MU-NLPC/Calc-aqua_rat huggingface dataset:
A 25 cm wide path is to be made around a circular garden having a diameter of 4 meters. Approximate area of the path is square meters is Choose the correct choice from the following answers
A) 3.34  B) 3.36  C) 3.76  D) 3.88  E) 3.22

Solution: Explanation:   3.34rea of the path = 3.34rea of the outer circle - 3.34rea of the inner circle = ∏{4/2 + 25/100}2 - ∏[4/2]2   = ∏[2.252 - 22] = ∏(0.25)(4.25) { (a2 - b2 = (a - b)(a + b) }   = (3.14)(1/4)(17/4) = 53.38/16 = 3.34 sq m   3.34nswer: Option 3.34
Answer: A
On a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water. On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water. On both days, all the orangeade that was made was sold. If the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $0.60 per glass on the first day, what was the price W per glass on the second day?  Choose the most appropriate option
A) $015 B) $0.20 C) $0.30 D) $0.40 E) $0.45

Solution: On the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade;   On the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade;   So, the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3. Naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3.   We are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day.   Say the price of the glass of the orangeade on the second day was $x then 2*0.6=3*x --> x=$0.4.   Answer: $0.40.
Answer: D
If the length and breadth of a rectangular room are each increased by 1 m, then the area of floor is increased by 21 sq. m. If the length is creased by 1 m and breadth is decreased by 1m, then the area is decreased by 5 sq. m. The perimeter of the floor is: Pick:
A) 27
B) 35
C) 40
D) 49
E) 38

Solution: Let length = x meters and breadth = y meters.   Then,   (x + 1) (y + 1) - xy = 21   x + y = 20 Ã¢â‚¬Â¦Ã¢â‚¬Â¦Ã¢â‚¬Â¦Ã¢â‚¬Â¦Ã¢â‚¬Â¦Ã¢â‚¬Â¦1   And, xy - [(x + 1) (y - 1)] = 5   x - y = 6 Ã¢â‚¬Â¦Ã¢â‚¬Â¦Ã¢â‚¬Â¦Ã¢â‚¬Â¦Ã¢â‚¬Â¦Ã¢â‚¬Â¦..2   Solving (i) and (ii), we get : x = 13 and y = 7   So, length = 13 m and breadth = 7 m.   Perimeter = [2 (13 + 7)] m = 40 m.   answer : 40
Answer: C
A dealer purchased an article at 3/4 of its list price and sold 50% more than the list price. Find his gain percent?
Answers.
A) 108%	B) 120%	C) 160%	D) 101%	E) 100%

Solution: MP = 100   CP = 75   SP = 150   ------   75 ---- 75   100 ---- ? =>   100%   Answer: 100%
Answer: E
A 6 litre sol is 35% alcohol .How many litres of pure alcohol must be added to produce a sol that is 50% alcohol ? Select the correct option
A) A.0.6
B) B.1
C) C.2.1
D) D.1.8
E) E.5.4

Solution: 35% of 6 = 2.1   50% of 6 = 3   shortage is 0.9   so we need to have 0.9/50% to get 50% alcohol content.   = 1.8 D.1.8
Answer: D
The sale price of an article including the sales tax is Rs. 616. The rate of sales tax is 10%. If the shopkeeper has made a profit of 12%, then the cost price of the article is:
Choose the correct choice:
A) 500
B) 334
C) 555
D) 664
E) 5598

Solution: 110% of S.P. = 616   S.P. = (616 * 100)/110 = Rs. 560   C.P = (110 * 560)/112 = Rs. 500   500nswer: Option 500
Answer: A
How many squares are there on a chess board ???  Choices:  A) 208  B) 204  C) 201  D) 205  E) 202

Solution: 204   204   Total 204 squares is there on chess board, including all sizes.
Answer: B
James took a 3-hour bike ride. In the second hour he travlled 24 miles, which was 20 percent farther than he traveled the first hour. If he traveled 25 percent farther in the third hour than he did in the second hour, how many miles did jose travel during the entire ride? Select the correct option.
A) 74.0	B) 54.9	C) 55.5	D) 57.0	E) 63.0

