MU-NLPC/Calc-aqua_rat huggingface dataset:
The average age of 20 persons in a office is 15 years. Out of these, the average age of 5 of them is 14 years and that of the other 9 persons is 16 years. The age of the 15th person is?  Choose the correct choice from the following answers.
A) 79 B) 86 C) 95 D) 72 E) 80

Solution: Age of the 15th student = 20*15 - (14*5+16*9) =300-214= 
300-214 = 86
86 years   Answer is 86
Answer: B
The rate of spin of a certain gyroscope doubled every 10 seconds from the moment a particular stopwatch started. If after a minute and a half the gyroscope reached a speed of 3200 meters per second, what was the speed, in meters per second, when the stopwatch was started? Choose one:
A) 25/3 B) 25/4 C) 25/8 D) 25/16 E) 25/32

Solution: Let x be the original speed when the stopwatch was started.   In 90 seconds, the speed doubled 9 times.   2^9 * x = 3200   x = (2^7 * 25) / 2^9 = 25/4   The answer is 25/4.
Answer: B
In Township K, 1/4 of the housing units are equiped with cable Tv. If 1/10 of the housing units, including 1/3 of those that are equiped with cable tv, are equipped with videocassette recorders, what fraction of the housing units have neither cable tv nor videocassette recorders?
Answers:	A) 23/30	B) 11/15	C) 7/10	D) 1/6	E) 2/15

Solution: 1/4 -- cable TV (This includes some data from video cassette recorder)   1/10 -- video cassette recorder including 1/3(equiped with cable tv) i.e. 1/3(1/4) = 1/12   therefore only video cassette recorder = 1/10 - 1/12 = 1/60   Total = 1/4+1/60+neither cable tv nor videocassette recorders   1 = 4/15 + neither cable tv nor videocassette recorders   therefore neither cable tv nor videocassette recorders = 1-4/15 = 11/15   Hence 11/15.
Answer: B
In 1982 and 1983, Company B’s operating expenses were $11.0 million and $14.0 million, respectively, and its revenues were $15.6 million and $18.8 million, respectively. What was the percent increase in Company B’s profit (revenues minus operating expenses) from 1982 to 1983 ?	Select.
A) 3% B) 16 2/3% C) 25% D) 4 1/3% E) 60%

Solution: Profit in 1982 = 15.6 - 11= 
15.6 - 11 = 4.6
4.6 million $   Profit in 1983= 18.8 - 14= 
18.8 - 14 = 4.8
4.8 million $   Percentage increase in profit= (4.8-4.6)/4.6 * 100 %   = 4 1/3%   Answer 4 1/3%
Answer: D
How many even multiples of 55 are there between 549 and 1101?	Choose the correct choice from the following answers
A) 5
B) 6
C) 9
D) 10
E) 11

Solution: 550 = 10*55   1100 = 20*55   The even multiples are 55 multiplied by 10, 12, 14, 16, 18, and 20 for a total of 6.   The answer is 6.
Answer: B
The marks obtained by Polly and Sandy are in the ratio 5:6 and those obtained by Sandy and Willy are in the ratio of 3:2. The marks obtained by Polly and Willy are in the ratio of...?  Answers:
A) 3:2  B) 5:4  C) 7:6  D) 9:8  E) 11:10

Solution: Polly : Sandy = 5:6   Sandy : Willy = 3:2 = 6:4   Polly : Sandy : Willy = 5:6:4   Polly : Willy = 5:4   The answer is 5:4.
Answer: B
The speed of a railway engine is 63 Km per hour when no compartment is attached, and the reduction in speed is directly proportional to the square root of the number of compartments attached. If the speed of the train carried by this engine is 24 Km per hour when 9 compartments are attached, the maximum number of compartments that can be carried by the engine is:
Select the correct option:  A) 19  B) 18  C) 16  D) 17  E) 23

Solution: the reduction in speed is directly proportional to the square root of the number of compartments attached   Does reduction mean amount subtracted? or percentage decrease? There are at least two interpretations, and the wording does not provide a clear interpretation between them.   Evidently what the question intends is the subtraction interpretation. What is subtracted from the speed is directly proportional to the square root of the number of compartments attached.   In other words, if S = speed, and N = number of compartments, then   S = 63 - k*sqrt(N)   where k is a constant of the proportionality. In general, if A is directly proportional to B, we can write A = k*B and solve for k.   If N = 9, then S = 24   24 = 63 - k*sqrt(9) = 63 - 3k   k = 13   Now, we need to know: what value of N makes S go to zero?   0 = 63 - 13*sqrt(N)   13*sqrt(N) =63   n = 23   With 24 compartments, the train does not budge. Therefore, it would budge if there were one fewer cars. Thus, 23 is the maximum number of cars the engine can pull and still move.   23
Answer: E
A man buys a cycle for Rs.1200 and sells it at a loss of 15%. What is the selling price of the cycle?  Select the correct option:
A) Rs.1090  B) Rs.1020  C) Rs.1190  D) Rs.1202  E) NONE

