MU-NLPC/Calc-aqua_rat huggingface dataset:
A shopkeeper buys mangoes at the rate of 6 a rupee and sells them at 4 a rupee. Find his net profit or loss percent?	Choices.
A) 34 %	B) 39 %	C) 50 %	D) 35 %	E) 33 %

Solution: The total number of mangoes bought by the shopkeeper be 24.   If he buys 6 a rupee, his 50 %P = 4   He selling at 4 a rupee, his SP = 6   Profit = SP - 50 %P = 6 - 4= 
6 - 4 = 2
2   Profit Percent= 2/4 * 100= 
2/4 * 100 = 50
50 %   Answer:50 %
Answer: C
A boat running up stram takes 6 hours to cover a certain distance, while it takes 10 hours to cover the same distance running down stream. what is the ratio between the speed of the boat and the speed of water current respectively?  Options:	A) 2 : 3	B) 5 : 6	C) 4 : 1	D) 7 : 1	E) 8 : 1

Solution: Explanation:   Let speed of boat is x km/h and speed stream is y km/hr   6(x+y) = 10(x-y)   6x+6y = 10x-10y   16y = 4x   4y = x   x/y = 4/1   4 : 1   Answer: Option 4 : 1
Answer: C
A bank issued credit card numbers and the corresponding PIN (Personal Identification Number). Both are 3-digit numbers up to 996. Pinaki was the last to get the credit card and so he had the last possible credit card number.
He was afraid of forgetting his PIN. He wrote down the number 124 in his diary to remember his PIN. He also wrote out the way to calculate 124 : "Multiply the card number by PIN. Divide the product by 997. The remainder is 124".
Once, Prafull saw his diary in which Pinaki wrote this number 124. Prafull did a lot of purchasing, as he now knows Pinaki's PIN. What is Pinaki's PIN?	Answers: A) 874 B) 875 C) 876 D) 877 E) 873

Solution: Explanation :   Let, the PIN is x.   According to the question,   The card number =996 and Remainder =124.   Thus, (996 × x)/997=124.   =>x= 873.   Answer : 873
Answer: E
A tank has 5 inlet pipes. Three pipes are narrow and two are wide. Each of the three narrow pipes works at 1/2 the rate of each of the wide pipes. All the pipes working together will take what fraction K of time taken by the two wide pipes working together to fill the tank?	Select:
A) 1/2	B) 2/3	C) 3/4	D) 3/7	E) 4/7

Solution: I always plug in for these questions.. I find them easier   Let 2 large pipes each work fill 10lts/hr   small ones = 1/2*10= 
1/2*10 = 5
5   total 5= 10+10+5+5+5= 
10+10+5+5+5 = 35
35 lts/hrs   now assume the total capacity= 140 lts ( LCM of 20,35)   Qn :All the pipes working together will take what fraction of time taken by the two wide pipes working together to fill the tank   all working together will take 140/35= 
140/35 = 4
4 hrs   two large pipes working will take   140/20= 
  140/20 = 7
7 hrs   hence ratio K= 4/7 = 4/7
Answer: E
A box measuring 36 inches long by 45 inches wide by 18 inches deep is to be filled entirely with identical cubes. No space is to be left unfilled. What is the smallest number of cubes that can accomplish this objective?	Choose the correct option
A) 32  B) 34  C) 38  D) 40  E) 42

Solution: least number of cubes will be required when the cubes that could fit in are biggest.   9 is the biggest number that could divide all three, 36, 45 and 18.   Thus side of cube must be 9, and total number of cubes = 36/9 * 45/9*18/9= 
36/9 * 45/9*18/9 = 40
40   Ans 40.
Answer: D
Find the sum lend at C.I. at 5 p.c per annum will amount to Rs.441 in 2 years?	Choose the correct answer.
A) 387	B) 400	C) 776	D) 268	E) 181

