MU-NLPC/Calc-aqua_rat huggingface dataset:
Which of the following cannot be true if the sum of k consecutive integers is 0?
I. The product of the k integers is positive
II. The smallest of the k integers is zero
III. The largest of the k integers is negative
Choose the correct choice from the following:
A) I only
B) II only
C) III only
D) I and III
E) I, II and III

Solution: For the sum of k consecutive integers to be 0 we must have one of the following cases: {0}, {-1, 0, 1}, {-2, -1, 0, 1, 2}, ..., {..., -3, -2, -1, 0, 1, 2, 3, ...}.   I. The product of the k integers is positive. As you can see the product of the integers in either of these sets is always 0, thus I cannot be true.   II. The smallest of the k integers is zero. If the set is {0}, then it's possible.   III. The largest of the k integers is negative. As you can see the largest of the integers is always more than or equal to zero, thus III cannot be true.   Answer: I and III.
Answer: D
The population of a town increases by 10% per annum for two years then decreases by 10% per annum for the next two years, if the population of the town four year ago was 10000, what would it be today?
Pick one.
A) 9500	B) 9801	C) 10100	D) 9000	E) None of these

Solution: Explanation :   Increase of population = (100+10)= 
(100+10) = 110
110%= 1.1   Reduction of population = (100 -10)= 
(100 -10) = 90
90%= 0.9   Total effect = 1.1 X 1.1 X 0.9 X 0.9 = 0.9801,   Population = 10000 X 0.9801 = 9801   Answer : 9801
Answer: B
Which of the following options is the correct value of z if the greatest common divisor of (z-1)!,(z+2)!, and (z+4)! is 120.  Select the correct option.
A) 9  B) 5  C) 6  D) 7  E) 8

Solution: GCD of (z-1)!,(z+2)!, and (z+4)! is 120. Find z.   Best way to find n is substitute each of the answer and find out the correct one.   Only option C gave the correct answer.   Option C: 6 and find GCD or 5!, 8! and 10!. 5! itself is 120 and 5! which is contained in the other two factorials. This satisfies the condition, hence answer is 6.   Answer is 6.
Answer: C
The speed of a bus including stoppages is 35 kmph and excluding stoppages is 70 kmph. Of how many minutes does the train stop per hour?	Choose the correct choice:
A) 7
B) 15
C) 25
D) 30
E) 35

Solution: Explanation:   T = 35/70 * 60= 
35/70 * 60 = 30
30   Answer: Option 30
Answer: D
ASvennumber is defined as a five-digit number which goes according to the following rules: the leftmost digit is even, any digit to the right of an even digit must be an odd digit, and any digit to the right of an odd digit can only be one of the digits 1 or 9. How many different 5-digit numbers areSvennumbers?
Select
A) 20  B) 80  C) 160  D) 220  E) 250

Solution: ASvennumber is defined as a five-digit number which goes according to the following rules: the leftmost digit is even, any digit to the right of an even digit must be an odd digit, and any digit to the right of an odd digit can only be one of the digits 1 or 7. How many different 5-digit numbers areSvennumbers?   4/9*5/10*2/10*2/10*2/10=160/9000   E. 250
Answer: E
A number when divided by 45, gives 432 as quotient and 0 as remainder. What will be the remainder when dividing the same number by 21	Choose the correct choice from the following choices: A) A)15 B) B)3 C) C)4 D) D)6 E) E)7

Solution: Explanation:   P ÷ 45 = 432   => P = 432 * 45= 
432 * 45 = 19_440
19440   P / 31= 19440 / 21 = 925, remainder = 15   15nswer: Option 15
Answer: A
A certain no. whendivided by 35leaves a remainder 25, what is the remainder if the same no.be dividedby 15? Choose the correct choice.
A) 2 B) 4 C) 7 D) 8 E) 9

Solution: Explanation:   35 + 25= 
35 + 25 = 60
60/15= 
60/15 = 4
4 (Remainder)   4
Answer: B
How many S ways are there of placing 6 marbles in 4 bowls, if any number of them can be placed in each bowl?  Choose the most appropriate option:
A) 6C4 B) 6P4 C) 4^6 D) 6^4 E) 6!

