MU-NLPC/Calc-aqua_rat huggingface dataset:
If there are half as many women as men in a group and an equal number of men and women do not own cars - a group that is 30% of the total. What fraction of the total is men who own cars?  Pick one
A) 3⁄20  B) 31⁄60  C) 9⁄40  D) 1⁄3  E) 11⁄20

Solution: Consider a group of 100 women and 200 men, a total of 300 people. 30% of them, which is 90, form a group of people who don't own a car.   Half of them are men, and the other half are women, more precisely 45.   It means that there are 200 - 45= 
200 - 45 = 155
155 men who own a car, and this represents 155/300= 31/60 of the total.   Answer 31⁄60
Answer: B
The radius of the two circular fields is in the ratio 3: 5 the area of the first field is what percent less than the area of the second?
Select the correct option:
A) 74%	B) 44%	C) 68%	D) 64%	E) 234%

Solution: r = 3 πr2 = 9   r = 5 πr2 = 25   25 π – 16 π   100 ---- ? => 64%   Answer: 64%
Answer: D
Running at the same constant rate, 6 identical machines can produce a total of 390 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?	Choose the correct option
A) 648	B) 1800	C) 2600	D) 10800	E) 10900

Solution: Let the required number of bottles be x.   More machines, More bottles (Direct Proportion)   More minutes, More bottles (Direct Proportion)   Machines	6	:	10	:: 390 : x   Time (in minutes)	1	:	4   6 x 1 x x = 10 x 4 x 390   x =	(10 x 4 x 390)/(6)   x = 2600.   ANSWER:2600
Answer: C
Each child has 2 pencils and 13 Skittles. If there are 11 children, how many pencils are there in total?
Select:	A) 16	B) 12	C) 18	D) 22	E) 08

Solution: 2*11= 
2*11 = 22
22.Answer is 22.
Answer: D
Line R has the equation 3x + y = 7. Which of the following lines is perpendicular to Line R?	Choose the correct option:	A) y = 3x + 4	B) y = –3x – 6	C) y = (1/3)x – 1	D) y = (–1/3)x + 2	E) y = (–7/3)x – 5

Solution: I first rewrote the equation in the standard y=mx+b form. Therefore, Line R as presented, 3x + y = 7, can be rewritten as follows: y=-3x+7.   Thought process next is what line would be perpendicular to Line R? Any line with a reciprocal of the slope but in the opposite direction. The reciprocal of any fraction/integer is 1 over that number/integer. Therefore the reciprocal of -3 is -1/3 - need to drop the negative sign because the line would kinda run parallel and we want perpendicular. Scan the answers choices and notice y = (1/3)x – 1 as the only one.
Answer: C
In a village the average age of n people is 42 years. But after the verification it was found that the age of a person had been considered 20 years less than the actual age, so the new average, after the correction,increased by 1. The value of n is?	Options
A) 33  B) 20  C) 88  D) 37  E) 16

Solution: It is the same as a person with 20 years more age replaces an existing person of the group ( or village)   Since the total age of the village having n persons, is being increased by 20 years and the average age of village is being increased by 1 year, hence there are total 20 people in the village.   Alternatively : ( n x 42 ) + 20 = ( n x 43 )   => n=20   Answer: 20
Answer: B
The average (arithmetic mean) of the even integers from 0 to 80 inclusive is how much greater than the average (arithmetic mean) of the even integers from 0 to 40 inclusive?	Select the correct option:
A) 20
B) 24
C) 28
D) 36
E) 40

Solution: The sum of even numbers from 0 to N is 2 + 4 +...+ N   = 2(1 + 2 + ...+ N/2)   = 2(N/2)(N/2+1)/2 = (N/2)(N/2+1)   The average is (N/2)(N/2+1)/(N/2+1) = N/2   The average of the even numbers from 0 to 80 is  80/2= 
 80/2 = 40
40   The average of the even numbers from 0 to 40 is  40/2= 
 40/2 = 20
20   The answer is 20.
Answer: A
A train, 130130 metres long travels at a speed of 4545 km/hr crosses a bridge in 3030 seconds. The length of the bridge is  Choose the most appropriate option
A) 270 metres B) 245 metres C) 235 metres D) 220 metres E) 260 metres