Solution: 441 = P(21/20)2   P = 400   Answer:400
Answer: B
A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that all the four bulbs are defective? Choose the correct answer:
A) 1/127	B) 1/183	C) 1/126	D) 1/122	E) 1/126

Solution: Out of nine, five are good and four are defective. Required probability   = ⁴C₄/⁹C₄ = 1/126   Answer: 1/126
Answer: E
If a, b, y are integers, 33 = aby, and a < b < y, what is the smallest possible value of a?
Select the correct option.
A) -33  B) -3  C) 1  D) 3  E) 11

Solution: Given : a * b * y = 33.   33 is a Positive Odd number.Side Note:Thus, all 3 numbers will be odd.   Prime factorization will also give you numbers. 1, 3, 11. The 3 numbers will be combination of these 3 numbers with possible variation in sign(+/-).   We could have any 2 digits as negative. --> negative * negative * positive. We have negative values in answer option, so eliminate C, D and E from answer choices.   -33 * -1 * 1= 
-33 * -1 * 1 = 33
33.   Correct answer is -33
Answer: A
Two trains each 250 m in length are running on the same parallel lines in opposite directions with the speed of 80 kmph and 70 kmph respectively. In what time will they cross each other completely?
Choices:
A) 15 sec
B) 19 sec
C) 12 sec
D) 10 sec
E) 11 sec

Solution: Explanation:   D = 250 m + 250 m = 500 m   RS = 80 + 70= 
80 + 70 = 150
150 * 5/18= 125/3   T = 500 * 3/125= 
500 * 3/125 = 12
12 sec   Answer: Option 12 sec
Answer: C
A certain team has 8 members, including Joey. A three-member relay team will be selected as follows: one of the 8 members is to be chosen at random to run first, one of the remaining 7 members is to be chosen at random to run second, and one of the remaining 6 members is to be chosen at random to run third. What is the probability that Joey will be chosen to run second or third?
Choose the correct option:	A) 1/1320	B) 1/132	C) 1/110	D) 1/12	E) 1/4

Solution: Total outcomes= 8*7*6   Favorable Outcomes= 7*1*6 and 7*6*1   P=2*7*6*1/8*7*6   P=1/4   Ans 1/4
Answer: E
Two trains are running in opposite directions with the same speed. If the length of each train is 120 m and they cross each other in 8 sec, then the speed of each train is?	Choices:
A) 54  B) 77  C) 36  D) 88  E) 21

Solution: Let the speed of each train be x m/sec.   Then, relative speed of the two trains = 2x m/sec.   So, 2x = (120 + 120)/8 => x = 15   Speed of each train = 15 m/sec.   = 15 * 18/5 =- 54 km/hr.54nswer: 54
Answer: A
If a tire rotates at 400 revolutions per minute when the car is traveling 168km/h, what is the circumference of the tire?
Answers.
A) 7 meters B) 9 meters C) 8 meters D) 5 meters E) 3 meters

Solution: 400 rev / minute = 400 * 60 rev / 60 minutes   = 24,000 rev / hour   24,000 * C = 168,000 m : C is the circumference   C = 3 meters   correct answer 7 meters
Answer: A
Each month, after Jill pays for rent, utilities, food, and other necessary expenses, she has one fifth of her net monthly salary left as discretionary income. Of this discretionary income, she puts 30% into a vacation fund, 20% into savings, and spends 35% on eating out and socializing. This leaves her with $105 dollar, which she typically uses for gifts and charitable causes. What is Jill’s net monthly salary?	Options: A) $2400 B) $3200 C) $3500 D) $6400 E) $9600

Solution: let x be the monthly salary   15%of 1/5*x=105   x=3500   answer $3500
Answer: C
75 persons Major in physics, 83 major in chemistry, 10 not at major in these subjects u want to find number of students majoring in both subjects  Choose the correct option
A) 65
B) 66
C) 67
D) 68
E) 69

