MU-NLPC/Calc-aqua_rat huggingface dataset:
A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, the son's age five years back was:	Select the correct option:
A) 14 years
B) 19 years
C) 33 years
D) 38 years
E) 48 years

Solution: Let the son's present age be x years. Then, (38 - x) = x   2x = 38.   x = 19.   Son's age 5 years back (19 - 5)= 
(19 - 5) = 14
14 years. 14 yearsnswer: Option 14 years
Answer: A
anup manages to draw 7 circles of equal radii with their centres on the diagonal of a square such that two extreme circles touch two sides of the square and each middle circle touches two circles on either side. find the ratio of radius of the circles to the side of the square.
Select
A) 1:(2+6^(1/2))  B) 1:(4+7^(1/3))  C) (2+7^(1/2)):1  D) (2+7^(1/2)):2  E) None of these

Solution: diagonal of square=(2*r)*7+(2^(1/2)*r-r)*2   diagonal has 7 squares diameters length +little distance between extreme squares to the end point [form a square of side r from center of extreme circle to the extreme end to find distance]   distance=2^(1/2)*r-r   D=a*2^(1/2)   a=2^(1/2)*[6*r + 2^(1/2)*r]   r/a =1:[2+6*2^(1/2)]   answer is none of the above   ANSWNone of theseR:None of these
Answer: E
There are 3 numbers A, B and C. If A:B = 3/4, B:C = 4/5, C:D = 5/6, then C:D will be? Answers.
A) 1 : 2	B) 3 : 5	C) 5 : 7	D) 5:6	E) 5 : 3

Solution: Sol. A : B = 3 : 4, B : C = 4 : 5, C : D = 5 : 6   ∴A∶B∶C∶D= 3 : 4 : 5 : 6.   Thus, C: 5:6 = 5 : 6   5:6
Answer: D
In the xy plane line m has the equation 4x + y = e. Line n passes through the origin and is perpendicular to line m. If point p has the coordinates (r, r+1) and is on both line n and m what is the value of r? Choose the most appropriate option
A) -4/3  B) 1/4  C) -4  D) 3/4  E) 4/3

Solution: The equation of line m is y=-4x+e. Now, since line n is perpendicular to line m, then its slope is negative reciprocal of the slope of line m, so the slope of n is 1/4. Next, as line n passes through the origin (0, 0) and has the slope of 1/4 then its equation is y=1/4*x.   Point (r, r+1) lies on line n means that (r+1)=1/4*r --> r( +1)= 
( +1) = 1
1/4*r --> r=-4/3.   -4/3nswer: -4/3.
Answer: A
What is the sum of all 3 digit positive integers that can be formed using the digits 1, 5, and 8, if the digits are allowed to repeat within a number Y? Choose the correct answer
A) 126
B) 1386
C) 3108
D) 308
E) 13986

Solution: As we are using digits 1,5, 8 and digits are allowed to repeat. Each of the unit, tenth and hundredth digit can be used by each of three digits.   So,Total possible numbers with these digits=3 X 3 X 3 =27.   First, As we have 27 three digit number, Sum will be for sure more than 2700..Eliminate options A,B,D   Second, If you imagine numbers Y with the given digits 1,5,8. We have numbers like 888,885,855,858,851. Sum is for sure more than 4000.Eliminate option C.   You are left withanswer 13986.
Answer: E
A train crosses a 120-metre and a 70-metre long plat form in 17 seconds and 12 seconds respectively. What is the speed of the train ?  Select the correct option:
A) 10 ms-1	B) 16 ms-1	C) 20 ms-1	D) 24 ms-1	E) 45 ms-1

Solution: Explanation :   let the length of the train be x   ∴ 120+x/17 = 70+x/12   1440 + 12x = 1190 + 17x   ∴ x = 250/5= 
250/5 = 50
50m   ∴ Speed= 120+50/17 = 170/17= 
170/17 = 10
10 ms-1   10 ms-1nswer : Option 10 ms-1
Answer: A
What is the dividend. divisor 17, the quotient is 9 and the remainder is 5?	Choose the correct choice from the following:
A) 150 B) 54 C) 158 D) 160 E) 180

