MU-NLPC/Calc-aqua_rat huggingface dataset:
The sum of three numbers is 98. The ratio of the first to the second is 2/3, and the ratio of the second to the third is 5/8. The second number is: Choices:
A) 15
B) 20
C) 30
D) 32
E) 33

Solution: Let the three numbers be x, y and z.   Sum of the numbers is 98.   x + y + z = 98………………(i)   The ratio of the first to the second is 2/3.   x/y = 2/3.   x = 2/3 ? y.   x = 2y/3.   The ratio of the second to the third is 5/8.   y/z = 5/8.   z/y = 8/5.   z = 8/5 ? y.   z = 8y/5.   Put the value of x = 2y/3 and z = 8y/5 in (i).   2y/3 + y + 8y/5 = 98   49y/15 = 98.   49y = 98 ? 15.   49y = 1470.   y = 1470/49.= 
1470/49. = 30
30 .   Therefore, the second number is 30   correct answer 30
Answer: C
The retirement plan for a company allows employees to invest in 10 different mutual funds. Six of the 10 funds grew by at least 10% over the last year. If Sam randomly selected 4 of the 10 funds, what is the probability T that 3 of Sam’s 4 funds grew by at least 10% over last year?  Pick one.
A) 6C3 / 10C4  B) 6C3 * 4C1 / 10C4  C) 6C3 * 4C1 / 10P4  D) 6P3 * 4P1 / 10C4  E) 6P3 * 4P1 / 10P4

Solution: Look at the answers. B is the only answer choice that uses only combination formulas and takes into account all the factors.   We know this is a combination, not a permutation. This rules out choices C, DE.   A clearly isn't the answer because T= 6C3 only accounts for 3 of the funds he chose. 10C4, the denominator, is correct, so the numerator must be wrong.   6C3 * 4C1 / 10C4 it is.
Answer: B
Roy is now 8 years older than Julia and half of that amount older than Kelly. If in 2 years, Roy will be twice as old as Julia, then in 2 years what would be Roy’s age multiplied by Kelly’s age?
Choose the correct choice from the following answers
A) 160
B) 168
C) 176
D) 184
E) 192

Solution: R = J+8 = K+4   R +2= 
 +2 = 2
2(J+2)   (J+8)+2= 2J+4   J = 6   R 2 +4= 
2 +4 = 6
6   R= 14   K = 10   In 2 years (R+2)(K+2) = 16*12= 
16*12 = 192
192   The answer is 192.
Answer: E
Ravi invested certain amount for two rates of simple interests at 6% p.a. and 7% p.a. What is the ratio of Ravi's investments if the interests from those investments are equal?	Choose the correct choice from the following choices:
A) 7:9
B) 7:5
C) 7:2
D) 7:6
E) 7:1

Solution: Let x be the investment of Ravi in 6% and y be in 7%   x(6)(n)/100   = y(7)(n)/100   => x/y = 7/6   x : y = 7 : 6   Answer: 7:6
Answer: D
A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is?	Choose the correct answer.
A) 8	B) 8/11	C) 8/13	D) 8/15	E) None

Solution: A's 1 day's work =	1	;   15   B's 1 day's work =	1	;   20   (A + B)'s 1 day's work =	(	1	+	1	)	=	7	.   15	20	60   (A + B)'s 4 day's work =	(	7	x 4	)	=	7	.   60	15   Therefore, Remaining work =	(	1 -	7	)	=	8	.   15	15   Option 8/15
Answer: D
The greatest number by which the product of three consecutive multiples of 3 is always divisible is  Choose one.
A) 54
B) 76
C) 152
D) 162
E) None of these

Solution: Solution   Required number	= Product of first three multiplies of 3   = (3 × 6 × 9)= 162.   Answer 162
Answer: D
For a drama, Jack need to select 5 dramatist from a team of 8 members. What is the possible way to select dramatist?
Choose the correct choice:
A) 60
B) 56
C) 48
D) 25
E) 10

Solution: The question is out of 8 members, john needs 5 members.   So the combination is 8C5.   8C5=8!/3!*5!   =8*7*6*5!/5!*3*2*1   =56 ways to select.   Option 56 is answer
Answer: B
A man walked diagonally across a square lot. Approximately, what was the percent saved by not walking along the edges? Choose one:
A) 30
B) 39
C) 87
D) 27
E) 91

