MU-NLPC/Calc-aqua_rat huggingface dataset:
From the integer n, if n*n*n*n*n is odd, then what is true from below options? Choose the correct choice from the following options
A) n is odd
B) n*n is even
C) n is odd, n*n is even, n*n*n is odd, n*n*n*n is even and n*n*n*n*n is odd
D) n is even
E) None

Solution: n is odd   Option n is odd
Answer: A
A dishonest dealer uses a scale of 90 cm instead of a metre scale and claims to sell at cost price. His profit is
Choose the correct choice from the following choices:	A) 9%	B) 10%	C) 12%	D) None of these	E) Cannot be determined

Solution: Solution   Gain%	= (10 / 90 x 100)%   = 11 1/9.   Answer None of these
Answer: D
The number of sequences in which 7 players can throw a ball, so that the youngest player may not be the last is ?	Choose the correct choice from the following answers:
A) 4328  B) 4328  C) 4320  D) 7862  E) 1242

Solution: x Not younger   The last ball can be thrown by any of the remaining 6 players. The first 6 players can throw the ball in 6P6 ways.   The required number of ways = 6(6!)   = 4320   Answer:4320
Answer: C
There are n members in a certain department, including Michael. Two representatives are to be selected to attend a company conference. If there are 66 possible combinations in which Michael is not selected, what is the value of n?  Pick one:  A) 11  B) 12  C) 13  D) 14  E) 15

Solution: The combinations of two people, in which Michael was not selected = 28   The number of ways two people can be selected from m people = m*(m-1)/2   Let m be the number of people excluding Michael.   Then m*(m-1) = 132 = 12*11   Thus, n = m + 1(Michael) = 13   The answer is 13.
Answer: C
In the equation s = 36.12t, t and s are integers. If s/t leaves a remainder of r, which of the following must divide into r?
Choose the most appropriate option:
A) 2  B) 3  C) 4  D) 6  E) 12

Solution: 1) It says it is a equation, so s=36.12t should be 36.12 * t..   2) It says t is an integer, again it means 36.12 * t..   Otherwise t would be just a digit and it would be mentioned..   Although not clearly mentioned that 36.12t is actually 36.12 * t, BUT entire info points towards that..   and that is why I have taken s/t = 36.12
Answer: B
In a 100 m race, A can give B 10 m and C 28 m. In the same race B can give C : Choose the correct answer:
A) 10 m B) 15 m C) 20 m D) 30 m E) 25 m

Solution: "A can give B 10 m".   In a 100 m race, while A starts from the starting point, B starts 10 meters ahead from the same starting point at the same time.   "A can give C 28 m"   In a 100 m race, while A starts from the starting point, C starts 28 meters ahead from the same starting point at the same time.   i.e., in a 100-10= 
100-10 = 90
90 m race, B can give 20 m 28-10= 
28-10 = 18
18 m   In a 100 m race, B can give 20 m18/90×100= 20 m   Answer is 20 m
Answer: C
Find 94 ×× 97  Choose one
A) 93/198 B) 93/12 C) 93/18 D) 93/10 E) 93/11

Solution: Here both numbers are less than 100. So they are deficient of - 6 and - 3 compared with 100. So   Answer:	93/18
Answer: C
A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
Choose the correct choice from the following choices
A) 177 B) 168 C) 120 D) 882 E) 122

Solution: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.   Length of the train = 20 * 6= 
20 * 6 = 120
120 m.Answer:120
Answer: C
Torry has submitted 3/5 of his homework assignments, and he received an average grade of 75 for those assignments. If he wishes to receive an average grade of 90 for all his homework assignments, the average grade for Torry's remaining homework assignments must be what percent greater than the average grade for the assignments he has already submitted?  Choose the correct choice
A) 15% B) 20% C) 25% D) 33 1/3% E) 50%

Solution: 0.6*75 + 0.4x = 90   45 + 0.4x=90   0.4x = 45   x= 112.5   112.5/75= 
112.5/75 = 1.5
1.5   Ans:50%
Answer: E
The ratio of number of boys and girls in a school is 1:2. If there are 90 students in the school, find the number of girls in the school?	Choose the correct choice from the following options:
A) 45  B) 50  C) 60  D) 75  E) 90

Solution: Let the number of boys and girls be x and 2x   Total students = 100   Number of girls in the school = 2*90/3= 
2*90/3 = 60
60   Answer is 60
Answer: C
If you roll a fair-sided die twice, what is the probability of getting a double? Answers:
A) 1/3
B) 1/6
C) 1/12
D) 1/24
E) 1/36

