MU-NLPC/Calc-aqua_rat huggingface dataset:
The smallest value of n, for which 2n is not a prime number, is
Choose the correct choice:
A) 2,3,4
B) 1,3,5
C) 2,5,6
D) 4,8,9
E) 12,14,16

Solution: (2Ã—1) = 2.   (2Ã—2) = 4.   (2Ã—3) = 6.   (2Ã—4) = 8.   which is not prime , n=2,3,4.   2,3,4NSWER:2,3,4
Answer: A
The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero ?	Choose the correct answer
A) 0
B) -1
C) 1
D) 2
E) none of these

Solution: Explanation:   Average of 20 numbers = 0.   Sum of 20 numbers = (0 * 20)= 
(0 * 20) = 0
0.   It is quite possible that 19 of these numbers may be positive and if their sum is a, then 20th number is (- a). 0nswer: 0
Answer: A
In a shop, 40% socks are white and rest are black. 60% socks are made of cotton and rest are made of wool. 25% white socks are made of cotton and 20 of the black socks are made of wool. How many black socks are made of cotton?	Options.
A) 100	B) 80	C) 60	D) 50	E) 25

Solution: 40% is white -> wht = 0.4x   Blk = 0.6 x   also 60% socks are made of cotton - > ct = 0.6x   wl = 0.4x   we know 25% of the white socks is cotton --> 1/4 (0.4x) = 0.1x = wh-ct   => 0.3x = wh-wl   total wool is 0.4x => black wool socks = 0.4 x (total) - 0.3 x (wh-wl) = 0.1x given as 20   => total number of socks = 200   = > total black socks = .6x = 120   total cotton black socks = 120 - 20 (bl-wl) = 100 hence 100
Answer: A
How many years will it take John’s investment to double at a simple interest rate of 4% per annum.  Answers.
A) 20  B) 30  C) 15  D) 25  E) 19

Solution: P = (P*4*R)/100   100P = P*4*R   100 = 4R   Therefore R = 25   25 = 25 Years
Answer: D
A bus from city M is traveling to city N at a constant speed while another bus is making the same journey in the opposite direction at the same constant speed. They meet in point P after driving for 2 hours. The following day the buses do the return trip at the same constant speed. One bus is delayed 24 minutes and the other leaves 36 minutes earlier. If they meet 24 miles from point P, what is the distance E between the two cities? Choose the correct choice from the following choices.
A) 48	B) 72	C) 96	D) 120	E) 192

Solution: Hmmm I did this question a while ago and got it wrong so trying again   Rate x time = distance.   For the initial trip lets the distance E to the midpoint be represented by P.   EQN1: R x 2 = P   For the second trip we know one bus left late and one left early. Together this is just a tricky way of saying one bus left an hour after the other. We know the total trip takes 4 hours (since getting to P is 2 hours). The second trip can be represented by:   Since the trip takes 4 hours if a bus leaves one hour early, the reminaining 3 hours are split between the two buses, ie. 1 + 3/2 = 2.5   EQN2: R x 2.5 = P + 24   EQN2-EQN1 : 0.5R=24   R=48   So the distance is rate x time = 48 x 4 = 192.   ANS = 192
Answer: E
A 300 meter long train crosses a platform in 33 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
Pick one.
A) 250 B) 266 C) 230 D) 288 E) 271

Solution: Speed = [300 / 18] m/sec = 50/3 m/sec.   Let the length of the platform be x meters.   Then, x + 300 / 33 = 50/3   3(x + 300) = 1650 è x = 250m.   250nswer: 250
Answer: A
A palindrome is a number that reads the same forward and backward, such as 242. How many odd three-digit numbers are palindromes? Select:
A) 40
B) 400
C) 50
D) 5,000
E) 100,000

Solution: 3rd digit 1,3,5,7,9   2nd digit 0 through 9   i.e 10*5 = 50 numbers   first digit is going to be same as 3rd . so it would still be 50 numbers.   Answer is 50.
Answer: C
Two men Amar and Bhavan have the ratio of their monthly incomes as 6:5. The ratio of their monthly expenditures is 3:2. If Bhavan saves one-fourth of his income, find the ratio of their monthly savings?  Choose the correct choice from the following choices.
A) 3:19  B) 3:10  C) 3:12  D) 3:11  E) 3:22

