MU-NLPC/Calc-aqua_rat huggingface dataset:
A computer manufacturer produces a certain electronic component at a cost of $80 per component. Shipping costs for delivering the components are $2 per unit. Further, the manufacturer has costs of $16,200 a month related to the electronic component regardless of how many it produces. If the manufacturer produces and sells 150 components a month, what is the lowest price it can sell them for such that the costs don't exceed the revenues? Choose the correct answer:
A) $28
B) $82
C) $110
D) $190
E) $192

Solution: This question can be solved easily using a equation model.   150*p = 16200(fixed cost) + 150*80+150*2.   = 16200+ 12000+300= 
16200+ 12000+300 = 28_500
28500   P= $190.   $190
Answer: D
Carl is facing very difficult financial times and can only pay the interest on a $10,000 loan he has taken. The bank charges him a quarterly compound rate of 8%. What is the approximate interest he pays annually?	Answers
A) 1500 B) 1750 C) 2000 D) 3500 E) 2500

Solution: An easy way too attempt this is by approximation:   For the first quarter, he pays 8% of 10,000 which is $800.   So for the four quarters in the year, he will approximately play  800*4= 
 800*4 = 3_200
3200 over the entire year.   Because of compound interest it will be more than 3200. Approx. option D is correct.   Answer :3500
Answer: D
In Jeevans opinion, his weight is greater than 65 kg but less than 72 kg. His brother does not agree with Jeevan and he thinks that Jeevans weight is greater than 60 kg but less than 70 kg. His mothers view is that his weight cannot be greater than 68 kg. If all of them are correct in their estimation, what is the average of different probable weights of Jeevan?	Choose the correct choice from the following answers.
A) 67 kg	B) 68 kg	C) 69 kg	D) None of these	E) Cannot be determined

Solution: Explanation :   Let Jeevans weight be X kg.   According to Jeevan, 65 < X < 72.   According to Jeevan's brother, 60 < X < 70.   According to Jeevan's Mother, X <= 68   The Values satisfying all the above conditions are 66, 67 and 68 .   Required average = (66 + 67+68)/3 = 201/3= 
201/3 = 67
67 kg.   67 kgnswer : 67 kg
Answer: A
The interest on Rs. 750 for 2 years is the same as the true discount on Rs. 960 due 2 years hence. If the rate of interest is the same in both cases, it is:	Choose the most appropriate option: A) 12% B) 13% C) 14% D) 15% E) 18%

Solution: S.I. on Rs. 750 = T.D. on Rs. 960.   This means P.W. of Rs. 960 due 2 years hence is Rs. 750.   T.D. = Rs. (960 - 750) = Rs. 210.   Thus, S.I. on R.s 750 for 2 years is Rs. 210.   Rate =(100 x 210)/(750 x 2)%	= 14% ANSWER : 14%
Answer: C
How many 0's are there in the binary form of 6*1024 + 4*64 + 2  Pick:  A) 6  B) 7  C) 8  D) 10  E) 9

Solution: 6*1024 + 4*64 + 2 = 6144+256 +2= 
6144+256 +2 = 6_402
6402   in binary code   6402 base 10= 11001 000000 10 in base 2.   so 9 zeros are there.   ANSW9R:9
Answer: E
Jerome anticipated that the WebWeb.com stock price would fall and sold all his WebWeb.com stocks for $5 per stock. He paid $10,000 tax on the revenue. A week later, Jerome became convinced that the WebWeb.com stock price would rise, and he used the money that he had gotten from selling the WebWeb.com stocks to purchase them again, this time at $6 per stock. If Jerome ended up having 5000 WebWeb.com stocks fewer than the number he had before selling them, how many WebWeb.com stocks did he have originally? Choose the correct choice:
A) 10,000  B) 11,600  C) 12,000  D) 15,000  E) 16,400