Solution: Explanation:   Solution 1Speed =45 km/hr=45Ã—518 m/s=12.5 m/s=45 km/hr=45Ã—518 m/s=12.5 m/s   Time =30 s=30 s   Distance travelled =12.5Ã—30=375 m=12.5Ã—30=375 m   Length of the bridge =375âˆ’130=245 m   ANSWER IS 245 metres
Answer: B
Jake, Lena, Fred, John and Inna need to drive home from a corporate reception in an SUV that can seat 8 people. If only Inna or Jake can drive, how many seat allocations are possible? Pick one:
A) 30	B) 42	C) 120	D) 360	E) 1680

Solution: 5 people ,8 seats, only 2 can drive   if inna is in one seat remaining, 4 people can be arranged in 4p4 i.e 4! =24 ways   since any one can drive total ways = 24 *2= 
24 *2 = 48
48 ways   4 seats can be chosen out of remaining 7 seats in 7c4 ways= 7!/(5!*2!)= 35 ways     48*35= 
  48*35 = 1_680
1680   1680
Answer: E
At what rate percent per annum will the simple interest on a sum of money be 1/5 of the amount in 10 years?	Choose the correct choice from the following answers:
A) 2%	B) 7%	C) 9%	D) 3%	E) 1%

Solution: Let sum = x. Then, S.I. = x/5, Time   = 10 years.   Rate = (100 * x) / (x * 5 * 10)   = 2%   2%nswer: 2%
Answer: A
45 x ? = 35% of 900
Pick.
A) 16.2  B) 7  C) 5  D) 500  E) None

Solution: Answer   Let 45 x A = (35 x 900)/100   ∴ A = (35 x 9)/45 = 7   Correct Option: 7
Answer: B
If a% of b is the same as 8/9 of 450, then the value of ab is? Answers.
A) 40000
B) 45120
C) 65200
D) 32560
E) 45878

Solution: a/100 * b = 8/9 * 450= 
8/9 * 450 = 400
400*100= 
400*100 = 40_000
40000   40000nswer is 40000
Answer: A
How many four-digit numbers are there, if the two leftmost digits are even, the other digits are odd and the digit 4 cannot appear more than once in the number.  Choose the correct option:
A) 480	B) 475	C) 485	D) 490	E) 495

Solution: N=(4*5-1)*5*5= 
(4*5-1)*5*5 = 475
475   where   4 cases of first digit {2,4,6,8}   5 cases of second digit {0,2,4,6,8}   1 case of 44 for two leftmost digit   5 cases of third digit {1,3,5,7,9}   5 cases of fourth digit {1,3,5,7,9}   475
Answer: B
The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 5 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each? Choose the most appropriate option: A) Rs. 4800 B) Rs. 3600 C) Rs. 3560 D) Rs. 4530 E) None of these

Solution: Area of the four walls = 2h(l + b)   Since there are doors and windows, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.   Total cost = 906 * 5 = Rs. 4530   ANSWER:Rs. 4530
Answer: D
A watch was sold at a loss of 15%. If it was sold for Rs.400 more, there would have been a gain of 5%. What is the cost price?  Answers
A) 1600 B) 2998 C) 2778 D) 2788 E) 2991

Solution: 85%   120%   --------   25% ---- 400   100% ---- ? => Rs.1600   1600nswer:1600
Answer: A
Look at this series: 22, 21, 23, 22, 24, 23, ... What number should come next? Choose the correct choice from the following:
A) 22  B) 24  C) 25  D) 26  E) 27

Solution: Explanation: In this simple alternating subtraction and addition series; 1 is subtracted, then 2 is added, and so on.   Answer: Option 25
Answer: C
If the Average of 10 consecutive integers is 22.5 then the 10th integer is :-  Choose the correct choice from the following options:
A) 15	B) 20	C) 23	D) 27	E) 25

Solution: The average falls between the 5th and 6th integers,   integer 5 = 22, integer 6 = 23.   Counting up to the tenth integer   we get 27.   ANSWER:27
Answer: D
The entrance ticket at the Imax theatre in Chennai is worth Rs 250. The sale of tickets increased by 50% when the price of the ticket was lowered. However, the collections recorded a decrease of 17.5%. The price of the ticket is reduced by how much rupees?	Choose the correct choice from the following choices:
A) Rs150
B) Rs112.50
C) Rs105
D) Rs120
E) Rs180

