MU-NLPC/Calc-aqua_rat huggingface dataset:
A man cheats while buying as well as while selling. While buying he takes 10% more than what he pays for and while selling he gives 20% less than what he claims to. Find the profit percent, if he sells at 13% below the cost price of the claimed weight.  Choose the correct option
A) 19.63%  B) 20%  C) 37.5%  D) 25%  E) 37.5%

Solution: There is a one step calculation method too. It requires more thought but is faster.   The man takes 10% more than what he pays for. So if he claims to take 100 pounds, he pays $100 but he actually takes 110 pounds for which he will take from the customer $110. Hence, in effect, there is a 10% mark up.   While selling, he sells 20% less. This means, he claims to sell 100 pounds and gets $100 but actually sells only 80 pounds and should have got only $80 for it. So this is again a mark up of $20 on $80 which is 25%.   But he also sells at 13% less   (1 + m1%)(1 + m2%)(1 - d%) = (1 + p%)   11/10 * 5/4 * 87/100 = (1 + p%)   profit % = 19.63%   19.63%
Answer: A
How many numbers from 32 to 97 are exactly divisible by 9?
Choose the correct choice from the following answers
A) 5  B) 7  C) 9  D) 11  E) 12

Solution: Option '7'   32/9 = 3 and 97/9 = 10 ==> 10 - 3= 
10 - 3 = 7
7 Numbers
Answer: B
On dividing a number by 5, we get 3 as remainder. What will be the remainder when the square of this number is divided by 5 ? Answers
A) 0 B) 1 C) 3 D) 4 E) 2

Solution: Let the number be x and on dividing x by 5, we get k as quotient and 3 as remainder.   x=5k+3   x^2=(5k+3)^2=(25k^2+30k+9)   =5(5k^2+6k+1)+4   on dividing x^2 by 5,we get 4 as remainder.   Answer is 4
Answer: D
A train with a length of 100 meters, is traveling at a speed of 72 km/hr. The train enters a tunnel 3.5 km long. How many minutes does it take the train to pass through the tunnel from the moment the front enters to the moment the rear emerges?  Select the correct option.
A) 3  B) 4.2  C) 3.4  D) 5.5  E) 5.7

Solution: 72 km/hr = 1.2 km/min   The total distance is 3.6 km.   3.6 / 1.2= 
3.6 / 1.2 = 3
3 minutes   The answer is 3.
Answer: A
If a card is drawn from a well shuffled pack of cards, the probability of drawing a spade or a king is ? Choose the correct answer.
A) 4/18 B) 4/12 C) 4/15 D) 4/13 E) 4/16

Solution: P(SᴜK) = P(S) + P(K) - P(S∩K), where S denotes spade and K denotes king.   P(SᴜK) = 13/52 + 4/52 - 1/52 = 4/13   Answer: 4/13
Answer: D
An article is bought for Rs.475 and sold for Rs.525, find the gain percent?  Answers.
A) 33 1/7% B) 33 1/6% C) 33 1/3% D) 10.53% E) 33 2/3%

Solution: 475 ---- 50   100 ---- ? => 10.53%   Answer: 10.53%
Answer: D
In an animal behavior experiment, 40 tagged white pigeons and 200 tagged gray pigeons were released from a laboratory. Within one week, 88 percent of the white pigeons and 80.5 percent of the gray pigeons had returned to the laboratory. What percent of the total number of pigeons returned to the laboratory?	Options:
A) 80.5  B) 82  C) 81.75  D) 85  E) 86.5

Solution: Weighted mix method is best here....   Ratio is 1:5 for 88:80.5...   So the answer required = 80.5+ (88-80.5)*1/6=80.5+7.5*1/5   80.5+1.25= 
80.5+1.25 = 81.75
81.75   81.75
Answer: C
What annual installment will discharge a debt of $1092 due in 3 years at 12% simple interest? Choose the correct choice:
A) $210
B) $115
C) $295
D) $325
E) $415

Solution: Let each installment be x   [x + (x*12*1/100)] + [x + (x*12*2/100)] + x = 1092   28x/25 + 31x/25 + x = 1092   x = 325   Answer is $325
Answer: D
A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
Choose the correct choice from the following:
A) 769m B) 678m C) 350m D) 168m E) 198m