Solution: D = d * Q + R   D = 17 * 9 + 5   D = 153 + 5= 
153 + 5 = 158
158   158)
Answer: C
The cost of a car was $3,000 in 1960. In 2010, the price had increased to $5,000. What was the percent increase in the cost of the car?
Select the correct option:	A) 33.3%	B) 45%	C) 60%	D) 66.6%	E) 55.8%

Solution: Increase = 5000-3000= 
5000-3000 = 2_000
2000   % increase= 2000*100/3000 = 66.6%   Answer: option 66.6%
Answer: D
A patient was given a bottle of tablets by the doctor and he was asked to take five tablets in a gap of 30 minutes.
In how much time will he be able to take all the five tablets? Options:
A) 1 Hour.  B) 2 Hour.  C) 3 Hour.  D) None  E) Cannot be determined

Solution: Suppose he takes the first tablet at 8:00 pm. Then the second will be consumed by him at 8:30, third at 9:00, fourth at 9:30 and fifth at 10:00.   Time = 2 hour   Answer 2 Hour.
Answer: B
If n is a positive integer and n^2 is divisible by 150, then what is the largest positive integer that must divide n?	Choose the correct choice from the following:  A) 10  B) 20  C) 30  D) 40  E) 50

Solution: 150 =   2 * 3 * 5= 
  2 * 3 * 5 = 30
30   The answer is 30.
Answer: C
A can do a piece of work in 10 days and B can do the same work in 12 days. A and B worked together for 3 days. How many more days are required to complete the remaining work if they work together?	Select the correct option
A) 3 (5/18)  B) 3 (5/16)  C) 2 (5/11)  D) 3 (5/13)  E) 3 (5/21)

Solution: A can do 1/10 of the work in a day.   B can do 1/12 of the work in a 1 day.   Both of them together can do (1/10 + 1/12) part of work in 1 day = (6 + 5)/60 = 11/60   They take 60/11 days to complete the work together.   Given that they already worked for 3 days.   The number of days required to complete remaining work => 60/11 - 3 = 27/11 = 2 (5/11) days.   Answer:2 (5/11)
Answer: C
A carpenter worked alone for 1 day on a job that would take him 6 more days to finish. He and another carpenter completed the job in 6 more days. How many days would it have taken the second carpenter to do the complete job working alone?
Pick:  A) 4 2/3  B) 7  C) 9  D) 24  E) 21

Solution: A carpenter worked only 1 day on something that takes him 6 MORE days.   Means;   Carpenter finishes his work in 7 days.   Let his buddy finish the same task in x days.   Respective rates per day:   1/7 AND 1/x   To complete 1 work:   First guy worked for 5 days @ rate=1/7 per day.   Second one worked for 6 days @ rate=1/x per day   Expression:   Days*Rate=Work   5*1/7+6*1/x=1   5x+42=7x   2x=42   x=21 days.   Ans:21
Answer: E
How many factors of 240 are also multiples of 3 ?	Choose the correct choice:  A) 5  B) 8  C) 9  D) 10  E) 20

Solution: take factors of 240   240= 2^4*3^1*5^1   Total factors of 240= (4+1)*(1+1)*(1+1)   =5*2*2= 
5*2*2 = 20
20   out of total factors of 20, half will have 0 as power of 3 and half will have 1 as power of 3. It is because we have considered only 0 and 1 as power of 3 to compute total factors of 240.   Therefore factors that are multiple of 3= 20/2= 
20/2 = 10
10   Ans - 10
Answer: D
The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:  Choose the correct choice from the following answers:	A) 243 m	B) 240 m	C) 245 m	D) 249 m	E) 242 m