Solution: let the no. of tickets sold before = x   then the no. of tickets sold after = 1.5x   Collection Rs112.50efore = x*250   Collection after = 1.5x* = (250x*82.5)100   =137.5   change in price =250 - 137.5= 
250 - 137.5 = 112.5
112.5   ANSWER:Rs112.50
Answer: B
Harkamal purchased 8kg of grapes at the rate of 90 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper? Choose the correct choice from the following
A) A)1055 B) B)1215 C) C)1065 D) D)1070 E) E)1080

Solution: Cost of 8 kg grapes = 90 × 8 = 720.   Cost of 9 kg of mangoes = 55 × 9 = 495.   Total cost he has to pay = 720 + 495= 
720 + 495 = 1_215
1215.   1215)
Answer: B
The ‘moving walkway’ is a 300-foot long conveyor belt that moves continuously at 3 feet per second. When Bill steps on the walkway, a group of people that are also on the walkway stands 120 feet in front of him. He walks toward the group at a combined rate (including both walkway and foot speed) of 6 feet per second, reaches the group of people, and then remains stationary until the walkway ends. What is Bill’s average rate of movement R for his trip along the moving walkway?	Pick.
A) 2 feet per second B) 2.5 feet per second C) 3 feet per second D) 4 feet per second E) 5 feet per second

Solution: I get E.   Their rate is 3 ft/sec and his is 6 ft/sec. Their distance is d-120 and his distance is d.   So we get two equations:   3t=d-120   6t=d   Substituting, we get 3t=6t-120, or t=40 which means that d=240 so Bill traveled 240 ft and they traveled 120 ft. (They were at 240 on the conveyor belt when they met.   So, Bill's average rate of movement is R:   He traveled 6 ft/sec for 240 ft and 40 seconds. He traveled 3 ft/sec for the remaining 60 ft for 20 seconds.   (240+60)/(20+40)= 
(240+60)/(20+40) = 5
5 ft/sec=5 feet per second
Answer: E
A store sells eight different kinds of shirts. If we want to buy two different kinds of shirts, how many possible combinations of two shirts can we buy? Pick one.
A) 22	B) 24	C) 26	D) 28	E) 30

Solution: 8C2=28.   The answer is 28.
Answer: D
A 280 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 one:
A) 230 B) 288 C) 267 D) 256 E) 220

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 + 280)/9 = 500/9 => x = 220.   Answer: 220
Answer: E
In a barrel of juice there is 40 liters; in a barrel of beer there are 80 liters. If the price ratio between barrels of juice to a barrel of beer is 3:4, what is the price ratio between one liter of juice and one liter of beer? Answers:
A) 3:2.	B) 2:1.	C) 3:1.	D) 4:3.	E) 3:4

Solution: Price of 40 L juice= 3x   1L= 3x/40   Price of 80 L beer= 4x   1L= 4x/80   Ratio of 1 L price = 3x/40/4x/80= 3:2   3:2. is the answer
Answer: A
A individuals pledged to pay equal contributions so that a charity’s goal of $x could be reached. If d of the contributors failed to pay their share, which of the following represents the additional number of dollars that each of the remaining individuals would have to pay in order to allow the charity to reach its goal?  Choose the correct choice
A) dx/A(A - d)	B) dx	C) a	D) A-d	E) nA-d

Solution: Number of individuals = dx/A(A - d)   dx/A(A - d)mount paid by each individual = n   Total expected amount = Charity's goal = ndx/A(A - d) = x   n = x/dx/A(A - d)   Number of individuals who fail to pay = d   Contribution from individuals who would fail to pay = dx/dx/A(A - d) --> dx/A(A - d)dditional amount   Number of individuals who are paying = dx/A(A - d) - d   dx/A(A - d)dditional amount has to be divided among the (dx/A(A - d) - d) individuals --> dx/dx/A(A - d)(dx/A(A - d) - d)   dx/A(A - d)
Answer: A
A girl was riding her scooter. Her father wanted to calculate her speed. He knew that the street was 600 meters from end to end. He saw his daughter make the roundtrip 6 times. It took her 20 minutes to complete those 6 trips. How fast was the girl riding her scooter in kilometers per hour? Choose the correct answer:  A) 2  B) 2.4  C) 1.2  D) 2.1  E) 2.7

Solution: The distance of the street was 600 meters.   The made the roundtrip 6 times, which would be 2 trips for each roundtrip.   Multiply 12 times 600 to get the total distance. 600 * 12 = 7200 meters of 7.2 km.   The question asked for the speed in km/hour and 20 minutes is one third of an hour.   Multiply 7200 by 1/3 to get approximately 2400 meters.   Correct answer is 2.4
Answer: B
An staff identification code consists of a vowel followed by a 3-digit number greater than 200. Exactly 2 of the 3 digits in the code should be identical. How many different codes is it possible to form?  Choose the correct choice from the following choices.
A) 211  B) 216  C) 1075  D) 1080  E) 2160

