MU-NLPC/Calc-aqua_rat huggingface dataset:
One ball will drop from a certain height. The height it will reach after rebounding from the floor is 50 percent of the previous height. The total travel is 150cm when it touches the floor on third time. What is the value of the original height? Choose the correct answer.
A) 60cm B) 90cm C) 100cm D) 120cm E) 130cm

Solution: when Ball comes down, Then i have indicated the distance covered in green   when Ball goes up, Then i have indicated the distance covered in red   Distance travelled uptil the ball touches the floor 3rd time:h+0.5h+0.5 h+0.5*0.5 h+0.5*0.5 h   h + 2 * 0.5 * h + 2 * 0.25 * h = h (1+2*0.5+2* 0.25) = h (1+1+0.5) = 150   2.5 h = 150   h = 60.   60cm is the answer.
Answer: A
If the price of gold increases by 25%, find by how much the quantity of ornaments must be reduced, so that the expenditure may remain the same as before?
Answers:
A) 331/8%	B) 331/3%	C) 631/3%	D) 332/3%	E) 20%

Solution: 100   125   ------   125-------25   100-------? => 20%   Answer:20%
Answer: E
Let f(x) = x^2 + bx + c. If f(1) = 0 and f(-9) = 0, then f(x) crosses the y-axis at what y-coordinate?  Choose the correct choice from the following answers
A) -9  B) -1  C) 0  D) 1  E) 9

Solution: When x = 1 and when x = -9, the expression f(x) = x² + bx + c equals 0.   Then f(x) = (x-1)(x+9)   f(0) = -9   The answer is -9.
Answer: A
In triangle PQR, the angle Q = 90 degree, PQ = 2 cm, QR = 8 cm. X is a variable point on PQ. The line through X parallel to QR, intersects PR at Y and the line through Y, parallel to PQ, intersects QR at Z. Find the least possible length of XZ	Choose the correct choice from the following answers:  A) 1.6 cm  B) 2.4 cm  C) 4.8 cm  D) 2.16 cm  E) 3.2 cm

Solution: Look at the diagram below:   Now, in case when QY is perpendicular to PR, two right triangles PQR and PQY are similar: QY:QP=QR:PR --> QY:2=8:10 --> QY=1.6.   1.6 cmnswer: 1.6 cm.
Answer: A
A boat having a length 5 m and breadth 2 m is floating on a lake. The boat sinks by 1cm when a man gets on it. The mass of the man is:  Pick one.
A) 100 kg
B) 60 kg
C) 72 kg
D) 96 kg
E) None of these

Solution: Explanation:   Volume of water displaced = (5 x 2 x 0.01) m3   = 0.10 m3.   ∴ Mass of man = Volume of Water displaced x Density of water   = (0.10 x 1000)kg   = 100 kg.   100 kgnswer: 100 kg
Answer: A
The price of a coat in a certain store is $500. If the price of the coat is to be reduced by $250, by what percent is the price to be reduced?	Choose the correct choice from the following answers:  A) 10%  B) 15%  C) 50%  D) 25%  E) 30%

Solution: price of a coat in a certain store = $500   the price of the coat is to be reduced by $250   % change = (Final Value - Initial Value)*100 / Initial Value   % Reduction= (Reduction in Price)*100 / Initial Value   i.e. % Reduction= (250)*100 / 500= 
(250)*100 / 500 = 50
50%   Answer: Option 50%
Answer: C
A marching band of 240 musicians are to march in a rectangular formation with s rows of exactly t musicians each. There can be no less than 8 musicians per row and no more than 30 musicians per row. How many different rectangular formations X are possible?  Choose the correct choice from the following answers:
A) 3  B) 4  C) 5  D) 6  E) X=8