Solution: Speed =45 x5/18 m/sec=25/2m/sec.   Time = 30 sec.   Let the length of bridge be x metres.   Then,130 + x/30=25/2   2(130 + x) = 750   x = 245 m.   Answer 245 m
Answer: C
In a company the manager wants to give some gifts to all of the workers. In each block there are about 200 workers are there. The total amount for giving the gifts for all the workers is $6000. The worth of the gift is 2$. How many blocks are there in the company?  Select:
A) 10  B) 12  C) 18  D) 20  E) 15

Solution: 15ach employee will get a gift worth of = $2   total employees = 6000/2= 
6000/2 = 3_000
3000   total blocks= 3000/200= 
3000/200 = 15
15   correct option is 15
Answer: E
A sells a bike to B at a profit of 20%. B sells it to C at a profit of 25%. If C pays Rs. 225 for it, the cost price of the bike for A is: Pick one:  A) 150  B) 230  C) 120  D) 430  E) 200

Solution: 150   125% of 120% of 150 = 225   125/100 * 120/100 * 150= 
125/100 * 120/100 * 150 = 225
225   150= 225 * 2/3= 
225 * 2/3 = 150
150.
Answer: A
A train covers a distance in 50 min, if it runs at a speed of 48kmph on an average. The speed at which the train must run to reduce the time of journey to 40min will be Choose the correct choice from the following answers.
A) 47 kmph
B) 60 kmph
C) 69 kmph
D) 37 kmph
E) 80 kmph

Solution: 60 kmph   60 kmph   Time = 50/60 hr = 5/6hr   Speed = 48mph   distance = S*T = 48 * 5/6= 
48 * 5/6 = 40
40km   time= 40/60hr = 2/3hr   New speed = 40* 3/2= 
40* 3/2 = 60
60kmph
Answer: B
The average mark of the students of a class in a particular exam is 80. If 5 students whose average mark in that exam is 30 are excluded, the average mark of the remaining will be 90. Find the number of students who wrote the exam.  Select the correct option:
A) 22 B) 27 C) 25 D) 99 E) 30

Solution: Let the number of students who wrote the exam be x.   Total marks of students = 80 x.   Total marks of (x - 5) students = 90(x - 5)   80x - (5 * 30) = 90(x - 5)   300 = 10x => x = 30.Answer: 30
Answer: E
A certain collage has total of 600 seniors each majoring in exactly one of six subjects. A minimum of 20 seniors major in each six subjects. If three quarter of the seniors major in one of four subjects, what is the greatest possible number of seniors majoring in one of the other two subjects?	Pick.
A) 100
B) 130
C) 75
D) 60
E) 50

Solution: Answer 130   600 = 450 + 20 + x => x = 130   = 3/4 * 600 in 4 subjects + 20 min for 5th subject + x = 600
Answer: B
Sonika deposited Rs.8000 which amounted to Rs.9200 after 3 years at simple interest. Had the interest been 1.5% more. She would get how much?  Pick:  A) 9560  B) 96288  C) 26667  D) 1662  E) 2882

Solution: (8000*3*1.5)/100= 
(8000*3*1.5)/100 = 360
360   9200   --------   9560   9560nswer:9560
Answer: A
A textile worker’s wages are increased by 10% and afterwards decreased by 10 %. Find the change percentage in his wages.  Pick one:
A) 1% decrease
B) 2% decrease
C) 5% decrease
D) 7% decrease
E) 8% decrease

Solution: Explanation:   Let workers wages = X   1% decrease 10% increase would mean new wages   = (110/100) X   1% decrease 10% decrease would mean new wages   = (90/100) (110/100 X)   = 99/100 X which means a decrease of 1 %   1% decreaseNSWER: 1% decrease
Answer: A
One week, a certain truck rental lot had a total of 18 trucks, all of which were on the lot Monday morning. If 50% of the trucks that were rented out during the week were returned to the lot on or before Saturday morning of that week, and if there were at least 12 trucks on the lot that Saturday morning, what is the greatest number of different trucks that could have been rented out during the week? Choose the correct choice from the following:
A) 18
B) 16
C) 12
D) 8
E) 4