Solution: Speed = [300 / 18] m/sec = 50/3 m/sec.   Let the length of the platform be x meters.   Then, x + 300 / 39 = 50/3   3(x + 300) = 1950 è x = 350m.   Answer: 350m
Answer: C
A batsman in his 18th innings makes a score of 150 runs and there by increasing his Average by 6.
Find his average after 18th innings.  Select:  A) 150  B) 18  C) 6  D) 17  E) 42

Solution: Let the average for 17 innings is x runs   Total runs in 17 innings = 17x   Total runs in 18 innings = 17x + 150   Average of 18 innings = 17x + 150/18   : . 17x + 150/18 = x + 6 -- > x = 42   Thus, average after 18 innings = 42   Answer is 42.
Answer: E
Two trains leave a station traveling in the same direction. Train A leaves traveling at a constant speed of 50 mph, while train B leaves traveling at a constant speed of 80 mph. If train B left the station 30 minutes after train A left, in how many minutes will train B overtake train A?  Select: A) 30 B) 40 C) 50 D) 60 E) 70

Solution: We can use a form of the equation D=RT [distance=rate*time]   Train A will have traveled for 30 minutes longer when train B overtakes it so   time of train A: T + 30 minutes = T + 1/2 hours (switch to hours since the rates are in hours)   time of train B: T   rate of train A: 50 mph   rate of train B: 80 mph   the distance traveled by each will be the same when B overtakes A so set the right side of D=RT equal to each other for the two trains   50*(T+1/2)=80*T   50T+25=80T   25=30T   25/30=T   5/6 hours = T which is 5/6*60= 
5/6*60 = 50
50 minutes   50
Answer: C
How many natural numbers between 23 and 137 are divisible by 7?
Choices: A) 12 B) 17 C) 16 D) 13 E) 15

Solution: Solution : These numbers are 28, 35, 42,…., 133.   This is in A.P. in which a= 28, d=(35-28)= 
(35-28) = 7
7 and L=133.   Let the number of there terms be n. then, Tn=133   a+(n-1)d=133 by solving this we will get n=16.   Answer 16
Answer: C
The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ 26.50 per metre is Rs. 5300, what is the length of the plot in metres?	Answers.
A) 40
B) 45
C) 125
D) Data inadequate
E) None of these

Solution: Explanation:   Let breadth = x metres.   Then, length = (x + 20) metres.   Perimeter = 5300/26.50= 
5300/26.50 = 200
200 m   2[(x + 20) + x]= 200   2x + 20 = 100   2x = 80   x = 40.   Hence, length = x + 20 = 60 m.   Answer: None of these
Answer: E
In a group of cows and hens, the number of legs are 20 more than twice the number of heads. The number of cows is :  Choose the correct choice from the following answers
A) 5  B) 6  C) 7  D) 10  E) 12

Solution: Let no of cows be x, no of hens be y.   So heads=x+y   Legs=4x+2y   Now, 4x+2y = 2(x+y)+ 20   2x = 20   x = 10.   ANSWER:10
Answer: D
A train 300 m long passed a pole in 30 sec. How long will it take to pass a platform 1000 m long?  Pick one.
A) 90 sec	B) 100 sec	C) 110 sec	D) 120 sec	E) 130 sec

Solution: Speed = 300/30= 
300/30 = 10
10 m/sec.   Required time= (300 + 1000)/10= 
(300 + 1000)/10 = 130
130 sec   Answer:130 sec
Answer: E
If population of certain city increases at the rate of 5%. If population in 1981 was 138915, then population in 1978 was?  Select
A) 12,0000 B) 130000 C) 261000 D) 627000 E) 12690

Solution: Explanation:   X * (105/100) * (105/100) * (105/100) = 138915   X = 138915/1.157625= 
138915/1.157625 = 120_000
120000   12,0000nswer: Option 12,0000
Answer: A
One water pump can fill half of a certain empty tank in 3 hours. Another pump can fill half of the same tank in 312312 hours. Working together, how long will it take these two pumps to fill the entire tank? Choose the correct choice from the following choices:	A) 1 7/13	B) 1 5/8	C) 3 1/4	D) 3 3/13	E) 3 1/2

Solution: One pump can fill a tank in 3 hours and another in 3.5 hours   so the rate at which both can half fill the tank is (1/3+1/3.5) => 13/21   Thus half of the tank can be filled in 21/13   so for filling the complete tank => 21/13*2 = 42/13   ANSWER:3 3/13
Answer: D
Cost is expressed by the formula tb^4. If b is doubled, the new cost Q is what percent of the original cost?
Choose one.
A) Q=200  B) Q=600  C) Q=800  D) Q=1600  E) Q=50

