MU-NLPC/Calc-aqua_rat huggingface dataset:
Two dogsled teams raced across a 300 mile course in Wyoming. Team A finished the course in 3 fewer hours than team T. If team A's average speed was 5 mph greater than team T's, what was team T's average mph?  Choices: A) 12 B) 15 C) 18 D) 20 E) 25

Solution: This is a very specific format that has appeared in a handful of real GMAT questions, and you may wish to learn to recognize it: here we have a *fixed* distance, and we are given the difference between the times and speeds of two things that have traveled that distance. This is one of the very small number of question formats where backsolving is typically easier than solving directly, since the direct approach normally produces a quadratic equation.   Say Team T's speed was s. Then Team T's time is 300/s.   Team A's speed was then s+5, and Team A's time was then 300/(s+5).   We need to find an answer choice for s so that the time of Team A is 3 less than the time of Team T. That is, we need an answer choice so that 300/(s+5) = (300/s) - 3. You can now immediately use number properties to zero in on promising answer choices: the times in these questions will always work out to be integers, and we need to divide 300 by s, and by s+5. So we want an answer choice s which is a factor of 300, and for which s+5 is also a factor of 300. So you can rule out answers A and C immediately, since s+5 won't be a divisor of 300 in those cases (sometimes using number properties you get to the correct answer without doing any other work, but unfortunately that's not the case here). Testing the other answer choices, if you try answer 20, you find the time for Team T is 15 hours, and for Team A is 12 hours, and since these differ by 3, as desired, 20 is correct.
Answer: D
The ages of two persons differ by 16 years. 6 years ago, the elder one was 3 times as old as the younger
one. What are their present ages of the elder person  Pick one: A) 15 B) 20 C) 25 D) 30 E) 35

Solution: Explanation:   Let's take the present age of the elder person = x   and the present age of the younger person = x � 16   (x � 6) = 3 (x-16-6)   => x � 6 = 3x � 66   => 2x = 60   => x = 60/2= 
60/2 = 30
30   Answer: Option 30
Answer: D
What is the greatest positive integer n such that 3^n is a factor of 36^50?  Pick:
A) 100
B) 200
C) 300
D) 600
E) 900

Solution: 36 = 3^2 * 2^2.   36^50 = 3^100 * 2^100   The answer is 100.
Answer: A
At a monthly meeting, 3/5 of the attendees were males and 4/5 of the male attendees arrived on time. If 5/6 of the female attendees arrived on time, what fraction of the attendees at the monthly meeting did not arrive on time?	Choose the correct choice from the following options
A) 6/25 B) 11/50 C) 14/75 D) 23/100 E) 31/150

Solution: Males who did not arrive on time are 1/5*3/5 = 3/25 of the attendees.   Females who did not arrive on time are 1/6*2/5 = 1/15 of the attendees.   The fraction of all attendees who did not arrive on time is 3/25 + 1/15 = 14/75   The answer is 14/75.
Answer: C
If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is? Choose the correct choice.
A) 1/8 B) 1/2 C) 1/6 D) 1/1 E) 1/5

Solution: The number of exhaustive outcomes is 36.   Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then   = 18/36 = 1/2   P(E)   = 1 - 1/2 = 1/2.   Answer: 1/2
Answer: B
A train 500 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is? Choose the correct choice from the following answers
A) 298 m
B) 279 m
C) 500 m
D) 289 m
E) 800 m

Solution: Speed = 78 * 5/18 = 65/3 m/sec.   Time = 1 min = 60 sec.   Let the length of the train be x meters.   Then, (500 + x)/60 = 65/3   x = 800 m.   Answer: 800 m
Answer: E
Which of the following integers is a divisor of(15!+14)?
Choose the correct answer
A) 15 B) 14 C) 13 D) 7 E) 2

Solution: When we say 15!, it just means 1*2*3*4*5*...*13*14*15   So you need to find the integer which is a divisor of   (1*2*3*4*5*...*13*14*15 + 14) = 14 (1*2*3*4*5*...*12*13*15 + 1) We obtain this by taking 14 common.   Hence 14 is definitely a divisor of (15! + 14).   14
Answer: B
The faces of storage box are to be painted by 6 different colors. In how many ways can be this be done?
Select the correct option:
A) A.720
B) B.256
C) C.1
D) D.12
E) E.36

Solution: If I have to paint 6 sides with 6 different colour...   First face can have 6c1 options,   2nd would have 5c1, and subsequent ones would have 4c1, 3c1, 2c1 and 1 options respectively.   Total options = 6c1 X 5c1 x 4c1 x 3c1 x 2c1 x 1 = 720 distinct ways   Correct answer - A.720
Answer: A
Tom can hit a target 3times in 6shots, Karan can hit the target 2times in 6 shots & Ashwini can hit 4 times in 4 shots. What is the probability that at least 2 shots hit the target ? Choose the correct choice from the following options.
A) 2/5
B) 3/7
C) 2/3
D) 2/5
E) 3/11

Solution: Ashwini hits the target definitely, hence required probability that atleast 2 shots hit the target is given by   Karan hits tha target and Raja not hit the target.   or   Karan does not hit the target and Raja hits the target.   or.   Karan hits the target and Raja hits the target   = 2/6 x 3/6 + 4/6 x 3/6 + 2/6 x 3/6   = 24/36 = 2/3   2/3
Answer: C
If h and g are distinct prime numbers less than 10, which of the following cannot be the product of h and g?
Answers:
A) 6 B) 9 C) 10 D) 14 E) 15