Solution: Let the monthly incomes of Amar and Bhavan be 6x and 5x respectively.   Let the monthly expenditures of Amar and Bhavan be 3y and 2y respectively.   Savings of 3:10havan every month = 1/4 (5x)   =(his income) - (his expenditure) = 5x - 2y   => 5x = 20x - 8y => y = 15x/8   Ratio of savings of Amar and 3:10havan   = 6x - 3y : 1/4 (5x) = 6x - 3(15x/8) : 5x/4   = 3x/8 : 5x/4 => 3:10   Answer:3:10
Answer: B
Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is -.	Choose the correct choice from the following answers:
A) 5/12
B) 4/13
C) 5/17
D) 3/12
E) 8/9

Solution: Using question number 11 and 12, we get the probability as   1 - (1/36 + 5/9) = 5/12   5/12NSWER 5/12
Answer: A
In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 52, the dividend is: Answers:	A) 6832	B) 6814	C) 6816	D) 6812	E) 6810

Solution: Divisor = (5 * 52)= 
(5 * 52) = 260
260= 10 * Quotient = Divisor   => Quotient = 260/10= 
260/10 = 26
26   Dividend= (Divisor * Quotient) + Remainder   Dividend = (260 * 26) + 52= 
(260 * 26) + 52 = 6_812
6812.   6812
Answer: D
There are 20 poles with a constant distance between each pole. A car takes 25 second to reach the 12th pole. How much will it take to reach the last pole.
Select the correct option:	A) 43.1543	B) 43.1818	C) 43.45128	D) 43.41288	E) 43.41222

Solution: Assuming the car starts at the first pole.   To reach the 12th pole, the car need to travel 11 poles (the first pole doesn't count, as the car is already there).   11 poles 25 seconds   1 pole (25/11) seconds   To reach the last (20th) pole, the car needs to travel 19 poles.   19 pole 19 x (25/11) seconds   = 43.1818 seconds   Answer:43.1818
Answer: B
For an employee to qualify for early retirement at a certain company, the sum of the employee’s age and years of service must be at least 65, If Sue was K years old when she was hired by the company, what is the minimum age at which she could possibly qualify for early retirement. Choose the correct option.
A) K+35	B) 2K+35	C) (70+K)/2	D) (65+K)/2	E) 2(70-K)

Solution: Say Sue was hired when she was already 65 years old (k=65), then she could retire right away, at the age of 65. Now, plug k=65 in the answer choices and see which yields 65. Only C fits.   Answer: (65+K)/2.
Answer: D
2 no's are respectively 40% & 60% more than 3rdnumber. Find the ration of two numbers ?
Choose the correct option.
A) 3 : 4 B) 4 : 5 C) 7 : 8 D) 8 : 9 E) 8 : 11

Solution: Step 1: Let the third number is A   Then first number is 140% of A = 140 x A / 100 = 7A / 5 and second number is 160% of B = 160 x B / 100 = 8B /5.   Step 2: now ratio of first and second number is 7A / 5 : 8B / 5 = 35A : 40B = 7 : 8.   7 : 8
Answer: C
An alloy of copper and aluminum has 40% copper. An alloy of Copper and Zinc has Copper and Zinc in the ratio 2:7. These two alloys are mixed in such a way that in the overall alloy, there is more aluminum than Zinc, and copper constitutes x% of this alloy. What is the range of values x can take?  Choose the correct choice from the following options.
A) 30% ≤ x ≤ 40% B) 32.5% ≤ x ≤ 40% C) 32.5% ≤ x ≤ 42% D) 33.33% ≤ x ≤ 40% E) 33.33 % ≤ x ≤ 42%

Solution: The maximum aluminium you can have is when you mix copper and aluminium alloy (say alloy A) with infinitesimally small amount of copper and zinc alloy (alloy B). In that case, you will have almost 40% of copper in the mix (because alloy A has 40% of copper). So x% < 40%.   Minimum case:   60% of alloy 30% ≤ x ≤ 40% > (7/9) of alloy B   30% ≤ x ≤ 40%/B > 35/27   If the two alloys are mixed in this ratio, the copper concentration will be:   Using weighted average:   Cavg = (2/5 * 35 + 2/9 * 27)/(35 + 27)   Cavg = (14 + 6)/62= 20/62 = 32.26% (rounded to 2 decimal places)   So x% > 32.26%   30% ≤ x ≤ 40%nswer: 32.26 < x < 40   30% ≤ x ≤ 40%NSWER:30% ≤ x ≤ 40%
Answer: A
For four days of work, a clerk had daily earnings of $180, $170, $180, and $180 respectively. In which of the following intervals does the standard deviation of the daily earnings lie?
Select:  A) Between $10 and $100  B) Between $10 and $50  C) Between $50 and $75  D) Between $50 and $100  E) Between $0 and $10