Solution: Consider the number of total students = n(T) = 100   number of persons Major in physics = n(P) = 75   number of persons Major in chemistry = n(C) = 83   According to the question ;   10 not at major in these subjects = n(P'∩ C') = 10   n(P'∩ C') = n(P U C)' = 10   n(P U C)' = n(T) - n(P U C)   10 = 100 - n(P U C)   n(P U C) = 90   n(P U C) = n(P) + n(C) - n(P ∩ C)   90 = 75 + 83 - n(P ∩ C)   n(P ∩ C) = 158 - 90   n(P ∩ C) = 68   number of students majoring in both subjects WILL be 68   ANSWER:68
Answer: D
A man, his wife and daughter worked in a graden. The man worked for 3 days, his wife for 2 days and daughter for 4 days. The ratio of daily wages for man to women is 5 : 4 and the ratio for man to daughter is 5 : 3. If their total earnings is mounted to Rs. 105, then find the daily wage of the daughter.  Choose the most appropriate option:
A) Rs. 15
B) Rs. 12
C) Rs. 10
D) Rs. 9
E) NONE OF THE ABOVE

Solution: EXPLANATION:   Assume that the daily wages of man, women and daughter are Rs 5x, Rs. 4x, Rs 3x respectively.   Multiply (no. of days) with (assumed daily wage) of each person to calculate the value of x.   [3 x (5x)] + [2 x (4x)] + [4 x (3x)] = 105   [15x + 8x + 12x] = 105   35x = 105   x = 3   Hence, man's daily wage = 5x = 5 x 3 = Rs. 15   Wife's daily wage = 4x = 4 x 3 = Rs. 12   Daughter's daily wage = 3x = 3 x 3 = Rs. 9   ANSWER IS Rs. 9
Answer: D
Of the 160 people at a party, 70 were women, and 50 women tried the appetizer. If 50 people did not try the appetizer, what is the total number of men who tried the appetizer?
Choose the most appropriate option:
A) 40
B) 50
C) 60
D) 70
E) 80

Solution: Total people at party=160   Women=70   so Men  160-70= 
 160-70 = 90
90   No. of pple who tried appetizer=160-50 (given info)=110   No of women who tried appetizer=50   So Remaining ppl(men) who tried the appetizer =110-50= 
110-50 = 60
60   60orrect Option 60
Answer: C
One pipe can fill a pool 1.5 times faster than a second pipe. When both pipes are opened, they fill the pool in five hours. How long would it take to fill the pool if only the slower pipe is used?	Choose the correct choice from the following:  A) 11.25  B) 11.52  C) 12.5  D) 9  E) 7.2

Solution: Say the rate of the slower pipe is R pool/hour, then the rate of the faster pipe would be 1.5R=3R/2. Since when both pipes are opened, they fill the pool in five hours, then their combined rate is 1/5 pool/hour.   Thus we have that R + 3R/2 = 1/5 --> R = 2/25 pool/hour --> time is reciprocal of rate thus it's 25/2= 
25/2 = 25/2 = around 12.5
12.5 hours.   Answer: 12.5.
Answer: C
A cistern 6m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:
Choose the correct choice from the following.
A) 49 m2
B) 50 m2
C) 53.5 m2
D) 55 m2
E) 58

Solution: Area of the wet surface	= [2(lb + bh + lh) - lb]   = 2(bh + lh) + lb   = [2 (4 x 1.25 + 6 x 1.25) + 6 x 4] m2   = 49 m2.   49 m2nswer: Option 49 m2
Answer: A
Find the ratio between 1hr 30 minutes and 2hrs 40 minutes. Choose the correct choice from the following answers: A) 9:16 B) 5:9 C) 12:17 D) 13:24 E) None of these

Solution: Solution: The ratio = 1hr 30 min : 2hr 40 min. 90 min : 160 min = 9 : 16.   9:16NSWER IS 9:16
Answer: A
A man can row upstream at 25 kmph and downstream at 31 kmph, and then find the speed of the man in still water?
Choose the correct choice:
A) 22	B) 28	C) 30	D) 27	E) 18