Solution: ways you can get double - 6...as each dice showing any number from 1 to 6...   total ways = 6∗6=36.6∗6=36..   P=6/36=1/6   ANSWER: 1/6
Answer: B
What is 35% of 4/13 of 715? Choose the correct choice:
A) 44 B) 55 C) 66 D) 77 E) 88

Solution: This problem can be solved easily if we just use approximation: 35% is a little over 1/3, while 4/13 is a little less than 4/12, which is 1/3. Thus, the answer is about 1/3 of 1/3 of 715, or 1/9 of 715. Since the first 1/3 is a slight underestimate and the second 1/3 is a slight overestimate, the errors will partially cancel each other out. Our estimate will be relatively accurate.   The number 715 is about 720, so (1/9)*715 will be a bit less than 80.   Keeping track not only of your current estimate, but also of the degree to which you have overestimated or underestimated , can help you pinpoint the correct answer more confidently.   The closest answer is 77, so this is the answer to choose.   The answer is 77.
Answer: D
Dinesh speaks truth in 3/4 cases and Abhishek lies in 1/5 cases. What is the percentage of cases in which both Dinesh and Abhishek contradict each other in stating a fact? Choose one: A) 60% B) 35% C) 20% D) 15% E) None of these

Solution: Explanation :   D and A will contradict each other when one speaks truth and other speaks lies.   Probability of D speak truth and A lies   =>(3/4)×(1/5).   =>3/20.   Probability of A speak truth and D lies   =>(4/5)×(1/4).   =>1/5.   The two probabilities are mutually exclusive. Hence, probabilities that D and A contradict each other:   =>(3/20)+(1/5).   =>7/20.= 
7/20. = 0.35
>0.35×100%=>35%   Answer : 35%
Answer: B
A man drive his car to the office at 20miles/hr.
After reaching office, he realize that its a new year holiday so he went back home at a speed of 30miles/hr.
Discounting the time spent in the stoppage what was his average speed of his journey ? Select
A) 23miles
B) 25miles
C) 22miles
D) 24miles
E) 26miles

Solution: 24miles   24miles/hr (not 25miles/hr which might be guessed by many)   24miles : distance traveled   T1 : time of going to office   T2 : time of returning back   Y : Average Speed   24miles = 20 * T1   T1 = 24miles/20   24miles = 30 * T2   T2 = 24miles/30   224miles = Y(T2 + T1)   224miles = Y(24miles/20 + 24miles/30)   224miles = Y(324miles/60 + 224miles/60)   224miles = Y(524miles/60)   Y = 12024miles/524miles   => Y = 24
Answer: D
The average (arithmetic mean) of 22, 33, and 53 is 8 less than the average of 30, 56, and x. What is x?	Choose the correct choice from the following choices.
A) 42	B) 44	C) 46	D) 48	E) 50

Solution: The average of 22, 33, and 53 is  108/3= 
 108/3 = 36
36.   The average of 30, 56 and x is 44.   Then 30 + 56 + x= 132.   x = 46.   The answer is 46.
Answer: C
Abby and Bobby type at constant rates of 80 words per minute and 60 words per minute, respectively. Bobby begins typing before Abby and has typed 600 words when Abby begins typing at 1:30 pm. If they continue typing at their respective rates, at what time will Abby have typed exactly 300 more words than Bobby?  Choose the correct choice.
A) 1:40 PM B) 1:50 PM C) 2:00 PM D) 2:15 PM E) 2:20 PM

Solution: Say time needed for Abby to type 200 more words than Bobby is t. In that time she would type 80t words and Bobby would type 60t words.   Now, total words typed by Bobby would be 600+60t and we want that number to be 200 less than 80t: 600+60t=80t-300 --> t=45.   1:30 PM + 45 minutes = 2:15 PM.   Answer: 2:15 PM.
Answer: D
Three runners E, B and C run a race, with runner E finishing 12m ahead of runner B and 18m ahead of runner C, while runner B finishes 8m ahead of runner C. Each runner travels entire distance at a constant speed. What was the length of the race?	Select the correct option.
A) 36m
B) 48m
C) 60m
D) 72m
E) 84m