Solution: Let the number of shares be x.   5*x -10000(money paid in taxes) = 6(x- 5000)   Solving for x, we get the shares as 15000.   Ans :(Option 15,000)
Answer: D
A train 125 m long passes a man, running at 4 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
Choose the correct choice from the following answers
A) 49 kmph
B) 50 kmph
C) 51 kmph
D) 52 kmph
E) 53 kmph

Solution: Explanation:   Speed of the train relative to man   = (125/10) m/sec = (25/2) m/sec.   [(25/2) x (18/5)] km/hr = 45 km/hr.   Let the speed of the train be 'x' km/hr.   Then, relative speed = (x - 4) km/hr.   x - 4 = 45 => x = 49 km/hr.   49 kmphNSWER IS 49 kmph
Answer: A
If a is an integer and (a^2)/(12^3) is odd, which of the following must be an odd integer? Choose the correct option
A) a/4  B) a/12  C) a/27  D) a/36  E) a/72

Solution: we can rewrite: a^2 / 2^6 x 3^3   so a^2 must be at least 2^6*3^4   or a is at least 2^3 * 3^2   A. if we divide by 4, or 2^2, we still have a factor of 2 left out, which will make an even integer..so no   B. if we divide by 12 (3x2^2), we are still left with a factor of 2- so no   C. 27=3^3. it might be even a non-integer, so no. moreover, we are left with 2^3 ..which will make the number even.   D. 36 = 2^2 * 3^2. still we have at least one factor of 2, so no.   E. by poe, E is left..72=2^3 * 3^2. since we know that a is at least this number (other variations would include another odd factor)..then dividing it by this will always yield an odd integer.   ANSWa/72R:a/72
Answer: E
Rs.800 amounts to Rs.920 in 3 years at simple interest. If the interest is increased by 3%, it would amount to how much?  Choose the correct choice from the following choices:
A) 3387  B) 277  C) 223  D) 992  E) 213

Solution: (800*3*3)/100= 
(800*3*3)/100 = 72
72   920 + 72= 
920 + 72 = 992
992   Answer: 992
Answer: D
If the diameter of circle R is 50% of the diameter of circle S, the area of circle R is what percent of the area of circle S?  Choose the correct choice from the following options
A) 35%  B) 25%  C) 20%  D) 15%  E) 10%

Solution: Let diameter of circle R , dr = 50   and diameter of circle S , ds = 100   Radius of circle R , Rr = 25   Radius of circle S , Rs = 50   Area of circle R/ Area of circle S = (pi * Rr ^2 ) /( pi * Rs^2 )   = (25/50)^2 = (5/10)^2   =25%   Answer :25%
Answer: B
A survey of n people in the town of Eros found that 50% of them preferred Brand A. Another surveyof 100 people in the town of Angie found that 60% preferred Brand A. In total, 55% of all the people surveyed together preferred Brand A. What is the total number of people surveyed?	Pick one:
A) 50 B) 100 C) 150 D) 200 E) 250

Solution: 50% of n people from Eros prefer brand A.   50% of n is 50/100 x n = n/2.   60% of 100 people from Angie prefer brand A.   60% of 100 is 60/100 x 100 = 60.   Of the total n+ 100 people surveyed, n/2 + 60 prefer brand A.   Given that this is 55%,   we have   (n/2+60)/(n+100) x100 =55   Solving the equation   (n/2+60)/(n+100) x100= 55   (n/2+60) = 55/100x(n+100)   (n/2+60) = 11/20n+55   0 = 11n /20 –n/2+55-60   Now subtracting n/2 and 60 from both sides   0=n/20-5   Adding 5 on both sides   5=n/20   n=100   Hence, the total number of people surveyed is   n + 100= 
 + 100 = 100
100 + 100= 
100 + 100 = 200
200.   ANSWER:200
Answer: D
In a certain Parallelogram the degree measure of one angle exceeds that of the other by 20 what is the degree measure of the smaller angle?
Pick: A) 75 B) 80 C) 85 D) 90 E) 95

Solution: In a parallelogram opposite angles are equal and the angles at each side are supplementary to each other (supplementary angles are two angles that add up to 180°).   Given: x+(x+20)=180 --> x=80.   Answer: 80.
Answer: B
In the third grade of Windblown School there are 96 students, one third of them failed the math test and 1/6 failed that literature test. At least how many students failed both tests?
Answers:
A) 0.	B) 6.	C) 8.	D) 10.	E) 12.

