MU-NLPC/Calc-aqua_rat huggingface dataset:
The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?
Choose the correct answer:
A) 8 years
B) 16 years
C) 4 years
D) 18 years
E) 12 years

Solution: Let the age of first child be x years.   since all the children got birth in interval of 3 years so the age of 2nd,3rd,4th and 5th child would be x-3 , (x-3)-3 ,((x-3)-3)-3 ,(((x-3)-3)-3)-3 respectively,   also the sum of ages of all children is 50,   = x+(x-3)+(x-6)+(x-9)+(x-12)=50   =5x-30=50   =5x=80   =x=16   so the age of youngest child would be   16-12= 
  16-12 = 4
4 years. ANSWER : 4 years
Answer: C
Jamboree and GMAT Club Contest Starts
QUESTION #20:
How many words (with or without meaning) can be formed using all the letters of the word “SELFIE” so that the two E’s are not together?  Options: A) 660 B) 600 C) 500 D) 300 E) 240

Solution: The question is asking the total number of arrangements possible with the letters of the word “SELFIE” where two E’s are not together.   Arrangements when two E’s are not together = Total arrangements - Arrangements when two E’s are together   In total there are 6 letters but two are identical. so we can arrange in 6! ways. but we divide for those objects that are identical. so divide by 2!. Hence,   Total arrangements = 6!/2!   Now two E's are coupled together. Consider this couple (EE) as one letter. apart from this there are 4 more letters. so we can arrange these 5 different objects in 5! ways.   Two E's can arrange themselves in 2! ways, but we divide for those objects that are identical. so divide by 2!. so arrangement for E's would be 2!/2!.   Hence, Arrangements when two E’s are together = 5! * (2!/2!)   Arrangements when two E’s are not together = 6!/2! - 5! = 5! * ( 6/2 -1 ) = 120 * 2= 
120 * 2 = 240
240.   Option 600 is correct!
Answer: B
Which of the following lines has x-intercept and y-intercept that are integers W? Choose the correct choice from the following answers:
A) y=3x+1	B) y=√x+1	C) y=-2/x	D) y=x^2-1	E) xy=1

Solution: Values that satisfy y=x^2-1 are (x,y)=(-1,0),(1,0),(0,-1). Hence, they are all integers W and the correct answer is y=x^2-1.
Answer: D
A no.when divided by 224 gives a remainder 43, what remainder will beobtained by dividingthe same no.17?  Choose the most appropriate option.
A) 2	B) 7	C) 9	D) 11	E) 12

Solution: 224 + 43= 
224 + 43 = 267
267/17= 12 (Remainder)   12
Answer: E
In X game of billiards, X can give Y 20 points in 60 and he can give Z 30 points in 60. How many points can Y give Z in X game of 80?	Choose the correct choice from the following answers.
A) 30  B) 20  C) 25  D) 40  E) 50

Solution: X scores 60 while Y score 40 and Z scores 30.   The number of points that Z scores when Y scores 80 = (80 * 30)/40= 
(80 * 30)/40 = 60
60.   In X game of 100 points, Y gives (80 - 60)= 
(80 - 60) = 20
20 points to C.   20
Answer: B
Stella buys an advertising agency for rs.16,000,000 and sells it for rs.20,000,000. Find her gain %.  Choose the correct choice.
A) 9%  B) 20%  C) 14%  D) 87%  E) 25%

Solution: sol. cp=rs16,000,000, sp=rs 20,000,000   gain=rs(20,000,000 –16,000,000)=rs4,000,000   so gain%={(4,000,000/16,000,000)*100}=25%   Answer is 25%.
Answer: E
Two dice are rolled. What is the probability the sum will be greater than 8?
Choose the most appropriate option:	A) 2/9.	B) 1/12.	C) 5/36.	D) 7/36.	E) 1/5.

Solution: Combinations possible: (6,6) , (5,6) , (6,5) , (4,6), (6,4) , (5,5) , (5,4), (4,5) = 8   Total combinations possible:   6*6= 
  6*6 = 36
36   2/9.nswer= 8/36 = 2/9 Option 2/9..
Answer: A
The length and breadth of a room are 8 m and 6 m respectively. A cat runs along all the four walls and finally along a diagonal order to catch a rat. How much total distance is covered by the cat?
Select the correct option:
A) 22
B) 88
C) 38
D) 99
E) 11

Solution: Answer: 38) 38
Answer: C
A bag of potatoes weighs 12 lbs divided by half of its weight. How much does the bag of potatoes weight?
Pick
A) 20 lb	B) 18 lb	C) 12 lb	D) 15 lb	E) 5 lb