Solution: N - Not rented trucks; R - Rented trucks   N + R = 18   N + R/2 = 12   R = 12   12
Answer: C
In a village of 2,600 people, 800 people are over 70 years old and 850 people are female. It is known that 40 percent of the females are younger than 70 years old. If no one in the village is 70 years old, what is the probability that a person chosen at random is either a female or younger than 70 years old? Choose the correct choice from the following answers:
A) 231/260	B) 117/130	C) 51/65	D) 23/32	E) 11/16

Solution: The number of people younger than 70 years old is   2600-800= 
  2600-800 = 1_800
1800   The number of females older than 70 years old is   0.6*850= 
  0.6*850 = 510
510   The number of people who are either female or younger than 70 is  1800+510= 
 1800+510 = 2_310
2310.   P(a person is younger than 70 or male)= 2310/2600 = 231/260   The answer is 231/260.
Answer: A
A manufacturer of a certain product can expect that between 0.4 percent and 0.5 percent of the units manufactured will be defective. If the retail price is $2,500 per unit and the manufacturer offers a full refund for defective units, how much money can the manufacturer expect to need to cover the refunds on 20,000 units?	Answers.
A) Between $15,000 and $25,000
B) Between $30,000 and $50,000
C) Between $200,000 and $250,000
D) Between $150,000 and $250,000
E) Between $300,000 and $500,000

Solution: Number of defective units is between = .4 % of 20000 and .5% of 20000   = 80 and 100   Retail Price per unit = 2500 $   Expected price of refund is between = 2500 x 80 and 2500 x 100   =2,00,000 and 2,50,000 dollars   Answer Between $200,000 and $250,000
Answer: C
Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is	Pick one
A) 17/28	B) 17/27	C) 17/19	D) probability of 17/20	E) 17/22

Solution: n(S) = 20   n(Even no) = 10 = n(E)   n(Prime no) = 8 = n(P)   P(EᴜP) = 10/20 + 8/20 - 1/20 = 17/20   Answer: probability of 17/20
Answer: D
A certain factory produces buttons and buckles at a uniform weight. If the total weight of 2 buttons and 2 buckles is one third of 11 buckles and 3 buttons, then the weight of 3 buttons and 4 buckles is how many times that of 5 buckles and 6 buttons?	Options:
A) 7/15.
B) 4/9.
C) 6/11.
D) 3/5.
E) 8/15.

Solution: 2buttons + 2buckles = 1/3(11buckles + 3buttons)   6buttons + 6buckles = 11buckles + 3buttons   3buttons = 5buckles   Weight of 3buttons and 4buckles = 5buckles + 4buckles = 9buckles   Weight of 6buttons and 5buckles = 10buckles + 5buckles = 15buckles   (3buttons and 2buckles) = x * (6buttons and 5buckles)   9 = x*15   x = 9/15=3/5   Answer: 3/5.
Answer: D
A truck travels 20 miles due north, 30 miles due east, and then 20 miles due north. How many miles is the truck from the starting point?
Choose the correct choice:
A) 20.3  B) 44.7  C) 50  D) 70  E) 120

Solution: We have two right angle triangles with sides 20 and 15   The distance between starting and end point = sum of the hypotenuse of both the triangles.   Hypotenuse = [400 + 225]^(1/2) = 25   Hence the total distance between end point and starting point = 25 + 25= 
25 + 25 = 50
50   50orrect Option: 50
Answer: C
what is the next term of this series6,10,9,15,..?
Pick one
A) 9  B) 10  C) 11  D) 12  E) 15