Solution: Total = 96   failed in math = 96/3= 
96/3 = 32
32   failed in literature=108/6=16   the least failed in both can be 0   while max can be 16   0.nswer 0.
Answer: A
The fourth proportional to 12, 14 and 18 is?  Choose the correct answer
A) 21	B) 66	C) 55	D) 88	E) 61

Solution: (14*18)/12= 
(14*18)/12 = 21
21   21nswer:21
Answer: A
A pupil's marks were wrongly entered as 73 instead of 63. Due to the average marks for the class got increased by half. The number of pupils in the class is?  Choose the correct choice from the following answers:
A) 18  B) 82  C) 20  D) 27  E) 29

Solution: Let there be x pupils in the class.   Total increase in marks   = (x * 1/2) = x/2   x/2 = (73 - 63) => x/2   = 10 => x = 20.   Answer: 20
Answer: C
A box measuring 72 inches long by 48 inches wide by 24 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? Answers:
A) 17 B) 18 C) 54 D) 108 E) 162

Solution: least number of cubes will be required when the cubes that could fit in are biggest.   8 is the biggest number that could divide all three, 72, 48 and 24.   Thus side of cube must be 8, and total number of cubes = 72/8 * 48/8*24/8= 
72/8 * 48/8*24/8 = 162
162   Ans 162 it is.
Answer: E
Given that G and H are events such that
Q(G)= 0.30
Q(H)=0.9
Q(GnH)=0.9
find Q (G|H) and Q(G|H) Choose the correct choice from the following options.
A) 1/5	B) 1/6	C) 1/3	D) 1/6	E) 1/3

Solution: Here, G and H are events   Q(G|H) = Q(GnH)/Q(H) = 0.9/0.9= 
0.9/0.9 = 1
1   Q(G|H)= Q(GnH)/Q(G) = 0.9/0.30 = 1/3   Answer is 1/3
Answer: C
How many 2 digits number are there which when subtracted from the number formed by reversing its digits as well as when added to the number formed by reversing its digit, result is a perfect square.  Choices:	A) 63	B) 64	C) 65	D) 66	E) 67

Solution: If xy is number, then 11(x+y) and 9*(x-y) should be perfect square.   which is possible when   x+y=11 and x-y = 1,4,9   value of x,y is valid only when x-y=1, then x=6,y=5   so number is 65.   ANSWER:65
Answer: C
How many pieces can a square pizza be cut into by making 6 linear cuts?  Choose the correct answer
A) 20
B) 21
C) 22
D) 23
E) 24

Solution: 1 cut makes 2 pieces   a second cut can make 4 pieces by cutting through both pieces   a third cut can make 7 pieces by cutting through 3 of the pieces   a fourth cut can make 11 pieces by cutting through 4 of the pieces   a fifth cut can make 16 pieces by cutting through 5 of the pieces   a sixth cut can make 22 pieces by cutting through 6 of the pieces   22
Answer: C
What is the greatest prime factor of 4^16 - 2^28? Choose one:	A) 2	B) 3	C) 5	D) 7	E) 11