Solution: US = 25   DS = 31   M = (31 + 25)/2= 
(31 + 25)/2 = 28
28   Answer:28
Answer: B
The length of the bridge, which a train 130 m long and traveling at 45 km/hr can cross in 30 sec is?
Pick:
A) 187 m
B) 279 m
C) 245 m
D) 279 m
E) 222 m

Solution: Speed = 45 * 5/18 = 25/2 m/sec.   Time = 30 sec   Let the length of bridge be x meters.   Then, (130 + x)/30 = 25/2   x = 245 m.   Answer: 245 m
Answer: C
A, B AND C TOGETHER EARN RS. 300 PER DAY WHILE A AND C TOGETHER EARN RS. 188 AND B AND C TOGETHER EARN RS. 152. THE DAILY EARNING OF C IS:	Choose the correct option.
A) RS. 40	B) RS. 68	C) RS. 112	D) RS. 150	E) NONE OF THESE

Solution: B'S DAILY EARNING = RS. (300-188)=RS. 112   A'S DAILY EARNING = RS. (300=152)-RS. 148.   C'S DAILY EARNING = RS. (300-(112+148))=RS. 40   CORRECT OPTION: RS. 40
Answer: A
A rectangular field has a length 10 meters more than it is width. If the area of the field is 119, what is the length (in meters) of the rectangular field?
Select the correct option
A) 13 B) 15 C) 17 D) 19 E) 21

Solution: area = l * w = (L) * (L-10) = 171   trial and error:    20*10= 
 20*10 = 200
200 (too high)   19*9= 
19*9 = 171
171 (too high)   18*8= 
18*8 = 144
144 (too high)   17*7= 
17*7 = 119
119   The length is 17 meters.   The answer is 17.
Answer: C
Find the value of y from (12)^3 x 6^4 ÷ 432 = y?	Select:  A) 3452  B) 2343  C) 2435  D) 2578  E) 5184

Solution: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184   432 12 x 62   5184
Answer: E
A tailor trims 6 feet from opposite edges of a square piece of cloth, and 5 feet from the other two edges. If 80 square feet of cloth remain, what was the length of a side of the original piece of cloth?  Choose one.
A) 16
B) 18
C) 20
D) 24
E) 32

Solution: Let the original side of the square be x.   (x-12)*(x-10) = 80 = 8*10   x = 20   The answer is 20.
Answer: C
How much pure alcohol should be added to 400ml of a 15% solution to make the strength of solution 28%?
Options.
A) 100 ml  B) 60 ml  C) 120 ml  D) 140 ml  E) 150 ml

Solution: we can also go by answer choices   Tke 100 ml for eg   400 (old)+100 (new concentr)ml     500*28/100= 
  500*28/100 = 140
140 ml (40ml is de old concentration +100 ml (newly added)   Answer 140 ml
Answer: D
The ratio of the ages of three people is 4:6:7. Six years ago, the sum of their ages was 50. Find their present ages.	Choose the correct answer: A) 12,18,21 B) 16,24,28 C) 20,30,35 D) 24,36,42 E) 28,42,49

Solution: Let the present ages be 4x, 6x, 7x.   (4x-6) + (6x-6) + (7x-6) = 50   17x = 68   x = 4   Their present ages are 16, 24, and 28.   The answer is 16,24,28.
Answer: B
The symphony sells two kinds of tickets: orchestra, for $30, and upper tiers, for $12. On a certain night, the symphony sells 90 tickets and gets $1800 in revenue from the sales. How many orchestra tickets did they sell?
Choices.
A) 20  B) 30  C) 40  D) 50  E) 60

Solution: Let x be the number of orchestra tickets.   Then 90-x is the number of upper tier tickets.   30x + 12(90-x) = 1800   18x = 1800-1080   x = 40   The answer is 40.
Answer: C
what is the sum of all 5 digits numbers which can be formed with the digits 0,1,2,3,4 without repetition
Choose the correct choice:
A) 2599980
B) 2699980
C) 2799980
D) 2509980
E) 2499980

