MU-NLPC/Calc-aqua_rat huggingface dataset:
Naomi drives to the beauty parlor in 60 minutes. On the way back, her average speed is half the average speed as it was to the way to the parlor. How much time will it take Naomi to travel two round trips to the beauty parlor? Select:
A) 3 hours.  B) 4 hours.  C) 4 hours and 20 minutes.  D) 5 hours and 50 minutes  E) 6 hours.

Solution: s1=2s2   since, speed is inversely proportional to time   we have,   s1/s2=2/1= 
2/1 = 2
t2/t1   therefore , the time taken for one trip= 60+120= 
60+120 = 180
180 minutes   total= 180*2= 
180*2 = 360
360 minutes= 6 hours   ANSW6 hours.R:6 hours.
Answer: E
If the price of 20 toys is 540, then what will the price of 15 toys ? Choose one
A) 144
B) 405
C) 117
D) 287
E) 112

Solution: One toy price = 540/20= 
540/20 = 27
27   15 toy price= 15 * 27= 
15 * 27 = 405
405   Answer : 405
Answer: B
A clock loses two minutes every three hours for 4 days and gains 1% in the subsequent 6 days. If it was set right on Friday at 11 AM, what will be the time at the end of 10 days?
Answers
A) 11:54:40 AM	B) 11:56:24 AM	C) 12:16:40 PM	D) 11:22:24 AM	E) 12:06:36 PM

Solution: Clock loses: 2 minute in 3 hours = 16 minutes in 24 hours = 64 minutes in 4 days.   Clock gains: 1% in the subsequent 6 days = 1% in 6*24*60 minutes = 86.40 minute in 6 days;   Net gain in 10 days = 86.40 - 64= 
86.40 - 64 = 22.4
22.4 minutes.   11AM + 22.4 minutes= 11:22 and 4/10th of a minute or 24 seconds.   Answer: 11:22:24 AM.
Answer: D
A salesman sold twice as much pears in the afternoon than in the morning. If he sold 360 kilograms of pears that day, how many kilograms did he sell in the morning and how many in the afternoon?	Choose the most appropriate option:
A) 120
B) 140
C) 240
D) 320
E) 100

Solution: Let x be the number of kilograms he sold in the morning.Then in the afternoon he sold 2x kilograms. So, the total is   x+2x=3x. This must be equal to 360.   3x=360   x=360/3= 
360/3 = 120
120   Therefore, the salesman sold 120 kg in the morning and   2*120= 
  2*120 = 240
240 kg in the afternoon.   Answer is 240.
Answer: C
If the bus had traveled 60 kmh faster than it actually did, the trip of 120 km would have lasted 1 hour less. Find the speed of the bus.
Choose the correct choice from the following choices:
A) 55 kmh
B) 30 kmh
C) 80 kmh
D) 60 kmh
E) 75 kmh

Solution: Time = Distance/Speed   Difference in time = 1 hr   120/x - 120/(x + 60) = 1   Substitute the value of x from the options. --> x = 60 --> 120/60 - 120/120 = 2 - 1= 
2 - 1 = 1
1   Answer: 60 kmh
Answer: D
The sum of two numbers is 95. Their difference is 5. The bigger number is  Choose the correct choice from the following choices:	A) 20	B) 50	C) 30	D) 35	E) 45

Solution: X + Y = 95   X - Y = 5   Adding 2X = 100 ==> X = 50 and Y = 95 - 50= 
95 - 50 = 45
45   50igger number is X= 50   Answer 50.
Answer: B
A card is drawn from a pack of 52 cards. The probability of getting a queen of club or a king of heart is  Choose the correct choice from the following answers.
A) 1/13
B) 2/13
C) 1/26
D) 1/52
E) None