Solution: Original Cost C1=t1*b1^4   New Cost C2=t2*b2^4....only b is doubled so t2=t1 and b2=2b1   C2=t2*(2b1)^4   =16(t1*b1^4)   =16C1   16 times C1=>1600% of C1   Ans Q=1600 =1600
Answer: D
What is the smallest possible common multiple of three integers, all larger than 26?	Choose one:
A) 27
B) 54.
C) 846.
D) 19,656
E) 21,924

Solution: The Least common positive multiple would be for the immediate least number(s) after 26 i.e 27.   Since nowhere is it stated that the three integers must be different, the integers could be 27,27 and 27...   leading to least possible positive common multiple to be 27.   27nswer 27.
Answer: A
A man walking at the rate of 5 km/hr crosses a bridge in 15 minutes. The length of the bridge (in metres) is? Answers:	A) 2267	B) 1162	C) 2276	D) 1250	E) 1262

Solution: Explanation:   speed = (5x5/18)m/sec   = 25/18 m/sec.   Distance covered in 15 minutes = (25/18 x 15 x 60)m   = 1250 m.   Answer: 1250
Answer: D
If a card is drawn from a well shuffled pack of cards, the probability of drawing a spade or a king is ?	Choose the most appropriate option: A) 4/29 B) 4/20 C) 4/23 D) 4/13 E) 4/92

Solution: P(SᴜK) = P(S) + P(K) - P(S∩K), where S denotes spade and K denotes king.   P(SᴜK) = 13/52 + 4/52 - 1/52   =4/13   Answer: 4/13
Answer: D
If the probability R of rain on any given day in city x is 50% what is the probability it with rain on exactly 3 days in a five day period?  Pick one:	A) 8/125	B) 2/25	C) 5/16	D) 8/25	E) 3/4

Solution: 55/163 (1/2)^3(1/2)^2   = (5 * 4 * 3!)/2!3! * 1/32   R= 5/16   Answer - 5/16
Answer: C
In what ratio P:Q should the Mixture P of milk and water in the ratio of 2:1 be mixed with another Mixture Q of milk and water in the ratio 1:5 so that the resultant mixture contains equal quantities of milk and water?
Choices:
A) 3:2	B) 2:1	C) 4:3	D) 3:5	E) 3:1

Solution: (2/3)*P +(1/6)*Q = (1/3)*P+(5/6)*Q   2P=4Q   P/Q = 2/1   The answer is 2:1.
Answer: B
What is the simple interest on Rs 7000 at 10% per annum for the period from 16th January 2017 to 8th April 2017.
Select:
A) Rs.77.8
B) Rs.95.8
C) Rs.47.8
D) Rs.97.8
E) Rs.90.8

Solution: Explanation:   One thing which is tricky in this question is to calculate the number of days.   Always remember that the day on which money is deposited is not counted while the day on which   money is withdrawn is counted.   So lets calculate the number of days now,   Time = (15+28+8)= 
(15+28+8) = 51
51/365 years   P= 7000   R = 10%   S.I. = =7000Ã—10Ã—51/(365*100)=97.8   Answer: Rs.97.8
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 the correct option
A) 7/88	B) 7/78	C) 7/11	D) 7/12	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 = ⁷C₂/¹⁵C₂ + ⁸C₂/¹⁵C₂   = 7/15   Answer: 7/15
Answer: E
Calculate the percentage gain if a trader bought a bicycle for Rs.550 and sold it for Rs.650? Options:
A) 11.18%  B) 13.18%  C) 18.18%  D) 19.18%  E) 12.18%

Solution: C.P. = 500   S.P. = 650   Gain = 650-550 ---- 100   % Gain => 100/550*100 => 18.18%   Answer:18.18%
Answer: C
If a certain sample of data has a mean of 30.0 and a standard deviation of 3.5, which of the following values is more than 2.5 standard deviations from the mean?
Choose the correct choice:  A) 12.0  B) 13.5  C) 17.0  D) 23.5  E) 26.5

Solution: The standard deviation is 3.5. 2.5 standard deviations, which is just 2.5 x 3.5 is 8.75. The only answer more than 8.75 away from the mean is 12.0.
Answer: A
In a graduate physics course, 70 percent of the students are male and 30 percent of the students are married. If two-sevenths of the male students are married, what fraction of the female students is married? Choose the most appropriate option.
A) 2/7 B) 1/3 C) 1/2 D) 2/3 E) 5/7