Solution: Let distance of race be x mtrs. Then when E finishes x m , B has run (x- 12)mtrs and C has run x-18 mtrs. so at this point B is 6 m ahead of C. Now to finish race b needs to run another 12 m, so he runs another 12 m. when B finishes race he is 8 m ahead of C. so last 12 m B has run, C has run 10 m.   as speeds are constant, we have equation,   x-12/ x-18 = 12/10 > x = 48.   Answer 48m
Answer: B
A man saves 20% of his monthly salary. If an account of dearness of things he is to increase his monthly expenses by 20%, he is only able to save Rs. 260 per month. What is his monthly salary?	Choose the most appropriate option:
A) 5000  B) 2999  C) 2878  D) 2990  E) 6500

Solution: Income = Rs. 100   Expenditure = Rs. 80   Savings = Rs. 20   Present Expenditure 80*(20/100) = Rs. 96   Present Savings = 100 â€“ 96 =Rs. 4   100 ------ 4   ? --------- 260 => 6500   Answer: 6500
Answer: E
letters in the word ABUSER are permuted in all possible ways and arranged in alphabetical order then find the word at position 49 in the permuted alphabetical order? Choose the correct answer.
A) KASJJHJ
B) DGUJKL
C) ARBESU
D) ILUGUO
E) HDIWWD

Solution: Ans: The best way to solve this problems is Just ask how many words starts with A. If we fix A, then the remaining letters can be arranged in 5! ways = 120. So the asked word must start with A.   Arrange all the given letters in alphabetical order. ABERSU   Let us find all the words start with AB. AB**** = 4!= 24 ways   Now we find all the words start wit AE. AE****= 4!= 24 ways   So next word start with AR and remaining letters are BESU   Answer:ARBESU
Answer: C
If 1/12 of the passengers on a ship are from North America, 1/4 are Europeans, 2/9 are from Africa, 1/6 are from Asia and the remaining 50 people are citizens of other continents, then how many passengers are on board the ship? Choose the correct choice from the following choices.
A) 120	B) 140	C) 150	D) 160	E) 180

Solution: 1/12 + 1/4 + 2/9 + 1/6 = (3+9+8+6)/36 = 13/18   Let x be the number of passengers on the ship.   50 = (5/18)x   x = 180   The answer is 180.
Answer: E
If it takes 6 identical printing presses exactly 4 hours E to print 5,000 newspapers, how long would it take 3 of these presses to print 3,000 newspapers? Choose the correct choice
A) 3 hours, 20 minutes	B) 4 hours, 20 minutes	C) 4 hours, 48 minutes	D) 5 hours, 48 minutes	E) 6 hours, 50 minutes

Solution: 6 presses - 5,000 newspapers - 4 hours ;   3 presses - 2,500 newspapers - 4 hours ;   3 presses - 3,000 newspapers - 4 hours + 1/5*4 hours = 4 hours, 48 minutes (since 2,500+1/5*2,500=3,000) = E.   Answer: 4 hours, 48 minutes.
Answer: C
A fast food hotel sells chicken in orders of 6, 9, and 20.
What is the largest number of pieces of chicken you cannot order from this hotel ?
Choose the correct choice from the following answers:
A) A)23
B) B)33
C) C)43
D) D)53
E) E)63

Solution: 43.   After 6 all numbers divisible by 3 can be ordered (because they can all be expressed as a sum of 6's and 9's). After 26, all numbers divisible by three when subtracted by 20 can be obtained. After 46, all numbers divisible by three when subtracted by 40 can be obtained. After 46, all numbers fit into one of these 3 categories, so all numbers can be obtained. 43 is the last number that doesn't fall into one of these categories (44 = 20 + 6 * 4, 45 = 6 * 6 + 9). answer is 43
Answer: C
A person walks at a speed of 4 km/hr and runs at a speed of 8 km/hr. How many hours will the person require to cover a distance of 8 km, if the person completes half of the distance by walking and the other half by running?
Options
A) 0.5  B) 1.5  C) 2.5  D) 3.5  E) 4.5

Solution: time = 4/4 + 4/8 = 12/8= 
12/8 = 3/2 = around 1.5
1.5 hours   The answer is 1.5.
Answer: B
How many positive integers less than 200 are there such that they are multiples of 13 or multiples of 12?	Pick one:  A) 28  B) 29  C) 30  D) 31  E) 32