Solution: Let the distance travelled in the first hour be x. Thus, 1.2x = 24 , x = 20. Now, the distance travelled in the 3rd hour = 24+1/4âˆ—24= 30.   = 24+20+30= 
24+20+30 = 74
74   74.0NSWER:74.0
Answer: A
A sum of money place at compound interest doubles itself in 10 years. In how many years will it amount to eight times itself?	Choose the correct choice from the following options:
A) 20
B) 30
C) 40
D) 50
E) 60

Solution: 100 ---- 200 ---- 10   400 ---- 10   800 ---- 10   ------   12 years   Answer: 30
Answer: B
In an election between two candidates, the first candidate got 80% of the votes and the second candidate got 240 votes. What was the total number of votes?	Select:
A) 600
B) 900
C) 1200
D) 1500
E) 1800

Solution: Let V be the total number of votes.   0.2V = 240   V = 1200   The answer is 1200.
Answer: C
A can do a piece of work in 10 days and B can do it in 15 days and C can do it 20 days. They started the work together and A leaves after 2 days and B leaves after 4 days from the beginning. How long will work lost?
Choose the most appropriate option:
A) 10 2/5 B) 10 2/0 C) 10 2/3 D) 10 2/1 E) 10 2/3

Solution: 2/10 + 4/15 + x/20 = 1   x = 32/3 = 10 2/3 Answer: 10 2/3
Answer: C
If q is the smallest positive integer that is not prime and not a factor of 50!, what is the sum of the factors of q?	Choices
A) 51	B) 54	C) 72	D) 50!+2	E) 162

Solution: In fact 51=3*17 IS a factor of 50!.   The smallest positive integer that is NOT prime and NOT a factor of 50! is 106=2*53. The sum of the factors of 106 is 162.   Answer: 162.
Answer: E
A rectangular-shaped carpet that measures x feet by y feet is priced at $35. What is the cost of the carpet, in dollars per square yard? (1 square yard = 9 square feet)  Choose the correct option.
A) 180xy B) 180/(xy) C) 20xy D) 315/(xy) E) xy/180

Solution: The area of the carpet in feet is xy.   The area in square yards is xy / 9.   The price per square yard is 35 / (xy/9) = 315/(xy).   The answer is 315/(xy).
Answer: D
If x and b are integers and (15^x + 15^(x+1))/4^b = 15^b what is the value of x? Pick
A) 2  B) 3  C) 4  D) 5  E) Cannot be determined

Solution: \frac{15^x( 1+ 15)}{4^b} = 15^b   (15^x . 4^2 ) / 4^b = 15^b. 4^0   15^x . 4^(2-b) = 15^b. 4^0   Equating the powers, x = b; 2-b = 0; So x = b = 2=2
Answer: A
Out of 6 fruits in a basket, 2 are rotten. If two fruits are drawn at random from the basket, the probability of both being rotten is
Choose the most appropriate option:	A) 1/15	B) 10/13	C) 21/15	D) 15/21	E) 2/21

Solution: The number of exhaustive events = 6C2 = 15.   Let E be event of the 2 fruits being rotten. The number of favourable cases are   2C2 = 1 way.   Required probability = 1/15.   1/15NSWER:1/15
Answer: A
What is the difference between the banker's discount and the true discount on Rs.8100 for 3 months at 5% Pick one:
A) Rs. 2  B) Rs. 1.25  C) Rs. 2.25  D) Rs. 0.5  E) None of these