Solution: Each marble has 4 options, so there are total of S= 4*4*4*4*4*4=4^6 ways.   Answer: C.   The total number of ways of dividing n identical items among r persons, each one of whom, can receive 0,1,2 or more items is (n+r -1)4^6(r-1).
Answer: C
A and B can do a piece of work in 8 days. With the help of C they finish the work in 5 days. C alone can do that piece of work in?  Options:
A) 30 DAYS	B) 35 DAYS	C) 40 DAYS	D) 8 DAYS	E) 3 DAYS

Solution: 40 DAYS = 1/5 – 1/8= 1/40 => 40 days   Answer:40 DAYS
Answer: C
A starts a business with a capital of Rs. 9,000. B joins in the business with Rs.18,000 after some time. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1? Choose the correct answer
A) 2 months  B) 6 months  C) 7 months  D) 8 months  E) None of these

Solution: Explanation :   Let B joins for x months. Then   A:B = 9000*12 : x* 18000 = 3 : 1   => 9*12 : 18x= 3 : 1   => 9*12/ 18x = 3/1= 
3/1 = 3
3=> 9*4 /18x = 1   => 2/x = 1   => x = 2. 2 monthsnswer : Option 2 months
Answer: A
The sum of five consecutive odd numbers of set p is 435. What is the sum of five consecutive numbers of another set q. Whose largest number is 45 more than the largest number of set p?
Pick one:	A) 530	B) six hundred seventy	C) 730	D) 770	E) None of these

Solution: Let the five consecutive odd numbers of set p be 2n - 3, 2n - 1, 2n + 1, 2n + 3, 2n + 5.   Sum of these five numbers   = 2n - 3 + 2n - 1 + 2n + 1 + 2n + 3 + 2n + 5   = 10n + 5 = 435 => n = 43   Largest number of set p = 2(43) + 5 = 91   The largest number of set q = 91 + 45= 
91 + 45 = 136
136=> The five numbers of set q are 132, 133, 134, 135, 136.   Sum of above numbers = 132 + 133 + 134 + 135 + 136= 
132 + 133 + 134 + 135 + 136 = 670
670.   ANSWER:six hundred seventy
Answer: B
Length of a rectangular plot is 20 mtr more than its breadth. If the cost of fencin gthe plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr?  Choices.
A) 50 m	B) 60 m	C) 65 m	D) 70 m	E) 75 m

Solution: Let breadth = x metres.   Then, length = (x + 20) metres.   Perimeter = 5300 m = 200 m.   26.50   2[(x + 20) + x] = 200   2x + 20 = 100   2x = 80   x = 40.   Hence, length = x + 20 = 60 m   60 m
Answer: B
Find the one which does not belong to that group ?  Answers
A) 23776  B) 28287  C) 84284  D) 28278  E) 83484

Solution: Explanation:   42624, 37573, 74347 and 93339 are palindromes but not 84284.   Answer: 84284
Answer: C
In a certain pond, 50 fish were caught, tagged, and returned to the pond. A few days later, 50 fish were caught again, of which 8 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what is the approximate number of fish in the pond?
Answers.
A) 400 B) 625 C) 1,250 D) 2,500 E) 312

Solution: total fish = x   percentage of second catch = (8/50)*100= 
(8/50)*100 = 16
16%   so, x * 16%= 50   x = 312 ans.312
Answer: E
What is the sum of all remainders obtained when the first 100 natural numbers are divided by 8?	Choose the correct option
A) 397
B) 401
C) 403
D) 405
E) 399