Solution: Total Multiples of 13: 15 (First multiple:13, last multiple:195)   Total Multiples of 12:16 (First multiple: 12,Last multiple: 192)   Multiple of 12 and 13: 1 (156)   15+16-1= 
15+16-1 = 30
30   ANSWER:30
Answer: C
Find the sum of all odd numbers upto 100.
Choose the correct answer.
A) 2200 B) 2900 C) 2700 D) 2500 E) 2800

Solution: The given numbers are 1, 3, 5, 7, ..., 99.   This is an A.P. with a = 1 and d = 2.   Let it contain n terms. Then,   1 + (n - 1) x 2 = 99 or n = 50.   Therefore, Required sum = n/2 (first term + last term)   = 50/2 (1 + 99) = 2500.   Answer is 2500.
Answer: D
A and B can together finish a work in 40days. They worked together for 10days and then B left. After another 9days, A finished the remaining work. In how many days A alone can finish the job?
Choose the correct answer:	A) 12	B) 25	C) 60	D) 30	E) 20

Solution: 12+B 10days work = 10*1/40 = 1/4   Remaining work = 1-1/4 = 3/4   3/4 work is done by 12 in 9 days   whole work will be done by 12 in  9*4/3= 
 9*4/3 = 12
12 days   12nswer is 12
Answer: A
The sum of the squares of three consecutive natural number is 2030. What is the middle number?	Choose the correct choice from the following options.
A) 25  B) 26  C) 27  D) 28  E) 29

Solution: Let the numbers be x, x+1 and x+2   X2+(x+1)2+(x+2)2=2030   3x2+6x-2025=0   (x+27)(x-25)=0   X=25   The middle number is 26   ANSWER 26 26
Answer: B
A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 47, then how old is B? Select the correct option
A) 17 years B) 19 years C) 18 years D) 10 years E) 12 years

Solution: Let C's age be x years.   Then, B's age = 2x years.   A's age = (2x + 2) years.   (2x + 2) + 2x + x = 47   5x = 45 => x = 9   Hence, B's age = 2x = 18 years.   Answer: 18 years
Answer: C
In a mixture of 60 liters, the ratio of milk and water is 4:1. What amount of water must be added to make the ratio of milk and water as 1:4?	Choose the correct option
A) 60 liters  B) 42 liters  C) 68 liters  D) 65 liters  E) 62 liters

Solution: 4:1 --- 60   1:4   2:8   ---------------   5   5 ----------- 60   5 ----------- ? => 60 liters   60 litersNSWER:60 liters
Answer: A
At a local appliance manufacturing facility, the workers received a 10% hourly pay raise due to extraordinary performance. If one worker decided to reduce the number of hours that he worked so that his overall pay would remain unchanged, by approximately what percent would he reduce the number of hours that he worked?	Choose the correct choice from the following answers:  A) 83%  B) 80%  C) 20%  D) 17%  E) 9%

Solution: Let's say he works usually 10 hours and earns 100 per hour.   10 * 100= 
10 * 100 = 1_000
1000   10 * 110= 
10 * 110 = 1_100
1100 (this are the new earnings after the raise)   To figure out how much he needs to work with the new salary in order to earn the original 1000:   1000/110= 9.09   So he can reduce his work by 0.91 hours. Which is >9%.   Answer 9%
Answer: E
The profit earned by selling an article for 812 is equal to the loss incurred when the same article is sold for 448. What should be the sale price of the article for making 50 per cent profit?  Choose the correct choice
A) 960	B) 1060	C) 1,200	D) 945	E) None of these

Solution: Let the profit or loss be x   and 812 – x = 448 + x or, x = 364⁄2 = 182   \ Cost price of the article = 812 – x = 448 + x = 630   \ SP of the article = 630 × 150⁄100 = 945   Answer 945
Answer: D
What will be the difference between simple and compound interest at 10% per annum on a sum of Rs. 1000 after 4 years?	Choose the correct choice
A) 64.19	B) 64.12	C) 62.1	D) 64.1	E) 64.11

Solution: S.I. = (1000 * 10 * 4)/100 = Rs. 400   C.I. = [1000 * (1 + 10/100)4 - 1000] = Rs. 464.10 Difference = (464.10 - 400) = Rs. 64.10   Answer: 64.1
Answer: D
In a certain game, you perform three tasks. You flip a coin, and success would be heads. You roll a single die, and success would be a three. You pick a card from a full playing-card deck, and success would be picking a spades card. If exactly one of these three tasks is successful, then you win the game. What is the probability of winning?	Choose one:
A) 11/16 B) 15/32 C) 14/36 D) 17/56 E) 23/48