Solution: There is a simplest formula for solving these type of questions when we are using numbers along with 0 for finding sum.   i,e........(sum of numbers)*{(n-1)!*(111...........n times)-(n-2)!*(111..........(n-1)times) }   so,here by putting the values as,   (0+1+2+3+4){(5-1)!*(11111)-(5-2)!*1111}   = 10{(4!*11111)-(3!*1111)}   = 10{266664-6666}   = 2599980   2599980NSWER:2599980
Answer: A
A merchant sold two items for Rs.1700 each, and makes a profit of 25% from the first item and a loss of 20% from the second item. calculate the total gain or loss.
Select the correct option.
A) 7	B) 5	C) 3	D) 6	E) 4

Solution: (25*20)/100= 
(25*20)/100 = 5
5%loss   Answer: 5
Answer: B
I have only 1$ and 2$ note. I want to give 95$ to John. How many maximum number of 2$ note I need?
Choose the correct choice from the following options
A) 39	B) 95	C) 47	D) 55	E) 76

Solution: 47heck whether 95 is divisible by 2 then that is maximum no of 2$ note   else check next maximum term before 95   so 94/2= 
94/2 = 47
47   ans is 47
Answer: C
An amount of money is to be divided among P, Q and R in the ratio of 4 : 9 : 16. If R gets 4 times more than P, what is Q’s share in it?
Choose the correct choice:
A) 1,800
B) 2,700
C) 3,600
D) Data inadequate
E) None of these

Solution: Here, neither the total amount nor the individual amount is given. So the share of Q cannot be determined.   Answer Data inadequate
Answer: D
If x is an integer and y = 3x + 7, which of the following CANNOT be a divisor of y?	Choose the correct option.
A) 4	B) 5	C) 7	D) 9	E) 8

Solution: For any value of x, the expression 3x + 2 would never be divisible by 3,6,9...... onwards   So answer = 6 = 9
Answer: D
Mr. Kramer, the losing candidate in a two-candidate election, received 942,568 votes, which was exactly 25 percent of all votes cast. Approximately what percent of the remaining votes would he need to have received in order to have won at least 50 percent of all the votes cast?
Choose the correct choice from the following choices:
A) 10%
B) 12%
C) 15%
D) 17%
E) 33%

Solution: Lets assume that candidate got 25% votes and total votes is 100.   Candidate won = 25   Remaining = 75   To get 50%, candidate requires 25 votes from 100 which is 25% and 25 votes from 75.   25/75 = 33.33%   Which is approx 33%. Hence the answer is 33%
Answer: E
Addison High School’s senior class has 200 boys and 160 girls. If 60% of the boys and 75% of the girls attended college, what percentage of the total class that did not attend college?	Choose the correct choice from the following answers
A) 33.33  B) 60  C) 80  D) 66.67  E) 64

Solution: Number of boys attending the college: 0.60*200= 
0.60*200 = 120
120   number of girls attending the college: 0.75*160= 
0.75*160 = 120
120   Total attending= 120+120= 
120+120 = 240
240   Total people= 200+160= 
200+160 = 360
360   % of people attending= 240/360 = 66.67%. 66.67 is the correct answer
Answer: D
How many seconds will a 500 metre long train moving with a speed of 63 km/hr, take to cross a man walking with a speed of 3 km/hr in the direction of the train ?	Choose the most appropriate option.
A) 30 B) 40 C) 50 D) 20 E) 15

Solution: Dist = 500 m   relative speed = (63-3)= 
(63-3) = 60
60 km/hr   60*5/18= 50/3 m/s   time taken = 500/(50/3)= 
500/(50/3) = 30
30 sec   30NSWER 30
Answer: A
Two trains, one from Hyderabd to Bangalore and the other from Bangalore to Hyderabad, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is ?  Choose the correct choice from the following choices: A) 2 : 3 B) 3 : 2 C) 3: 4 D) 1 : 2 E) 4 : 3