Solution: 3&2=6;    5*2= 
 5*2 = 10
10;    3*3= 
 3*3 = 9
9;    3*5= 
 3*5 = 15
15.   3*4= 
3*4 = 12
12   ANSWER:12
Answer: D
Suppose you answer the last three questions on this test at random. What is the most likely
number of these three questions that you will answer correctly?  Choose the correct choice from the following answers
A) 0
B) 1
C) 2
D) 3
E) it is impossible to determine

Solution: There are five answers to each question The probabilities you will correctly answer   respectively 0, 1, 2, and 3 are   4/5   4/5   4/5   =   64/125   ;   3   1/5   4/5   4/5   =   48/125   ;   3   1/5   1/5   4/5   =   12/125   ;   1/5   1/5   1/5   =   1/125   :   The first is the most likely possibility. Indeed, it is more probable than the other three combined   correct answer 0
Answer: A
A customer went to a shop and paid a total of $30, out of which $1.28 was for sales tax on taxable purchases. If the tax rate was 8%, then what was the cost of the tax free items?
Options:  A) $9.84  B) $10.68  C) $11.26  D) $12.72  E) $13.54

Solution: The total cost was $30.   The tax was $1.28   Let the original price of the taxable items = x   Given that tax rate = 8%   0.08x = 1.28   x = $16   The cost of the tax free items was $30 - $16 - $1.28 = $12.72   The answer is $12.72.30 -  16 -  1.28= 
30 -  16 -  1.28 = 12.72
$12.72   The answer is $12.72.
Answer: D
What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 20%?  Choose the correct choice from the following answers
A) 20%
B) 70%
C) 80%
D) 40%
E) 10%

Solution: Explanation:   SP2 = 2/3 SP1   CP = 100   SP2 = 80   2/3 SP1 = 80   SP1 = 120   100 --- 20 => 20%   20%nswer: 20%
Answer: A
In a college, 280 students study Hindi, 254 students study Sanskrit and 280 students study English.
97 students study Hindi as well as physics, 138 students study Sanskrit as well as English and 152 students study Hindi as well as English.
73 students study all the three languages.
How many total number of students are there in that college?
Pick:  A) 350  B) 500  C) 650  D) 235  E) 450

Solution: 500
Answer: B
A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is:  Choices
A) 100 m	B) 125 m	C) 130 m	D) 150 m	E) 170 m

Solution: Let the length of the train be x meters and its speed be y m/sec.   They, x / y = 15 => y = x/15   x + 100 / 25 = x / 15   x = 150 m.   ANSWER:150 m
Answer: D
In covering distance,the speed of A & B are in the ratio
of 3:4.A takes 30min more than B to reach the destion.The time
taken by A to reach the destinstion is.  Choose the correct choice from the following choices: A) 4 hrs B) 9 hrs C) 3 hrs D) 5 hrs E) 2 hrs

Solution: Ratio of speed = 3:4   Ratio of time = 4:3   let A takes 4x hrs,B takes 3x hrs   then 4x-3x = 30/60 hr   x = ½ hr   Time taken by A to reach the destination is 4x = 4 * ½ = 2 hr   Answer is 2 hrs.
Answer: E
Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 35 kmph. Of how many minutes does the train stop per hour? Choose the correct choice:  A) E982  B) 27  C) 12  D) 121  E) 13.3

Solution: 13.3xplanation:   T = 10/45 * 60 = 13.3   Answer: Option 13.3
Answer: E
5 blue marbles, 3 red marbles and 4 purple marbles are placed in a bag. If 4 marbles are drawn without replacement, what is the probability that the result will not be 2 blue and 2 purpl e marbles?
Pick one
A) 4/33
B) (5/36)^2
C) 1/2
D) (31/36)^2
E) 29/33

Solution: Answer is 29/33.   The probability of 2 blue and 2 purple marbles selected is 5C2.4C2/12C4 =4/33.   Subtracting the above from 1 we get 29/33 29/33
Answer: E
Find the simple interest on $1200 for 5 years at 20% per annum? Choose the correct choice.
A) $1200  B) $1000  C) $500  D) $1100  E) $1500