Solution: Solution   Here, n(S) = 52   Let E = event of getting a queen of club or a king of heart.   Then, n(E) = 2.   P(E)	= n(E) / n(S)   = 2/52   ‹=›1/26.   Answer 1/26
Answer: C
Three people each took 5 tests. If the ranges of their scores in the 5 practice tests were 17, 28 and 34, what is the minimum possible range in scores of the three test-takers?  Options.
A) a 17  B) b) 34  C) c) 35  D) d) 45  E) e) 80

Solution: It is finding the minimum range between all their scores, if all test taker scores are between 0 and maximum range we will have:   A- 0 and 17   B- 0 and 28   C- 0 and 35   therefore the minimum range is 34, it cant be any lower however you play with the numbers.   b) 34
Answer: B
You buy a piece of land with an area of âˆš400, how long is one side of the land plot?	Select the correct option.
A) 28  B) 29  C) 30  D) 20  E) 32

Solution: Try filling the numbers into the answer y x y =   Find the closest to 400.   Answer 20
Answer: D
#p is defined as 2p-20 for any number p. What is p, if #(#(#p))=12?  Choose the correct option.
A) –108	B) 19	C) 10	D) 16	E) 18

Solution: #p = 2p-20 --->#(#p) = 2(2p-20)-20 = 4p-60 and thus #(4p-60) = 2(4p-60)-20 = 8p-140 = 12 ---> 8p= 152 ---> p = 19, 19 is the correct answer.
Answer: B
The circumferences of two circles are 264 meters and 352 meters. Find the difference between the areas of the larger and the smaller circles?  Choose the correct choice from the following options.
A) 1976 sq m B) 2176 sq m C) 4312 sq m D) 1269 sq m E) 2679 sq m

Solution: Let the radii of the smaller and the larger circles be s m and l m respectively.   2∏s = 264 and 2∏l = 352   s = 264/2∏ and l = 352/2∏   Difference between the areas = ∏l2 - ∏s2   = ∏{1762/∏2 - 1322/∏2}   = 1762/∏ - 1322/∏   = (176 - 132)(176 + 132)/∏   = (44)(308)/(22/7) = (2)(308)(7) = 4312 sq m   Answer:4312 sq m
Answer: C
If 4 men can colour 48 m long cloth in 2 days, then 2 men can colour 36 m long cloth in	Choose the correct answer
A) 1 day
B) 2 days
C) 3 days
D) 4 days
E) 5 days

Solution: The length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m   No. of days required to paint 36 m cloth by 6 men = 36/ 6 × 2 = 3 day.   3 days
Answer: C
A sum of Rs.4700 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years.
Choices:
A) Rs.2520
B) Rs.3055
C) Rs.3320
D) Rs.2760
E) None of these

Solution: Let A be the amount received at the end of the three years.   A = 4700[1 + 10/100][1 + 20/100][1 + 25/100]   A = (4700 * 11 * 6 * 5)/(10 * 5 * 4)   A = Rs.7755   So the interest = 7755 - 4700 = Rs.3055   ANSWER:Rs.3055
Answer: B
A dress on sale in a shop is marked at $X. During the discount sale its price is reduced by 15%. Staff are allowed afurther 10% reduction on thedis counted price. If a staff member buys thedress what will she have to pay in terms of X?  Choose the correct option.
A) 0.560X  B) 0.560X  C) 0.765X  D) 0.608X  E) 0.895X

Solution: If the price is reduced by 15 %, then the new price will be 0.85D   If this new price is further reduced by 10%, the discounted price will be 0.9 x 0.85X = 0.765X   0.765X
Answer: C
Cost of 2 bats and 3 balls is Rs.1300. The cost of 3 bats and 2 balls is Rs.1200. The cost of each balls is more than that of each bat by?	Choose the correct option:
A) 50
B) 100
C) 110
D) 120
E) 130

Solution: 2100ats + 3100all = 1300 --- (1)   3100ats + 3100all = 1200 --- (2)   Subtracting 2nd from 1st, we get   -100ats  + 100= 
 + 100 = 100
100=> 100all - 100ats = 100   100
Answer: B
If 11 and 13 are prime numbers, which of the following CANNOT be the sum of a and b?  Pick one.
A) 24  B) 48  C) 72  D) 47  E) 96