Solution: let assume there are 100 students of which 70 are male and 30 are females   if 30 are married then 70 will be single.   now its given that two-sevenths of the male students are married that means 2/7 of 70 = 20 males are married   if 30 is the total number of students who are married and out of that 20 are males then the remaining 10 will be females who are married.   total females = 30   married females = 10   then single females = 30-10= 
30-10 = 20
20   we need to find the fraction of female students who are single i.e single female students / total female student= 10/30 = 1/3 [1/3]
Answer: B
One fourth of a solution that was 8% sugar by weight was replaced by a second solution resulting in a solution that was 16 percent sugar by weight. The second solution was what percent sugar by weight?  Select:
A) 40% B) 24% C) 22% D) 18% E) 8.5%

Solution: Instead of using complex calculations and remembering formulae, why dont u directly get to weighted average.   3 parts of 8% + 1 part of x (unknown) % = 4 parts of 16%   => x% = 64%-24% = 40%   ans 40% it is.64 -24= 
64 -24 = 40
40%   ans 40% it is.
Answer: A
If you cut a 22ft piece of wood into two pieces making one piece 4ft longer than the other. What size is the smaller piece?
Select the correct option
A) 4ft	B) 6ft	C) 8ft	D) 10ft	E) 9ft

Solution: Total length is 22ft, one piece is 4ft longer (x+4), leaving the other piece to figure out (x).   (x)+ (x+4)=22   x+x+4-4=22-4   2x=18   2x/2=18/2= 
18/2 = 9
9   The piece is 9ft) 9ft.
Answer: E
A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?
Select
A) 7
B) 4
C) 3
D) 2
E) 9

Solution: M = 45   S = 1.5   DS = 6   US = 3   AS = (2 * 6 * 3) /9= 
(2 * 6 * 3) /9 = 4
4   Answer: 4
Answer: B
L2Q,L6S,P12U,R20W,T30U,?	Answers.
A) V42Y
B) U47Y
C) V47Z
D) V47Y
E) V46X

Solution: L - Q = 2   L - S = 6   P - U = 12   R - W = 20   T - W = 30   1^2 + 1 , 2^2 + 2 , 3^2 + 3 , 4^2 + 4 , 5^2 + 5 ---> V42Ys per number sequence   => next number = 6^2 + 6 = 42   V - Y = 42 => V42Y   V42YNSWER:V42Y
Answer: A
If two sides of a triangle have lengths 5 and 7, which of the following could be the perimeter of the triangle?
I. 9
II. 15
III. 19
Choose the correct choice from the following options.
A) None
B) I only
C) II only
D) II and III only
E) I, II, and III

Solution: Let x be the length of the third side.   7-5 < x < 7+5   2 < x < 12   14 < perimeter < 24   The answer is II and III only.
Answer: D
If TIER is written as 7163 and BRAIN is written as 23415, how is RENT coded ?  Answers.
A) 3653	B) 3657	C) 2977	D) 2790	E) 2711

Solution: Explanation:   Given :   Letter : T I E R B A N   Code : 7 1 6 3 2 4 5   Thus, the code for RENT is 3657.   ANSWER:3657
Answer: B
A dishonest dealer professes to sell goods at the cost price but uses a weight of 780 grams per kg, what is his percent?	Options
A) 28%	B) 25%	C) 55%	D) 28%	E) 28.2%

Solution: 780 --- 220   100 --- ? => 28.2%   Answer: 28.2%
Answer: E
Of the final grades received by the students in a certain math course, 1/5 are A's, 1/4 are B's, 1/2 are C's, and the remaining 40 grades are D's. What is the number of students in the course? Choose the correct choice from the following answers
A) 80  B) 110  C) 160  D) 800  E) 400

Solution: We start by creating a variable for the total number of students in the math course. We can say:   T = Total number of students in the math course   Next, we can use variable T in an equation that we translate from the given information. We are given that, of the final grades received by the students in a certain math course, 1/5 are A's, 1/4 are B's, 1/2 are C's, and the remaining 40 grades are D's. Since this represents all the grades in the class, it represents all the students in the class. Thus we know:   #A’s + #B’s + #C’s + #D’s = Total number of students in the class   1/5(T) + ¼(T) + ½(T) + 40 = T   We can multiply the entire equation by 20 to cancel out the denominators of the fractions and we have:   4T + 5T + 10T + 800 = 20T   19T + 800 = 20T   800 = T   There are a total of 800 students in the math class.   Answer is 800.
Answer: D
What percent of 16 is 16 percent of 1? Answers.
A) 0.001 B) 1 C) 0.1 D) 100 E) 101.