Solution: An staff identification code will be of the type -,-,-,-   first digit can be selected from any of the 5 vowels in 5C1 ways   now for the remaining three digit lets consider the following two cases   case 1: when the number is greater than 200 but less than 300   number will be of the type 2,_,_. now suppose repeating number is same as first digit number i.e. 2. and the third number is one of the remaining 9 numbers (we are rejecting 2 here, because it will result in 222, which is not acceptable as per the given condition). thus these two number can arrange themselves in two blank spaces in 2! ways. hence total number of numbers in which repeating digit is same as the first digit = 1.9.2! =18   now, suppose that repeating number is different than first digit. thus possible case in this case are 8 as listed below:   211   233   244   255   266   277   288   299   here again we have rejected 200( because number must be greater than 200) and 222 ( exactly two repeating digits are allowed)   thus total possible cases are 18 + 8= 
18 + 8 = 26
26   case 2: number ranging from 300 to 999   here for first digit we have 7 cases (3,4,5,6,7,8,9)   now if the repeating number is same as the first number then we will have 18 cases ( same reasoning as mentioned in the previous case)   if the repeating number is different than first digit number then we will have 9 cases ( because here number ending with two zeros are allowed)   hence total number of ways= 7(18+9) = 189   thus different number of codes = 5(189+26) = 1075   hence 1075
Answer: C
A thief is spotted by a policeman from a distance of 100metres. When the policeman starts the chase, the thief also starts running. If the speed of the thief be 15km/hr and that of the policeman 20km/hr, how far the thief will have run before he is overtaken ?	Select:  A) A)1km  B) B)300m  C) C)650m  D) D)750m  E) E)800m

Solution: Relative speed of the policeman = 20-15= 
20-15 = 5
5 km/hr   time taken by policeman to cover 100m= (100/1000)*(1/5) = 1/50 hr   In 1/50 hr the thief covers a distance of 15/50 km = 3/10 km = 300m   Answer is 300m
Answer: B
The total of the ages of Jayant, Prem and Saransh is 93 years. Ten years ago, the ratio of their ages was 2 : 3 : 4. What is the present age of Jayant?	Choose the correct option
A) 24 years
B) 32 years
C) 34 years
D) 38 years
E) None

Solution: Solution   Let the ages of Jayant, Prem and Saransh 10 years ago be 2x, 3x and 4x years respectively. Then,   (2x + 10)+(3x + 10)+(4x + 10)	= 93.   ‹=›9x = 63   x = 7.   ∴ Jayant's present age = 2x + 10 = 24 years.   24 yearsnswer 24 years
Answer: A
Cereal A is 8% sugar by weight, whereas healthier but less delicious Cereal B is 2% sugar by weight. To make a delicious and healthy mixture that is 4% sugar, what should be the ratio of Cereal A to Cereal B, by weight?	Pick one.
A) 2:9
B) 2:7
C) 1:2
D) 1:4
E) 1:3

Solution: (8/100)A+(2/100)B = (4/100)(A+B)   4A =2B   => A/B = 1/2   Answer is 1:2.
Answer: C
What is the range of all the roots of |x^2 - 3| = x ?
Choose one
A) 4 B) 3 C) 2 D) 1 E) 0

Solution: we get 2 quadratic equations here ..   1) x^2-x-3=0 ....... roots 2 , -1   2) x^2+x-3=0 ........ roots -2, 1   Inserting each root in given equation , it can be seen that -1 and -2 do not satisfy the equations .   So value of x for given equation .... x=3 or x=1   I guess range is   3-1= 
  3-1 = 2
2   2
Answer: C
Will must choose a 3-character computer password, consisting of 3 distinct digits, in any order.From how many different passwords can Will choose?  Choose one.
A) 390	B) 2,340	C) 4,320	D) 7,020	E) 14,040

Solution: 10C1*9C1*8C1 = 720.   =>720 * 3 ! = 4320.   Option E is correct answer...but OA is 4,320.
Answer: C
An order was placed for a carpet whose length and width were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and width were in the ratio 1 : 1 but were was no change in its perimeter. What is the ratio of the areas of the carpets?  Select.
A) 4:5	B) 9:10	C) 14:15	D) 19:20	E) 24:25