Solution: Explanation :   F = Rs. 8100   R = 5%   T = 3 months = 1/4 years   BD = FTR/100 = (8100 × (1/4) × 5)/100 = 2025/20 = 405/4 = Rs. 101.25   TD = FTR/(100+TR) = (8100 × (1/4) × 5)/(100 + (1/4 × 5) = (2025 × 5)/(100+(5/4))   = (2025 × 5 × 4)/(400+5) = (2025 × 5 × 4)/405 = (405 × 5 × 4)/81 = (45 × 5 × 4)/9   = 5 × 5 × 4 = Rs. 100   BD - TD = Rs. 101.25 - Rs. 100 = Rs. 1.25 Answer : Option Rs. 1.25
Answer: B
A worker is paid a regular rate of Rs.30 for completing a survey. The worker completes 100 surveys per week. For any survey involving the use of her cellphone, she is paid at a rate of that is 20% higher than her regular rate. If she completed 50 surveys involving the use of her cellphone, how much did she get that week?	Choose the correct answer:
A) 2200
B) 1100
C) 2500
D) 2800
E) 3300

Solution: Amount earned using her cell phone = 50 * 36= 
50 * 36 = 1_800
1800   earned for remaining surveys= 50 * 30= 
50 * 30 = 1_500
1500   Total earning= 3300   Answer :3300
Answer: E
There are 24 students in a class one of them who is 18 years old left the class and a new comer filled his place. If the avg age of the class was there by lowered by one month . The age of new comer is  Select
A) 14years  B) 15years  C) 16 years  D) 17 years  E) 18 years

Solution: Let new comer age was x.   Average age decreased by = 1 month = 1/12 years.   You can use this formula for these type of problems.   No. of students in class* aged decreased = difference of replacement   24 * 1/12 = 18 - x   2 = 18 - x   x = 16 years.   Age of new comer age was 16 years.   Answer: Option 16 years
Answer: C
The manager of a produce market purchased a quantity of tomatoes for $0.80 per pound. Due to improper handling, 10 percent of the tomatoes, by weight, were ruined and discarded. At what price per pound should the manager sell the remaining tomatoes if she wishes to make a profit on the sale of the tomatoes equal to 8 percent of the cost of the tomatoes.  Choose the correct answer:
A) $0.94	B) $0.96	C) $0.98	D) $1.00	E) $1.20

Solution: Assume the manager bought 100 tomatoes.   Cost Price = 80   Given: 10% are damaged --> Available tomatoes to sell = 90   90 * x - 80 = 0.08 * 80   90x - 80 = 6.4   90x = 86.64   x = 86.64/90 = 87/90 (approx) = 29/30 = 0.966   x is slightly under 0.9666 = 0.96   Answer: $0.96
Answer: B
A and B can do a piece of work in 6 2/3 days and 5 days respectively. They work together for 2 days and then A leaves. In how many days after that B will complete the work alone.
Select the correct option
A) 1 1/8 days  B) 1 1/2 days  C) 3 1/2 days  D) 1 1/5 days  E) 1 5/2 days

Solution: 3/20 * 2 + (2 + x)/5 = 1   x = 1 1/2 days   Answer:1 1/2 days
Answer: B
If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number?  Select:
A) 5 : 3  B) 2 : 6  C) 5 : 6  D) 6 : 4  E) 2 : 5

Solution: Let 40% of A =(2/3)B   Then,40A/100=2B/3   2A/5=2B/3   A/B =(2/3 x 5/2) = 5/3   A : B = 5 : 3.   5 : 3NSWER 5 : 3
Answer: A
Find the principle on a certain sum of money at 5% per annum for 3 1/5 years if the amount being Rs.2030? Choose the correct answer:  A) Rs.2000  B) Rs.1750  C) Rs.2010  D) Rs.2005  E) None of these

Solution: Explanation:   2030 = P [1 + (5*16/5)/100]   P= 1750   Answer: Option Rs.1750
Answer: B
If the cost of 12 books is equal to the selling price of 10 books, the profit per cent in the transaction is	Choose the correct choice from the following answers:
A) 16 2/3%	B) 18%	C) 20%	D) 25%	E) 30%