Solution: ans =47
Answer: D
A and B started a partnership business investing some amount in the ratio of 3 : 5. C joined then after six months with an amount equal to that of B. In what proportion should the profit at the end of one year be distributed among A, B and C? Pick one.
A) 3 : 5 : 2 B) 3 : 5 : 5 C) 6 : 10 : 5 D) 8 : 12 : 4 E) Data inadequate

Solution: Explanation:   Let the initial investments of A and B be 3x and 5x.   A : B : C = (3x x 12) : (5x x 12) : (5x x 6) = 36 : 60 : 30 = 6 : 10 : 5.   Answer is 6 : 10 : 5
Answer: C
A shop keeper had some books. He sells 40% books and still has 420 books. Originally, he had  Choose the correct choice from the following choices.
A) 588 books	B) 600 books	C) 620 books	D) 700 books	E) None of these

Solution: Explanation :   Suppose originally he had x books.   Then,(100-40)% of x = 420.   =>60/100x = 420   =>x = (420 100 / 60   =>x=700.   Answer : 700 books
Answer: D
There were totally 100 men.81 are married.75 have T.V, 85 have radio,70 have A.C. How many men have T.V, radio, A.C and also married?
Choose the most appropriate option.
A) 11	B) 12	C) 13	D) 14	E) 15

Solution: 100-(100-81)-(100-75)-(100-85)-(100-70)= 100-19-25-15-30=100-89= 
100-89 = 11
11   11NSWER:11
Answer: A
When 200 is divided by positive integer x, the remainder is 5. What is the remainder when 395 is divided by x?	Choose the correct choice from the following answers: A) 2 B) 3 C) 4 D) 6 E) 5

Solution: if 200/x leaves a reminder 5 then (200-5) i.e. 195 is divisible by x   So (200+195)/x leaves a reminder rem(200/x)+rem(195/x)=> 5+0= 
5+0 = 5
5   Answer :5
Answer: E
A = {2, 3, 5, 7, 11}
B = {2, 4, 6, 17}
Two integers will be randomly selected from sets A and B, one integer from set A and one from set B, and then multiplied together. How many different products can be obtained?	Choose the correct choice from the following answers:
A) 15 B) 16 C) 19 D) 20 E) 36

Solution: Step 1: Find out the number of products you get.   5 distinct numbers in set A and 4 distinct in set B so number of products = 5*4= 
5*4 = 20
20   Step 2: Remove the products that appear more than once.   Notice that 5, 7, 11 and 13 are primes and none of their multiples are in either set. So ignore them. We just need to focus on 2 and 3 of set A and 2, 4 and 6 of set B.   2, 3   2, 4, 6   The only product repeated when you take a number from each set is 12. (3*4 and 2*6) Rest all are distinct.   Answer= 20 - 1 = 20   Note here that the second step will involve manual calculation since it will depend on the specific numbers you have in the two sets.   20
Answer: D
A 270m long train running at the speed of 120kmph crosses another train running in opposite direction at the speed of 80kmph in 9 second. What is the length of the other train?
Choose the correct choice from the following answers
A) 150m
B) 230m
C) 290m
D) 310m
E) 420m

Solution: Relative speed = 120+80= 
120+80 = 200
200*5/18= 500/9 m/s   Let the length of the other train be x meters   x+270/9 = 500/9   x = 230m   Answer is 230m
Answer: B
A sum of 15,600 amounts to 21,200 in 5 years at the rate of simple interest. What is the rate of interest?
Choose the correct choice from the following answers.
A) 2%	B) 1%	C) 7%	D) 5%	E) 8%