Solution: Sol.   12÷1 = 12.   Answer : 12 lb
Answer: C
The difference between simple and compound interests annually on a particular sum of money for 2 years at 4% per annum is Rs. 1. What is the sum? Select the correct option
A) 600  B) 625  C) 650  D) 675  E) 700

Solution: sum consider as x   CI = (x(1+4/100)^2-x) = 676/625x-x   =>51/625x   SI = x*4*2/100 = 2x/25   51x/625 - 2x/25 = 1   x= 625   ANSWER 625
Answer: B
If the length of a certain rectangle is decreased by 4 cm and the width is increased by 3 cm, a square with the same area as the original rectangle would result. Find the perimeter of the original rectangle.  Choose the correct choice from the following answers
A) 33
B) 38
C) 77
D) 50
E) 29

Solution: Explanation:   Let x and y be the length and breadth of the rectangle respectively.   Then, x - 4 = y + 3 or x - y = 7 ----(i)   Area of the rectangle =xy; Area of the square = (x - 4) (y + 3)   (x - 4) (y + 3) =xy <=> 3x - 4y = 12 ----(ii)   Solving (i) and (ii), we get x = 16 and y = 9.   Perimeter of the rectangle = 2 (x + y) = [2 (16 + 9)] cm = 50 cm.   Answer: 50) 50
Answer: D
A man starts walking at 3 pm, He walks at a speed of 4 km/hr on level ground and at a speed of 3 km/hr on uphill, 6 km/hr downhill and then 4 km/hr on level ground to reach home at 9 pm. What is the distance covered on one way?	Answers:	A) 8	B) 9	C) 10	D) 11	E) 12

Solution: if x km is level ground and y km is hill road, then   x/4 + y/3 +y/6+x/4= 6   6(x+y)=72   x+y=12 km   so one side distance is 12 kms.   ANSW12R:12
Answer: E
The average of six numbers is 3.95. The average of two of them is 3.4, while the average of the other two is 3.85. What is the average of the remaining two numbers?	Pick one.
A) 4.5  B) 4.6  C) 4.7  D) 4.8  E) 4.9

Solution: Sum of the remaining two numbers   = (3.95 × 6) – [(3.4 × 2) + (3.85 × 2)]   = 23.70 – (6.8 + 7.7)   = 23.70 – 14.5 = 9.20   ∴ Required average = (9.2⁄2) = 4.6   Answer 4.6
Answer: B
What day of the week was 1 January 1901 Choose the most appropriate option:  A) Monday  B) Tuesday  C) Saturday  D) Friday  E) None of these

Solution: Explanation :   1 Jan 1901 = (1900 years + 1-Jan-1901)   We know that number of odd days in 400 years = 0   Hence the number of odd days in 1600 years = 0 (Since 1600 is a perfect multiple of 400)   Number of odd days in the period 1601-1900   = Number of odd days in 300 years   = 5 x 3 = 15 = 1   (As we can reduce perfect multiples of 7 from odd days without affecting anything)   1-Jan-1901 = 1 odd day   Total number of odd days = (0 + 1 + 1)= 
(0 + 1 + 1) = 2
2   2 odd days= Tuesday   Hence 1 January 1901 is Tuesday.   Answer : Option Tuesday
Answer: B
Car A runs at the speed of 50km/hr & reaches its destination in 8hr. Car B runs at the speed of 25 km/h & reaches its destination in 4h. What is the respective ratio of distances covered by Car A & Car B? Choose one
A) 4 : 1	B) 11 : 8	C) 13 : 7	D) 15 : 7	E) 16 : 9

Solution: Sol. Distance travelled by Car 4 : 1 = 50 × 8 = 400 km   Distance travelled by Car B = 25 × 4 =100 km   Ratio = 400/100= 
400/100 = 4
4 : 1   4 : 1nswer : 4 : 1
Answer: A
A tradesman by means of his false balance defrauds to the extent of 18%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?  Choose the correct choice from the following options:	A) 44%	B) 48%	C) 94%	D) 45%	E) 39%

Solution: g% = 18 + 18 + (18*18)/100   = 39%   Answer: 39%
Answer: E
If x and y are positive integers such that (3x + 7y) is a multiple of 11, then which of the following will be divisible by 11 ?	Choose the correct choice:
A) 9
B) 11
C) 17
D) 21
E) 27