Solution: Let the side of the square(ABCD) be x meters.   Then, AB + BC = 2x metres.   AC = = (1.41x) m.   Saving on 2x metres = (0.59x) m.   Saving % = = 30% (approx)   30nswer:30
Answer: A
Convert 150 inches into centimeter?  Choices:
A) 312cm  B) 381cm  C) 350cm  D) 310cm  E) 354cm

Solution: 1 inch = 2.54cm   150 inches = 110*2.54 = 381cm   Answer is 381cm
Answer: B
In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?	Pick:  A) 800  B) 880  C) 720  D) 1500  E) 1110

Solution: The word 'OPTICAL' has 7 letters. It has the vowels 'O','I','A' in it and these 3 vowels should always come together. Hence these three vowels can be grouped and considered as a single letter. That is, PTCL(OIA).   Hence we can assume total letters as 5 and all these letters are different.   Number of ways to arrange these letters   =5!=5×4×3×2×1=120   All the 3 vowels (OIA) are different   Number of ways to arrange these vowels among themselves   =3!=3×2×1=6   Hence, required number of ways   =120×6=720   720
Answer: C
If goods be purchased for Rs.840 and one-fourth be sold at a loss of 20% at what gain percent should the remainder be sold so as to gain 20% on the whole transaction?  Choices:
A) 36 1/3%
B) 37 1/3%
C) 33 1/3%
D) 33 1/8%
E) 31 1/3%

Solution: 1/4 33 1/3%P = 210 SP = 21*(80/100) = 168   SP = 840*(120/100)= 
840*(120/100) = 1_008
1008   1008 - 168= 
1008 - 168 = 840
840   3/4 SP= 630   Gain = 210   630 --- 210   100 --- ? => 33 1/3%   Answer:33 1/3%
Answer: C
What number comes next in this Number series.
3 4 4 6 9 7 8 ?
*Hint: check calender
Choose the correct choice from the following answers:
A) 8
B) 3
C) 6
D) 1
E) 9

Solution: E   8 (the number of letters in the month December)   May : 3 letters   June : 4 letters   July : 4 letters   8ugust: 6 letters   September : 9 letters   October : 7 letters   November : 8 letters
Answer: A
A chair is bought for Rs. 800/- and sold at a loss of 10% find its selling price  Choose the correct choice from the following options.
A) Rs. 720/- B) Rs. 600/- C) Rs. 630/- D) Rs. 820/- E) Rs. 970

Solution: Explanation:   100 % ------> 800 (100 * 8 = 800)   90 % ------> 720 (90 * 8 = 720)   Selling price = Rs. 720/-   Rs. 720/-nswer: Option Rs. 720/-
Answer: A
The surface area of a sphere is 4πR2, where R is the radius of the sphere. If the area of the base of a hemisphere is 3, what is the surface area E of that hemisphere?  Choose the correct option
A) 6/π	B) 9/π	C) 6	D) 9	E) 12

Solution: Given Area of the base of a hemisphere is 3 = PI * R^2   Thus R = Sqrt ( 3 / PI ) .   Surface area of whole sphere = 4*PI*R^2 .   = 4 * PI * 3 / PI   = 12 .   Since the hemisphere is half of a sphere the Surface area of the hemisphere = 12 / 2= 
12 / 2 = 6
6 ( curved part , not including the flat rounded base ) .   But the total surface area= 6 + Area of the base of a hemisphere .   = 6 + 3= 
6 + 3 = 9
9.   Answer is 9 !!
Answer: D
A person purchased a TV set for Rs. 1000 and a DVD player for Rs. 650. He sold both the items together for Rs. 2500. What percentage of profit did he make?	Choose the correct choice from the following choices.
A) 51.51% B) 96.96% C) 10.11% D) 15.12% E) 23.32%

Solution: The total CP = Rs. 1000 + Rs. 650   = Rs. 1650 and SP = Rs. 2500   Profit(%)   = (2500 - 1650)/1650 * 100   = 51.51%   51.51%nswer: 51.51%
Answer: A
What is the probability of getting a sum 9 from two throws of a dice?  Choose the correct answer:
A) 5/5	B) 1/9	C) 5/1	D) 5/7	E) 5/2

Solution: In two throws of a dice, n(S) = (6 x 6) = 36.   Let E = event of getting a sum ={(3, 6), (4, 5), (5, 4), (6, 3)}.   The probability = 4/36 = 1/9.   Answer: 1/9
Answer: B
On a ferry, there are 38 cars and 12 trucks. The cars have an average mass of 950 kg and the trucks have an average mass of 3100 kg. What is the average mass of all 50 vehicles on the ferry?  Choices.
A) 1442	B) 1448	C) 1454	D) 1460	E) 1466