Solution: Let us name the trains as A and B.   Then, (A's speed) : (B's speed)   = √b : √a = √16 : √9 = 4:3   Answer : 4 : 3
Answer: E
If n is a positive integer, what is the remainder when (6^(4n+3))(6^n) is divided by 10?	Choose one:
A) 7
B) 2
C) 4
D) 6
E) 8

Solution: This one took me bout 3 1/2 min. Just testin numbers and what not.   First notice that n is positive. Save time by noticing thatI worked out one solution where n=0 only to find that thats not an option :p.   1-7 stands for ^1 thru 6   1: 7*1=7   2: 7*7=9   3: 7*9=3   4: 7*3=1   5: 7*1=7   6: 7*7=9   7: 7*9=3   Pattern repeats every @ 5. Notice every ^4 or multiple of 4 is always going to be 1. This is just for future notice for similar problems.   so 7^4n+3 ---> if n=1 then its ((7^7)*6))/10 which can say is going to be 3*8--> 18/10 --> R=8   Now from here if id double check just to make sure.   7^4(2)+3*6= 
3*6 = 18
18/10 ---> R=7.   7 or J in this problem.
Answer: A
An amount of Rs. 55000 is invested in two types of shares. The first yields an interest of 9% p.a and the second, 11% p.a. If the total interest at the end of one year is 9 3/4 %, then the amount invested in each share was?  Choose the correct answer:
A) s. 52500; Rs. 47500	B) s. 34375; Rs. 20625	C) s. 72500; Rs. 27500	D) s. 82500; Rs. 17500	E) s. 72500; Rs. 17500

Solution: Let the sum invested at 9% be Rs. x and that invested at 11% be Rs. (55000 - x). Then,   (x * 9 * 1)/100 + [(55000 - x) * 11 * 1]/100 = (55000 * 39/4 * 1/100)   (9x + 605000 - 11x)/100 = 39000/4 = 10725/2   x =34375   Sum invested at 9% = Rs. 34375   Sum invested at 11% = Rs. (55000 - 34375) = Rs. 20625   ANSWER:s. 34375; Rs. 20625
Answer: B
The greatest number of four digits which is divisible by 10, 13, 40 and 60 is:  Choose one.
A) 9200	B) 9300	C) 9400	D) 7800	E) 8700

Solution: Greatest number of 4-digits is 9999.   L.C.M. of 10, 13, 40 and 60 is 600.   On dividing 9999 by 7800, the remainder is 2199.   Required number  (9999 - 2199)= 
 (9999 - 2199) = 7_800
7800.   ANSWER :7800
Answer: D
If
1 = 3
2 = 6
3 = 9
4 = 12
5 = 15
Then 9 = ?
Hint: Its a logic Riddle not a mathematical riddle	Choose the correct choice from the following.
A) 1
B) 2
C) 3
D) 4
E) 5

Solution: 3   3   As stated   3=9 => 9=3   Answer is 3
Answer: C
Simple interest on a sum at 4% per annum for 2 years is Rs.80.The compound interest on the same sum for the same period is :
Options:
A) Rs.81.60  B) Rs.160  C) Rs.1081.60  D) None of these  E) Cannot be determined

Solution: Explanation:   Principal = Rs. (100×80/4×2) = Rs.1000   C.I = Rs. [{1000×(1+4/100)2−1000}] = Rs.81.60   Correct Option: Rs.81.60
Answer: A
The charge for a single room at Hotel P is 25 percent less than the charge for a single room at Hotel R and 10 percent less than the charge for a single room at Hotel G. The charge for a single room at Hotel R is what percent greater than the charge for a single room at Hotel G ?	Choose the correct option:	A) 15%	B) 20%	C) 40%	D) 50%	E) 150%

Solution: Let rate in R = 100x   then P = 75x   G = 100y   P = 90y   Thus   75 x=90y   or x = 1.20 y   Ans R = 120y   so increase = 20%   Answer: 20%.
Answer: B
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 answer
A) 2 years	B) 3 years	C) 5 years	D) 4 years	E) 1 years