Solution: Solution   S.P	= 85% of Rs.1200   = Rs.(85/100×1200)   Rs.1020.   Answer Rs.1020
Answer: B
An angry Arjun carried some arrows for fighting with Bheeshm. With half the arrows, he cut down the arrows thrown by Bheeshm on him and with six other arrows he killed the Chariot driver of Bheeshm. With one arrow each he knocked down respectively the Chariot, the flag and the bow of Bheeshm. Finally, with one more than four times the square root of arrows he laid Bheeshm unconscious on an arrow bed. Find the total number of arrows Arjun had.	Choose the correct choice
A) 90	B) 100	C) 110	D) 120	E) 130

Solution: x/2 + 6+3+1+4 sqrt(x) = x   x/2 +10 + 4 sqrt(x) = x   4sqrt(x) = x/2 - 10   squaring on both sides   16x = x²/4 +100 -10x   simplifying x² -104x +400=0   x =100, 4   x=4 is not possible therefore x=100   ANSWER:100
Answer: B
Village P’s population is 800 greater than Village Q's population. If Village Q’s population were reduced by 500 people, then Village P’s population would be 3 times as large as Village Q's population. What is Village Q's current population?	Select
A) 1100
B) 1150
C) 1200
D) 1250
E) 1300

Solution: P = Q+800.   P=3(Q-500).   3(Q-500)=Q+800.   2Q=2300.   Q=1150.   The answer is 1150.
Answer: B
A 4 digit no may consist of the digits 6,2,7,5 where none of the nos are repeated.Find the possible no of combinations divisible by 36?	Choose the correct choice:
A) 18 B) 36 C) 38 D) 48 E) 58

Solution: lcm of 36 = 3 *3 * 4 the four digit number should be divisible by 3 and 4 then it is divisible by 36 adding all the digits   6+2+7+5= 
  6+2+7+5 = 20
20 not divisible by 20 so   any 4 digit number formed by this is not divisible by 36   ANSWER:36
Answer: B
0, 3, 9, 18, 30, 45, 63, ?What number should replace the question mark? Select:
A) 78  B) 74  C) 79  D) 72  E) 84

Solution: 84 84add 3,6,9,12,15,.....
Answer: E
How many X ways can you group 3 people from 4 sets of twins if no two people from the same set of twins can be chosen? Choose one:
A) 3
B) 16
C) 28
D) 32
E) 56

Solution: Ways to select 3 people from 8 people (4 twins x 2) = 8C3 = 56   Ways to select 1 twin + 1 people = 4C1*6C1 = 24   Ways to select a group 3 people from 4 sets of twins if no two people from the same set of twins can be chosen X= 56 - 24= 
56 - 24 = 32
32   Ans: 32
Answer: D
A walks at 4 kmph and 4 hours after his start, B cycles after him at 10 kmph. How far from the start does B catch up with A? Choose the correct choice from the following options:	A) 25km	B) 26.7km	C) 30km	D) 32.5km	E) 31.2km

Solution: Suppose after x km from the start B catches up with A. Then, the difference in the time taken by A to cover x km and that taken by B to cover x km is 4 hours.   x/4 - x/10 = 4   x = 26.7 km   Answer is 26.7km
Answer: B
Machine A and machine B are each used to manufacture 440 sprockets. It takes machine A 10 hours longer to produce 440 sprockets than machine B. Machine B produces 10 percent more sprockets per hour than machine A. How many sprockets per hour does machine A produces?  Pick
A) 5	B) 6	C) 4	D) 3	E) 2

Solution: Machine B: Takes x hours to produce 440 sprockets   Machine A: Takes (x+10) hours to produce 440 sprockets   Machine B: In 1 hour, B makes 440/x sprockets   Machine A: In 1 hour, A makes 440/(x+10) sprockets   Equating:   1.1(440/(x+10)) = 440/x   484/(x+10) = 440/x   484x = 440x+4400   44x = 4400   x = 100   A makes   440/(110)= 
  440/(110) = 4
4 sprockets per hour   Answer : 4
Answer: C
It takes Joey the postman 1 hours to run a 4 mile long route every day. He delivers packages and then returns to the post office along the same path. If the average speed of the round trip is 5 mile/hour, what is the speed with which Joey returns?
Choose the correct choice from the following choices: A) 5 B) 12 C) 13 D) 14 E) 15