Solution: The total mass of the vehicles is 38*950+12*3100= 
38*950+12*3100 = 73_300
73300   The average mass is   73300/50= 
  73300/50 = 1_466
1466   The answer is 1466.
Answer: E
How long will a boy take to run round a square field of side 20 meters, if he runs at the rate of 12km/hr?
Choose the correct choice from the following answers.
A) 52sec	B) 45sec	C) 60sec	D) 24sec	E) 39sec

Solution: Speed = 12 km/hr = 12*5/18 = 10/3 m/sec   24secistance = 20*4= 
20*4 = 80
80m   Time taken= 80*3/10= 
80*3/10 = 24
24sec   Answer is 24sec
Answer: D
In a party every person shakes hands with every other person. If there were a total of 105 handshakes in the party then what is the number of persons present in the party ?  Choose the most appropriate option.
A) 15
B) 16
C) 17
D) 18
E) 19

Solution: Explanation :   Let the number of persons be n   âˆ´ total handshakes = nC2 = 105   n(n-1)/2 = 105 âˆ´ n = 15   15nswer : 15
Answer: A
A collection of books went on sale, and 2/3 of them were sold for $3.50 each. If none of the 40 remaining books were sold, what was the total amount received for the books that were sold?
Pick.
A) $180  B) $250  C) $260  D) $280  E) $300

Solution: If 40 books constitute 1/3rd of the total, then 2/3rd of the total = 80 books   Amount received for sold books = 80 * 3.5= 
80 * 3.5 = 280
$280   Answer :$280
Answer: D
Of the three-digit integers greater than 500, how many have two digits that are equal to each other and the remaining digit different from the other two?
Answers.
A) 90  B) 82  C) 80  D) 45  E) 36

Solution: To satify the given condition,   required no. of cases = total numbers - numbers with all digits different - numbers when all three digits are same,   number greater than 700;   total numbers = 1*10*10= 
1*10*10 = 100
100   numbers with all digits different= 1*9*8= 
1*9*8 = 72
72   numbers when all three digits are same (777)= 1   req. = 100- 72 - 1= 
100- 72 - 1 = 27
27   considering the numbers between 700999= 27*3=46   Answer is 80 ('cause 700 can't be included)   Answer (45).
Answer: D
8, 19, 30, 41, 52, ….
Given the sequence above, what is the sum of the 12th and the 20th terms?
Select
A) 324	B) 335	C) 346	D) 357	E) 368

Solution: The first term is 8 = 11 – 3. The second term is 19 = 22 – 3, the third term is 30 = 3 × 11 – 3, the fourth term is 41 = 4 × 11 – 3, etc.   Thus, 11n – 3 describes the values in the sequence where n is the number of the term.   The 12th term is 12 × 11 – 3 = 129   The 20th term is 20 × 11 – 3 = 220 – 3 = 217.   The sum of these two values is 346.   The correct answer is choice (346).
Answer: C
When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k+n is a multiple of 39?  Choose the correct answer
A) 3
B) 8
C) 12
D) 32
E) 35

Solution: n = 5p + 1 = 6,11,16,21,26,31   n 5  + 1= 
5  + 1 = 6
6,11,16,21,26,31   n= 7q + 3 = 3,10,17,24,31   =>n = 39m + 31   To get this, we need to take LCM of co-efficients of p and q and first common number in series.   So we need to add 8 more to make it   39m + 39   Answer - 8
Answer: B
The avearge score of a cricketer for ten matches is 38.9 runs. If the average for the first six matches is 45. Then find the average for the last four matches?  Select:  A) 33.25  B) 33.5  C) 34.25  D) 29.75  E) none

Solution: Solution   Required average	=(38.9 x 10)-(45 x 6)/ 4   = 119 / 4.= 
119 / 4. = 29.75
29.75   Answer 29.75
Answer: D
In order to fence a square Manish fixed 48 poles. If the distance between two poles, is 2 metres then what will be the area of the square so formed?  Choose the correct choice from the following choices: A) 133 cm2 B) 276 cm2 C) 2500 cm2 D) 576 cm2 E) None of these