Solution: C   7%   S.I. = (21200 - 15600)= 
(21200 - 15600) = 5_600
5600.   Rate= (100 x 5600)/(15600x5)% = 7%
Answer: C
10 books are placed at random in a shelf. The probability that a pair of books will always be together is  Choose the correct choice from the following answers:
A) 1/9  B) 1/7  C) 1/5  D) 1/6  E) 1/3

Solution: 10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2!   Required probability = 1/5   Answer: 1/5
Answer: C
Lilly has 10 fish and Rosy has 14 fish. In total, how many fish do they have in all?
Answers.
A) 21  B) 22  C) 23  D) 24  E) 25

Solution: 10+14= 
10+14 = 24
24   The answer is 24.
Answer: D
What quantity of water should be added to reduce 20 liters of 80% acidic liquid to 20% acidic liquid? Pick.
A) 30liters
B) 50liters
C) 60liters
D) 70liters
E) 80liters

Solution: Acid in 20 liters = 80% of 20 = 16 liters   Suppose x liters of water be added.   Then 16 liters of acid in 20+x liters of diluted solution   20% of 20+x = 16   20+x = 80   x = 60liters   Answer is 60liters
Answer: C
Ashis's height is 25% more than Babji, by how much percent Babji's height is less than Ashis. Choose the correct answer
A) 30%
B) 25%
C) 75%
D) 20%
E) None of these

Solution: Explanation :   Solution: Babji is less than Ashis by (25/(100+25) * 100)= 
(25/(100+25) * 100) = 20
20%   Answer : 20%
Answer: D
A bullet train 140 m long is running at 60 kmph. In how much time will it pass a platform 210 m long?  Pick one
A) 34 Seconds  B) 22 Seconds  C) 21 Seconds  D) 24 Seconds  E) 29 Seconds

Solution: Distance travelled = 140 + 210= 
140 + 210 = 350
350m   Speed= 60 * 5/8 = 50/3m   Time = 350 * 3/50= 
350 * 3/50 = 21
21 Seconds   ANSWER 21 Seconds
Answer: C
Incomes of two companies A and B are in the ratio of 5 : 8. Had the income of company A been more by 35 lakh, the ratio of their incomes would have been 5 : 4. What is the income of company B?  Pick:
A) 80 lakh	B) 56 lakh	C) 40 lakh	D) 60 lakh	E) None of these

Solution: Let the incomes of two companies A and B be 5x and 8x respectively.   From the question,   5x+35/8x=5/4 ⇒ 20x + 140 = 40x   ∴ x = 7   ∴ Income of company 56 lakh = 8x = 56 lakh   Answer 56 lakh
Answer: B
Two employees X and Y are paid a total of Rs. 550 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?  Options
A) Rs.250  B) Rs.300  C) Rs.320  D) Rs.340  E) Rs.400

Solution: Let the amount paid to X per week = x   and the amount paid to Y per week = y   Then x + y = 550   But x = 120% of y = 120y/100 = 12y/10   ∴12y/10 + y = 550   ⇒ y[12/10 + 1] = 550   ⇒ 22y/10 = 550   ⇒ 22y = 5500   ⇒ y = 5500/22 = 500/2 = Rs.250   Rs.250
Answer: A
If N is the least positive integer that is divisible by every integer from 3 to 10 inclusive, then N/7 is = Select
A) 360
B) 720
C) 2520
D) 3960
E) 6720

Solution: The integer should be divisible by: 3, 4, 5, 6, 7, 8, 9 and 10, that is 3, 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5. The least common multiple of these integers is the product of 7, 5, 3^2 and 2^3. Then, N/7 is (7 * 5 * 3^2 * 2^3)/7 = 5*9*8= 
5*9*8 = 360
360.   360nswer: 360.
Answer: A
If A got 70 marks and B got 60 marks, then what percent of A's mark is B's mark?	Choose the correct answer.
A) A)60% B) B)85.7% C) C)65% D) D)75% E) of these