Solution: The standard deviation is between 0 and 10.   The reason is that none of the numbers in the set is further away from the mean than 10(or rather Abs(170-(180*3+170)/4)). I am not fully sure how to calculate the standard deviation(I simply remember that there were some formula for calculating the average of the squared distances from the mean for all items in the set from statistics classes - variation), but I believe this will suffice for any GMAT question related to standard deviation.   Answer : Between $0 and $10
Answer: E
In a single throw of a die, what is the probability of getting a number greater than 2? Select the correct option
A) 1/2  B) 2/5  C) 1/3  D) 2/7  E) 2/3

Solution: S = {1,2,3,4,5,6}   2/3 = {3,4,5,6}   Probability = 4/6 = 2/3   Answer is 2/3
Answer: E
10 men can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 men and 10 children take to complete the work?  Choose the correct choice from the following choices:
A) 4	B) 7	C) 3	D) 5	E) nONE

Solution: 1 man's 1 day's work = 1   70   1 child's 1 day's work = 1   140   (5 men + 10 children)'s day's work = 5 + 10 = 1 + 1 = 1   70 140 14 14 7   5 men and 10 children will complete the work in 7 days.   Correct Answer is 7
Answer: B
A man can row a boat at 20 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 60 km downstream? Choose the correct choice from the following options:  A) 20/6 hours  B) 27/2 hours  C) 30 hours  D) 30/13 hours  E) 20/13 hours

Solution: Speed downstream = 20 + 6= 
20 + 6 = 26
26 kmph.   Time required to cover 60 km downstream= d/s = 60/26 = 30/13 hours   ANSWER:30/13 hours
Answer: D
Kamal started a business with Rs.25000 and after 4 months, Kiran joined him with Rs.60000. Kamal received Rs.58000 including 10% of profit as commission for managing the business. What amount did Kiran receive? Choose the most appropriate option:
A) 75000  B) 70000  C) 72000  D) 78000  E) None of these

Solution: Explanation :   Ratio of the profits = 25000*12 : 60000*8   = 25*12 : 60*8 = 5*3 : 12:2 = 5 : 4*2   = 5:8   Let the total profit = x.   Then Kamal received 10x/100 = x/10 as commission for managing the business   Remaining profit = x- x/10 = 9x/10 which is shared in the ration 5:8   Kamal's share = x/10 + (9x/10) * (5/13) = 58000   => x + 9x(5/13) = 580000   => x(1 + 45/13) = 580000   => x ( 58/13) = 580000   => x ( 1/13) = 10000   => x = 130000   Kiran's share = 130000 - 58000= 
130000 - 58000 = 72_000
72000. Answer : Option 72000
Answer: C
How many arrangements of the letters of the word BEGIN can be made, without changing the place of the vowels in the word?	Choose the most appropriate option:
A) 6 ways	B) 7 ways	C) 9 ways	D) 11 ways	E) 13 ways

Solution: E,I fixed. Consonants can be arrangements in 3P3 = 3! = 6 ways   6 ways)
Answer: A
In a division sum, the quotient is 120, the divisor 456 and the remainder 333, find the dividend?
Choose the correct option:
A) 55287
B) 29887
C) 27768
D) 55053
E) 17191

Solution: Explanation:   120 * 456 + 333= 
120 * 456 + 333 = 55_053
55053   Answer: 55053
Answer: D
A family made a down payment of $25
and borrowed the balance on a set of
encyclopedias that cost $400. The
balance with interest was paid in 28
monthly payments of $16 each and a
final payment of $19. The amount of
interest paid was what percent of the
amount borrowed? Choose the correct choice from the following answers.
A) 6.75% B) 12.25% C) 14.23% D) 16.66% E) 24.53%

Solution: interest paid = 16*28+19 - 375= 
16*28+19 - 375 = 92
92   % off the balance= (92/375) * 100 = 24.53%   Answer is 24.53%.
Answer: E
4 dice are thrown simultaneously on the board. Find the probability show the same face. Choose the correct choice from the following answers
A) 2/213	B) 3/115	C) 1/216	D) 4/221	E) 5/229