Solution: Answer: Option 4 years   28 * 2= 
28 * 2 = 56
56   20 * 3= 
20 * 3 = 60
60   -----------   4 years
Answer: D
A can do a piece of work in 36 days, B in 54 days and C in 72 days. All the three began the work together on the Dec. 15, 2000, but A left 8 days and B 12 days before the completion of the work. If C took the rest for a week then in how many days, the work was finished from the day it started ? Sol. Let the total time taken be x days.	Answers:
A) 1 B) 70 C) 5 D) 7 E) 776

Solution: Answer:776
Answer: E
A technician makes a round-trip to and from a certain service center by the same route. If the technician completes the drive to the center and then completes 30 percent of the drive from the center, what percent of the round-trip has the technician completed?
Choose one
A) 5%
B) 10%
C) 25%
D) 40%
E) 65%

Solution: The complete round trip consists of driving to the service center and then back home again.   So, once the technician drives to the service center he/she has already competed 50% of the entire trip.   Since the technician completes a portion of the trip back home,the correct answer must be greater than 50%   so  0.5+0.5*0.3= 
 0.5+0.5*0.3 = 0.65
0.65   Answer:   65%
Answer: E
If x^2+(1/x^2)=5, x^4+(1/x^4)=?	Select the correct option.
A) 23 B) 11 C) 12 D) 14 E) 15

Solution: -> x^4+(1/x^4)=(x^2)^2+(1/x^2)^2=(x^2+1/x^2)^2-2x^2(1/x^2)=5^2-2=23.   Thus, the answer is 23.
Answer: A
In the xy-plane, the line y = k is the perpendicular bisector of the line segment PQ and the line x = d is the perpendicular bisector of the line segment RQ. If the coordinates of the point R are (-d, -k), then what are the coordinates of the point P? Pick one:
A) (-5d, -5k) B) (-3d, -3k) C) (2d, 2k) D) (3d, 3k) E) (5d, 5k)

Solution: firstly the Question tells us that RQ and PQ are perpendicular at Q..   Now the coordinates of the point R are (-d, -k), so R is at a distance of 2d from line x and at dist of 2k from line Y..   as line X bisect RQ .... length of RQ =4d and coord (3d,-k)..   as line Y bisect PQ .... length of PQ =4k and coord (3d,3k).ans (3d, 3k)
Answer: D
Ross has 60 shirts, 3/4 of the shirts are green and 1/10 is without buttons. Therefore Ross has between ___ and ___ shirts with buttons that are not green. Choices
A) 9 ; 15.  B) 2 ; 15.  C) 4 ; 10.  D) 5 ; 25.  E) 3 ; 10.

Solution: Total shirts = 60   Green shirts = 3/4*60= 
3/4*60 = 45
45, Non green shirts= 15   Shirts without button = 1/10*60= 
1/10*60 = 6
6, shirts with button= 24   Required: Range of shirts with buttons that are not green.   Maximum non green shirts with buttons = number of non green shirts = 15   Minimum non green shirts with buttons (9 ; 15.ll without button shirts are non green) = Non green shirts - shirts without button = 15 - 6 = 6   Hence the range would be (9, 15)   Correct Option: 9 ; 15.
Answer: A
A is a working partner and B is a sleeping partner in the business. A puts in Rs.15000 and B Rs.25000, A receives 10% of the profit for managing the business the rest being divided in proportion of their capitals. Out of a total profit of Rs.9600, money received by A is?
Options
A) 1978
B) 2707
C) 7728
D) 4200
E) 7291

Solution: 15:25 => 3:5   9600*10/100= 
9600*10/100 = 960
960   9600 - 960= 
9600 - 960 = 8_640
8640   8640*3/8= 
8640*3/8 = 3_240
3240 + 960= 
3240 + 960 = 4_200
4200   Answer: 4200
Answer: D