Solution: Let C.P. of 12 books = Rs 12   Therefore, S.P. of 10 books = Rs 12   C.P. of 10 books = Rs 10   Therefore, Profit = 20%   ANSWER:20%
Answer: C
For which of the following values of s is (40+s)/s an integer?  Options:
A) 3
B) 4
C) 9
D) 11
E) 40

Solution: This problem has to be solved by checking the options   (40 + s)/s   For this entity to be an integer, 50 + s should be divisible by s   Option A: 43/3 - Not an Integer   Option B:44/4 - Not an Integer   Option C: 49/9 - Not an integer   Option D: 51/11 - Not an integer   Option 40 - 80/40- Integer   Correct Option: 40
Answer: E
A basket contains one dozen flowers. 7 of the flowers are Roses, three are sunflowers, and two are jasmine. If two flowers are randomly selected from the basket, one after the other, what is the probability that both will be rose flower? Choose the correct choice from the following answers:	A) 1/11	B) 11/4	C) 7/22	D) 5/4	E) 8/9

Solution: Probability of getting the first Rose flower - 7/12   Probability of getting the second Rose flower - 6/11   total probability = 7/12*6/11 = 7/22   correct option 7/22
Answer: C
Tom and Jerry enter into a partnership by investing $700 and $300 respectively. At the end of one year, they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business. If Tom received $800 more than Jerry did, what was the profit made by their business in that year?
Options
A) 3000	B) 4000	C) 5000	D) 6900	E) 6677

Solution: Say the profit was $x.   Tom share = x/6 (half of the third) + (x-x/3)*0.7   Jerry share = x/6 (half of the third) + (x-x/3)*0.3   Thus (x-x/3)*0.7-(x-x/3)*0.3=800 --> x=3000.   answer is 3000
Answer: A
A train 350 m long, running with a speed of 63 km/hr will pass a tree in?  Choose one.
A) 15 sec B) 16 sec C) 18 sec D) 20 sec E) 25 sec

Solution: Speed = 63 * 5/18 = 35/2 m/sec   Time taken = 350 * 2/35= 
350 * 2/35 = 20
20 sec   ANSWER: 20 sec
Answer: D
A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day? Choose the correct option:  A) 12 days  B) 15 days  C) 16 days  D) 18 days  E) none

Solution: A's 2 day's work = (1/20 * 2) = 1/10   (A + B + C)'s 1 day's work = (1/20 + 1/30 + 1/60) = 6/60 = 1/10   Work done in 3 days = (1/10 + 1/10) = 1/5   Now, 1/5 work is done in 3 days.   Whole work will be done in (3 x 5) = 15 days.   Answer = 15 days
Answer: B
The average age of students of a class is 15.8 years. The average age of boys in the class is 16.4 years and that of the girls is 15.4 years, The ratio of the number of boys to the number of girls in the class is  Choose the most appropriate option.
A) 2 : 9  B) 2 : 3  C) 2 : 2  D) 2 : 1  E) 2 : 7

Solution: Let the ratio be k : 1. Then,   k * 16.4 + 1 * 15.4 = (k + 1) * 15.8   <=> (16.4 - 15.8) k = (15.8 - 15.4) <=> k = 0.4/0.6 = 2/3.   Required ratio = 2/3 : 1 = 2 : 3.   Answer: 2 : 3
Answer: B
A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are drawn what is the probability that one is yellow and two are red?	Answers:
A) 24/455
B) 3/91
C) 12/455
D) 15/91
E) None of these

Solution: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.   When three marbles are drawn, the probability that one is yellow and two are red   = (²12/455₁)(⁴12/455₂)/¹⁵12/455₃   = (2 * 4 * 3 * 3 * 2)/(1 * 2 * 15 * 14 * 13) = 12/455   ANSWER:12/455
Answer: C
If a man lost 4% by selling oranges at the rate of 12 a rupee at how many a rupee must he sell them to gain 44%?  Choose the correct choice:
A) 6 B) 8 C) 9 D) 5 E) 2