Solution: The answer is 23/48   Probability of just one enent will be happining   So, Probability heads=1/2   Probability number 3 =1/6   Probability picking a spades card =1/4   so, Probability win by getting tails= 1/2*5/6*3/4 = 15/48   Probability win by getting number 6 = 1/2*1/6*3/4 = 3/48   Probability win by picking a spades card =1/2*5/6*1/4=5/48   Probability wining= 15/48+3/48+5/48 =23/48
Answer: E
For a recipe for triple berry pie calls for cups of strawberries, raspberries, and blueberries in a ratio of 1:2:3. How many total cups of fruit will you need to make the pie?	Options:
A) 2 B) 3 C) 4 D) 5 E) 6

Solution: The ratio 1:2:3 represents 1 cup strawberries: 2 cups raspberries: 3 cups blueberries.   1+2+3= 
1+2+3 = 6
6   6 cups will be used for the pie.   The answer is 6
Answer: E
Mahesh can do a piece of work in 30days. He works at it for 20days and then Rajesh finished it in 30days. How long will Y take to complete the work? Options
A) 90 B) 25 C) 37 D) 41 E) 30

Solution: Work done by Mahesh in 30days = 20*1/30 = 2/3   Remaining work = 1 - 2/3 = 1/3   1/3 work is done by Rajesh in 30days   Whole work will be done by Rajesh is   30*3= 
  30*3 = 90
90days   90nswer is 90
Answer: A
After M students took a test, the average score was 72%. If the test has 50 questions, what is the least number of questions that the next student has to get right to bring the average score up to 75%?  Choose the correct option.
A) 1.5M + 36
B) 72 - 1.5M
C) 1.5M + 37.5
D) 0.75 + 1.5M
E) 1.5M + 0.72

Solution: The total number of correct answers for M students is (0.72)*50*M=36*M   For an average of 75%: (total correct answers) / (M+1) = 0.75*50= 
0.75*50 = 37.5
37.5   Let x be the number of correct answers for the next student.   (x + 36M) / M+1= 37.5   x + 36M= 37.5M+37.5   x = 1.5M + 37.5   The answer is 1.5M + 37.5.
Answer: C
By selling 80 pens, a trader gains the cost of 20 pens. Find his gain percentage?  Choose the most appropriate option:
A) 25%	B) 30%	C) 35%	D) 40%	E) 50%

Solution: Let the CP of each pen be Rs. 1.   CP of 80 pens = Rs. 80   Profit = Cost of 20 pens = Rs. 20   Profit% = 20/80 * 100= 
20/80 * 100 = 25
25%   25%nswer:25%
Answer: A
A train travels from station A to station B. If the train leaves station A and makes 75 km/hr, it arrives at station B 48 minutes ahead of scheduled. If it made 50 km/hr, then by the scheduled time of arrival it would still have 40 km more to go to station B. Find:
A) The distance between the two stations;
B) The time it takes the train to travel from A to B according to the schedule;
C) The speed of the train when it's on schedule.	Options.
A) 34  B) 27  C) 26  D) 28  E) 60

Solution: Let xx be the scheduled time for the trip from A to B. Then the distance between A and B can be found in two ways. On one hand, this distance equals 75(x−4860)75(x−4860) km. On the other hand, it is 50x+4050x+40 km. So we get the equation:   75(x−4860)=50x+4075(x−4860)=50x+40   x=4x=4 hr is the scheduled travel time. The distance between the two stations is 50⋅4+40=24050⋅4+40=240 km. Then the speed the train must keep to be on schedule is 2404=602404=60 km/hr.   Answer:60
Answer: E
In an examination, a pupil’s average marks were 63 per paper. If he had obtained 20 more marks for his Geography paper and 2 more marks for his history paper, his average per paper would have been 65. How many papers were there in the examination?
Options.
A) 8
B) 9
C) 10
D) 11
E) 12

Solution: Solution   Let the number pf papers be x.   Then, 63x + 20+2=65x   65x-63x=22   2x = 22   x = 11.   Answer 11
Answer: D
Maddie has 18 apples, if she give 12 to mike, how many does she have left?	Choose the correct choice from the following options:
A) 1
B) 6
C) 3
D) 4
E) 5