Solution: The combinations could be {(1,240),(2,120),(3,80),(4,60),(5,48),(6,40),(8,30),(10,24),(12,20),)15,16),(16,15),(20,12),(24,10),(30,8),(40,6), (48,5),(60,4),(80,3),(120,2),(240,1)}   Of these we are told 8<=t<=30 So we can remove these pairs, and we are left only with.   {(8,30,(10,24),(12,20),(15,16),(16,15),(20,12),(24,10),(30,8)}   Hence 8.X=8
Answer: E
The respective ages of father and his son are 51 and 16 years. In how many years will the father be twice as old as his son ?
Choose the most appropriate option
A) 19 years	B) 9 years	C) 10 years	D) 15 years	E) 12 years

Solution: Suppose x years later the father will be twice as old as his son.   x + 51 = 2 (x + 16)   x = 51 - 32= 
51 - 32 = 19
19 years   answer : 19 years
Answer: A
What inequality represents the condition 1<x<13?	Select: A) |x|<3 B) |x+5|<4 C) |x-7|<6 D) |-5+x|<4 E) |3+x|<5

Solution: 1<x<13 represents segment with   length:   13-1= 
  13-1 = 12
12   center:   (13+1)/2= 
  (13+1)/2 = 7
7   For any |x-a|<b a is a center and b is a half of length. So, |x-7|<12/2 represents our inequality (answer |x-7|<6)
Answer: C
It takes one machine 4 hours to complete a production order and another machine 9 hours to complete the same order. How many hours would it take both amhcines working simultaneously at their respective rates to complete the order?  Choose the correct choice
A) a) 7/12  B) b) 2 10/13  C) c) 1 5/7  D) d) 3 1/2  E) e) 7

Solution: RT = W   Given:   R = 1/9 + 1/4 = 13/36   T = ?   W = 1   T = 1 / (13/36) = 36/13 = 2 10/13   Answer: b) 2 10/13
Answer: B
A sells a Cricket Bat to B at a profit of 20%. B sells it to C at a profit of 25%. If C pays $231 for it, the cost price of the Cricket Bat for A is:	Pick:
A) 150 B) 120 C) 154 D) 160 E) 210

Solution: 125% of 120% of A = 231   125/100 * 120/100 * A = 231   A = 231 * 2/3= 
231 * 2/3 = 154
154.   ANSWER 154
Answer: C
A basket has 5 apples and 7 oranges. Three fruits are picked at random. What is the probability that at least 2 apples are picked?	Answers:	A) 2/7	B) 4/11	C) 5/11	D) 7/22	E) 15/44

Solution: The total possible choices are 12C3 = 220   The ways to choose 3 apples: 5C3 = 10   The ways to choose 2 apples: 5C2 * 6C1 = 60   P(at least 2 apples) = 70/220 = 7/22   The answer is 7/22.
Answer: D
Pipe A can fill a tank in 5 hours, pipe B in 10 hours and pipe C in 30 hours. If all the pipes are open,in how many hours will the tank be filled ? Pick
A) 2  B) 2.5  C) 3  D) 3.5  E) 4

Solution: 1/5+1/10+1/30=10/30=1/3. soo 3 hrs   ANSWER:3
Answer: C
A seven-digit phone number is divisible by 5. After adding the two digits of the area code the number is not divisible by 3, which of the following cannot be the area code?	Choose one.
A) 05. B) 06. C) 03. D) 04. E) 02.

Solution: Given that 7 digit number is divisible by 5   we know any number will not be divisible by 5 if the sum of all digits of the number is not the multiple of5.   Hence looking at the option we can say that the number that should be added to the seven digit number must be 06 as adding it will make it divisible by 5... hence answer is 05.
Answer: A
In how many ways, a committee of 5 members can be selected from
6 men and 5 ladies, consisting of 3 men and 2 ladies?  Options: A) 450 B) 750 C) 130 D) 250 E) 200

Solution: (3 men out 6) and (2 ladies out of 5) are to be chosen.   Required number of ways = (6c3x5c2)   = [6x5x4/3x2x1] x [5x4/2x1]   = 200.   Ans: 200
Answer: E
Carmen made a sculpture from small pieces of wood. The sculpture is 2 feet 10 inches tall.Carmen places her sculpture on a base that is 2 inches tall. How tall are the sculpture andbase together? Choose the correct option.
A) 3.1 feet
B) 3.2 feet
C) 3.3 feet
D) 3.0 feet
E) 3.5 feet