Solution: Let the side of the square be x m.   ∴ Perimeter of the square = 48 × 2 = 4x ∴ x = 24 m   ∴ Area = (24)2 = 576 m2   Answer 576 cm2
Answer: D
While flying over the Pacific, an airplane makes a 25° turn to the right to avoid a storm. If, as a result, the airplane is traveling in a direction 7° east of north, in what direction was it originally flying? Select the correct option:
A) (a) 30° west of north
B) (b) 30° east of north
C) (c) 18° west of north
D) (d) 18° east of north
E) (e) 5° west of north

Solution: After a turn of 25° you are 7°North East, with a 18° turn you would be perfectly pointing at north. So you were, before the turn, 18° to the other side (West).   Answer (c) 18° west of north)
Answer: C
How many of the positive factors of 45 , 16 and how many common factors are there in numbers? Choose the correct choice from the following:  A) 1  B) 2  C) 3  D) 4  E) 5

Solution: factors of 45 - 1, 3, 9, 15 and 45   factors of 16 - 1 , 2, 4, 8 and 16   Comparing both, we have three common factors of 45,16-1   1nswer(1)
Answer: A
Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will be:  Options.
A) Rs. 169  B) Rs. 169.50  C) Rs. 175.50  D) Rs. 180  E) Rs. 180.50

Solution: Since first and second varieties are mixed in equal proportions.   So, their average price = Rs. 126 + 135 = Rs. 130.50   2   So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x.   By the rule of alligation, we have:   Cost of 1 kg of 1st kindCost of 1 kg tea of 2nd kind   Rs. 130.50	Mean Price   Rs. 153	Rs. x   (x - 153)	22.50   x - 153	= 1   22.50   x - 153 = 22.50   x = 175.50   Option Rs. 175.50
Answer: C
A fair die is rolled once and a fair coin is flipped once. What is the probaility that either the die will land on 3 or that the coin will land on heads?
Pick
A) 5/12	B) 7/12	C) 11/12	D) 3/4	E) 7/4

Solution: Event A = Fair die is rolled once   Event B = Fair coin is flipped once.   P(A or 7/12) = P(A) + P(7/12) - P(A and 7/12)   = 1/6 + 1/2 - (1/6)(1/2)   = 7/12   ANSWER 7/12
Answer: B
Two identical machines have the ability to produce both nuts and bolts. However, it takes 3 second to produce a bolt but 1 seconds to produce a nut. What is the fastest the two machines, working together, can produce 1,000 nuts and 1,000 bolts? Choose the correct choice from the following answers.
A) 1,250 seconds	B) 1,500 seconds	C) 1,750 seconds	D) 2,000 seconds	E) 3,000 seconds

Solution: To minimize the amount of time, we should make both machines work all the time while producing 1,000 nuts and 1,000 bolts.   Two machines to produce 1,000 bolts will need (1,000*3)/2 = 1500 seconds.   Two machines to produce 1,000 nuts will need (1,000*1)/2 = 500 seconds.   Total = 1500 + 500= 
1500 + 500 = 2_000
2000.   Answer: 2,000 seconds
Answer: D
A train takes 6 hours to cover a distance of 540 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
Choose the correct choice from the following answers.
A) 50 Kmph	B) 54 Kmph	C) 60 Kmph	D) 59 Kmph	E) 60 Kmph

Solution: Time = 6   Distance = 540   3/2 of 6 hours = 6 * 3/2= 
6 * 3/2 = 9
9 Hours   Required speed= 540/9= 
540/9 = 60
60 Kmph   60 Kmph)
Answer: C
How many seconds will a 400 metre long train take to cross a man running with a speed of 6 km/hr in the direction of the moving train if the speed of the train is 46 km/hr?  Choose the correct choice from the following options
A) 25
B) 30
C) 40
D) 45
E) 36

Solution: Explanation :   Speed of train relatively to man = ( 46 - 6)km/hr   = 40 km /hr   = (40 x 5 / 18)m/sec   = 11.11 m/sec   Time taken to pass the man = (400/ 11.11)sec = 36 sec.   Answer : 36
Answer: E
Walking across campus, a student interviewed a group of students. 25% of the students took a finance class last semester, 55% took a marketing class last semester, and 40% took neither a finance nor a marketing class last semester. What percent of the students in the group took both a finance and a marketing class?  Choose the correct answer.
A) 60%  B) 50%  C) 25%  D) 20%  E) 10%

Solution: {Total} = {finance} + {marketing} - {both} + {neither}   100 = 25 + 55 - {both} + 40   {both} = 20%.   Answer: 20%.
Answer: D
The volume of water inside a swimming pool doubles every hour. If the pool is filled to its full capacity within 8 hours, in how many hours was it filled to one quarter of its capacity?
Choose the most appropriate option: A) 2 B) 4 C) 5 D) 6 E) 7