Solution: let his speed for one half of the journey be 4 miles an hour   let the other half be x miles an hour   now,   avg speed =5 mile an hour   2*4*x/4+x=5   8x=4x+20=>x=5   5
Answer: A
Dacid obtained 90, 92, 85, 87 and 85 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?	Choose the correct option:
A) 67  B) 26  C) 88  D) 90  E) 75

Solution: Average   = (90+ 92+ 85+ 87+ 85)/5   = 439/5 = 87.8.   Answer: 88
Answer: C
What is the greatest positive integer x such that 5^x is a factor of 125^10?
Choose the correct choice
A) 5	B) 9	C) 10	D) 20	E) 30

Solution: 125^10 = (5^3)^10 = 5^30   ANSW30R:30
Answer: E
A and B started a business in partnership. A invested Rs. 40000 for 6 months. A received Rs.6000 as his share out of the total profit of Rs. 9000, What was the amount invested by B for the whole year?	Choices:  A) Rs. 10000  B) Rs. 10002  C) Rs. 10009  D) Rs. 10007  E) Rs. 122122

Solution: Explanation:   Profits of A and B are distributed in the same ratio of their investment and period of investments.   Investment of A/ Investment of B = Profit of A/ Profit of B = 6000/3000   (40000*1/2)/X*1 = 2/1   Therefore, X = B's investment amount = Rs. 10,000.   Rs. 10000NSWER:Rs. 10000
Answer: A
In a certain city, 60% of the registered voters are democrats and the rest are republicans.In a mayoral race, if 70% of the registered voters who are democrats and 20% of the registered voters who are republicans are expected to vote for candidate A,What % of the registered voters are expected to vote for candidate A?
Choose the correct choice from the following choices:  A) a) 50%  B) b) 53%  C) c) 54%  D) d) 55%  E) e) 57%

Solution: Let total voters = 100   so d) 55%= 60, vote for the mayor 60*75%=45 (60*3/4)   R= 40, vote for the mayor 40*20%= (40*1/5)   45+8= 
45+8 = 53
53   53/100*100=55%   d) 55%
Answer: D
In how many minimum number of complete years, the interest on 212.50 P at 3% per annum will be in exact number of rupees?  Choices:
A) 6
B) 8
C) 9
D) 7
E) None of these

Solution: Interest for one year = 212.50 × 3⁄100 × 1 = 51⁄8   Thus in 8 years, the interest is 51.   Answer 8
Answer: B
The annual budget of a certain college is to be shown on a circle graph. If the size of each sector of the graph is to be proportional to the amount of the budget it represents, how many degrees of the circle should be used to represent an item that is 35 percent of the budget? Choose the correct choice from the following options
A) 126 °	B) 15 °	C) 54 °	D) 90 °	E) 150 °

Solution: 100 percent = 360 degrees   35 percent = 360*35/100= 
360*35/100 = 126
126 degrees   126 °nswer is 126 °.
Answer: A
300 first-time customers of a fashion store were surveyed for their shopping experience right after leaving the store. 60% of the customers in the survey had purchased clothes for less than $100. 40% of the customers in the survey reported they were overall satisfied with their purchase. 65% of the customers that had purchased clothes for less than $100 reported they were overall satisfied with their purchase. What percent of the customers surveyed purchased clothes for at least $100 and reported that they were NOT overall satisfied with their purchase?	Choose the correct option
A) 1	B) 25	C) 35	D) 45	E) 75

Solution: Out of 300 - 180 purchased for less than 100$120 for more   Out of 300 - 120 responded as satisfied and 180 responded disatisfied   Out of 180 ( Purchased less than 100$) - 65% = 117 responded as satisfied, So remaining Satisfied are  120 - 117= 
 120 - 117 = 3
3   so 3 is what percentage of 300 - 1%   So the answer should be 1
Answer: A
A car started running at a speed of 29 km/hr and the speed of the car was increased by 2 km/hr at the end of every hour. Find the total distance covered by the car in the first 10 hours of the journey. Choose the correct choice from the following choices
A) 41 km  B) 76 km  C) 25 km  D) 15 km  E) 30 km