Solution: Let the length and width of one carpet be 3x and 2x.   Let the length and width of the other carpet be y and y.   2(3x + 2x) = 2(y + y)   5x = 2y   (5/2) * x = y   The ratio of the areas of the carpet in both cases:   = 3x * 2x : y * y   = 6x^2 : y^2   = 6x^2 : (25/4) * x^2   = 24 : 25   The answer is 24:25.
Answer: E
A train moves past a post and a platform 264 metre long in 8 seconds and 20 seconds respectively. What is the speed of the train?	Pick one
A) 79.2 km/hr
B) 82.4 km/hr
C) 69.7 km/hr
D) 49.8 km/hr
E) 78.9 km/hr

Solution: The train can cover a distance equal to its length in 8 seconds. Therefore, additional   (20âˆ’8)=12 seconds was taken to cross the platform.   Hence, speed of the train=264/12= 
264/12 = 22
22 m/s=22 Ã— 18/5=79.2 km/hr   79.2 km/hrNSWER:79.2 km/hr
Answer: A
A person buys 18 local tickets for Rs 110. Each first class ticket costs Rs 10 and each second class ticket costs Rs 3. What will another lot of 18 tickets in which the numbers of first class and second class tickets are interchanged cost?	Select
A) 112  B) 118  C) 121  D) 124  E) None of these

Solution: Explanation :   Let, there are x first class ticket and (18-x) second class tickets.   Then,   110 = 10x + 3(18−x).   =>110=10x+54−3x.   =>7x=56.   =>x=8.   If the number of the first class and second class tickets are interchanged, then the total cost would be 10×10 + 3 × 8=124.   Answer : 124
Answer: D
In traveling from a dormitory to a certain city, a student went 1/5 of the way by foot, 2/3 of the way by bus, and the remaining 6 kilometers by car. What is the distance, in kilometers, from the dormitory to the city?  Select.
A) 30
B) 58
C) 60
D) 90
E) 120

Solution: I believe there is a better way to do it.   Basically one of the options should satisfy the given criteria.   60 did    1/5 *60= 
 1/5 *60 = 12
12   2/3*60= 
2/3*60 = 40
40   so total distance   52 + remaining 6=58   Answer 58
Answer: B
A meal cost $ 35.50 adn there was no tax. If the tip was more than 2 pc but less than 12pc of the price, then the total amount paid should be:
Choose the correct choice: A) 40-43 B) 39-42 C) 39-42 D) 38-41 E) 36-40

Solution: 2%(35.5) = 0.71   12%(35.5) = 4.26   total amount could have been 35.5+0.71 and 35.5+4.26   => could have been between 36.21 and 39.76   => approximately between 36 and 40   Answer is 36-40.
Answer: E
A monkey ascends a greased pole 26 meters high. He ascends 2 meters in the first minute and then slips down 1 meter in the alternate minute. If this pattern continues until he climbs the pole , in how many minutes would he reach at the top of the pole ?
Options:
A) 50th minute
B) 41st minute
C) 45th minute
D) 42nd minute
E) 49th minute

Solution: The money is climbing 1meter in 2min. This pattern will go on till he reaches 24meters. I mean this will continue for first  24*2= 
 24*2 = 48
48mins. he would have reached 24meters. After that he will climb 2meters and he will reach the pole. So total time taken= 48 + 1= 
48 + 1 = 49
49 mins.   So, asnwer will be 49th minute
Answer: E
Percentage of profit earned by selling a book for $1680 is equal to the percentage loss incurred by selling the same book for $1120. What price should the book be sold to make 25% profit?	Choose the correct choice from the following:  A) $1250  B) $1050  C) $1550  D) $1750  E) $2050

Solution: Let C.P. be $ x.   Then, (1680 - x)	x 100 =(x - 1120)x 100   1680 - x = x - 1120   2x = 2800   x = 1400   Required S.P. = 125% of 1400 = 1.25 x 1400 = $1750   Answer : $2050
Answer: E
The price of a microchip declines by 67 percent every 6 months. At this rate, approximately how many years will it take for the price of an $81 microchip to reach $1? Choose the correct choice from the following answers
A) 1.5 years	B) 2 years	C) 3 years	D) 13 years	E) 13.5 years

