B) 12:49pm C) 12:52pm D) 1:00pm E) 1:05pm

Solution: Train A: going from K to T   Train B: going from T to K   First I calculated how far Train A will have travelled by the time Train B starts at 12:10:   10 minutes at 240 mph    1/6*240= 
 1/6*240 = 40
40miles   They have 320-40= 
320-40 = 280
280 miles to travel to meet each other.   I found the combined rate of the two trains   Rate(A) + Rate(B)= 400mph   Divide Distance/Rate to find total time each will travel:   280/400>>> 42 Minutes to meet   12:10+42 minutes = 12:52 or Answer 12:52pm
Answer: C
Each person who attended a company meeting was either a stockholder in the company, an employee of the company, or both. If 62 percent of those who attended the meeting were stockholders and 46 percent were employees, what percent were stockholders who were not employees?  Choose the correct choice.
A) 34%	B) 38%	C) 54%	D) 53%	E) 62%

Solution: Let M represent the number of meeting attendees. Then, since 62% of M or 0.62M   were stockholders and 46% of M or 0.47M were employees, it follows that 0.62M +   0.46M = 1.08M were either stockholders, employees, or both. Since 1.08M exceeds   M, the excess 1.08M − M = 0.08M must be the number of attendees who were both   stockholders and employees, leaving the rest 0.62M − 0.08M = 0.54M, or 54%, of   the meeting attendees to be stockholders but not employees.   The correct answer is 54%.
Answer: C
A portion of the 90% solution of chemicals was replaced with an equal amount of 20% solution of chemicals. As a result, 40% solution of chemicals resulted. What part of the original solution was replaced?
Select the correct option:
A) 5/7	B) 6/7	C) 9/5	D) 13/9	E) 13/6

Solution: This is a weighted average question. Say x% of the solution was replaced --> equate the amount of chemicals: 0.90(1-x)+0.2*x=0.4 --> x=5/7.   5/7nswer: 5/7.
Answer: A
The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 70 metres? Choose the correct choice from the following answers.
A) 22 seconds	B) 65 seconds	C) 78 seconds	D) 12 seconds	E) 14 seconds

Solution: Speed of the boat downstream   = 15 + 3= 
15 + 3 = 18
18 kmph= 18 * 5/18= 
18 * 5/18 = 5
5 m/s   Hence time taken to cover 60 m= 70/5= 
70/5 = 14
14 seconds.   Answer:14 seconds
Answer: E
There are 8 people and 5 chairs. In how many different ways people can occupy the chairs?
Pick one.
A) 1640  B) 1650  C) 1660  D) 1670  E) 1680

Solution: number of ways = 8*7*6*5= 
8*7*6*5 = 1_680
1680   Answer is 1680
Answer: E
Two Trains starting at same time from two stations 320km apart and going in opposite directions cross each other at a distance of 140km from first stations. What is the ratio of their speeds	Pick one.
A) 6:7	B) 4:7	C) 7:9	D) 7:11	E) 7:12

Solution: Explanation:   As the two trains are starting at same time   Total distance is 320km   7:9rossed each other 140km from first stations   Therefore first train speed = 140kmph   And other one is 320-140= 
320-140 = 180
180kmph   Ratio of the two train speeds 140:180= 7:9   Answer: Option 7:9
Answer: C
Which of the following is closer to (9!+8!)-(9!-8!)? Choices
A) 80460 B) 80640 C) 80540 D) 80440 E) 80740

Solution: 9!+8!)-(9!-8!)=362880+40320-362880+40320= 
362880+40320-362880+40320 = 80_640
80640   Answer: 80640
Answer: B
A certain boxer has agreed to pay his opponent a fee of 3% of his total purse for every pound over the specified weight limit he weighs in. If the boxer pays his opponent a fee of $26,250 after weighing in seven pounds over the specified limit, what was the boxer's purse?
Choose the most appropriate option:
A) $65,625	B) $105,000	C) $125,000	D) $183,750	E) $1,050,000

Solution: .03*7= 
.03*7 = 0.21
.21   26250/.21= $125,000   Answer: $125,000
Answer: C
A basketball team composed of 12 players scored 100 points in a particular contest. If none of the individual players scored fewer than 7 points, what is the greatest number of points L that an individual player might have scored?	Choose the most appropriate option.
A) 7 B) 13 C) 16 D) 21 E) 23

Solution: General rule for such kind of problems:   to maximize one quantity, minimize the others;   to minimize one quantity, maximize the others.   Thus to maximize the number of points of one particular player minimize the number of points of all other 11 players.   Minimum number of points for a player is 7, so the minimum number of points of 11 players is 7*11= 
7*11 = 77
77.   Therefore, the maximum number of points L for 12th player is  100-77= 
 100-77 = 23
23.   Answer: 23.
Answer: E
What number is that, to which if 1, 5, and 13, be severally added, the first sum shall be to the second, as the second to the third? Select the correct option.
A) 1 B) 2 C) 3 D) 4 E) 5

Solution: Solution   Let x= the number required.   By the conditions, x+1:x+5 = a+5:x+13   Subtracting terms, (Art. 385,2.) x+1:4 = x+5:8   Therefore 8x+8 = 4x+20. And x = 3.   Answer 3
Answer: C
A man sells an article at a profit of 25%. If he had bought it at 20% less and sold it for Rs.8.40 less, he would have gained 30%. Find the cost of the article.	Select the correct option:	A) 30	B) 40	C) 50	D) 60	E) 70