Solution: SI = PTR/100   = 1200*5*20/100= 
1200*5*20/100 = 1_200
$1200   $1200nswer is $1200
Answer: A
Sagar purchased 10 kg of rice at the rate of Rs. 15 per kg and 25 kg of rice at the rate Rs. 14 per kg. He mixed the two and sold the mixture. Approximately at what rate per kg should he sell the mixture to make 40 % profit in the transaction?	Choose the correct choice from the following options.
A) Rs. 20.00	B) Rs. 20.08	C) Rs. 20.02	D) Rs. 20.008	E) Rs. 20.021

Solution: Explanation:   Rice variety	Quantity(Kg)	Rate(Rs/Kg)	Cost(in Rs)   First	10	15	150   Second	25	14	350   Total	500   By 40% profit on cost price,   Selling price of mixture = 140/100 * 500   = Rs. 700   Therefore, selling price per kg of mixture = 700/35 = Rs. 20'   Rs. 20.00NSWER:Rs. 20.00
Answer: A
Three bells commence tolling together and toll at intervals of 3,6,9 seconds respectively. In 60 minutes, how many times do they toll together?  Choose the correct choice from the following answers:
A) 4	B) 10	C) 15	D) 21	E) 17

Solution: L.C.M of 3,6,9 is 18. i.e after each 3 min they will toll together.So in 60 min they will toll 20 times.As they have initially tolled once,The answer will be  20+1= 
 20+1 = 21
21.   ANSWER:21
Answer: D
The product of two consecutive negative even integers is 24. Find the numbers.	Choose the correct choice from the following options.
A) -2, -4
B) -10, -12
C) -6, -8
D) -4, -6
E) -12, -14

Solution: (n)(n + 2) = 24   n2 + 2n = 24   n2 + 2n – 24 = 0   (n + 6)(n – 4) = 0   Then the solutions are n = –6 and n = 4. Since the numbers I am looking for are negative, I can ignore the "4" and take n = –6. Then the next number is n + 2 = –4   Answer: -4, -6
Answer: D
In how many ways can a three-letter password be chosen, using the letters A, B, C, D, E, and/or F, such that at least one letter is repeated within the password?  Choose the correct choice from the following options:
A) 72
B) 86
C) 90
D) 96
E) 1,296

Solution: Total number of four letter passwords = 6*6*6= 
6*6*6 = 216
216 ------(1)   Total number of passwords in which no letter repeats= 6C3*3!= 20*6= 
20*6 = 120
120------(2)   therefore required value= (1)-(2)= 216-120= 
216-120 = 96
96   96
Answer: D
A bag contains 7 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is ? Choose one:
A) 7/17
B) 7/22
C) 7/18
D) 7/19
E) 7/15

Solution: Drawing two balls of same color from seven green balls can be done in ⁷C₂ ways.   Similarly from eight white balls two can be drawn in ⁸C₂ ways.   P = 7C2/¹15C2 + 8C2/15C2   = 7/15   Answer: 7/15
Answer: E
find value for x from given equation? x + 1 = -3  Choose the correct choice from the following: A) 1 B) -x=-4 C) -3 D) -5 E) 5

Solution: 1. Subtract 1 from both sides:   x + 1 - 1 = -3 - 1   2. Simplify both sides:   x = -4   -x=-4
Answer: B
In how many ways can 10 people line up at a ticket window of a railway station?
Choose the correct answer
A) 36,28,800  B) 34,82,800  C) 33,44,800  D) 33,28,800  E) None of these