Solution: 16 % of 1 = (16/100) * 1 = 16/100   To determine what percentage of 16 this is :   [16][/100*16] *100 = 1%   Ans : 1
Answer: B
If “&” implies “Add”, “@” implies “multiply”, “#” implies “subtract”, “$” implies “division”,
12 & 3 @ 2 # 32 $ 4 = ? Choose the correct choice from the following options.
A) 10
B) 99
C) 27
D) 29
E) 16

Solution: Explanation:   Given:   12 & 3 @ 2 # 32 $ 4 = ?   By substituting appropriate mathematical symbols, we get,   12 + 3 * 2 – 32/4 = ?   12 + 3 * 2 – 8 = ?   12 + 6 – 8 = ?   18 – 8 = 10   10NSWER:10
Answer: A
In how many years, Rs. 150 will produce the same interest at 6% as Rs. 800 produce in 2 years at 4½% ?  Choose the correct answer.
A) 4 years  B) 6 years  C) 8 years  D) 9 years  E) 10 years

Solution: Explanation:   Let Simple Interest for Rs.150 at 6% for n years = Simple Interest for Rs.800 at 4½ % for 2 years   (150×6×n)/100 = (800 × (9/2) × 2)/100   (150 × 6 × n) = (800 × (9/2) × 2   150 × 6 × n = 800 ×9   3 × 6 × n = 16 × 9   6 × n = 16 × 3   2 × n = 16   n = 8 years   Answer: Option 8 years
Answer: C
A certain team has 10 members, including Joey. A three-member relay team will be selected as follows: one of the 10 members is to be chosen at random to run first, one of the remaining 9 members is to be chosen at random to run second, and one of the remaining 8 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 choice from the following answers.
A) 1/5  B) 3/10  C) 4/15  D) 3/20  E) 6/25

Solution: Each member has an equal probability to run second (1/10) or third (1/10).   The probability that Joey runs second or third is 1/10 + 1/10 = 1/5   The answer is 1/5.
Answer: A
A hare and a jackal are running a race. Three leaps of the hare are equal to four leaps of the jackal. For every six leaps of the hare, the jackal takes 7 leaps. Find the ratio of the speed of the hare to the speed of the jackal. Choose the correct choice from the following answers
A) 64:25 B) 8:7 C) 5:8 D) 25:64 E) 6:7

Solution: The hare takes 6 leaps and the jackal takes 7 leaps.   1 hare leap = 4/3 jackal leaps   Thus the hare's 6 leaps = 6*(4/3)= 
6*(4/3) = 8
8 jackal leaps.   The ratio of their speeds is 8:7.   The answer is 8:7.
Answer: B
A committee that includes 6 members is about to be divided into 2 subcommittees with 3 members each. On what percent of the possible subcommittees that Michael is a member of is David also a member?	Pick: A) 10% B) 20% C) 25% D) 40% E) 50%

Solution: Committee #1: 50% chance that David will be a member, leaving 2 possible spots the other 5 people. Michael's chances of being one of those 2 is 2/5 or 40%. Chances of David and Michael being on this committee is   50%x40%=20%.   Committee #2: Same.   20% + 20% = 40%.   ANSWER:40%20  + 20= 
20  + 20 = 40
40%.   ANSWER:40%
Answer: D
50 liters of a mixture contains milk and water in the ratio 3:2. If 5 liters of this mixture be replaced by 5 liters of milk, the ratio of milk to water in the new mixture would be? Choose the correct choice from the following options: A) 6:5 B) 6:2 C) 6:4 D) 7:4 E) 7:2

Solution: Quantity of milk in 50 liters if mix = 50*3/5= 
50*3/5 = 30
30 liters   Quantity of milk in 55 liters of new mix= 30+5= 
30+5 = 35
35 liters   Quantity of water in it= 55-35= 
55-35 = 20
20 liters   Ratio of milk and water in new mix= 35:20 = 7:4   Answer is 7:4
Answer: D
If the cp of 12 rubbers is equal to the sp of 8 rubbers, the gain %is ?
Options:
A) 30%  B) 40%  C) 50%  D) 60%  E) 70%