Solution: A positive integer can give only the following 9 remainders when divided by 9: 1, 2, 3, 4, 5, 6, 7, 8, and 0.   1 divided by 9 gives the remainder of 1;   2 divided by 9 gives the remainder of 2;   ...   8 divided by 9 gives the remainder of 8;   9 divided by 9 gives the remainder of 0.   We'll have 11 such blocks, since  99/9= 
 99/9 = 11
11. The last will be:   91 divided by 9 gives the remainder of 1;   92 divided by 9 gives the remainder of 2;   ...   98 divided by 9 gives the remainder of 8;   99 divided by 9 gives the remainder of 0.   The last number, 100, gives the remainder of 1 when divided by 9, thus the sum of all remainders will be:   11(1+2+3+4+5+6+7+8+0)+1=401.   Answer: 401.
Answer: B
A thief goes away with a SANTRO car at a speed of 35 kmph. The theft has been discovered after half an hour and the owner sets off in a bike at 100 kmph when will the owner over take the thief from the start?
Choose the correct answer.
A) 12/3 hours B) 2/7 hours C) 7/13 hours D) 1/3 hours E) 2/5 hours

Solution: -----------35--------------------|   100 35   D = 35   RS = 100 â€“ 35 = 65   T = 35/65 = 7/13 hours   ANSWER:7/13 hours
Answer: C
Three numbers are in the ratio 3:5:7. The largest number value is 42. Find difference between Smallest & largest number is?	Choose the most appropriate option
A) 20  B) 22  C) 24  D) 26  E) 28

Solution: == 3:5:7   Total parts = 15   = The largest number value is 42   = The largest number is = 7   = Then 7 parts -----> 42 ( 7 * 6 = 42 )   = smallest number = 3 & Largest number = 7   = Difference between smallest number & largest number is = 7 - 3= 
7 - 3 = 4
4= Then 4 parts -----> 24 (4 * 6 = 24)   24
Answer: C
If X^y denotes x raised to the power y, then find last two digit of
1507^3381+1457^3757  Answers.
A) 64	B) 65	C) 66	D) 75	E) 84

Solution: 1507^3381+1457^3757   => 07^3381+57^3757   49^1690×7 + 49^1878 × 57   => (100-51)^1690 ×7 + ( 100-51)^1878×57   => 51^1690 × 7 + 51^1878×57   => 07+57=64   64NSWER:64
Answer: A
A car dealer purchased new cars at 80% of their list price and sold them for 90% of their list price. What is his percent gain? Choices: A) 11 B) 12.5 C) 15 D) 16 E) 20

Solution: Cost = 80% of List Price = .8*LSale = 90% of List Price = .9*LGain Ratio = (Sale - Cost) / Cost = (.9*L - .8*L) / .8*L = .1*L / .8*L = .125Gain Percent = 100 * Gain Ratio = 100 * .125= 
100 * .125 = 12.5
12.5%= Answer 12.5
Answer: B
A goods train leaves a station at a certain time and at a fixed speed. After ^hours, an express train leaves the same station and moves in the same direction at a uniform speed of 90 kmph. This train catches up the goods train in 4 hours. Find the speed of the goods train.	Select the correct option.
A) 24 kmph
B) 36 kmph
C) 56 kmph
D) 32 kmph
E) 46 kmph

Solution: Let the speed of the goods train be x kmph.   Distance covered by goods train in 10 hours= Distance covered by express train in 4 hours   10x = 4 x 90 or x =36.   So, speed of goods train = 36kmph.   Ans: 36 kmph
Answer: B
Out of 10 persons working on a project, 6 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them?
Choices:	A) 29/7	B) 29/3	C) 29/1	D) 29/30	E) 29/20

Solution: P(at least one graduate) = 1 - P(no graduates)   = 1 - 4C₃/¹⁰C₃ = 1 - (4*3*2)/(10 * 9 * 8)   = 29/30   Answer: 29/30
Answer: D
How much time will it take for an amount of 1000 to yield 100 as interest at 5% per annum of simple interest?
Choose the correct choice from the following options
A) 3 years	B) 4 years	C) 2 years	D) 5 years	E) 7 years