Solution: we know 1 feet =12 inch then   2 feet =24 inch     24+10= 
  24+10 = 34
34 then     34+2= 
  34+2 = 36
36   36/12= 
36/12 = 3
3.0 feet   ANSWER:3.0 feet
Answer: D
When Q is divided by W, the quotient is R and the remainder is r. Which of the following expressions is equal to r?  Choose the correct choice from the following:
A) RW + Q  B) Q - RW  C) RW - Q  D) QW - R  E) Q/R

Solution: Q/W = R + r/W   Q -RW = r   Amswer: Q - RW
Answer: B
If a coin is tossed twice what is the probability that it will land either heads both times or tails both times?  Choices
A) 1/8	B) 1/6	C) 1/4	D) 1/2	E) 1

Solution: Prob to get 2 heads = 1/2*1/2 = 1/4   Prob to get 2 tails = 1/2*1/2 = 1/4   So, Prob to get either 2 heads or 2 tails = 1/4+1/4 = 1/2   Answer will be 1/2.
Answer: D
What is the least value of x. So that 4x569 is divisible by 3?  Choose one:
A) 2  B) 5  C) 1  D) 0  E) 7

Solution: The sum of the digits of the number is divisible by 3, then the number is divisible by3.   4 + x +5 + 6 + 9 =24 + x   Least value of x may be 0   Therefore  24+0= 
 24+0 = 24
24 is divisible by 3.   0
Answer: D
A shipment of 1500 heads of cabbage, each of which was approximately the same size, was purchased for $600. The day the shipment arrived 2/3 of the heads were sold, each at 25% above the cost per head. The following day the rest were sold at a price equal to 20% less than the price each head sold for on the day before. What was the total gross profit on this shipment.	Choose the correct choice from the following answers:
A) $100
B) b $115
C) c $125
D) d $130
E) e $135

Solution: Purchase cost = 600/1500= 
600/1500 = 2/5 = around 0.4
$ 0.4   25% above the cost per head= (125/100)*0.4= 
(125/100)*0.4 = 0.5
$ 0.5   2/3 of the heads were sold means 2/3*1500= 
2/3*1500 = 1_000
1000 ,Selling amount for 1000 cabbage= 1000 * 0.5= 
1000 * 0.5 = 500
$ 500   Remaining were sold at a price equal to 20% less than the price each head sold for on the day before i.e , (80/100)*0.5= $ 0.4   Hence selling cost for the remaining cabbage = 500 * 0.4= 
500 * 0.4 = 200
$ 200   Total selling cost= 500 + 200= 
500 + 200 = 700
$ 700   Gross profit= $ 700 - $ 600 = $ 100   Hence $100nswer is $100.
Answer: A
The ratio of a to b to c is 2 to 3 to 4, and a, b, c are positive integers. If the average (arithmetic mean) of the three numbers is 42, what is the value of a?
Choose the most appropriate option:
A) 24 B) 25 C) 28 D) 30 E) 32

Solution: Let a=2k, b=3k, and c=4k.   a+b+c = 2k+3k+4k = 9k   Since the average is 42:   9k/3 2 +3 +4= 
2 +3 +4 = 9
9k   Since the average is 42:   9k/3= 42   3k = 42   k=14   Then a=28.   The answer is 28.
Answer: C
What is the remainder when 9^1 + 9^2 + 9^3 +...+ 9^9 is divided by 3?	Choose one:
A) 0 B) 3 C) 2 D) 5 E) None of the above

Solution: Notice that in the brackets we have the sum of 8 odd multiples of 3, which yields remainder of 0 upon division by 3.   0nswer : 0
Answer: A
A number is doubled and 5 is added. If the resultant is trebled, it becomes 117. What is that number?  Select the correct option
A) 12	B) 29	C) 27	D) 17	E) 99