Solution: I think the fastest way is   81 *(1/3)^n = 1   n =4   So 2 yrs   ANSWER:2 years
Answer: B
Find the invalid no.from the following series 13, 18, 25, 30, 37, 40
Pick one: A) 23 B) 26 C) 40 D) 42 E) 49

Solution: The differences between two successive terms from the beginning are 7, 5, 7, 5, 7, 5. So, 40 is wrong.   40
Answer: C
20% of major airline companies equip their planes with wireless internet access. 70% of major airlines offer passengers free on-board snacks. What is the greatest possible percentage of major airline companies that offer both wireless internet and free on-board snacks? Choose the correct choice from the following
A) 20%  B) 30%  C) 40%  D) 70%  E) 90%

Solution: To maximize the percentage of companies offering both, let's assume that all 20% of companies which offer wireless internet also offer snacks.   The answer is 20%.
Answer: A
A reduction of 40% in the price of bananas would enable a man to obtain 64 more for Rs.40, what is reduced price per dozen?
Choose the correct choice
A) 5 B) 6 C) 2 D) 3 E) 9

Solution: 40*(40/100)= 
40*(40/100) = 16
16 --- 64   ? --- 12=> Rs.3   Answer: 3
Answer: D
A trader purchased two colour televisions for a total of Rs. 35000. He sold one colour television at 30% profit and the other 40% profit. Find the difference in the cost prices of the two televisions if he made an overall profit of 32%?
Choose the correct option.
A) Rs. 21000 B) Rs. 17500 C) Rs. 19000 D) Rs. 24500 E) None of these

Solution: Let the cost prices of the colour television sold at 30% profit and 40% profit be Rs. x and Rs. (35000 - x) respectively.   Total selling price of televisions = x + 30/100 x + (35000 - x) + 40/100 (35000 - x)   => 130/100 x + 140/100 (35000 - x) = 35000 + 32/100 (35000)   x = 28000   35000 - x = 7000   Difference in the cost prices of televisions = Rs. 21000   Rs. 21000NSWER:Rs. 21000
Answer: A
Mother,her daughter and her grand child weighs 140 kg. daughter and her daughter(child) weighs 60 kg. child is 1/5th of her grand mother. What is the age of the daughter? Choose the correct choice from the following answers:
A) 44  B) 47  C) 48  D) 49  E) 50

Solution: mother + daughter + child = 140kg   daughter + child = 60kg   mother = 140 - 60= 
140 - 60 = 80
80kg   child= 1/5th of mother = (1/5)*80= 
(1/5)*80 = 16
16kg   So now daughter= 140 -(mother + child) = 140 - (80+16)= 
140 - (80+16) = 44
44kg   44NSWER:44
Answer: A
If two dice are thrown simultaneously, then find the probability that the sum of numbers appeared on the dice is 6 or 7?  Answers:	A) 5/6	B) 7/36	C) 5/36	D) 11/36	E) 12/36

Solution: The sum of numbers appeared is 6 or 7. Therefore, the required sums are 6 or 7, i.e., the required events are (1,5), (5,1), (2,4), (4,2), (3,3), (1,6), (6,1), (2,5), (5,2), (3,4), (4,3)   i.e., for 6, n(E) = 5 and for 7, n(E) = 6   Therefore, the required probability = n(E)/n(S) = 11/36.   ANSWER:11/36
Answer: D
The average age of 36 students in a group is 14 years. When teacher's age is included to it, the average increases by one. What is the teacher's age in years ?
Choose the correct choice from the following answers
A) 66 B) 77 C) 51 D) 98 E) 99

Solution: Explanation:   Age of the teacher = (37 * 15 - 36 * 14)= 
(37 * 15 - 36 * 14) = 51
51 years.   Answer: 51) 51 years
Answer: C
If a car went the first third of the distance at 80 kmh, the second third at 18 kmh, and the last third at 48 kmh, what was the average speed of the car for the entire trip?  Choose the correct choice from the following answers.
A) 34 kmh  B) 40 kmh  C) 42 kmh  D) 44 kmh  E) 50 kmh

Solution: 34 kmhssume D/3 = 720 (this number is convenient because it is divisible by 80, 18 and 48)   So:   720 = 80*T1 = 9 hrs   720 = 18*T2 = 40 hrs   720 = 48*T3 = 15 hrs   T = T1 + T2 + T3 = 64 hrs   D = RT   (720*3) = R*64   R = 33.75   34 kmhNSWER: 34 kmh
Answer: A