Solution: 41 km   41 km   The total distance covered by the car in the first 10 hours = 32 + 34 + 36 + 38 + 40 + 42 + 44 + 46 + 48 + 50 = sum of 10 terms in 41 kmP whose first term is 32 and last term is 50 = 10/2 [32 + 50] = 410 km.
Answer: A
Three bottles contain equal mixtures of spirit and water in the ratio 6 : 1, 5 : 2 and 3 : 1 respectively. If all the solutions are mixed together, the ratio of spirit to water in the final mixture will be Choose the correct choice from the following options:
A) 64 : 65
B) 65 : 64
C) 19 : 65
D) 65 : 19
E) none of these

Solution: Given that all bottles contain equal amount of mixture say V.   So in the first vessel -> water : spirit =1/7 : 6/7   In the second bottle -> 2/7 : 5/7   In the third bottle -> l/4:3/4.   Hence, the final ratio is=((6/7) + (5/7) + (3/4)) / ((1/7) + (2/7) + (1/4))   = 65/19   ANSWER:65 : 19
Answer: D
When a student Joe, weighing 43 kg, joins a group of students whose average weight is 30 kg, the average weight goes up by 1 kg. Subsequently, if two students, excluding Joe, leave the group the average weight comes back to 30 kg. What is the difference between the average weight of the two students who left and the weight of Joe?
Choose the correct option: A) 5.5 kg B) 11 kg C) 30 kg D) 6.5 kg E) 71 kg

Solution: After two persons leave the group the average remains the same. That means the weight of the two persons = 43+30= 
43+30 = 73
73   So, the average the two persons= 36.5   That gives the answer  43-36.5= 
 43-36.5 = 6.5
6.5   Answer 6.5 kg
Answer: D
What is the remainder when 7777* 8888 * 101010 is divided by 33
Pick one
A) 110  B) 220  C) 330  D) 440  E) 550

Solution: 7777/33==> Remainder=22   8888/33==> Remainder=11   101010/33==> Remainder=30   =22*11*30= 
22*11*30 = 7_260
7260/33==> Remainder=220   Answer:220
Answer: B
In a class of 78 students 41 are taking French, 22 are taking German. Of the students taking French or German, 9 are taking both courses. How many students are not enrolled in either course?
Answers.
A) 23 B) 12 C) 24 D) 27 E) 11

Solution: You could solve this by drawing a Venn diagram. A simpler way is to realize that you can subtract the number of students taking both languages from the numbers taking French to find the number taking only French. Likewise find those taking only German. Then we have:Total = only French + only German + both + neither   78 = (41-9) + (22-9) + 9 + neither.   Not enrolled students = 24   Answer: 24
Answer: C
10 books are placed at random in a shelf. The probability that a pair of books will always be together is	Choose the most appropriate option:	A) 1/9	B) 1/7	C) 1/5	D) 1/1	E) 1/2

Solution: 10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2!   Required probability = 1/5   Answer: 1/5
Answer: C
Six points are marked on a straight line and five points are marked on another line which is parallel to the first line. How many straight lines, including the first two, can be formed with these points?	Choose the correct choice from the following answers:	A) 6	B) 73	C) 72	D) 35	E) 32

Solution: We know that, the number of straight lines that can be formed by the 11 points in which 6 points are collinear and no other set of three points, except those that can be selected out of these 6 points are collinear.   Hence, the required number of straight lines   = ¹¹C₂ - ⁶C₂ - ⁵C₂ + 1 + 1   = 55 - 15 - 10 + 2= 
55 - 15 - 10 + 2 = 32
32   Answer:32
Answer: E
If difference between compound interest and simple interest on a sum at 10% P.a. for 2 years is Rs.61 then sum is	Pick:
A) s.6100
B) s.5100
C) s.5800
D) s.6000
E) s.6200

Solution: p(r/100)^2=C.I-S.I   P(10/100)^2=61   6100   s.6100NSWER:s.6100
Answer: A
In 1985 a company sold a brand of shoes to retailers for a fixed price per pair. In 1986 the number of pairs of the shoes that the company sold to retailers decreased by 20 percent, while the price per pair increased by 20 percent. If the company’s revenue from the sale of the shoes in 1986 was $3.0 million, what was the approximate revenue from the sale of the shoes in 1985 ?	Choose the correct choice from the following answers.
A) $2.4 million	B) $2.9 million	C) $3.0 million	D) $3.1 million	E) $3.6 million