Solution: I'm happy to help with this.   We know 4 = 2^2, so 4^17 = (2^2)^17 = 2^(2*16) = 2^32   That takes advantage of a law of exponents that says (a^n)^m = a^(n*m)   So, 4^16 - 2^28 = 2^32 - 2^28 = 2^(28 + 4) - 2^28 = (2^28)*(2*4) - 2^28 = (2^4 - 1) *(2^28)   = (16 - 1)*(2^28) = 15*(2^28)   The prime factors of 63 are 3*5, so the largest prime factor is 7, answer choice D.   Here's a blog you may find helpful.   http://magoosh.com/gmat/2012/gmat-math-factors/   Does all that make sense? Please let me know if you have any further questions.   Mike   Wow. I am floored by how great of an explanation you provided. Posts like that make me really think that doing thousands of practice problems with good explanations beats out reading books on math every day of the week.   5
Answer: C
A bat is bought for Rs.400 and sold at a gain of 30% find its selling price?	Choose the correct choice from the following answers:
A) s.460/-	B) s.480/-	C) s.500/-	D) s.520/-	E) s.540/-

Solution: 100 % ------> 400 (100 * 4 = 400)   130 % ------> 520 (130 * 4 = 520)   Selling price = Rs.520/-   Option 's.520/-'
Answer: D
In a division, a student took 87 as divisor instead of 36. his answer was 24 . The correct answer is-	Choose the correct answer:
A) 42
B) 32
C) 48
D) 28
E) 58

Solution: X/87 = 24.   X = 24 *87.   So correct answer would be,   (24 *87) /36= 
(24 *87) /36 = 58
58.   ANSW58R : 58
Answer: E
The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is:	Pick.
A) 40	B) 25	C) 30	D) 35	E) 48

Solution: Sum of the present ages of husband, wife and child = (27 * 3 + 3 * 3)= 
(27 * 3 + 3 * 3) = 90
90 years.   Sum of the present age of wife and child= (20 * 2 + 5 * 2)= 
(20 * 2 + 5 * 2) = 50
50 years.   Husband's present age= (90 - 50)= 
(90 - 50) = 40
40 years.   40NSWER 40
Answer: A
Matt gets a $1,000 commission on a big sale. This commission alone raises his average commission by $150. If Matt's new average commission is $550, how many sales has Matt made?
Choose the correct answer:
A) 3 B) 4 C) 5 D) 6 E) 7

Solution: Let, Average Commission = x   No. of items sold = y   Total Commission = xy   New Commission = xy+1000   New Average = (xy+1000) / (y+1) = 150+x   i.e. (xy+1000) = (y+1)* (150+x)   i.e. (xy+1000) = (xy+x+150y+150)   i.e. (850) = (x+150y)   New Commission = 550 = 150+x   i.e. x=400   i.e. y = 3   New Sales = y+1 = 4   Answer: option 4
Answer: B
The Cottage Grove Loop Line travels the distance between the north side and the south side of the city in two hours, at a rate of speed of 100 km/h. How long is a round trip, measured in kilometers?
Select the correct option
A) 100 km B) 150 km C) 200 km D) 300 km E) 400 km

Solution: Distance covered in 2 hours: 100 x 2 = 200 km   Duration of a return trip: 2 x 2 = 4 hours   Distance covered in 4 hours: 100 x 4 = 400 km   IMO, correct answer is "400 km."
Answer: E
A vending machine randomly dispenses four different types of fruit candy. There are twice as many apple candies as orange candies, twice as many strawberry candies as grape candies, and twice as many apple candies as strawberry candies. If each candy cost $0.1, and there are exactly 90 candies, what is the minimum amount of money required to guarantee that you would buy at least three of each type of candy?  Choices.
A) $8.30 B) $20.75 C) $22.50 D) $42.75 E) $45.00

Solution: Let number of Apple , Orange , strawberry and grape candies be A, O ,S and G respectively .   A= 2O   S= 2G   A= 2S   A= 4G   A+O+S+G = 90   =>A + A/2 + A/2 +A/4 = 90   => 9A/4 = 90   => A = 40   O = 20   S = 20   G = 10   Cost of each candy = .1 $   Mininum amount of money required to guarantee that you would buy at least three of each type of candy   We can buy 40 Apple candies , 20 orange candies , 20 strawberry candies and 3 grape candies to ensure atleast 3 of each type of candies .   Total = 83 candies   $8.30mount required = 83 * .1= 
83 * .1 = 8.3
8.30 $   $8.30nswer $8.30
Answer: A
A completes a work in 12 days and B complete the same work in 24 days. If both of them work together, then the number of days required to complete the work will be?  Choose the correct option:
A) 8 days	B) 11 days	C) 21 days	D) 22 days	E) 24 days