Solution: By hit and trial, we put x = 5 and y = 1 so that (3x + 7y) = (3 x 5 + 7 x 1) = 22, which is divisible by 11.   (4x + 6y) = ( 4 x 5 + 6 x 1) = 26, which is not divisible by 11;   (x + y + 4 ) = (5 + 1 + 4)= 
(5 + 1 + 4) = 10
10, which is not divisible by 11;   (9x + 4y)= (9 x 5 + 4 x 1) = 49, which is not divisible by 11;   (4x - 9y) = (4 x 5 - 9 x 1) = 11, which is divisible by 11.   Option 11
Answer: B
A cycle is bought for Rs.900 and sold for Rs.1350, find the gain percent? Choose the correct answer
A) 27% B) 20% C) 50% D) 30% E) 24%

Solution: 900 ---- 450   100 ---- ? => 50%   Answer: 50%
Answer: C
which number need to add to 859622 to get a number exactly divisible by 456?  Answers.
A) 454365  B) 412343  C) 546573  D) 567683  E) 859622

Solution: Dividend = Quotient * Divisor + Reminder   859622 / 456 gives quotient = 1885 and reminder = 62.   So, the next number divisible by 456 is 456 places infront of 456 * 1885   Which means 456 – 62 = 394 should be added to 859622.   859622
Answer: E
What is the maximum number of pieces that a circular pizza can be cut into with 5 linear cuts? Choose the correct answer:  A) 10  B) 14  C) 15  D) 16  E) 17

Solution: 1 cut makes 2 pieces   a second cut can make 4 pieces   a third cut can make 7 pieces by cutting through 3 of the pieces   a fourth cut can make 11 pieces by cutting through 4 of the pieces   a fifth cut can make 16 pieces by cutting through 5 of the pieces   16
Answer: D
A furniture dealer purchased a desk for $150 and then set the selling price equal to the purchase price plus a markup that was 50% of the selling price. If the dealer sold the desk at the selling price, what was the amount of the dealer's gross profit from the purchase and the sale of the desk?  Choose the correct choice from the following answers
A) $40  B) $60  C) $80  D) $90  E) $150

Solution: Purchase price = 150   Selling price = x   150 + 0.5*x = x   0.5*x = 150   x = 300   Profit = 300 - 150= 
300 - 150 = 150
150   ANSW$150R:$150
Answer: E
A meeting has to be conducted with 5 managers. Find the number of ways in which the managers be selected from among 8 managers, if 2 managers will not attend the meeting together?	Choose the most appropriate option.
A) 40	B) 36	C) 42	D) 45	E) 47

Solution: we can either choose all 5 people from 6 manager who have no problems or choose 4 from the 6 and 1 from the 2 managers who have a problem sitting together   so 6C5 + (6C4 * 2C1)   this is   6 + 30= 
  6 + 30 = 36
36   Answer : 36
Answer: B
What is the are of an equilateral triangle of side 20 cm?  Answers:
A) 250√3
B) 150√3
C) 300√3
D) 200√3
E) 100√3

Solution: Area of an equilateral triangle = √3/4 S2   If S = 20, Area of triangle = √3/4 * 20 * 20   = 100√3 cm2;   Answer:100√3
Answer: E
If x^2 - 1 = 0 and x < 0, which of the following must be equal to 0 ?	Choose the correct choice from the following:
A) x^2 - 9x	B) x^2 - 9x + 20	C) x^2 - 2x + 3	D) x^2 + 2x - 3	E) x^2 + 5x + 4

Solution: x^2-1 = 0   x= +1 or x = -1   if we substitute x= -1 in the equation x^2 +5x+4 = 1-5+4= 
1-5+4 = 0
0   x^2 + 5x + 4 is also the answer
Answer: E
If x = y^2, and x and y are positive integers, which of the following numbers could be the value of x?
Select:  A) 9,343  B) 10,982  C) 11,881  D) 12,988  E) 13,547

Solution: The square of an integer can have a units digit of 0, 1, 4, 5, 6, or 9.   The answer is 11,881.
Answer: C
A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is? Choose the most appropriate option
A) 112  B) 50  C) 77  D) 14  E) 12

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 - 5) km/hr. x - 5 = 45 ==> x   = 50 km/hr.   Answer: 50
Answer: B
A teacher has 16 students, then she gets 7 more students. Now how many students does she have? Choose the correct choice from the following.
A) A)9
B) B)15
C) C)15
D) D)23
E) E)25