Solution: Time = (100 x 100)/(1000 x 5) years = 2 years.   answer 2 years
Answer: C
In the quiet town of "Nothintodo" there are 600 inhabitants, 400 are unemployed and 300 are somnambulists. If half of the somnambulists are unemployed, how many are employed and are not somnambulists? Pick one
A) 50. B) 100 C) 150 D) 200 E) 300

Solution: 400 are unemployed and 300 are somnambulists. So 200 are employed and 300 are Non-somnambulists.   Half of the somnambulists are unemployed = 150. So employed somnambulists = 300 -150= 
300 -150 = 150
150.   Employed and not somnambulists= 200 - 150= 
200 - 150 = 50
50.   Hence the answer is 50..
Answer: A
There are two positive numbers in the ratio 2:7. If the larger number exceeds the smaller by 30, then find the larger number?  Pick one:
A) 42
B) 38
C) 44
D) 36
E) 46

Solution: Let the two positive numbers be 2x and 7x respectively.   7x - 2x = 30   5x = 30 => x = 6   => Larger number = 7x = 42.   42nswer: 42
Answer: A
Four of the five parts numbered (a), (b), (c), (d) and (e) are exactly equal. Which of the parts is not equal to the other four? The number of that part is the answer. Choose the correct choice
A) (a + b)(a – 2b)
B) a2 – b(a + 2b)
C) a2 + b2 – ab – 3b2
D) (a + b)(a – b) + ab
E) (a – b)2 + b(a – 3b)

Solution: Others equal a2 – ab – 2b2 whereas (d) equals a2 + ab – b2 .   Answer (a + b)(a – b) + ab
Answer: D
In six successive games, a baseball team scored 2 runs once, 8 runs twice, and 12 runs three times.
What was the average (arithmetic mean) number of runs the team scored per game over the six-game period?  Choose the correct choice from the following answers.
A) 9	B) 7	C) 6	D) 5	E) 4

Solution: 2 runs once (one game)   8 runs twice (two game)   12 runs three times (three games)   SO we have (2*1 + 8*2 + 12*3)/6 = 54/6= 
54/6 = 9
9.   9NS: 9.
Answer: A
If xy ≠ 0 and x^2y^2 − xy = 20, which of the following could be y in terms of x?
I. 5/x
II. -4/x
III. 3/x	Choose the correct choice from the following.
A) I only B) II only C) I and II only D) I and III E) II and III

Solution: (x^2)(y^2) – xy - 20 = 0   (xy – 5)(xy + 4) = 0   xy – 5 = 0 or xy + 4 = 0   xy = 5 or xy = -4   Since we need y in terms of x, we can isolate y in both of our equations.   y = 5/x or y = -4/x   Answer: I and II only
Answer: C
A can run 2.7 km distance in 1 min 20 seconds, while B can run this distance in 1 min 30 sec. By how much distance can A beat B?	Choices:	A) 90 m	B) 30 m	C) 120 m	D) 300 m	E) 190 m

Solution: A takes time 1.20 minutes=80sec   B takes time 1.30 minutes=90sec   diffrence= 90-80= 
90-80 = 10
10sec   now we are to find distance covered in 10 sec by B   90sec=30m   1sec=30m   10sec=10x30=300m   ANSWER:300 m
Answer: D
3x^2 - 13x + 12 =	Select the correct option
A) (3x-4)(x-2)
B) (3x-4)(x+2)
C) (3x-4)(x-3)
D) (3x-2)(x+4)
E) none of above

Solution: 3x^2 - 13x + 12   = 3x^2 - 9x - 4x + 12   = 3x (x - 3) - 4 (x-3)   = (3x-4) (x-3)   Option (3x-4)(x-3)
Answer: C
The average temperature of the town in the first four days of a month was 58 degrees. The average for the second, third, fourth and fifth days was 60 degrees. If the temperatures of the first and fifth days were in the ratio 7 : 8, then what is the temperature on the fifth day ?
Answers:	A) 62 degrees	B) 64 degrees	C) 65 degrees	D) 66 degrees	E) 67 degrees