Solution: 18-12= 
18-12 = 6
6   B. 6
Answer: B
At a garage sale, all of the items were sold at different prices. If the price of a radio sold at the garage sale was both the 18th highest price and the 25th lowest price among the prices of the items sold, how many items were sold at the garage sale?	Choose the correct option:  A) 41  B) 42  C) 43  D) 44  E) 45

Solution: There were 17 items sold at a higher price than the radio and 24 items sold at a lower price than the radio. Including the radio, there were 17 + 24 + 1= 
17 + 24 + 1 = 42
42 items sold.   The answer is 42.
Answer: B
Two numbers are in the ratio of 5:7. If 25 be subtracted from each, they are in the ratio of 35:59. Find the numbers?	Choose the correct answer.
A) 60,85	B) 60,61	C) 60,18	D) 60,84	E) 60,15

Solution: =(5x-25):(7x-25) = 35:59   x = 12 => 60,84   Answer: 60,84
Answer: D
In a game of billiards, A can give B 20 points in 60 and he can give C 30 points in 60. How many points can B give C in a game of 130?
Choose the correct choice from the following:
A) 15 B) 77 C) 55 D) 18 E) 12

Solution: A scores 60 while B score 40 and C scores 30.   The number of points that C scores when B scores 100 = (100 * 30)/40 = 25 * 3= 
25 * 3 = 75
75.   In a game of 100 points, B gives (130 - 75)= 
(130 - 75) = 55
55 points to C.   Answer:55
Answer: C
How many of the following numbers are divisible by 14 ?
264, 396, 462, 792, 968, 2178, 5184, 6336 Choices:
A) 3 B) 4 C) 5 D) 6 E) 1

Solution: By using your calculator you can calculate that the following numbers are divisible by 14 : 462.   Required number of number = 1.   1
Answer: E
What is the least number of square tiles required to pave the floor of a room 50 m 00 cm long and 11m 25 cm broad?	Choose the correct option:
A) 724
B) 804
C) 814
D) 9000
E) None

Solution: Solution   Length of largest tile = H.C.F. of 5000cm & 1125cm = 25cm.   Area of each tile = (25 x 25)cm2   ∴ Required number of tiles	= [5000x1125/25x25]   = 9000.   Answer 9000
Answer: D
Karen places a bet with Tom that she will beat Tom in a car race by 4 miles even if Karen starts 4 minutes late. Assuming that Karen drives at an average speed of 60 mph and Tom drives at an average speed of 45 mph, how many Q miles will Tom drive before Karen wins the bet?  Choose the correct choice from the following choices
A) 15	B) 18	C) 21	D) 24	E) 27

Solution: Let K and T be the speeds of Karen and Tom respectively.   t be the time that Karen will travel ----> t+4/60 will be the total time Tom will travel by the time the distance between Karen and Tom is 4 miles.   Thus, per the question , K(t) - T(t+4/60) = 4 ---> t = 7/15 hours   Thus the distance traveled by Tom when Karen is 4 miles ahead of him : T*(t+4/60) = 45 (7/15+4/60) Q= 24 miles. 24 is the correct answer.
Answer: D
In Arun's opinion, his weight is greater than 65 kg but less than 72 kg. His brother doest not agree with Arun and he thinks that Arun's weight is greater than 60 kg but less than 70 kg. His mother's view is that his weight cannot be greater than 68 kg. If all are them are correct in their estimation, what is the average of different probable weights of Arun?  Answers.
A) 67 kg
B) 68 kg
C) 69 kg
D) Data inadequate
E) None of these

Solution: Explanation:   Let Arun's weight by X kg.   According to Arun, 65 < X < 72   According to Arun's brother, 60 < X < 70.   According to Arun's mother, X <= 68   The values satisfying all the above conditions are 66, 67 and 68.   Required average = 66 + 67 + 68/ 3 = 201	/ 3	= 67 kg.   67 kgNSWER IS 67 kg201 / 3= 
201 / 3 = 67
67 kg.   67 kgNSWER IS 67 kg
Answer: A
There are 27 different three-digit integers that can be formed using only the digits 1, 3, and 4. If all 27 of the integers were listed, what would their sum be?
Choose the correct choice from the following options:  A) 7592  B) 7692  C) 7792  D) 7892  E) 7992

Solution: There must be nine 1's in the hundreds place, nine 1's in the tens place, and nine 1's in the units place. This is also true for the 3's and 4's. Then the sum is:   9(111+333+444)=9*(888)= 
9*(888) = 7_992
7992.   The answer is 7992.
Answer: E