Solution: 96% ---- 12   144% ---- ?     96/144 * 12= 
  96/144 * 12 = 8
8   Answer: 8
Answer: B
Two trains, each 100 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is?  Choices.
A) 30 km/hr
B) 45 km/hr
C) 60 km/hr
D) 75 km/hr
E) 85 km/hr

Solution: Explanation:   Let the speed of the slower train be x m/sec.   Then, speed of the train = 2x m/sec.   Relative speed = ( x + 2x) = 3x m/sec.   (100 + 100)/8 = 3x => x = 25/3.   So, speed of the faster train = 50/3 = 50/3 * 18/5= 
50/3 * 18/5 = 60
60 km/hr.   ANSWER IS 60 km/hr
Answer: C
If a - b = 6 and a2 + b2 = 48, find the value of ab.  Choose the correct choice from the following options:	A) 8	B) 10	C) 12	D) 6	E) 19

Solution: 2ab = (a2 + b2) - (a - b)2   = 48 - 36= 
48 - 36 = 12
12   ab= 6.   Answer: 6
Answer: D
The average monthly income of A and B is Rs. 5050. The average monthly income of B and C is Rs. 6250 and the average monthly income of A and C is Rs. 5200. What is the monthly income of A?	Choose the correct choice from the following:
A) 2000  B) 3000  C) 4000  D) 5000  E) 6000

Solution: Explanation:   Let monthly income of A = a   monthly income of B = b   monthly income of C = c   a + b = 2 × 5050 .... (Equation 1)   b + c = 2 × 6250 .... (Equation 2)   a + c = 2 × 5200 .... (Equation 3)   (Equation 1) + (Equation 3) - (Equation 2)   => a + b + a + c - (b + c) = (2 × 5050) + (2 × 5200) - (2 × 6250)   => 2a = 2(5050 + 5200 - 6250)   => a = 4000   i.e., Monthly income of A = 4000   Answer: Option 4000
Answer: C
Express the ratio 3 2/3 : 7 1/3 in its simplest form.
Choose the correct choice from the following options
A) 1:21
B) 1:1
C) 2:1
D) 1:2
E) 2:11

Solution: Solution   We first convert the mixed numbers 3 2/3 and 7 1/3 into fractions   3 2/3 = 3*3 / 3 + 2 / 3 = 11 / 3   7 1/3 = 7*3 / 3 + 1 / 3 = 22 / 3   The ratio 3 2/3 : 7 1/3 can be expressed as   11 / 3 ÷ 22 / 3 = 11 / 3 × 3 / 22   Simplify   = 11 / 22 = 1 / 2   The ratio is 1 / 2 or 1:2   ANSWER IS 1:2
Answer: D
If k is a positive integer, which of the following must be divisible by 27?	Choose one:
A) (k – 4)(k)(k + 3)(k + 7) B) (k – 4)(k – 2)(k + 3)(k + 5) C) (k – 2)(k + 3)(k + 5)(k + 6) D) (k + 1)(k + 3)(k + 5)(k + 7) E) (k – 3)(k + 1)(k + 4)(k + 6)

Solution: 24=8*3.   Note that the product of two consecutive even integers is always divisible by 8 (since one of them is divisible by 4 and another by 2). Only option B offers two consecutive even numbers for any integer value of k: k-4 and k-2, if k=even or k+3 and k+5 if k=odd.   Also from the following 3 consecutive integers:(k-4), (k-3),(k-2)one must be divisible by 3, if it's not k-4 or k-2 then it must be k-3 (if it's k-4 or k-2 option B is divisible by 3 right away). But if it's k-3 then (k-3)+6=k+3must also be divisible by 3.   So, option B: (k – 4)(k – 2)(k + 3)(k + 5) is divisible by 8 and 3 in any case.   Answer: (k – 3)(k + 1)(k + 4)(k + 6).
Answer: E
Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 2.10 km and 1.4 km respectively. The time taken by the slower train to cross the faster train in seconds is?
Answers:
A) 99
B) 277
C) 84
D) 96
E) 22