Solution: Explanation:   Sum of temperatures on 1st, 2nd, 3rd and 4th days = (58 * 4)= 
(58 * 4) = 232
232 degrees ... (1)   Sum of temperatures on 2nd, 3rd, 4th and 5th days - (60 * 4)= 240 degrees ....(2)   Subtracting (1) From (2), we get :   Temp, on 5th day - Temp on 1st day = 8 degrees.   Let the temperatures on 1st and 5th days be 7x and 8x degrees respectively.   Then, 8x - 7x = 8 or x = 8. Answer: 64 degrees   Temperature on the 5th day = 8x = 64 degrees.
Answer: B
A company has a job to prepare certain number of cans and there are three machines A, B and C for this job. A can complete the job in 10 days, B can complete the job in 2 days and C can complete the job in 5 days. How many days the company will it take to complete the job if all the machines are used simultaneously?  Answers: A) 4/3 days B) 5/4 days C) 4/5 days D) 20days E) 14 days

Solution: Let the total number of cans to be prepared be 10.   The number of cans prepared by A in 1 day = 1.   The number of cans prepared by B in 1 day = 5.   The number of cans prepared by C in 1 day = 2.   Thus, the total number of cans that can be prepared by all the machines working simultaneously in a single day = 8.   Therefore, the number of days taken to complete the whole work = 10/8 = 5/4 days.   ANSWER:5/4 days
Answer: B
Krishan and Nandan jointly started a business. Krishan invested three times as Nandan did and invested his money for double time as compared to Nandan. Nandan earned Rs. 4000. If the gain is proportional to the money invested and the time for which the money is invested then the total gain was?
Choose the most appropriate option:
A) 28,008  B) 28,006  C) 28,005  D) 28,000  E) 28,001

Solution: 3:1   2:1   ------   6:1   1 ----- 4000   7 ----- ? => Rs.28,000.Answer:28,000
Answer: D
What should come in place of question mark (?)?
138.009 + 341.981 – 146.305 = 123.6 + ?	Select.
A) 210.85  B) 120.85  C) 220.085  D) 120.085  E) None of these

Solution: ? = 138.009 + 341.981 – 146.305 – 123.60   ∴ ? = 210.085   Answer None of these
Answer: E
Find the smallest number of five digits exactly divisible by 16,24,36 and 54.	Choose the correct choice:
A) 10368	B) 10638	C) 10836	D) 10863	E) None of them

Solution: Smallest number of five digits is 10000.   Required number must be divisible by L.C.M. of 16,24,36,54 i.e 432,   On dividing 10000 by 432,we get 64 as remainder.   Therefore, Required number = 10000 +( 432 – 64 ) = 10368.   10368nswer is 10368.
Answer: A
A train running at the speed of 60 km/hr crosses a pole in 12 seconds. What is the length of the train?
Select:
A) 286
B) 278
C) 255
D) 150
E) 200

Solution: Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train   = (Speed x Time) = (50/3 * 12)= 
(50/3 * 12) = 200
200 m.   Answer:200
Answer: E
The points A(0, 0), B(0, 4a - 5) and C(2a + 1, 2a +4) form a triangle. If angle ABC = 90, what is the area of triangle ABC? Choose the correct option.
A) 80	B) 75	C) 70	D) 60	E) 65

Solution: 1/2bh=1/2(2a+1)(2a+4)   Now 4a-5=2a+4   2a=9   Therefore,   A(0,0); B(0,13); C(10,13)   1/2*10*13= 
1/2*10*13 = 65
65   Answer: 65
Answer: E
Raj invested an amount of Rs.17400 for two years. Find the rate of compound interest that will fetch him an amount of Rs.1783.50 at the end of two years?	Choose the correct choice from the following choices
A) 1/208 B) 1/228 C) 1/229 D) 1/20 E) 1/213