Solution: 6
Answer: D
A pair of prime numbers that can be expressed in the form K{p, (p + 6)} is deﬁned as a pair of “sexy primes.” A “sexy triplet” is a group of three primes that can be expressed in the form {p, (p + 6), (p + 12)}. All of the following prime numbers are the middle term of a sexy triplet EXCEPT  Choose one:
A) 11
B) 13
C) 17
D) 19
E) 23

Solution: definetly a sitter.plug in the values for middle term and calculate.We can see clearly that K for 19 , 19+6 gives 25 which is not a prime   therefore correct answer 19
Answer: D
While working alone at their respective constant rates, server B uploads 480 files in 4 hours and server Y uploads 480 files in 8 hours. If all files uploaded by these servers are the same size, how long would it take the two servers, working at the same time and at their respective constant rates, to process a total of 480 files?  Choose the correct choice from the following answers: A) 2 hr B) 2hr 20 min C) 2hr 40 min D) 5 hr 40 min E) 6hr

Solution: Server B processes 480/4= 
480/4 = 120
120 per hour   Server Y processes 180/8 files per hour= 60 per hour   Total files processed per hour when B and Y work together = 120+60= 
120+60 = 180
180 files per hour   480/180= 2 2/3 hours=2hr 40 min
Answer: C
The average of runs of a cricket player of 10 innings was 32. How many runs must he make in his next innings so as to increase his average of runs by 4 ?
Pick: A) 98 B) 76 C) 23 D) 16 E) 12

Solution: Average = total runs / no.of innings = 32   So, total = Average x no.of innings = 32 x 10 = 320.   Now increase in avg = 4runs. So, new avg = 32+4= 
32+4 = 36
36runs   Total runs= new avg x new no. of innings = 36 x 11 = 396   Runs made in the 11th inning = 396 - 320= 
396 - 320 = 76
76   Answer 76
Answer: B
If the integer n has exactly three positive divisors, including 1 and n, how many positive divisors does n^3 have?
Select the correct option
A) 7 B) 5 C) 6 D) 8 E) 9

Solution: take the example of 4...   it has 3 positive divisors (1,2,4)   Now, take the example of 64...   it has only 7 divisors..   so 7 is the ans
Answer: A
Two employees M and N are paid a total of $605 per week by their employer. If M is paid 120 percent of the salary paid to N, how much is N paid per week? Options
A) $245  B) $255  C) $265  D) $275  E) $285

Solution: 1.2N + N = 605   2.2N = 605   N = 275   The answer is $275.
Answer: D
When 50 per cent of a number is added to another number the second number increases to its 140 per cent. What is the ratio between the first and the second number?  Select:
A) 3 : 4 B) 4 : 5 C) 3 : 2 D) Data inadequate E) None of these

Solution: Let the first and the second numbers be x and y respect then   y + 50% of x = 140% of y   or, y + 0.5x = 1.4y   or, 0.5x = 0.4y   ∴ x : y = 0.4 : 0.5 = 4 : 5   Answer 4 : 5
Answer: B
A company has 15 managers and 75 associates. The 15 managers have an average salary of $150,000. The 75 associates have an average salary of $30,000. What is the average salary for the company? Choose the correct choice
A) $35,000	B) $45,000	C) $50,000	D) $65,000	E) $75,000

Solution: Another method is to get ratios   Say 30000=a and   We know the # of people are in 1:5 ratio   Average=(5a*1+a*5)/6= 10a/6=50000   Answer is C. $50,000
Answer: C
Together, 15 type A machines and 7 type B machines can complete a certain job in 4 hours. Together 8 type B machines and 15 type C machines can complete the same job in 11 hours. How many Q hours would it take one type A machine, one type B machine, and one type C machine working together to complete the job (assuming constant rates for each machine)?	Choose the most appropriate option.
A) 22 hours	B) 30 hours	C) 44 hours	D) 60 hours	E) It cannot be determined from the information above.