Solution: Relative speed = 60 + 90= 
60 + 90 = 150
150 km/hr.= 150 * 5/18 = 125/3 m/sec.   Distance covered = 2.10 + 1.4= 
2.10 + 1.4 = 3.5
3.5 km= 3500 m.   Required time = 3500 * 3/125= 
3500 * 3/125 = 84
84 sec.   Answer:84
Answer: C
What is the unit digit in {(6374)1793 x (625)317 x (341491)}?  Choose the correct answer:	A) 0	B) 2	C) 3	D) 5	E) 7

Solution: Explanation:   Unit digit in (6374)1793 = Unit digit in (4)1793   = Unit digit in [(42)896 x 4]   = Unit digit in (6 x 4) = 4   Unit digit in (625)317 = Unit digit in (5)317 = 5   Unit digit in (341)491 = Unit digit in (1)491 = 1   Required digit = Unit digit in (4 x 5 x 1) = 0.   0NSWER IS 0
Answer: A
Last year a worker saved 10% of her annual salary. This year, she made 10% more money than last year and she saved 12% of her salary. The amount she saved this year was what percent of the amount she saved last year?	Choose the correct choice from the following answers:	A) 126%	B) 128%	C) 130%	D) 132%	E) 134%

Solution: Let x be the worker's salary last year.   Last year, she saved 0.1x.   This year, she saved 0.12(1.1x)=0.132x   0.132x/0.1x=132%   The answer is 132%.
Answer: D
Today is Thursday. The day after 59 days will be?
Choose the correct answer:  A) Monday  B) Tuesday  C) Saturday  D) Sunday  E) None of these

Solution: Explanation :   59 days = 8 weeks 3 days = 3 odd days   Hence if today is Thursday, After 59 days, it will be = (Thursday + 3 odd days)   = Sunday   Answer : Option Sunday
Answer: D
Father is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:	Choose one.
A) 20 years	B) 21 years	C) 22 years	D) 28 years	E) 25 years

Solution: age consider as x   (x + 24) + 2 = 2(x + 2)   x + 26 = 2x + 4   x = 22.   ANSWER 22 years
Answer: C
4/15 of 5/7 of a number is greater than 4/9 of 2/5 of the same number by 24. What is half of that number?	Choose the correct choice from the following options:  A) 670  B) 750  C) 945  D) 375  E) 315

Solution: Let no. be x   4/15*5/7*x - 4/9*2/5*x =8   by further solving   20x/105- 8x/45=8   4x/315=24   x=1890   we have to find x/2   =1890/2= 
1890/2 = 945
945   ANSWER:945
Answer: C
If pq > 0, which of the following must be negative?  Choose the correct option.
A) p/q B) -p/q C) -p/-q D) -p * -q E) pq

Solution: Given pq> 0 So both will be the positive integers. If both are positive, then A,C,D,E also positive.   Answer :-p/q
Answer: B
The ratio between the length and the breadth of a rectangular park is 3:2. If a man cycling along theboundary of the park at the speed of 12 km/hr completes one round in 8 min, then the area of the park (in sq. m) is?
Pick one:
A) 143530 m B) 145600 m C) 153600 m D) 134500 m E) 155600 m

Solution: Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m.   60   Let length = 3x metres and breadth = 2x metres.   Then, 2(3x + 2x) = 1600 or x = 160.   Length = 480 m and Breadth = 320 m.   Area = (480 x 320) m2 = 153600 m   153600 m
Answer: C
A can give B 150 meters start and C 300 meters start in a kilometer race. How much start can B give C in a kilometer race?  Choose the correct choice from the following:
A) 111.12	B) 111.67	C) 111.64	D) 111.11	E) 176.47