Solution: Let the rate of interest be R% p.a.   17400[1 + R/100]2 = 17400 + 1783.50   [1 + R/100]2 = (17400 + 1783.50)/17400   = 1 + 1025/10000 = 1 + 41/400   = 441/400 = [21/20]2   [1 + R/100] = 21/20   R/100 = 1/20   Answer:1/20
Answer: D
A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 610 m long?
Choose the correct choice from the following choices
A) 22  B) 89  C) 85  D) 278  E) 291

Solution: Speed = 240/24= 
240/24 = 10
10 m/sec.   Required time= (240 + 610)/10= 
(240 + 610)/10 = 85
85 sec.   Answer: 85
Answer: C
When 19 is divided by positive integer j, the remainder is 4. For how many values of j is this be true?  Choose the most appropriate option:
A) 1
B) 3
C) 5
D) 7
E) 9

Solution: When 19 is divided by j, the remainder is 4 i.e. 5 kiwis left over after grouping, so j must be greater than 5.   It also means that 15 is completely divisible by j.   Factors of 15 are 1, 3, 5, and 15.   Out of these, j can be 15.   1nswer is (1).
Answer: A
If n is the product of the integers from 1 to 9, inclusive, how many different prime factors greater than 1 does n have?
Select
A) Four  B) Five  C) Six  D) Seven  E) Eight

Solution: n = 1*2*3*4*5*6*7*8*9   The prime factors of n are 2, 3, 5, and 7.   There are 4 prime factors.   The answer is Four.
Answer: A
In 1940, a correspondent proposed the following question:
A man's age at death was one twenty-ninth of the year of his birth. How old was he in 1900? Choose one:  A) 14  B) 24  C) 34  D) 44  E) 54

Solution: He was 44 years old.   From the question you know the man died between 1900 and 1940. We also know his age at death (x) is one twenty-ninth of the year of his birth (29x). If you add his age at death to the year he was born you get the year he died (30x). Only one year between 1900 and 1940 is divisible by 30, 1920 (the year he died). The year he was born can now be found:  1920 * (29/30)= 
 1920 * (29/30) = 1_856
1856. So in 1900 he was   (1900 - 1856)= 
  (1900 - 1856) = 44
44 years old.
Answer: D
Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 34 kmph. Of how many minutes does the train stop per hour?
Choose the correct choice from the following answers
A) 73  B) 15  C) 12  D) 83  E) 28

Solution: Explanation:   T = 11/45 * 60 = 15   Answer: Option 15
Answer: B
The simple interest on a sum of money will be Rs.500 after 10 years. If the principal is trebled after 5 years what will be the total interest at the end of the tenth year?
Select the correct option
A) 700	B) 800	C) 900	D) 1000	E) 1100

Solution: P --- 10 ---- 500   P --- 5 ----- 250   3P --- 5 -----750   ------   => 1000   ANSWER:1000
Answer: D
By selling 50 meters of cloth. I gain the selling price of 15 meters. Find the gain percent?  Choose the correct choice from the following answers.
A) 72 6/7%	B) 82 6/7%	C) 22 6/7%	D) 42 6/7%	E) 82 2/7%

Solution: Explanation:   SP = CP + g   50 SP = 50 CP + 15 SP   35 SP = 50 CP   35 --- 15 CP gain   100 --- ? => 42 6/7%   Answer: 42 6/7%
Answer: D
A cyclist covers a distance of 750 m in 2 min 30 sec. What is the speed in km/hr of the cyclist?  Choose the correct choice from the following options:
A) 28 B) 18 C) 20 D) 22 E) 24

Solution: Speed = { 750 } m/sec =5 m/sec = { 5 * 18 } km/hr =18km/hr   Option 18
Answer: B
Calculate the percentage profit or loss if a trader bought the apples at 5 per rupee and sells 4 apples per rupee. Choose one
A) 11 %	B) 34 %	C) 25 %	D) 15 %	E) 35 %

Solution: Let he total number of oranges bought by the shopkeeper be 12.   If he buys 5 a rupee, his 25 %P = 4   He selling at 4 a rupee, his SP = 5   Profit = SP - 25 %P = 5 - 4= 
5 - 4 = 1
1   Profit Percent= 1/4 * 100= 
1/4 * 100 = 25
25 %   Answer: 25 %
Answer: C
In a class there are 20 boys and 23 girls. In how many ways can a boy and a girl be selected? Answers:
A) 508
B) 460
C) 800
D) 570
E) 503