Solution: 16+7= 
16+7 = 23
23. Answer is 23
Answer: D
Ravi can do a piece of work in 50 days while Prakash can do it in 75 days. In how many days will they finish it together?  Options
A) 30 days  B) 35 days  C) 25 days  D) 27 days  E) 29 days

Solution: 1/50 + 1/75 = 5/150   30/1= 
30/1 = 30
30 days   30 daysNSWER:30 days
Answer: A
Kiran travels from A to B by car and returns from B to A by cycle in 7 hours. If he travels both ways by car he saves 3 hours. What is the time taken to cover both ways by cycle? Choose the correct choice from the following answers:	A) 10 hours	B) 16 hours	C) 19 hours	D) 15 hours	E) 20 hours

Solution: Let the time taken to cover from A to B in car and cycle be x hours and y hours respectively.   x + y = 7 --- (1) ; 2x = 4 --- (2)   solving both the equations, we get y = 5   So, time taken to cover both ways by cycle = 2y hours   =10 hours.   10 hoursnswer: 10 hours
Answer: A
George and Mark can paint 720 boxes in 20 days. Mark and Harry in 24 days and Harry and George in 15 days. George works for 4 days, Mark for 8 days and Harry for 8 days. The total number of boxes painted by them is	Choose one
A) 28	B) H	C) 27	D) 29	E) 271

Solution: Answer:H
Answer: B
If x = a/(a – 1) and 1/(a – 1), then:	Choose the correct choice from the following.
A) x is equal to y B) x is equal to y only if a < 1 C) x is greater than y D) x is greater than y only if a < 1 E) y is greater than x only if a < 1

Solution: x = a/(a – 1) = 1 + 1/(a – 1) = 1 + y.   Therefore, x > y   x is equal to yNSWER:x is equal to y
Answer: A
In August,a cricket team that played 120 matches won 20% of the games it played.After a continuous winning streak,this team raised its average to 52%.How many matches did the team win to attain this average?
Choose the correct choice from the following choices.
A) 40	B) 52	C) 68	D) 80	E) 98

Solution: let the no of matches played more=x   so,   (120+x)*52/100=24+x   by solving we get x=80   ANSWER:80
Answer: D
An article was sold after a discount of 20% and therewas a gain of 20%. If the profit madeon it was Rs.6 less thanthe discount offered on it, find its SP?
Choose one:
A) Rs. 70	B) Rs. 71	C) Rs. 72	D) Rs. 90	E) Rs. 98

Solution: Let CP = Rs. 100x   SP = Rs. 120x   MP = 120x/80 * 100 = Rs. 150x   D = Rs. 150x - Rs. 120x = Rs. 30x   D - P = 30x - 20x = Rs. 6, 10x = Rs. 6   120x = 120/10 * 6 = Rs. 72   Rs. 72
Answer: C
A sun is divided among X, Y and Z in such a way that for each rupee X gets, Y gets 45 paisa and Z gets 30 paisa. If the share of Y is RS. 63, what is the total amount? Choose the correct choice from the following options:
A) 166
B) 105
C) 178
D) 177
E) 245

Solution: x:y:z = 100:45:30   20:9:6   9 --- 63   35 --- ? => 245   Answer: 245
Answer: E
The first doughnut is priced at $1 and then if you purchase additional doughnuts as dozens then the price is $6/dozen. What is the total number of doughnut purchased if you paid $19?	Answers.
A) 24
B) 25
C) 35
D) 36
E) 37

Solution: a is the number of dozen of doughnuts at a price of $6/dozen   1 + 6a = 19   a= 3   The total number of doughnuts purchased -->    1 + 3 * 12= 
 1 + 3 * 12 = 37
37   ANSW37R: 37
Answer: E
If (4.2)x = (0.42)y = 100, then (1/x) - (1/y) =  Choose one:	A) 1	B) 2	C) 1/2	D) 1/4	E) 2

Solution: (4.2)x = 100   => (42)x = 102+x   => 42 = 10(2/x+1) ---------- (i)   [42/100]y = 100 => 42y = 102+2y   => 42 = 102/y+2-------- (ii)   From (i) and (ii), 2/x - 2/y = 1   =>1/x - 1/y = 1/2.   ANSWER:1/2
Answer: C
In each of the following questions a number series is given with one term missing. Choose the correct alternative that will continue the same pattern and fill in the blank spaces.
2, 7, 14, 23, 34, ?
Choose the correct choice from the following options:	A) 31	B) 47	C) 36	D) 31	E) 33

Solution: B   47   The given sequence is +5, +7, +9, ——   ie. 2+ 5 = 7, 7 + 7 = 14, 14 + 9 = 23
Answer: B
Find the no.of ways of arranging 5 men and 5 ladies at a circular table so that no two ladies sit together ? Options
A) 4!x4!	B) 5!x5!	C) 4!x5!	D) 10!x10!	E) 25!x25!