Solution: A's marks = 70 ; B's marks = 60.   Let x% of A = B => x/100 *70 = 60   => x = (60 * 100)/80 = 85.7   B's marks is 85.7% of A's marks.   ANSWER:85.7%
Answer: B
A male leader is to be selected from a class of students having 15 boys and 20 girls. In how many ways can select?	Choose the correct choice from the following answers.
A) 50 ways
B) 7/3 ways
C) 3/7 ways
D) 35 ways
E) 15 ways

Solution: The number of boy student in the class is 15. Therefore required number of selection =15. Answer : 15 ways
Answer: E
How many seconds will a 500 meter 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 correct option.
A) 42	B) 50	C) 30	D) 28	E) 26

Solution: Explanation:   Distance = 500m   Speed = 63 -3 km/hr = 60 km/hr = 600/36 m/s = 50/3 m/s   Time taken = distance/speed = 500/(50/3)= 
500/(50/3) = 30
30 s   Answer: Option 30
Answer: C
Kid have 8 black balls and 8 white balls. He is trying to arrange a ball in a row then in how many ways can he arrange these balls in a row so that balls of different colors alternate?	Choose the correct option:
A) 3×(4!)^2 B) 1×(9!)^3 C) 2×(8!)^2 D) 2×(8!) E) 2×6^2

Solution: 8 black balls can be arranged in 8! ways ...(A)   Now we need to arrange white balls such that white balls and black balls are positioned alternatively. i.e., we can arrange 8 white balls either in the 8 positions marked as A,B,C,D,E,F,G,H or in the 8 positions marked as B,C,D,E,F,G,H,I as shown below.   8 white balls can be arranged in the 8 positions marked as A,B,C,D,E,F,G,H in 8! ways.   8 white balls can be arranged in the 8 positions marked as B,C,D,E,F,G,H,I in 8! ways.   8 white balls can be arranged in the 8 positions marked as A,B,2×(8!)^2,D,E,F,G,H or in the 8 positions marked as B,2×(8!)^2,D,E,F,G,H,I in 8!+8!=2×8! ways ...(B)   From (A) and (B),   required number of ways =8!×2×8!=2×(8!)^2   2×(8!)^2
Answer: C
If √x = x, then which of the following must be true?  Choose the correct answer
A) x is positive
B) x=1
C) x^2>x
D) x is non-negative
E) None of the above

Solution: Square both the sides we get   x = x^2   x^2 - x= 0   x(x-1)=0   either x=0 or x=1   So, answer will be x is non-negative
Answer: D
Andrew started saving at the beginning of the year and had saved $240 by the end of the year. He continued to save and by the end of 2 years had saved a total of $600. Which of the following is closest to the percent increase in the amount Andrew saved during the second year compared to the amount he saved during the first year? Choices:
A) 11%
B) 25%
C) 44%
D) 50%
E) 125%

Solution: Percent increase in the amount Andrew saved during the second year compared to the amount he saved during the first year.   Percentage Change = ( Change in value / Original value ) * 100   Percentage Change = [ (Saving in 2nd year - Saving in 1st year ) / Saving in 1st year ] * 100   Saving in 2nd year + Saving in 1st year = 600   Saving in 2nd year + 240 = 600   Saving in 2nd year = 600 - 240= 
600 - 240 = 360
360   Change in Value= 360 - 240= 
360 - 240 = 120
120   Original Value= 240   Percentage Increase = (120 / 240 ) * 100   = (1/2 ) * 100= 
(1/2 ) * 100 = 50
50 % ..... Answer 50%......
Answer: D
The total age of A and B is 12 years more than the total age of B and C. C is how many year younger than A
Select.
A) 11  B) 12  C) 13  D) 14  E) 15