Solution: We can select one boy from 20 boys in 20 ways.   We select one girl from 23 girls in 23 ways   We select a boy and girl in 20 * 23 ways i.e., = 460 ways.   Answer:460
Answer: B
A man bought 40 shares of Rs. 80 at 5 discount, the rate of dividend being 12 1/2%The rate of interest obtained is
Choose the correct option.
A) 13.33%	B) 15.5%	C) 14%	D) 14.25%	E) 14.95%

Solution: Explanation :   Face Value of a share = Rs.80   He bought each share at Rs.80 - Rs.5 = Rs.75   Number of shares = 40   Dividend = 12 1/2%=25/2%   Dividend per share = 80×25/2/100=Rs.10   Total dividend = (40 × 10)   ie, He got a dividend of (40 × 10) for an investment of Rs.(40 × 75)   Interest obtained = 40×10×100/40×75=13.33%   13.33%nswer : Option 13.33%
Answer: A
A rectangular lawn of dimensions 100 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m?
Choose the correct choice from the following choices:
A) s.3988	B) s.3900	C) s.4500	D) s.3922	E) s.3928

Solution: Area = (l + b – d) d   (100 + 60 – 10)10 => 1500 m2   1500 * 3   = Rs.4500   Answer:s.4500
Answer: C
There are 8 men and 10 women and you need to form a committee of 5 men and 6 women. In how many ways can the committee be formed?	Choose the correct choice: A) 11660 B) 11700 C) 11760 D) 11800 E) 11850

Solution: Explanation:   We need to select 5 men from 8 men and 6 women from 10 women   Number of ways to do this   = 8117605 × 10117606   = 8117603 × 10117604 [∵ n11760r = n11760(n-r)]   =   (   8   ×   7   ×   6   3   ×   2   ×   1   )   (   10   ×   9   ×   8   ×   7   4   ×   3   ×   2   ×   1   )   =   56   ×   210   =11760   Option 11760
Answer: C
A number is doubled and 9 is added. If the resultant is trebled, it becomes 63. What is that number?	Choose the correct answer:
A) 3.5	B) 6	C) 8	D) 7	E) 4

Solution: Let the number be x. Then,   3(2x + 9) = 63   2x = 12 => x = 6   ANSWER:6
Answer: B
Line m lies in the xy-plane. The y-intercept of line m is -2, and line m passes through the midpoint of the line segment whose endpoints are (2, 8) and (6, -4). What is the slope of line m?  Choose the correct option
A) -3
B) -1
C) -1/3
D) 0
E) 1

Solution: The midpoint of (2,8) and (6,-4) is (4,2).   The slope of a line through (0,-2) and (4,2) is (2-(-2))/(4-0) = 4/4= 
4/4 = 1
1   The answer is 1.
Answer: E
A palindrome is a number that reads the same forward and backward, such as 242. How many even eleven-digit numbers are palindromes? Choose the correct choice
A) 40  B) 400  C) 500  D) 5,000  E) 400,000

Solution: if the palindrome must be even, it must begin and end in 2,4 6 and 8 ( 4 ways) e.g 22122,44144.   The middle number in the eleven-digit could be 0-9 ( 10 ways), e.g 22522, 22822   The 2nd and fourth numbers , 3rd and 5th, 4th and 6th, 5th and 7th must also be same i.e 0-9( 10 ways)   we thus have, 4 *10*10*10*10*10* = 400000. 400,000
Answer: E
What will come in place of the x in the following Number series? 15, 60, X, 960, 3840  Choose the correct choice from the following answers
A) 280
B) 960
C) 820
D) 800
E) 980

Solution: (960)   15 x 4 = 60, 60 x 4 = 240, 240 x 4 = 960, 960 x 4 = 3840.
Answer: B