Solution: The no. of ways of 5 men may be arranged in 4! ways. The ladies can arranged in themselves in 5! ways. The required no. of ways of arranging them is 4!x5! . Ans:(4!x5!)
Answer: C
A man rows his boat 85 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?	Select:
A) 7 kmph  B) 6 kmph  C) 5 kmph  D) 8 kmph  E) 9 kmph

Solution: Speed downstream = d/t = 85/(2 1/2)   = 34 kmph   Speed upstream = d/t = 45/(2 1/2)   = 18 kmph   The speed of the stream = (34 - 18)/2= 
(34 - 18)/2 = 8
8 kmph   Answer: 8 kmph
Answer: D
How many words with or without meaning, can be formed by using all the letters of the word, â€˜WORKâ€™, using each letter exactly once?	Pick one
A) 700	B) 24	C) 32	D) 48	E) 28

Solution: The word â€˜WORKâ€™ contains 4 different letters.   Therefore, Required number of words= Number of arrangement of 4 letters, taken all at a time   =4P4   = 4!   = 4*3*2*1= 
4*3*2*1 = 24
24   ANSWER:24
Answer: B
If A invested 5 times of B and at the end of the year they got a profit of Rs.36,000 in their business then share. of B in the profit was (in Rs.)	Choose the correct choice from the following choices:
A) 5000 B) 4000 C) 3000 D) 6000 E) 3500

Solution: A:B=5:1   so b=1/6 *36000= 
1/6 *36000 = 6_000
6000   ANSWER:6000
Answer: D
By selling 12 toffees for a dollar, a man loses 20%. How many for a dollar should be sell to get a gain of 20%?
Choices.
A) 8	B) 5	C) 9	D) 4	E) 3

Solution: A   8   Let S.P. of 12 toffees be $x.   Then, 80:1 = 120:x or x = 120/180 = 3/2   For $3/2, toffees sold = 12.   For Re. 1, toffees sold = 12 * 2/3= 
12 * 2/3 = 8
8
Answer: A
In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 50, the dividend is:	Answers:  A) 5330  B) 6300  C) 5343  D) 5345  E) 5350

Solution: Divisor = (5 * 50)= 
(5 * 50) = 250
250= 10 * Quotient = Divisor   => Quotient = 250/10= 
250/10 = 25
25   Dividend= (Divisor * Quotient) + Remainder   Dividend = (250 * 25) + 50= 
(250 * 25) + 50 = 6_300
6300.   6300
Answer: B
From a Group of 8 People, Including Sachin and Rahul, 3 people are to be selected at random to work on a certain project. What is the probability that 3 people selected will include Sachin but not Rahul
Choose the correct choice
A) 5/56
B) 9/56
C) 15/56
D) 21/56
E) 25/56

Solution: Number of ways of selecting 3 people out of 8 people = 8C3   In the three members Sachin will always be there in the team. At this step we have vacancy for 2 more members and 7 members are available. Lina cannot be there in the team. So 2 members have to be selected and the number of available members = 7 - Rahul = 6   Number of ways to form a 3 member team that includes Sachin and excludes Rahul = 615/562   Probability = 615/562/815/563 = 15/56   Answer: 15/56
Answer: C
A man purchased a grinder for Rs. 120 and sold it at a profit of 10%. The selling price is:  Pick:
A) Rs. 736 B) Rs. 812 C) Rs. 132 D) None of these E) Cannot be determined

Solution: s.p.=110/100 × 120 = 132   Answer: Rs. 132
Answer: C
What percent of 5 letter combinations that can be made from the letters of the word VERMONT and in which each letter can be used only once are the combinations in which the first letter is a vowel and the last letter is a consonant?
A.
B.
C.
D.
E.	Choose the correct choice from the following choices.
A) 20% B) 23.8% C) 25% D) 30.2% E) 35%