Solution: If A can complete a work in x days and B can complete the same work in y days, then, both   of them together can complete the work in x y/ x+ y days   Therefore, here, the required number of days = 12 × 24/ 36 = 8 days.   Option '8 days'
Answer: A
If x is less than y by 20% then y exceed x by:	Choose the correct choice from the following answers:
A) 33.33% B) 25% C) 75% D) 66.66% E) None of these

Solution: Using formula (x/(100-x)*100) where x is Percentage decrease (here it is 20%)   => 20/(100-20)*100= 
20/(100-20)*100 = 25
25%   ANSWER:25%
Answer: B
A can do a piece of work in 4 days. B can do it in 8 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it?
Choose the correct choice.
A) 22 days
B) 8 days
C) 67 days
D) 1 days
E) 18 days

Solution: C = 1/2 - 1/4 - 1/8 = 1/8   => 8 days   Answer:8 days
Answer: B
What is the least common multiple of 15, 22 and 24?  Pick one:
A) 60
B) 120
C) 240
D) 1320
E) 1720

Solution: Let us first write the numbers in the form of prime factors:   15 = 3*5   22 = 2*11   24 = 2 * 17^1   The LCM would be the largest powers of the prime numbers from all these three numbers.   Hence LCM = 1320   Option 1320
Answer: D
It takes printer A 4 more minutes more than printer B to print 40 pages. Working together, the two printers can print 50 pages in 6 minutes. How long will it take Printer A to print 160 pages? Choose the correct choice from the following options
A) 12	B) 18	C) 48	D) 20	E) 30

Solution: If it takes 4 more minutes for A to print 40 pages than it takes B,   it takes 5 more minutes for A to print 50 pages than it takes B.   Thus if b is the number of minutes than B takes to print 50 pages,   we can write:   1/b+1/(b+5)=1/6 (since in 1 minute, they print 1/6th of the 50 page job)   6(2b+5)=b(b+5)   b^2-7b-30=0   (b-10)(b+3)=0   b=10   Thus it takes A 15 minutes to print 50 pages and   15*160/50= 
  15*160/50 = 48
48 minutes to print 160 pages (ANSWER 48)
Answer: C
Last year Sandy saved 6% of her annual salary. This year, she made 10% more money than last year, and she saved 9% of her salary. The amount saved this year was what percent of the amount she saved last year?  Choose the correct choice from the following answers
A) 140%  B) 152%  C) 165%  D) 176%  E) 190%

Solution: Let last year's salary be x.   Last year, Sandy save 0.06x   This year, Sandy saved  0.09*1.1= 
 0.09*1.1 = 0.099
0.099x   0.099x / 0.06x= 99/60= 
99/60 = 33/20 = around 1.65
1.65= 165%   The answer is 165%.
Answer: C
A boy is travelling from his home to school at 4 km/hr and reached 7 min late. Next day he traveled at 8 km/hr and reached 8 min early. Distance between home and school? Choose the correct choice from the following
A) 2km	B) 3km	C) 4km	D) 5km	E) 6km

Solution: Let the distance be x   T1 = x/4 hr   T2 = x/8hr   Difference in time = 7+8= 
7+8 = 15
15=1/4hr   x/4-x/8= 1/4   x/8=1/4   x =2 km   2kmnswer is 2km
Answer: A
In an exam, Dibi scored 25 percent, Balan scored 38 percent and Cristen 23 percent. The maximum score awarded in the exam is 1200. Find the average mark scored by all the three boys? Pick one: A) 322 B) 342 C) 344 D) 328 E) 320