Solution: Explanation:   Given that A+12= 
+12 = 12
12 + 12 + C=> A – C = 12 + 12 – 12 = 12   => C is younger than A by 12 years   Answer: Option 12
Answer: B
In an effort to plan out expenses, the Roberts family is representing its annual budget as a circle graph. Each sector of the graph is proportional to the amount of the budget it represents. If “clothes and shoes” takes up 54° of the chart, how much of the Roberts’s $20,000 annual budget is dedicated to clothes and shoes? Choose one
A) $1,500
B) $3,000
C) $4,500
D) $5,000
E) $5,400

Solution: Given for clothes and shoes” takes up 54° of the circular chart.   Then clothes and shoes = 54/360 * 20000.= 
54/360 * 20000. = 3_000
> 3000.   Answer:option $3,000 is correct answer...
Answer: B
In an automobile market of spare parts dealers and workshops, average earning of a spare parts dealer per day is $520 and the average earning of a workshop is $700. Considering there are 40 shops in market and number of spare parts dealer shops exceeds the workshops by 4. What is the average earning of this market consisting of only spare parts dealers and workshops.	Choose one:
A) 535
B) 562
C) 594
D) 601
E) 648

Solution: Let the number of workshops be x   number of s.p.d=x+4   x+x+4=40 = 2x=36 = x=18   workshops are 18 in number and spd are 22 in number   Average earning of the market= ((520x22)+(700x18))/40   =(11440+12600)/40   =24040/40= 
24040/40 = 601
601   Answer: 601
Answer: D
If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same sum at the rate and for the same time?  Choose the correct choice from the following answers:	A) 51.25	B) 51.29	C) 51.22	D) 51.38	E) 51.12

Solution: Sum = (50 * 100) / (2 * 5) = Rs. 500   Amount = [500 * (1 + 5/100)2] = Rs. 551.25   C.I. = (551.25 - 500)   = Rs.51.25.   51.25nswer: a
Answer: A
Each cell of a certain kind of bacteria produces two more cells. The life span of each cell is 10 minutes and each cell multiples only once in its life time, when it is exactly one minute old. If a new cell is placed in an empty box at time t = 0, then how many live cells will be there in the box just after t = 20 minutes?	Choose the most appropriate option
A) 2048 × 1023
B) 1024 × 1023 cells
C) (1024)²
D) 1023 × 1025
E) 1023 × 1026

Solution: see total cells created after   1min be 2^1   2min be 2^2   3 min be 2^3.......   thus after 20 min 2^20 will be created   now after 10 min 1 cell will die (2^0)   after 11 min 2 cells die (2^1)   similarly after 20 min 2^10 cells die   thus total cells remained=(2^20)-(1024)   or (1024)^2-1024   or1024*(1024-1)   i.e, 1024*1023   ANSWER:1024 × 1023 cells
Answer: B
A certain automobile company’s best-selling model is the Speedster. The Speedster, like all of their other models, comes in coupe and convertible styles. 2/3 of the current inventory is Speedsters, of which 4/5 are convertibles. If there are 60 vehicles that are not Speedsters, how many Speedster convertibles are there?
Select.
A) 36  B) 96  C) 100  D) 76  E) 72

Solution: Total Vehicle = 2/3 of speedster + 1/3 of others.   Speedster convertibles = 2/3 total vehicle * 4 /5   Given : 1/3 constitutes 60 Vehicles. hence 2/3 constitutes 120   Speedster convertibls = 120 * 4/5= 
120 * 4/5 = 96
96   96
Answer: B
The difference between the place values of two sevens in the numeral 69758472 is	Choose the most appropriate option:	A) 0	B) 100	C) 6993	D) 699930	E) None of these

Solution: Required difference = (700000 - 70)= 
(700000 - 70) = 699_930
699930   Answer: Option 699930
Answer: D
Average expenditure of a person for the first 3 days of a week is Rs. 310 and for the next 4 days is Rs. 420. Average expenditure of the man for the whole week is:  Choose the correct answer
A) 350  B) 370  C) 390  D) 430  E) None