Solution: Let C.P=100   Gain=25%   S.P=125   Supposed C.P=80   Gain=30%   S.P=(130*80)/100= 
(130*80)/100 = 104
104   Diff=(125-104)= 
(125-104) = 21
21   Diff 21 when C.P=100   then Diff 8.40 when C.P=(100*8.40)/21= 
(100*8.40)/21 = 40
40   ANSWER:40
Answer: B
Find the least number which when divided by 12,24,36,42 leaves remainder 9,21,33,39 respectively.  Choose the correct choice from the following options:
A) 499 B) 501 C) 452 D) 365 E) 325

Solution: The difference of 12-9= 
12-9 = 3
3 , 24-21= 3 , 36-33= 3 , 42-39 = 3   LCM of 12,24,36,42 = 504   Required number = 504 - 3= 
504 - 3 = 501
501   Answer is 501
Answer: B
Shweta buys a product at 25% discount rate. At what % over the cost price should she sell the product to make an overall 25% profit over the listed price?  Answers.
A) 25 B) 33.333 C) 66.667 D) 40 E) None of these

Solution: Explanation:   Let listed price of the product be x   Hence at 25% discount rate the 66.667ost Price will become: 3x/4   Now to make an overall profit of 25% over listed price:   SP = 66.667P+(25/100)66.667P   => SP = x+x/4   =>SP = 5x/4   =>Selling Price over 66.667ost price: (5x/4)-(3x/4)   =>x/2   =>%Selling price over 66.667ost price: (x/2)/(3x/4)*100   =>66.67%   ANSWER 66.667
Answer: C
When n is divided by 24, the remainder is 3. Find thee difference between previous remainder and the remainder when 9n is divided by 7 ?
Select:
A) 2  B) 7  C) 5  D) 3  E) 6

Solution: Let n=3 (leaves a remainder of 3 when divided by 24)   9n = 9(3) =27, which leaves a remainder of 6 when divided by 7.   difference = 6 - 3= 
6 - 3 = 3
3.   Answer 3
Answer: D
Peter age after 5 years will be 5 times his age 5 years back. what is the present age of Peter?  Choose one: A) A)20 B) B)25 C) C)15 D) D)22 E) E)10

Solution: Peter present age= x   after 5 years = x+5   5 years back = x-5   x +5= 
 +5 = 5
5(x-5)   x=20   20nswer is 20
Answer: A
A reduction of 20% in the price of salt enables a lady to obtain 10kgs more for Rs.100, find the original price per kg?	Choose the correct option.
A) Rs.2.8  B) Rs.2.4  C) Rs.2.5  D) Rs.2.2  E) Rs.2.1

Solution: 100*(20/100)= 
100*(20/100) = 20
20 --- 10   ? --- 1=> Rs.2   100 --- 80   ? --- 2 => Rs.2.5   Answer:Rs.2.5
Answer: C
What will be the output of the following code statements?
Integer a = 15, b = 30, c = 10 print (a × b / c) – c
Select:  A) 35  B) 26  C) 29  D) 26  E) 81

Solution: Explanation:   35pply BODM35S rule   15 × 30 = 450/10-10 =45 –10 =35   35nswer:35
Answer: A
A factory producing tennis balls stores them in either big boxes, 25 balls per box, or small boxes, 20 balls per box. If 126 freshly manufactured balls are to be stored, what is the least number of balls that can be left unboxed?  Choose the correct choice from the following
A) 2
B) 4
C) 1
D) 5
E) 3

Solution: We have to work with multiples of 20 and 25.   First, we must know the limits of this multiples, so:   126/25= 5....so the max is 5   126/20=6...so the max is 6   126-125= 
126-125 = 1
1 (5 big box or 5 small box +1 big box)   Answer : 1
Answer: C
My brother is 3 years elder to me. My father was 28 years of age when my sister was born while my mother was 26 years of age when I was bom. If my sister was 4 years of age when my brother was born, then, what was the age of my father and mother respectively when my brother was born?	Choose the correct choice from the following answers:	A) 32 yrs, 23 yrs	B) 32 yrs, 29 yrs	C) 35 yrs, 29 yrs	D) 35 yrs, 33 yrs	E) None

Solution: Solution   Clearly,my mother was born 3 years before I was born and 4 years after my sister was born.   So, father's age when brother was born	=(28+4)= 
(28+4) = 32
32 years.   mother's age when brother was born=(26 - 3)= 
(26 - 3) = 23
23 years.   32 yrs, 23 yrsnswer 32 yrs, 23 yrs
Answer: A
How many 4 digit numbers are there, if it is known that the first digit is even, the second is odd, the third is prime, the fourth (units digit) is divisible by 3, and the digit 7 can be used only once?	Options.
A) 20
B) 150
C) 304
D) 310
E) 320

Solution: 4 options for the first digit: 2, 4, 6, 8;   5 options for the second digit: 1, 3, 5, 7, 9;   4 options for the third digit: 2, 3, 5, 7;   4 options for the fourth digit: 0, 3, 6, 9.   Four digit # possible without the restriction (about the digit 2): 4*5*4*4=320   Numbers with seven 7-s,7X7X 4*1*1*4=16.   Thus there are 320-16= 
320-16 = 304
304 such numbers.   Answer: 304.
Answer: C