Solution: The total number of elementary events associated to the random experiments of throwing four dice simultaneously is:   =6×6×6×6=64=6×6×6×6=64   n(S)=64n(S)=64   Let XX be the event that all dice show the same face.   X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}   n(X)=6n(X)=6   Hence required probability,   =n(X)n(S)=664=n(X)n(S)=664   =1/216   1/216
Answer: C
On a sum of money, the S.I. for 2 years is Rs. 660, while the C.I. is Rs. 696.30, the rate of interest being the same in both the cases. The rate of interest is? Pick.
A) 23	B) 28	C) 12	D) 11	E) 18

Solution: Explanation:   Difference in C.I. and S.I for 2 years = (696.30 - 660) = Rs. 36.30.   S.I for one year = Rs. 330.   S.I. on Rs. 330 for 1 year = Rs. 36.30   Rate = (100 * 36.30)/(330 * 1)= 
(100 * 36.30)/(330 * 1) = 11
11%   Answer: 11
Answer: D
There are 24 students in a seventh grade class. They decided to plant birches and roses at the school's backyard. While each girl planted 3 roses, every three boys planted 1 birch. By the end of the day they planted 24 plants. How many birches and roses were planted?
Choose the correct option:
A) 3	B) 4	C) 5	D) 6	E) 7

Solution: Let x be the number of roses. Then the number of birches is 24−x, and the number of boys is 3×(24−x). If each girl planted 3 roses, there are x3 girls in the class.   We know that there are 24 students in the class. Therefore x3+3(24−x)=24   x+9(24−x)=3⋅24   x+216−9x=72   216−72=8x   1448=x   x=18   So, students planted 18 roses and 24 - x = 24 - 18= 
24 - 18 = 6
6 birches.   So answer is 6.
Answer: D
Raj drives slowly along the perimeter of a rectangular park at 24 kmph and completes one full round in 4 min. If the ratio of length to bredth of the park is 3 : 2, what are the dimansions?
Choose the correct choice from the following.
A) 100 m x 109 m B) 100 m x 102 m C) 100 m x 120 m D) 100 m x 100 m E) 100 m x 200 m

Solution: 24 kmph = 24×100060=40024×100060=400 m / min   In 4 minutes he covered 4 x 400 = 1600 m   This is equal to the perimeter 2 ( l + b) = 1600   But l : b = 3:2   Let l = 3k, b = 2k   Substituting, we get 2 ( 3k + 2k ) = 1600 => k = 180   So dimensions are 480 x 320   Answer:100 m x 100 m
Answer: D
How much interest will $10,000 earn in 3 months at an annual rate of 6%?
Pick one: A) $250 B) $150 C) $450 D) $550 E) $650

Solution: Soln:-   6 months = 1/4 of year;   6% = 6/100=3/50;   $10,000(principal)*3/50(interest rate)*1/4(time)=$150.   ANSWER:$150
Answer: B
The average of five numbers is 41. The average of first two numbers is 32 and the average of last two numbers is 38. What is the middle number? Pick one
A) 59 B) 64 C) 61 D) 72 E) 65

Solution: The total of five numbers = 5X41 = 205   The total of first 2 and last 2 numbers is = 2 X 32+2 X 38 = 140   So, the middle number is  (205 - 140 )= 
 (205 - 140 ) = 65
65   65
Answer: E
A dishonest shopkeeper professes to sell pulses at the cost price, but he uses a false weight of 950gm. for a kg. His gain is …%. Choose the correct answer.
A) 5.3 %  B) 8.2%  C) 4.3%  D) 8.3%  E) 8.0%

Solution: He sells 950 grams of pulses and gains 50 grams.   If he sells 100 grams of pulses then he will gain (50 / 950) *100 = 5.26   4. A software engineer has the capability of thinking 100 lines of code in five minutes and can type 100 lines of code in 10 minutes. He takes a break for five minutes after every ten minutes. How many lines of codes will he complete typing after an hour?   5.3 %nswer:5.3 %
Answer: A
The average price of three items of furniture is Rs. 15000. If their prices are in the ratio 3:5:7, the price of the cheapest item is :
Choose the correct choice from the following choices
A) 2348  B) 3888  C) 3988  D) 9000  E) 2882