Solution: Explanation:   Assumed mean = Rs. 310   Total excess than assumed mean = 4 × (Rs. 420 - Rs. 350) = Rs. 280   Therefore, Increase in average expenditure = Rs. 280/7 = Rs. 40   Therefore, Average expenditure for 7 days = Rs. 310 + Rs. 40 = Rs. 350   Correct Option: 350
Answer: A
Tom planted vegetables in a rectangular garden that was 25 feet long and 15 feet wide. He used
1/3 of the area for corn and 1/5 of it for peas. How many square feet are left for other vegetables?  Choose the correct choice from the following answers.
A) 175 sq. ft.
B) 176 sq. ft.
C) 177 sq. ft.
D) 178 sq. ft.
E) 179 sq. ft.

Solution: area of garden is 25 x 15 = 375 sq. ft.   1/3 x 375 = 125 sq. ft. for corn   1/5 x 375 = 75 sq. ft. for peas   125 + 75= 
125 + 75 = 200
200 sq. ft. used     375 - 200= 
  375 - 200 = 175
175 sq. ft. left over   correct answer 175 sq. ft.
Answer: A
If a certain coin is flipped, the probability that the coin will land heads is 1/2. If the coin is flipped 5 times, what is the probability that it will land heads up on the first flip but not on the last 4 flips?
Select the correct option.
A) 1/4 B) 1/8 C) 1/16 D) 1/32 E) 1/64

Solution: P(HTTTT) = 1/2*1/2*1/2*1/2*1/2 = 1/32   The answer is 1/32.
Answer: D
Aman started a business investing Rs. 70,000. Rakhi joined him after six months with an amount of Rs. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business ?  Choose the correct choice from the following choices.
A) 12 : 15 :19 B) 12 : 15 :29 C) 12 : 15 :11 D) 12 : 15 :16 E) 12 : 15 :13

Solution: Aman : Rakhi : Sagar = (70000 x 36) : (105000 x 30) : (140000 x 24)   = 12 : 15 : 16.   Answer: 12 : 15 :16
Answer: D
Bank account A contains exactly x dollars, an amount that will decrease by 10% each month for the next two months. Bank account B contains exactly y dollars, an amount that will increase by 20% each month for the next two months. If A and B contain the same amount at the end of two months, what is the ratio of x√x to y√y?
Options
A) 4 : 3  B) 3 : 2  C) 16 : 9  D) 2 : 1  E) 9 : 4

Solution: Explanation:   Account A has amount after 2 months = 0.9*0.9*x = 0.81*x   Account B has amount after 2 months = 1.2*1.2*y = 1.44*y   0.81*x=1.44*y --> √(x/y)=√(1.44/0.81) = 12/9 = 4/3.   4 : 3ns 4 : 3
Answer: A
|x+3| – |4-x| = |5+x| How many solutions will this equation have? Choose the correct option
A) 0	B) 1	C) 2	D) 3	E) 4

Solution: You have |x+3| - |4-x| = |8+x|   First, look at the three values independently of their absolute value sign, in other words:   |x+3| - |4-x| = |8+x|   (x+3) - (4-x) = (8+x)   Now, you're looking at x < - 8, so x is a number less than -8. Let's pretend x = -10 here to make things a bit easier to understand.   when x=-10   I.) (x+3)   (-10+3)   (-7)   II.) (4-x)   (4-[-10]) (double negative, so it becomes positive)   (4+10)   (14)   III.) (8+x)   (8+-10)   (-2)   In other words, when x < -8, (x+3) and (8+x) are NEGATIVE. To solve problems like this, we need to check for the sign change.   Here is how I do it step by step.   I.) |x+3| - |4-x| = |8+x|   II.) IGNOR4 absolute value signs (for now) and find the values of x which make (x+3), (4-x) and (8+x) = to zero as follows:   (x+3)   x=-3   (-3+3)= 
(-3+3) = 0
0   (4-x)   x=4   (4-4)= 
(4-4) = 0
0   (8+x)   x=-8   (8+-8) = 4   4
Answer: E