Solution: Let the number of pairs of shoes sold in 1985 = N   let price per pair of shoe sold in 1985 = P   In 1986,number of pairs of shoes sold decreased by 20 % = .8N   Price per pair increased by 20% = 1.2P   Company's revenue from sale of shoes in 1986 = 3 million$   => .8N * 1.2 P = 3   =>.96 NP = 3   => NP = 3/.96= 
3/.96 = 3.125
3.125 million $   Answer $3.1 million
Answer: D
Let S be the set of all positive integers that, when divided by 8, have a remainder of 5. What is the 81th number in this set?  Select the correct option.
A) 605 B) 608 C) 613 D) 616 E) 645

Solution: The set S = {5, 13, 21, 29, ..................... }   1st Number = 8 * 0 + 5= 
8 * 0 + 5 = 5
5   2nd Number= 8 * 1 + 5= 
8 * 1 + 5 = 13
13   3rd Number= 8 * 2 + 5= 
8 * 2 + 5 = 21
21   81th Number= 8 * (81-1) + 5= 
8 * (81-1) + 5 = 645
645   Answer= 645
Answer: E
When positive integer N is divided by positive integer J, the remainder is 14. If N/J = 134.07, what is value of J? Pick one.
A) 22 B) 56 C) 78 D) 200 E) 175

Solution: 1) We know that   decimal part of decimal quotient ={remainder/divisor}   So 0.07, the decimal part of the decimal quotient, must equal the remainder, 14, divided by the divisor J.   0.07 = 14/J   0.07*J = 14   J = 14/0.07 = 1400/7= 
1400/7 = 200
200   So J=200, answer = 200.
Answer: D
At what rate percent per annum will the simple interest on a sum of money be 3/5 of the amount in 10 years?  Choose the most appropriate option
A) 6%	B) 7%	C) 9%	D) 3%	E) 1%

Solution: Let sum = x. Then, S.I. = 2x/5, Time   = 10 years.   Rate = (100 * 3x) / (x * 5 * 10)   = 6%   6%nswer: 6%
Answer: A
The speed of a car is 90 km in the first hour and 60 km in the second hour. What is the average speed of the car?	Choices:
A) 228
B) 75
C) 299
D) 267
E) 312

Solution: S = (90 + 60)/2= 
(90 + 60)/2 = 75
75 kmph   Answer: 75
Answer: B
When 0.232323..... is converted into a fraction, then the result is
Choose one
A) 23/99
B) 24/99
C) 25/99
D) 22/99
E) 20/99

Solution: 0.232323... = 0.23   =	23/99   23/99nswer is 23/99.
Answer: A
The function f is defined by subtracting 25 from the square of a number and the function v is defined as the square root of one-half of a number. If v(f(x))=10, then which of the following is a possible value of x? Choose the correct answer:
A) -15 B) -5 C) 0 D) 5 E) 25

Solution: f(x) = x^2-25   v(x) = sqrt(x/2) not sqrt(x)/2, because the question clearly says its square root of (half of the number).   v(f(x)) = 10   v(x^2-25) =10   sqrt((x^2-25)/2) = 10   => (x^2-25)/2 = 100   =>x^2 = 225   => x = 15 or -15   -15nswer is -15.
Answer: A
John took a bus from home to market, that travels at 50 kmph. While walking back at 5 kmph,
halfway through, he suddenly realized he was getting late and he cycled back the remaining distance in 35 kmph. Find the average speed.	Choose the correct choice from the following.
A) 8.5 kmph B) 16.0 kmph C) 22.5 kmph D) 18.6 kmph E) none of these

Solution: Let the distance be 2x(one way)   Time taken by bus = 2x/50, by walking =x/5, by cycling = x/35 hours   :. Average speed = Total 18.6 kmphistance/Total time   = 5x / x/25 + x/5 + x/35   = 5 *60 / 2.4+12+1.7   = 18.6   ANSWER:18.6 kmph
Answer: D
Priya covers journey from kavali to nellore by car at average speed of 80 Km/hr. She returns back by scooty with an average speed of 40 Km/hr. Find her average speed during the whole journey? Choose the correct choice from the following choices.
A) 50Km/hr
B) 53.33Km/hr
C) 60Km/hr
D) 66Km/hr
E) 72km/hr

Solution: Explanation:   Average speed = 2 xy/x+y   = 2*80*40/120   = 53.33 Km/hr   Answer: Option 53.33Km/hr
Answer: B
There are two sets A and B. The range of set A is 7, and the range of set B is 13. If the two sets are combined and get a new set W, which cannot be the range of the set W?	Choose the correct choice:
A) 8
B) B.11
C) C.14
D) D.17
E) E.21