Solution: A runs 1000 m while B runs 850 m and C runs 700 m.   The number of meters that C runs when B runs 1000 m,   = (1000 * 700)/850 = 823.53 m.   B can give C = 1000 - 823.53= 
1000 - 823.53 = 176.47
176.47 m.   Answer:176.47
Answer: E
It is being given that (232 + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number? Choose the correct choice from the following answers:
A) (2^96 + 1)
B) (2^16 + 1)
C) (2^95 + 1)
D) (2^95 - 1)
E) (2^75 + 1)

Solution: Let 232 = x. Then, (232 + 1) = (x + 1).   Let (x + 1) be completely divisible by the natural number N. Then,   (296 + 1) = [(232)3 + 1] = (x3 + 1) = (x + 1)(x2 - x + 1), which is completely divisible by N, since (x + 1) is divisible by N.   (2^96 + 1))
Answer: A
The population of a town is 10000. It increases annually at the rate of 20% p.a. What will be its population after 2 years? Pick one:
A) 14000 B) 14400 C) 14500 D) 14600 E) 14700

Solution: Formula :   ( After =100 denominator   Ago = 100 numerator)   10000 × 120/100 × 120/100 = 14400   14400
Answer: B
A train 100 m long crosses a platform 180 m long in 14 sec; find the speed of the train?
Choose the correct choice from the following.
A) 72 kmph  B) 58 kmph  C) 54 kmph  D) 94 kmph  E) 59 kmph

Solution: D = 100 + 180= 
100 + 180 = 280
280   T= 14   S = 280/14 * 18/5= 
280/14 * 18/5 = 72
72 kmph   72 kmphnswer:72 kmph
Answer: A
As x increases from 169 to 155, which of the following must increase?
I. 2x - 5
II. 1 - 1/x
III. 1/(x^2 - x)	Choose the correct choice from the following options:
A) I only B) III only C) I and II D) I and III E) II and III

Solution: I. 2x - 5 --> x decreases from 169 to 155 --> 2x decreases --> 2x - 5 decreases.   II. 1 - 1/x --> x decreases from 169 to 155 --> 1/x increases --> 1 -1/x decreases.   III. 1/(x^2 - x) --> x decreases from 169 to 155 --> x^2-x decreases --> 1/(x^2 - x) increases.   Answer: III only.
Answer: B
Find the sum The difference between the compound and S.I. on a certain sum of money for 2 years at 10% per annum is Rs.15of money?
Choose the correct choice from the following answers:
A) 1500
B) 1528
C) 1298
D) 1528
E) 1282

Solution: P = 15(100/10)2   => P = 1500   1500nswer: 1500
Answer: A
Suppose you flip a fair coin five times. What is the probability that, in five flips, you get at least one head?  Pick one:
A) 27/32
B) 25/32
C) 17/32
D) 15/32
E) 31/32

Solution: Best way of solving an at least 1 type of question is to compute 1 - probability of flipping 0 heads   probability of flipping either a head or a tail = 1/2   probability of flipping 3 tails in a row (1/2)^5   probability of flipping at least 1 head = 1 - (1/2)^5 = 31/32   Answer : 31/32
Answer: E
What is the number of 7-element subsets of the set {1, 2, 3, 4, 5, 6, 7, 8, 9}
for which the sum of those 7 elements is a multiple of 3 ?	Choose the correct choice:  A) 10  B) 11  C) 12 number  D) 13  E) 14

Solution: We describe 2 solutions. Let S = {1, 2, . . . , 9}. Observe that the sum of the elements of S   is divisible by 3. So the problem is the same as asking for the number of ways that 2 elements   of S can be chosen so that their sum is divisible by 3 (the other 7 elements of S correspond to a   7-element set as in the problem). Choosing 2 elements of S with sum divisible by 3 corresponds   to either choosing 2 numbers divisible by 3 (which can be done in 3 ways) or choosing 1 number   that is one more than a multiple of 3 and 1 number that is one less than a multiple of 3 (which can   be done in 3 · 3 = 9 ways). Hence, the answer is 3 + 9= 
3 + 9 = 12
12.   correct answer 12 number
Answer: C