Solution: Say the rates of machines A, B and C are a, b, and c, respectively.   Together 15 type A machines and 7 type B machines can complete a certain job in 4 hours --> 15a + 7b = 1/4;   Together 8 type B machines and 15 type C machines can complete the same job in 11 hours --> 8b + 15c = 1/11.   Sum the above: 15a + 15b + 15c = 1/4 + 1/11 = 15/44 --> reduce by 15: a + b + c = 1/44 --> so, the combined rate of the three machines is 1/44 job/hour --> time is reciprocal of the rate, thus machines A, B and C can do the job Q in 44 hours.   Answer: 44 hours.
Answer: C
The price of pulses has fallen by 35. How many quintals can be bought for the same amount which was sufficient to buy 24 quintals at the higher price?
Choose the correct choice from the following answers:
A) 20.0	B) 22.5	C) 25.8	D) 36.9	E) 32.5

Solution: 80% of original price can buy = 24 quintals.   Therefore, he can buy ( 24 x 100 )/ 65 = 36.9 quintals at the lower price.   ANSWER:36.9
Answer: D
A man can swim in still water at 9 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?  Pick one:
A) 3 B) 7.5 C) 2.25 D) 1.5 E) 4

Solution: M = 9   S = x   DS = 9 + x   US = 9 - x   9 + x = (9 - x)2   9 + x = 18 -2x   3x = 9   x = 3   3NSWER:3
Answer: A
Two friends run the New York City marathon, one friend finishes the marathon in 400 minutes while the second friend finishes the marathon in 625 minutes. What is the ratio of their speed?
Choose the correct choice from the following:	A) 10 : 12	B) 1 : 2	C) 5 :10	D) 20 : 25	E) None

Solution: Solution   Let us name the friends   as A and B.	= ( Friend A'S speed) : (Friend B's speed)   =âˆšb : âˆša   = âˆš400 : âˆš625   = 20 : 25   Answer 20 : 25
Answer: D
The probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact?	Select the correct option:
A) 18/35
B) 18/38
C) 18/36
D) 18/16
E) 18/31

Solution: If both agree stating the same fact, either both of them speak truth of both speak false.   Probability   = 3/5 * 4/7 + 2/5 * 3/7   = 12/35 + 6/35   = 18/35   18/35nswer: 18/35
Answer: A
What is the lowest positive integer that is divisible by 4 through 7, inclusive? Choose the correct choice from the following choices:  A) 77  B) 270  C) 1600  D) 840  E) 980

Solution: The integer should be divisible by: 4, 5, 6 and 7. The least common multiple of these integers is LCM=4*5*6*7= 
4*5*6*7 = 840
840   Answer: 840
Answer: D
A, B and C shared profits in ratio of 5 : 3 : 8. Theypartnered for 14months, 8months and 7months respectively. What was he ratio of their investments ? Choose the correct answer:
A) 10 : 49 : 45	B) 20 : 49 : 64	C) 12 : 21 : 64	D) 20 : 29 : 64	E) 30 : 29 : 63

Solution: Simply multiply profit sharing ratio with investment ratio to get investment amount ratio.   Let X is the total investment   â‡’14 x = 5   â‡’ 8 x = 3   â‡’ 7x = 8   â‡’ Final investment ratio = 12 : 21 : 64   12 : 21 : 64
Answer: C
A type T machine can complete a job in 5 hours and a type B machine can complete the job in 7 hours. How many hours will it take 2 type T machines and 3 type B machines working together and independently to complete the job?	Answers:  A) 1/5  B) 29/35  C) 5/6  D) 35/29  E) 35/12

Solution: now D should be the answer.   T need 5 hours to complete   and B needs 7 hours to compete   so 2T + 3B will complete 2/5 + 3/7 or 29/35 portion of the job in 1 hour   so the whole job will take 35/29 hours....=35/29
Answer: D
A sales representative receives a salary of $150 per week and earns a commission of 15% on all sales she makes. How many dollars’ worth of sales does she need to make in order to bring her total weekly income to $1050? Choose the correct choice from the following answers: A) $3,000 B) $3,150 C) $4,000 D) $4,150 E) $6,000

Solution: We're told that a sales representative receives a salary of $150 per week and earns a commission of 15% on all sales she makes. We're asked how many dollars’ worth of sales will bring her total weekly income to $1050.   Since the salesperson receives a $150 salary, the remaining $900 has to be accounted for by the 15% commission. Since those numbers are rather specific, we're likely dealing with a 'round number' for total sales.   Let's TEST Answer C: $4,000   Since 15% of $1,000 = $150   15% of $4,000 = 4($150) = $600   This is TOO HIGH (it's supposed to be $900), so we need a LOWER total sales figure.   Let's TEST Answer E: $6,000   Since 15% of $1,000 = $150   15% of $6,000 = 6($150) = $900   This is an exact MATCH for what we were told, so this MUST be the answer.   Final Answer:   $6,000
Answer: E