Solution: The required number of ways = number of permutations of 10 people taking all 10 at a time.   P(10, 10) = 10!   = 10 x 9 × 8 x 7 x 6 × 5 x 4 x 3 × 2 x 1   = 36,28,800   36,28,800NSWER:36,28,800
Answer: A
The cost of 10 kg of apples is equal to the cost of 24 kg of rice. The cost of 6 kg of flour equals the cost of 2 kg of rice. The cost of each kg of flour is Rs.20.50. Find the total cost of 4 kg of apples, 3 kg of rice and 5 kg of flour?
Choose the correct choice from the following answers:	A) 877.49	B) 877.4	C) 877.45	D) 877.41	E) 877.43

Solution: :   Let the costs of each kg of apples and each kg of rice be Rs.a and Rs.r respectively.   10a = 24r and 6 * 20.50 = 2r   a = 12/5 r and r = 61.5   a = 147.6   Required total cost = 4 * 147.6 + 3 * 61.5 + 5 * 20.5   = 590.4 + 184.5 + 102.5 = Rs.877.40   Answer: 877.4
Answer: B
The population of a town is 8000. It decreases annually at the rate of 20% p.a. What will be its population after 3 years?
Answers:
A) 5100
B) 4096
C) 5200
D) 5400
E) 5500

Solution: Formula :   ( After =100 denominator   Ago = 100 numerator)   8000 Ã— 80/100 Ã— 80/100 x 80/100= 4096   Answer : 4096
Answer: B
In a certain country, 60 percent of the population likes basketball, and 35 percent of the population likes both basketball and golf. What percentage of the people who like basketball also like golf?  Options:
A) 20%
B) 33%
C) 40%
D) 58%
E) 67%

Solution: Correct Answer: (D).   Since this is a percent problem without concrete numbers, we can assign our own. If we assume that there are 100 people in the country, then 60 people like basketball, and 35 people like basketball and golf. We’re looking for people who like both divided by people who like basketball, so 35/60 = 58%, or choice 58%.
Answer: D
Sum of two number = 16 and product = 48, find the difference of the two number ??	Choose the correct option:
A) 1	B) 3	C) 4	D) 5	E) 8

Solution: (X-Y)2 = (X+Y)2 - 4 XY   (X-Y)2 = (16)2 - 4 x 48   (X-Y)2 = 256 - 192   (X-Y)2 = 64   X-Y = 8   ANSW8R 8
Answer: E
The average age of a husband and a wife is 23 years when they were married five years ago but now the average age of the husband, wife and child is 20 years(the child was born during the interval). What is the present age of the child?  Choose the correct choice.
A) 6	B) 5	C) 8	D) 4	E) 2

Solution: 28 * 2= 
28 * 2 = 56
56   20 * 3= 
20 * 3 = 60
60   -----------   4 years.Answer: 4
Answer: D
Excepting ‘seldom’ which means – rarely, infrequently and not often, is the antonym.	Choices: A) 22 B) 278 C) 267 D) 176 E) 971

Solution: Answer:176
Answer: D
A pharmaceutical company received $4 million in royalties on the first $50 million in sales of and then $12 million in royalties on the next $170 million in sales. By approximately what percentage did the ratio of royalties to sales decrease from the first $50 million in sales to the next $170 million in sales?  Choices.
A) 12% B) 15% C) 45% D) 52% E) 56%

Solution: (12/170)/(4/50) = 15/17 = 88% it means that 12/170 represents only 88%. Therefore a decrease of 12%.   12%nswer 12%
Answer: A
Which of the following must be true?
1) Every prime number greater than 5 can be written as either as 9n+1 or 9n-1
2) Every prime number greater than 5 can be written as 4n+1 or 4n-1
3) Every number greater than 5 of the form 9n+1 or 9n-1 is a prime number.	Select the correct option:	A) 1,2	B) 2,3	C) 1,2,3	D) only 1	E) only 2

Solution: Every prime number greater than 3 can be written in the form of 9n+1 or 9n-1 where n is an integer. So 1 can be possible.   3. This is not possible as 2 and 3 are being prime , we can't write then in the form of 9n+1 or 9n-1.   1,2
Answer: A