Solution: Let Set A has 1,8 as elements   B has 1,14 as elements.. So Range for Combined set W becomes  14-1= 
 14-1 = 13
13   For range to be 14,   A= 1,8   B= 2,15 (Range=14)   For range to be 17   A=1,8   B= 5,18   For range to be 21:   A=1,8   B= 9 ,22   So we are left with A and B.   Now consider A has elements A= -1,-8 and Thus Range =-1-(-8)= 
-1-(-8) = 7
7   So for Range of combined set to be 11, B needs to have largest elementxso that x- (-8)=11 or x=3...But if x=3, the largest element in Combined Set then smallest element in the combined set will be 3-y=13 or y=-10....And the range of combined set 3-(-10)=13...   Consider Option A   A=-1,-8   B= y,x where y and x are smallest and largest element in Set B   Elements of Combined Set: -8,-1,y and x   Now x-(-8)= 
-(-8) = 8
8 or x=0, then x-y=13 or y=-13...   Range of Combined Set: 0-(-13)= 13...   I don't see how range can be 8 or 11...Can you please post the source and explanation for the OA in spoiler...=B.11
Answer: B
How many of the following numbers are divisible by 3 but not by 9 ?
2133, 2343, 3474, 4131, 5286, 5340, 6336, 7347, 8115, 9276  Select
A) 5
B) 6
C) 7
D) None of these
E) Cannot be determined

Solution: Explanation: Marking (/) those which are are divisible by 3 by not by 9 and the others by (X), by taking the sum of digits, we get:s   2133 9 (X)   2343 12 (/)   3474 18 (X)   4131 9 (X)   5286 21 (/)   5340 12 (/)   6336 18 (X)   7347 21 (/)   8115 15 (/)   9276 24 (/)   Required number of numbers = 6.   Answer: Option 6
Answer: B
A can do a job in 10 days and B can do it in 30 days. A and B working together will finish twice the amount of work in ------- days?	Choose the correct choice from the following:
A) 21 ½ days  B) 22 ½ days  C) 23 ½ days  D) 15 days  E) None of these

Solution: Explanation:   1/10 + 1/30 = 4/30 = 2/15   15/2 = 15/2 *2= 
15/2 *2 = 15
15 days   Answer: 15 days
Answer: D
What is the square root of 6,561?  Choose the correct option.
A) 18
B) 9
C) 45
D) 62
E) 81

Solution: A square root of a number is a number times itself equals the original number.   Ex) The square root of 81 is 9 because 9 times itself(9) equals the original number(81).   81*81=6,561   6561 divided by x = 81   x=81   (81)81
Answer: E
In a sequence of 12 numbers, each term, except for the first one, is 12^13 less than the previous term. If the greatest term in the sequence is 12^14, what is the smallest term in the sequence?
Thus, A12 = A1+12-1d
Where d is the difference between each pairs of consecutive terms. Since each term is 1211 less than the previous term, d=-1211Click individual answer choices for specific explanations.
From what I undersltand the formula for an arithmetic sequence represents
some-number-in-the-sequence= first-number-in-sequence +the-place-of-that-number - 1x the-difference-of-each-#-in-the-sequence	Pick one.
A) −12^11	B) 0	C) 12^11	D) 11·12^11	E) 12^13

Solution: there are total 12 terms. andgreatestterm is 12^14. Each term is 12^13 less than previous one. What does this signify? This shows it is an AP - a decreasing one. (NoticeEach term is 12^11 less than previous one')   Therefore, 12^14 is the first term of the AP and -12^13 is the difference between successive terms, the smallest term should be the last one.   Last term = First term + (n-1)*d   therefore, Last term = 12^14 + 11*(-12^13)   => Last term = 12^14 - 11*12^13   => Last term = 12^13 (12-11) = 12^13   Which is the smallest term.   Hence Ans 12^13 it is.
Answer: E
Five years ago the average of the ages of A and B was 40 years and now the average of the ages of B and C is 48 years. What will be the age of the B ten years hence?
Select the correct option.
A) 66  B) 77  C) 66  D) 96  E) 51

Solution: Let the present ages of A, B and C be a, b and c respectively.   Given, [(a - 5) + (b - 5)] / 2 = 40 => a + b = 90 --- (1)   (b + c)/2 = 48 => b + c = 96 --- (2)   From (1) and (2), we cannot find b.   Answer: 96
Answer: D