Solution: Average mark scored by all the three boys =   [25/100 (1200) +38 /100 (1200) + 23/100 (1200)] / 3   300+456+276= 344   Answer: 344
Answer: C
The forth proportional to 1,2,3 is?
Choose the correct answer:
A) 2
B) 4
C) 8
D) 9
E) 6

Solution: Let the fourth proportional to 1,2,3 be x   then 1:2::3:x   1x = 2*3= 
2*3 = 6
6   Answer is 6
Answer: E
Two bus tickets from city A to B and three tickets from city A to C cost Rs. 77 but three tickets from city A to B and two tickets from city A to C cost Rs. 73. What are the fares for cities B and C from A ?  Choose the correct choice from the following answers:
A) Rs. 13, Rs. 19	B) Rs. 13, Rs. 17	C) Rs. 13, Rs. 12	D) Rs. 13, Rs. 11	E) Rs. 13, Rs. 10

Solution: Explanation:   Let Rs. x be the fare of city B from city A and Rs. y be the fare of city C from city A.   Then, 2x + 3y = 77 ...(i) and   3x + 2y = 73 ...(ii)   Multiplying (i) by 3 and (ii) by 2 and subtracting, we get: 5y = 85 or y = 17.   Putting y = 17 in (i), we get: x = 13.   Answer: B) Rs. 13, Rs. 17
Answer: B
An order was placed for the supply of a carper whose length and breadth were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and breadth were in the ratio 7 : 3 but were was no change in its parameter. Find the ratio of the areas of the carpets in both the cases. Choose the correct choice from the following options:
A) 4:3
B) 8 : 7
C) 4 : 1
D) 6 : 5
E) None of these

Solution: Explanation:   Let the length and breadth of the carpet in the first case be 3x units and 2x units respectively.   Let the dimensions of the carpet in the second case be 7y, 3y units respectively.   From the data,.   2(3x + 2x) = 2(7y + 3y)   => 5x = 10y   => x = 2y   Required ratio of the areas of the carpet in both the cases   = 3x * 2x : 7y : 3y   = 6x2 : 21y2   = 6 * (2y)2 : 21y2   = 6 * 4y2 : 21y2   = 8 : 7   ANSWER IS 8 : 7
Answer: B
Let the polynomials be:
P1(x)=3x2−7x+7,
P2(x)=−5x2−4x+2,
P1(x)+P2(x)=
Pick:  A) 2x2 + 11x - 7  B) -2x2 - 11x + 9  C) -2x2 - 11x + 6  D) 2x2 - 9x + 7  E) None of these

Solution: Solution:   P1(x)+P2(x)=(3x2−7x+7)+(−5x2−4x+2)=P1(x)+P2(x)=(3x2−7x+7)+(−5x2−4x+2)=   3x2−7x+7−5x2−4x+2=3x2−7x+7−5x2−4x+2=   −2x2−11x+9   Answer -2x2 - 11x + 9
Answer: B
In a game, one player throws two fair, six-sided die at the same time. If the player receives at least a five or a two on either die, that player wins. What is the probability that a player wins after playing the game once?  Select
A) 1/3	B) 4/9	C) 5/9	D) 2/3	E) 3/4

Solution: We're looking for the number of outcomes that include AT LEAST a 2 or a 5.   #getting a two in the 1st die = {(2,1), (2,2), ...(2,6) }= 6   #getting a two in 2nd die {(3,2), (4,2), ...(6,2) } = 4 [exclude 1,2 and 5,2] since it will be counted twice   #getting a five in 1st die {(5,1), (5,2), ...(5,6) }= 6   #getting a five in 1st die {(2,5), (3,5), ...(6,5) } = 4 [exclude 1,5 and 5,5] since it will be counted twice   Total possibilities = 20   Probability of rolling at least a 2 or a 5 on two dice: 20/36 = 5/9   5/9
Answer: C
The income of a broker remains unchanged though the rate of commission is increased from 4% to 5%. The percentage of slump in business is ?  Options
A) 8%
B) 1%
C) 20%
D) 80%
E) NONE