Solution: Explanation:   Let the number be x.   Therefore,   3(2x + 5) = 117   6x + 15 = 117   6x = 102   x = 17   ANSWER:17
Answer: D
What will the value replace by x if 210x0 is divisible by 5? Choices:
A) 4
B) 3
C) 2
D) All the Above
E) None

Solution: Divisibility of 5 is Last of the digit is 0 or 5.   In 210x0 has 0.So the Number must divisible by 5.   That is any number can be replaced in the place of x   Answer is All the Above
Answer: D
A certain restaurant offers 7 kinds of cheese and 2 kinds of fruit for its dessert platter. If each dessert platter contains an equal number of kinds of cheese and kinds of fruit, how many different dessert platters could the restaurant offer?	Choose the most appropriate option:
A) 8  B) 12  C) 15  D) 21  E) 35

Solution: As dessert platter should contain equal number of kinds of cheese and fruits, desert can contain:   A. 2 kinds of cheese and 2 kinds of fruits --> 7C2*2C2=21*1= 
21*1 = 21
21   B. 1 kind of cheese and 1 kind of fruit --> 7C1*2C1=7*2= 
7*2 = 14
14   A+B=21+14= 
21+14 = 35
35   Answer: 35.
Answer: E
A certain rectangular window is four times as long as it is wide. If its perimeter is 50 feet, what are its dimensions in terms of length by width?  Choose the correct option.
A) 12 by 2	B) 11 by 3	C) 20 by 5	D) 10 by 4	E) 9 by 3

Solution: 2x+2y=50   x+y=25   x+4x=25   5x=25   x=5   Answer 20 by 5
Answer: C
A motorcyclist goes from Bombay to Nagpur, a distance of 600 kms at an average of 120 kmph speed. Another man starts from Bombay by car 1 Â½ hours after the first, and reaches Nagpur Â½ hour earlier. What is the ratio of the speed of the motorcycle and the car?
Select the correct option:
A) 1:2  B) 1:7  C) 1:9  D) 3:5  E) 1:1

Solution: T = 600/120= 
600/120 = 5
5 h   T= 5 - 2= 
5 - 2 = 3
3   Time Ratio= 5:3   Speed Ratio = 3:5   Answer: 3:5
Answer: D
Three picked up 30 mangoes .In how many ways can they divide them if all mangoes be identical?  Options:
A) A)4^30 B) B)2^30 C) C)1^30 D) D)3^30 E) E)6^30

Solution: Each Mango can be given to any one of the Three people or in other words..1 mango can be divided into 3 ways...so all 30 can be divided in 3^30 ways   ANS:3^30
Answer: D
It is the New Year and Mandy has made a resolution to lose weight this year. She plans to exercise and do yoga. For exercise she plans to workout at the gym and ride her bicycle in the ratio of 2:3 everyday. She will also do yoga in the ratio, yoga:exercise = 2:3. If she rides her bike for 20 minutes, how much time will she spend doing yoga? (rounded to minutes)	Pick:
A) 10 min.
B) 33 min.
C) 17 min.
D) 23 min.
E) 25 min.

Solution: The ratio is 2:3 = gym:ride, so (20)(3/2) = 30 minutes at the gym, and   30 + 20= 
  30 + 20 = 50
50 minutes exercise, so (2/3)(50)= 33 minutes yoga.   Answer: 33 min.
Answer: B
53 x 22 = 1276 then (4221)n=()10? Pick
A) 3896
B) 3897
C) 3898
D) 3899
E) None

Solution: Sol:   As we don't know the base system here we take the base as n. So 53 in base n can be written as 5n+3, and 22 as 2n+2 and 1276 as n3+2n2+7n+6   ⇒⇒ (5n + 3)(2n + 2) = n3+2n2+7n+6   ⇒⇒ 10n2+16n+6=n3+2n2+7n+6   ⇒⇒ n3−8n2−9n=0   ⇒⇒ n(n2−8n−9)=0   ⇒⇒ (n + 1)(n - 9) = 0   So n = 9   (4221)9=4×93+2×92+2×9+1   = 3716 + 162 + 18 + 1= 
3716 + 162 + 18 + 1 = 3_897
3897   Answer 3897
Answer: B
Four friends, Thomas, Mike, Brian, and John, went on a fishing trip. If Mike caught 4 more than Brian did, John caught 12 less than Thomas did, and Thomas caught 4 more than Mike did, how many more fish did Brian catch than John did?
Choose the correct choice from the following:	A) 6	B) 4	C) 8	D) 1	E) 12