Solution: Explanation:   Let their prices be 3x, 5x and 7x.   Then, 3x + 5x + 7x = (15000 * 3) or x = 3000.   Cost of cheapest item = 3x = Rs. 9000.   Answer: 9000) 9000
Answer: D
The respective ratio between the angles of a quadrilateral is 1 : 2 : 3 : 4. What is the sum of the twice the smallest angle and half the largest angle together?	Choose one:	A) 22	B) 77	C) 62	D) 22	E) 71

Solution: Answer:77
Answer: B
Last year’s receipts from the sale of greeting cards during the week before Mother’s Day totaled $234 million, which represented 6 percent of total greeting card sales for the year. Total greeting card sales for the year totaled how many million dollars?	Choose the correct choice from the following options.
A) 17,010
B) 2,100
C) 3,900
D) 1,701
E) 2107

Solution: 6% ---- 234 millions   for 100% => ( 234 * 100% )/6% = 3900.   Option 3,900.( 234 * 100  )/6= 
( 234 * 100  )/6 = 3_900
3900.   Option 3,900.
Answer: C
A certain car averages 30 miles per gallon when driving in the city and 40 miles per gallon when driving on the highway. According to these rates, which of the following is closest to the number of miles per gallon that the car averages when it is driven 10 miles in the city and then 50 miles on the highway?	Select the correct option:  A) 28  B) 30  C) 33  D) 36  E) 38

Solution: Answer 38   No of Miles per Gallon = Total no of miles/Total no of Gallons   =10+50/(10/30+50/40) ~ 37.89
Answer: E
List I: 4, 8, 12, 16 List II: x,4, 8, 12, 16
Choose the correct option
A) 5	B) 4	C) 3	D) 10	E) 2

Solution: List I has even number of terms, thus its median is the average of two middle terms (when arranged in ascending/descending order), so median=(8+12)/2= 
(8+12)/2 = 10
10   List II has odd number of terms, thus its median is the middle term (when arranged in ascending/descending order). As no other number in the list equal to 10, then x=10.   Answer: 10
Answer: D
When a shop keeper sold 2/3 of an item, he got the cost price of the whole lot. What is the percentage of his profit?  Answers: A) 33 1/8% B) 66 2/3% C) 25% D) 50% E) None of these

Solution: Explanation:   If 2/3 of the cost of item amount to CP   Then the ½ of the cost of item amounts to gain   :. Profit percentage = 1 x 100/2= 
100/2 = 50
50%.   Answer: Option 50%
Answer: D
John bought 9.25m of cloth for $416.25. Find the cost price per metre.
Pick:
A) 46  B) 47  C) 45  D) 56  E) 54

Solution: 45loth bought by John = 9.25 m   45ost of 9.25 m = $416.25   45ost per metre = 416.25 ÷ 9.25   The cost of the cloth per metre = $ 45   Answers: 45
Answer: C
A shopkeeper bought 600 oranges and 400 bananas. He found 15% of oranges and 3% of bananas were rotten. Find the percentage of fruits in good condition?  Choose the correct choice from the following answers
A) 92.5%	B) 89.8%	C) 85.2%	D) 96.8%	E) 78.9%

Solution: Total number of fruits shopkeeper bought = 600 + 400= 
600 + 400 = 1_000
1000   Number of rotten oranges= 15% of 600   = 15/100 × 600   = 9000/100= 
9000/100 = 90
90   Number of rotten bananas= 3% of 400   = 12   Therefore, total number of rotten fruits = 90 + 12= 
90 + 12 = 102
102   Therefore Number of fruits in good condition= 1000 - 102= 
1000 - 102 = 898
898   Therefore Percentage of fruits in good condition= (898/1000 × 100)%   = (89800/1000)= 
(89800/1000) = 449/5 = around 89.8
89.8%   Answer:89.8%
Answer: B
The number of circles that can be drawn out of 10 points of which 7 are collinear is  Pick one:	A) 130	B) 85	C) 45	D) Cannot be determined	E) None

Solution: Solution   For drawing a circle we need 3 non collinear points.This can be done in:   3C3 + 3C2 × 7C1 + 3C1 × 7C2 = 1 + 21 + 63= 
1 + 21 + 63 = 85
85.   Answer 85
Answer: B
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) 2 C) 4.5 D) 5.5 E) 5