Solution: Answer   Let the business value change from A to B.   Then, 4% of A = 5% of B   ⇒ 4A/100 = 5B/100   ⇒ B = 4A/5   ∴ change in business = (A - 4A/5) = A/5   Percentage slump in business = {(A/5)/A} x 100 % = 20%   20%orrect Option: 20%
Answer: C
Two trains of length 200 m and 300 m are 200 m apart. They start moving towards each other on parallel tracks, at speeds 36 kmph and 72 kmph. In how much time will the trains cross each other?
Choices:	A) 70/8	B) 70/7	C) 70/5	D) 70/3	E) 70/1

Solution: Relative speed = (36 + 72)* 5/18 = 6 * 5= 
6 * 5 = 30
30 mps.   The time required= d/s = (200 +200 + 300)/30   = 700/30= 70/3 sec.   Answer: 70/3
Answer: D
What is the sum of this series?
1, 3, 5, 7, 9, ...... 45. Pick one:
A) 600
B) 529
C) 612
D) 512
E) 589

Solution: Number of odd numbers between 1 and 45 is  (45+1)/2= 
 (45+1)/2 = 23
23   Therefore Sum of odd numbers   23*23= 
  23*23 = 529
529   ANSWER: 529
Answer: B
Angelina walked 960 meters from her home to the grocery at a constant speed. She then walked 480 meters to the gym at double the speed. She spent 40 seconds less on her way from the grocery to the gym than on her way from home to the grocery. What was Angelina's speed, in meters per second, from the grocery to the gym? Choose the correct option:  A) 2  B) 13  C) 24  D) 36  E) 42

Solution: let the speed be X...   so time taken from home to grocery= 960/x..   the speed to gym = 2x..   so time taken = 480/2= 
480/2 = 240
240/x..   its given 960/x-240/x=40..   720/x=40..   x=18m/secs..   so grocery to gym=2*18= 
2*18 = 36
36m/s...   36
Answer: D
A mixture contains alcohol and water in the ratio 4 : 3. If 8 litres of water is added to the mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture Choose the correct choice from the following answers
A) 15 litres
B) 10 litres
C) 30 litres
D) 22 litres
E) 16 litres

Solution: Let the quantity of alcohol and water be 4x litres and 3x litres respectively   4x/(3x+8)=4/5   20x=4(3x+8)   8x=32   x=4   Quantity of alcohol = (4 x 4) litres = 16 litres.   Answer is 16 litres.
Answer: E
A 340-liter solution of Kola is made from 80% water, 6% concentrated Kola and the rest is made from sugar. If 3.2 liters of sugar, 10 liter of water and 6.8 liters of concentrated Kola were added to the solution, what percent of the solution is made from sugar? Choose the correct choice from the following choices
A) 6%. B) 7.5%. C) 9.2%. D) 10.5%. E) 14%.

Solution: Denominator:   340+10+3.2+6.8= 
340+10+3.2+6.8 = 360
360   Numerator:   340(1-.80-.06)+3.2   340(0.14)+3.2   47.6+3.2   50.8   Ratio:   50.8/360=0.14   Answer: 14%.
Answer: E
Tough and Tricky questions: Combinations.
Three students - 2 boys and 1 girls - are to sit side by side for a makeup exam. How many ways could they arrange themselves given that no two boys and no two girls can sit next to one another? Choose one
A) 2
B) 4
C) 72
D) 240
E) 720

Solution: 2!*1!*2 = 2*1*2= 
2*1*2 = 4
4 ways.   Ans. 4) 4
Answer: B
What is the remainder when 3^25 is divided by 5?	Options:
A) 0
B) 1
C) 2
D) 3
E) 4

Solution: The units digit of powers of 3 follow a repeating cycle of four: {3, 9, 7, 1}   25 has the form 4k+1, so the units digit of 3^25 is 3.   The remainder when dividing by 5 is 3.   The answer is 3.
Answer: D