Solution: In this word problem, the first key is to turn the story into equations:   Mike caught 4 more than Brian did: M = 4 + B   John caught 12 less than Thomas did: J = T - 12   Thomas caught 4 more than Mike did: T = 4 + M   Then, in classic GMAT style, the problem doesn't ask you to solve for a single variable, but instead to solve for the difference between B and J (how many more fish did Brian catch than John did?). This means that your goal is to get the equations in terms of B and J so that you can solve for the expression B - J.   Taking the first equation and solving for B, you have B = M - 4.   Taking the second equation and solving for J you have J = T - 12, and then with the third equation you can replace T with 4 + M so that both B and J are in terms of M: J = (4 + M) - 12.   So if 4 = M - 4 and J = M - 8, then:   4 - J = (M - 4) - (M - 8)   4 - J = M - 4 - M + 8 (remove the parentheses by distributing the multiplication)   4 - J = 4, so the answer is 4.
Answer: B
A group of 3 integers is to be selected one after the other, and at random and without replacement, from list L above. What is the probability that the 3 integers selected are not 3 consecutive integers?  Choices:
A) 3/5
B) 7/10
C) 3/4
D) 4/5
E) 14/15

Solution: Determining that there were 120 ways to select 3 numbers from that group was the perfect first step. Next, you just have to figure out which combinations of 3 involve three consecutive integers. Thankfully, it's not that hard - and you can list them out:   123   234   345   456   567   678   789   89&10   Thus there are 8 ways (out of 120) that ARE three consecutive integers and the other 112/120 are NOT three consecutive integers.   112/120 = 14/15   Final Answer:14/15
Answer: E
Ram's age and Shyam's age are in the ratio 3 : 4. Seven years ago the ratio of their ages was 2: 3. Find the ratio of their ages five years hence?
Choose the correct option:
A) 33:21  B) 44:44  C) 33:45  D) 26:33  E) 44:66

Solution: Let ages of Ramu and Shyamu be x and y respectively.   x/y = 3/4 => x = 3/4 y   Also (x - 7) / (y - 7) = 2/3   => 3x - 21 = 2y - 14   3x = 2y + 7   But x = 3/4 y   3 * 3/4 y = 2y + 7   9y = 8y + 28 => y = 28 years   Ratio of their ages five years hence   = (21 + 5) / (28 + 5) = 26/33.   Answer:26:33
Answer: D
Dick and Jane each saved $4,000 in 1989. In 1990 Dick saved 10 percent more than in 1989, and together he and Jane saved a total of $6,500. Approximately what percent less did Jane save in 1990 than in 1989?  Answers:
A) 20%	B) 70%	C) 50%	D) 30%	E) 40%

Solution: 1990   Dick saved = $ 4400   Jane saved = $ 2100 (jane saved $2800 less than she did the prior year)   Jane saved approximately $2800/4000$ (70%) less in 1990   Answer: 70%
Answer: B
2/5 of the fish in an aquarium are red and 1/4 of the fish are brown. 3/4 of the red fish and 3/5 of the brown fish are male. If the rest of the fish in the aquarium are female, what is the probability that a fish randomly picked from the aquarium is male? Options.
A) 2/5
B) 3/10
C) 7/10
D) 9/20
E) 11/20

Solution: 3/4*2/5 + 3/5*1/4 = 9/20   The answer is 9/20.
Answer: D
A young girl counted in the following way on the fingers of her left hand. She started collang the thumb 1, the index finger 2, the middle finger 3, the ring finger 4, the little finger 5, then reversed direction calling the ring finger 6, the the middle finger 7, the index finger 8, the thumb 9 then back to the index finger for 10, the middel finger for 11, and so on. She counted up to 1994. She ended on her  Choose the correct choice from the following options
A) thumb	B) the index finger	C) the middle finger	D) the ring finger	E) the little finger