Solution: (Explanation:Friends, we know we will need gain amount to get gain percent, right.   So lets get gain first.   Let the cost price of 1 pen is Re 1 50%ost of 8 pens = Rs 8 Selling price of 8 pens = 12   Gain = 12 - 8= 
12 - 8 = 4
4 Gain%=(Gain50%ost*100)%=(48*100)%=50%   50%
Answer: C
When a number is divided by 13, the remainder is 11. When the same number is divided by 17, then remainder is 9. What is the number ?	Choices: A) 349 B) 339 C) 400 D) 500 E) 600

Solution: x = 13p + 11 and x = 17q + 9   13p + 11 = 17q + 9   17q - 13p = 2   q =	2 + 13p   17   The least value of p for which q =	2 + 13p	=> p = 26   17   x = (13 x 26 + 11)   = (338 + 11)= 
(338 + 11) = 349
349   349NSWER 349
Answer: A
Foodmart customers regularly buy at least one of the following products: milk, chicken, or apples. 60% of shoppers buy milk, 50% buy chicken, and 15% buy apples. If 10% of the customers buy all 3 products, what percentage of Foodmart customers purchase exactly 2 of the products listed above?  Choose the correct choice from the following:
A) 5%	B) 10%	C) 15%	D) 25%	E) 30%

Solution: The formula is   n(AUBUC) = n(A)+n(B)+n(C)-B+A-N   where B is both (it will sum of (AB), (BC), (CA)).   and A is All   and N is neither   so plugging in we get   100 = 60+50+15+10-B-0   B = 35.   exactly two = 35 - 3(10) = 5   subtracting 10% three times as this value is including in all the (AB), (BC), (CA).   5%nswer 5%
Answer: A
The function f is defined for all positive integers w by the following rule. f(w) is the number of positive integers each of which is less than w and has no positive factor in common with w other than 1. If p is any prime, number then f(p)=  Choose the correct option:
A) p-1	B) p-2	C) (p+1)/2	D) (p-1)/2	E) 2

Solution: If not the wording the question wouldn't be as tough as it is now. The GMAT often hides some simple concept in complicated way of delivering it.   This question for instance basically asks: how many positive integers are less than given prime number p which have no common factor with p except 1.   Well as p is a prime, all positive numbers less than p have no common factors with p (except common factor 1). So there would be p-1 such numbers (as we are looking number of integers less than p).   For example: if p=4 how many numbers are less than 4 having no common factors with 4: 1, 2, 3, --> 4-1=3.   p-1nswer: p-1.
Answer: A
Abhijit started a business investing 2000. Anuja joined him after 8 months with an amount of 6000 and Sunil joined them with 60,000 after another 4 months. The amount of profit earned should be distributed in what ratio among Abhijit, Anuja and Sunil respectively, three years after Abhijit started the business?	Choose the most appropriate option:  A) 6 : 13 : 90  B) 5 : 12 : 90  C) 5 : 11 : 80  D) 6 : 11 : 90  E) 12 : 6 : 90

Solution: Ratio of their investments   = 2 × 36 : 6 × 22 : 60 × 18 = 6 : 11 : 90   Answer 6 : 11 : 90
Answer: D
If p and q are prime numbers, how many divisors does the product p^6 * q^7 have?
Choose the correct choice.
A) 40	B) 56	C) 60	D) 62	E) 70

Solution: when a number N=a^x*b^y, where a and b are prime numbers, and x, y are positive integers, the number of divisors of N=(x+1)(y+1)   Therefore, the answer is B. 7*8=56
Answer: B
If 9^y = 3^12, what is y?  Choose the correct answer.
A) 2
B) 2
C) 3
D) 4
E) 6

Solution: 3^2y = 3^12   2y=12, therefore y=6   6
Answer: E
A fruit drink is made of orange, watermelon, and grape juice, where 15 percent of the drink is orange juice and 60 percent is watermelon juice. If the drink is made with 35 ounces of grape juice, how many ounces is the drink total?	Answers
A) 120 B) 140 C) 160 D) 180 E) 200

Solution: Let the total number of ounces in the drink be x.   % of orange = 15%   % of watermelon = 60%   % of grape = 100% - 75% = 25%   0.25x 100  - 75= 
100  - 75 = 25
25%   0.25x= 35   x = 140   Therefore there are a total of 140 ounces in the drink.   The answer is 140.
Answer: B