Solution: 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:3.34
Answer: A
Evan ran a mile in 10 minutes Monday morning, and he ran the same mile in 8 minutes on Tuesday morning. On average, how many minutes did he take to run the mile over both days?
Choices:	A) 9	B) 18	C) 2	D) 80	E) 10

Solution: (10 + 8)/2= 
(10 + 8)/2 = 9
9   The correct answer is 9
Answer: A
A double decked bus can accomodate 90 passengers,40 in the upper deck and 50 in the lower deck.In how many ways can the passengers be accomodated if 15 refuse to be in the upper deck while 10 others refuse to be in the lower deck? Choose the most appropriate option
A) 1. 85!50!60!/40!45!
B) 2. 65!/30!35!
C) 3. 110!/50!60!
D) 4. 110!50!60!/40!45!
E) 5. 110!/40!45!

Solution: 90 passengers,40 in the upper deck and 50 in the lower deck.   25 passengers have issues as 15 refuse to be in the upper deck while 10 others refuse to be in the lower deck   So those 15 will be put in lower deck and 10 will be in upper deck   So from the rest 65 passengers(90-25), we need to find 30 people to put into upper deck and the rest go to lower deck   So the ways are: C(65,30) = 65!/30!35! . Answer 2. 65!/30!35!
Answer: B
What is the sum of the multiples of 4 between 53 and 145 inclusive?  Pick one:
A) 2000
B) 2200
C) 2300
D) 2450
E) 2500

Solution: the fastest way in an AP is to find the average and multiply with total integers..   between 53 and 145, the smallest multiple of 4 is 56 and largest =144..   average=(56+144)/2=100..   total numbers = (144-56)/4 + 1= 22+1=23..   sum=23*100= 
23*100 = 2_300
2300   ans 2300
Answer: C
A hat company ships its hats, individually wrapped, in 8-inch by 10-inch by 12-inch boxes. Each hat is valued at $6.0. If the company’s latest order required a truck with at least 288,000 cubic inches of storage space in which to ship the hats in their boxes, what was the minimum value of the order?  Options.
A) $960
B) $1,350
C) $1,725
D) $2,050
E) $1,800

Solution: Total Volume is 288000   Given LBH = 8*10*12.   the number of hats inside it = 288000/10 * 8 * 12 = 300.   price of each hat is 6 $ then total value is   300 * 6.0= 
  300 * 6.0 = 1_800
1800.   IMO option $1,800 is correct answer..
Answer: E
Let g(x) be a function such that g(x + 1) + g(x - 1) = g(x) for every real x. Then for what value of p is the relation g(x + p) = g(x) necessarily true for every real x?
Select: A) 7 B) 2 C) 6 D) 87 E) 21

Solution: g(x + 1) + g(x - 1) = g(x)   g(x + 2) + g(x) = g(x + 1)   Adding these two equations we get   ⇒⇒ g(x + 2) + g(x - 1) = 0   ⇒⇒ g(x + 3) + g(x) = 0 (By substituting x = x+1)   ⇒⇒ g(x + 4) + g(x + 1) = 0 (By substituting x = x+1)   ⇒⇒ g(x + 5) + g(x + 2) = 0 (By substituting x = x+1)   ⇒⇒ g(x + 6) + g(x + 3) = 0 (By substituting x = x+1)   ⇒⇒ g(x + 6) - g(x) = 0 ( g(x+3) + g(x) = 0 ⇒⇒ g(x+3) = - g(x))   ⇒⇒ g(x + 6) = g(x)   So for p = 6 the function is periodic.   7nswer:7
Answer: A
Ravi's 4days average income is 1025.68. But in a form he should write his average income as the greatest positive even integer less than or equal to his 4days average income. what is the difference between his real average and form filling average?	Choose one
A) 2
B) 4.3
C) 1.68
D) 1.5
E) 3.2

Solution: Since Ravi's 4days average income for form filling is defined as the greatest positive even integer less than or equal to his avg income, then avg income for form filling =1024 (the greatest positive even integer less than or equal to 1025.68 is 1024).   Hence the difference = 1025.68 - 1024= 
1025.68 - 1024 = 1.68
1.68   Answer: 1.68.
Answer: C
60% of a number is added to 120, the result is the same number. Find the number?	Choose the correct answer:
A) 300
B) 200
C) 400
D) 500
E) 600

Solution: (60/100) * X + 120 = X   2X = 600   X = 300   300NSWER:300
Answer: A