Solution: Notice the pattern. The thumb lands up at numbers 1,9,17,25,33,... so every 8th number   the index fingery this patter the thumb is also at number 1993 (multiple of 8 + 1)   Hence 1994 has to be the index finger   Answer is the index finger
Answer: B
How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 66 km/hr?	Choose the correct choice from the following choices
A) 11	B) 30	C) 29	D) 88	E) 61

Solution: Speed of train relative to man = 66 - 3= 
66 - 3 = 63
63 km/hr.= 63 * 5/18 = 35/2 m/sec.   Time taken to pass the man = 500 * 2/35 = 28.57 sec.   approx. 29 sec   Answer: 29
Answer: C
Raffle tickets numbered consecutively from 101 through 350 are placed in a box. What is the probability that a ticket selected at random will have a number with a hundreds digit of 1 ? Choose the correct choice from the following answers.
A) 2/5
B) 2/7
C) 33/83
D) 99/250
E) 98/250

Solution: SOLUTION   The number of integers from 101 to 350, inclusive is 250, out of which 100 (from 200 to 299) will have a hundreds digit of 2. Thus the probability is 98/250   Answer: 98/250
Answer: E
A group of 8 students are seated in a linear arrangement. There are 2 girls who must sit together always. in how many arrangements can the students sit? Select the correct option
A) A.1296  B) B.1850  C) C.2880  D) D.3546  E) E.10080

Solution: Glue two girls together: {AB}   6 units {AB}, {C},{D}, {E}, {F}, {G}, {H} can be arranged in 7! ways. Each girls within their unit can be arranged in 2! ways.   Therefore the final answer is 7!*2!=   Answer: E.10080.
Answer: E
A starts a business with a capital of Rs. 85,000. B joins in the business with Rs.42500 after some time. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1? Choose the correct answer
A) 8 months	B) 9 months	C) 1months	D) 12months	E) 23months

Solution: Let B joins for x months. Then   8 months:B = 85000*12 : x* 42500 = 3 : 1   => 850*12 : 425x= 3 : 1   => 850*12/ 425x = 3/1= 
3/1 = 3
3=> 850*4 /425x = 1   => 2*4/x = 1   => x = 8   8 monthsnswer is 8 months
Answer: A
Of three numbers, the third is four times the second and the second is two times the first. If their average is 165, the smallest of the three numbers is:
Choose the correct choice from the following answers
A) 18	B) 19	C) 45	D) 21	E) 22

Solution: Explanation:   Let first number be x.   So,2nd no. = 2x & 3rd no.=8x.   So,x+2x+8x=165 × 3 = 495   11x = 495/11   x = 495/11   Hence,smallest Number x=45   Answer: 45
Answer: C
Using all the letters of the word "NOOKIASS", how many words can be formed, which begin with N and end with S? Choose the correct choice from the following options.
A) 550 B) 160 C) 720 D) 620 E) 820

Solution: There are five letters in the given word.   Consider 8 blanks ....   The first blank and last blank must be filled with N and S all the remaining three blanks can be filled with the remaining 6 letters in 6! ways.   The number of words = 6! = 720.   Answer: 720
Answer: C
A 75m long train is running at 54 km/hr. In how much time will it cross an electric pole?	Choose the correct option:
A) 5  B) 10  C) 15  D) 20  E) 25

Solution: Speed of the train = ( 54 * 5 / 18) m/sec = 15 m / sec. Length of the train = (Speed x Time)   Time = (Length of the train / Speed)   =(75/ 15)= 
(75/ 15) = 5
5sec   5nswer: 5
Answer: A
At what time between 9’o clock and 10’o clock will the hands of a clock point in the opposite directions?  Pick one.
A) 16 4⁄11 minutes past 9  B) 16 4⁄11 minutes past 8  C) 55 5⁄61 minutes past 7  D) 55 5⁄61 minutes past 8  E) None of these