Solution: TOTAL number of 5 letter combinations = 7P5 = 7!/2! = 3*4*5*6*7   There are 2 vowels: e,o and 5 consonants: v,r,m,n,t   If A23.8%CDE is the required combination, A has 2 options, E has 5 options, 23.8% has 5, C has 4, and D has 3   Number of required combinations = 2*5*5*4*3   Answer = 2*5*5*4*3 / 3*4*5*6*7 = 5/21 = 23.8%   ANSWER: 23.8%
Answer: B
If each data point in a certain set Q is increased by a factor of 6, what happens with the set's standard deviation?  Choices:
A) Doesn't Change
B) Decreases by Factor 6
C) Increases by 6
D) Increases by Factor 6
E) Can't be determined

Solution: Standard deviation questions will always be conceptual in nature, because the GMAT does not require that you be able to calculate standard deviation.Veritasteaches a concept known as themapping strategyfor data sufficiency, which helps make a problem like this easily understandable. The mapping strategy is just looking at data sufficiency with sets of numbers like you would look at a map. Moving left and right on the map does not change the map's scale (which represents standard deviation in this analogy), just as adding or subtracting the same value in all numbers of a set does not change that set's standard deviation. For example, the set: 2, 5, 8, 11 has the same standard deviation of that same set after adding 5 to each number: 7, 10, 13, 16. Multiplying and dividing the entire set by a number other than 1, however, does affect standard deviation, and it does so proportionately. Multiplying by a number with an absolute value greater than 1 is like zooming in on a map...the standard deviation increases. Consider that same set multiplied by 2: 4, 10, 16, 22....this has a larger standard deviation than 2, 5, 8, 11. The opposite goes for division - dividing each number in a set of numbers by a number with an absolute value greater than 1 will reduce standard deviation, like zooming out on a map reduces the map's scale. Here because each number was multiplied by a factor of 6, the standard deviation will increase proportionately, giving us answer choice Increases by Factor 6.
Answer: D
if m>0 and b is m percent of a, then, in terms of m, a is what percent of b?	Choose the correct answer:
A) a)100m B) b)1/100m C) c)1/m D) d)10/m E) e)10^4/m

Solution: Given (m*a)/100=b   to find (a/b)*100   Rearranging first equation   a/b*100 = 100*100/m   =10^4/m   Answer e)10^4/m
Answer: E
The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 867 sq m, then what is the breadth of the rectangular plot?
Select:
A) 1 B) 17 C) 88 D) 12 E) 15

Solution: Let the breadth of the plot be b m.   Length of the plot = 3 b m   (3b)(b) = 867   3b2 = 867   b2 = 289 = 172 (b > 0)   b = 17 m.   Answer: 17
Answer: B
On flipping 3 coins together what is the outcomes for at least one head? Answers:	A) {HHH, HHT, HTH, THH, TTH, THT, TTT}	B) {HHH, HHT, HTH, THH, TTH, THT, HTT}	C) {HHH, HHT, HTH, TTT, TTH, THT, HTT}	D) {TTT, HHT, HTH, THH, TTH, THT, HTT}	E) None

Solution: Sample space, S = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}   Favorable outcomes for at least one heads   = favorable outcomes for exactly one heads and favorable outcomes for more than one heads   = {HHH, HHT, HTH, THH, TTH, THT, HTT}   {HHH, HHT, HTH, THH, TTH, THT, HTT}
Answer: B
One pipe can fill a tank four times as fast as another pipe. If together the two pipes can fill the tank in 40 minutes, then the slower pipe alone will be able to fill the tank in? Choose the correct choice from the following:
A) 100min
B) 150min
C) 200min
D) 250min
E) 300min

Solution: Let the slower pipe alone fill the tank in x minutes   Then, faster pipe will fill it in x/4 minutes   1/x + 4/x = 1/40   5/x = 1/40   x = 200 min   Answer is 200min
Answer: C
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? Select the correct option.
A) 31
B) 36
C) 51
D) 53
E) 57

Solution: age of the teacher=(37*15-36*14)= 
(37*15-36*14) = 51
51 years.   ANSWER:51
Answer: C
A car traveling at a certain constant speed takes 5 seconds longer to travel 1 km than it would take to travel 1 km at 90 km/hour. At what speed, in km/hr, is the car traveling?	Choices.
A) 70 B) 80 C) 74 D) 75 E) 78

Solution: Time to cover 1 kilometer at 80 kilometers per hour is 1/90 hours = 3,600/90 seconds = 40 seconds;   Time to cover 1 kilometer at regular speed is  40 + 5= 
 40 + 5 = 45
45 seconds= 45/3,600 hours = 1/80 hours;   So, we get that to cover 1 kilometer 1/80 hours is needed --> regular speed 80 kilometers per hour (rate is a reciprocal of time or rate=distance/time).   Answer: 80.
Answer: B