Solution: At 9’o clock, the Minute Hand is ahead of Hour Hand by 45 minutes. The hands will be opposite to each other when there is a space of 30 minutes between them.   This will happen when the Minute Hand gains 15 minutes space over Hour Hand.   Time taken by Minutes Hand to gain 15 minutes   = 15 × (1 + 1⁄11) = 15 + 15⁄11 = 15 + 14⁄11 + 16 4⁄11 minutes.   Hence the Hands are opposite to each other at 16 4⁄11 minutes past 9.   16 4⁄11 minutes past 9nswer 16 4⁄11 minutes past 9
Answer: A
Lina works 10 days a month at d dollars per day for m months out of the year. Which of the following represents her monthly pay?  Select the correct option:
A) m/(10d)
B) 5md/6
C) 10d
D) 10d/m
E) 10md

Solution: Total income of Lina in a year = d*10*m dollars. Now Monthly income = Total/12 = d*10*m / 12 = 5md/6 Answer is 5md/6
Answer: B
If 9x^2-16y^2=3x+4y,then what will give the answer?  Select the correct option:	A) 3x-4y=0	B) 3x-4y=2	C) 3x-4y=1	D) 3x+4y=0	E) 3x+4y=1

Solution: 9x^2-16y^2=3x+4y   (3x+4y)(3x-4y)=3x+4y   3x-4y=(3x+4y)/(3x+4y)   3x-4y=1   Answer is option 3x-4y=1
Answer: C
During one month at a particular restaurant, 1/5 of the burgers sold were veggie burgers and 1/4 of the rest of the burgers sold were double-meat. If x of the burgers sold were double-meat, how many were veggie burgers?  Select the correct option:	A) x/8	B) x	C) 2x/3	D) 3x/4	E) 4x/5

Solution: Let y be the number of total burgers.   veggie = y/5 , non veggie = 4y/5   1/4 of the rest of the burgers sold were double-meat   => 4y/5 * 1/4 = double meat = x   => y/5 = x= veggie   Hence x
Answer: B
A train 280 m long, running with a speed of 63 km/hr will pass a tree in?  Choose the correct choice from the following choices:
A) 15 sec
B) 16 sec
C) 18 sec
D) 20 sec
E) 22 sec

Solution: Speed = 63 * 5/18 = 35/2 m/sec   Time taken = 280 * 2/35= 
280 * 2/35 = 16
16 sec   ANSWER:16 sec
Answer: B
Tough and Tricky questions: Work/Rate Problems.
A group of 4 junior lawyers require 3 hours to complete a legal research assignment. How many hours would it take a group of three legal assistants to complete the same research assignment assuming that a legal assistant works at two-thirds the rate of a junior lawyer?
Source: Chili Hot GMAT
Select:
A) 13	B) 10	C) 9	D) 6	E) 5

Solution: # of people times the # of hours:   4*3= 
4*3 = 12
12 --> 3 lawyers do 12worksin 3 hours.   3*6/3= 
3*6/3 = 6
6 --> 3 assistants do 6 worksin 2 hours   So, since the amount of work the assistants do is half the work the lawyers do, the time will be double, soANS 6
Answer: D
A bowl contains 3 parts of which are milk and 5 parts water. How much of the mixture must be drawn off and replaced with milk sothat the mixture may be half milk and half water? Choose the correct choice from the following answers
A) 2/5
B) 3/5
C) 1/5
D) 1/7
E) 2/7

Solution: Suppose the vessel initially contains 8 litres of liquid.   Let x litres of this liquid be replaced with water.   Quantity of water in new mixture = 3 -	3x	+ x litres   8   Quantity of syrup in new mixture = 5 -	5x litres   8   3 -	3x	+ x = 5 -	5x   8	8   5x + 24 = 40 - 5x   10x = 16   x =	8	.   5   So, part of the mixture replaced = 8	x	1 =	1/5   5	8	5   1/5
Answer: C