Solution: If h and g are distinct prime numbers less than 10 prime numbers less than 10 are 2, 3, 5, 7   all except 9 is product of any two numbers picked from above set.   Ans: 9
Answer: B
Express of the following as a fraction:
36%	Choose the correct choice from the following:  A) 14/25  B) 13/25  C) 9/25  D) 17/25  E) None of them

Solution: 36% = 36/100= 9/25.   Answer is 9/25.
Answer: C
Milk is poured from a full rectangular container with dimensions 4 inches by 9 inches by 10 inches into a cylindrical container with a diameter of 6 inches. If the milk does not overflow, how many inches high will the milk reach?	Select the correct option.
A) 60/π	B) 24	C) 40/π	D) 10	E) 3π

Solution: Let the height of level of milk in the cylinder = h   Since , volume of milk is constant .   Therefore   4*9*10 = ππ* 3^2 * h   => π * h = 40   => h = 40/ (π )   Answer 40/π
Answer: C
A can do a piece of work in 10 days. He works at it for 4 days and then B finishes it in 9 days. In how many days can A and B together finish the work?
Choose the correct choice from the following options:
A) 6 days
B) 8 days
C) 8 ½ days
D) 7 ½ days
E) 9 days

Solution: Explanation:   4/10 + 9/x = 1 => x = 15   1/10 + 1/15 = 1/6 => 6 days   6 daysnswer: 6 days
Answer: A
The difference between compound and simple interest on a certain sum of money for 3 years at 6 2/3% p.a is Rs.184. Find the sum? Pick one:
A) 1789 B) 19799 C) 29918 D) 13500 E) 78181

Solution: P = (184*106) / [6 2/3 * 6 2/3 *(300*6 2/3)]   P = 13500   Answer:13500
Answer: D
A recipe for a large batch of fruit juice at a factory calls for 25% oranges, 25% lemons, and 50% limes. if 200 lemons are used, how many limes are needed? Answers
A) 100  B) 125  C) 400  D) 600  E) 800

Solution: 25%= 200 fruit   100%=800 fruit   50% of 800 fruit=400 fruit   400 limes   ANSWER:400
Answer: C
What are the two main types of access control lists (ACLs)? Choose the correct choice from the following choices:	A) 1 and 3	B) 1 and 2	C) 2 and 1	D) 1 and 5	E) 1 and 9

Solution: Explanation:   Standard and extended access control lists (ACLs) are used to configure security on a router.   1 and 3nswer: Option 1 and 3
Answer: A
Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is?  Choose the correct choice from the following choices:
A) 2/9
B) 3/2
C) 2/1
D) 2/7
E) 2/6

Solution: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train = 17 y meters. (27 x + 17 y) / (x + y) = 23 ==> 27 x + 17 y = 23 x + 23 y ==> 4 x = 6 y ==> x/y = 3/2.   Answer:3/2
Answer: B
How much water must be added to 10 gallons of 10% brine solution to decrease the concentration to 5%?	Pick one.
A) 0—1.5 gal
B) 1.5—3 gal
C) 3—4.5 gal
D) 4.5—6 gal
E) 6+ gal

Solution: Let amount of water that must be added in gallons to dilute concentration of brine solution = x   Amount of brine already present = 10/100 * 10= 
10/100 * 10 = 1
1 gallon   1/(10+x) *100= 5   =>100 = 50 + 5x   => x= 50/5= 
50/5 = 10
10   Answer 6+ gal
Answer: E
Some quantity of coffee is sold at Rs. 22 per kg, making 10% profit. If total gain is Rs. 88, what is the quantity of coffee sold?	Choose the most appropriate option:
A) 35 kg  B) 36 kg  C) 38 kg  D) 40 kg  E) 44 kg

Solution: Let CP of coffee was X.   SP = X + 10% of X   22 = 1.1X   X = 22/1.1 = Rs. 20.   Now,   Rs. 2 is gain on 20.   Rs, 1 gain = 20/2   Hence, 88 gain = (20 * 88)/2= 
(20 * 88)/2 = 880
880.   Quantity of coffee sold= 880/20= 
880/20 = 44
44 Kg.   answer : OPTION 44 kg
Answer: E
The value of a stock is X dollars. On Sunday the stock's value grew by half of its value, but on Monday its value dropped to a second of its new value. What is the stock's value at the end of Monday?  Choose the most appropriate option:
A) X.  B) X/2.  C) 2X/3.  D) X/3.  E) 3X/4.

Solution: Stock value= X   AT sunday end= x+.5X= 1.5 X   On monday the value drop to 1/2rd of its value on sunday   1.5x/2= .75x 1.5 /2= 
 1.5 /2 = 0.75
.75x= 3X/4   3X/4. is the answer
Answer: E
A cistern is normally filled in 12 hours but takes two hours longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in? Select the correct option
A) 33  B) 84  C) 40  D) 99  E) 11

Solution: 1/12 - 1/x = 1/14   x = 84   Answer: 84
Answer: B
The volume of a certain substance is always directly proportional to its weight. If 48 cubic inches of the substance weigh 114 ounces, what is the volume, in cubic inches, of 63 ounces of this substance? Pick one
A) 27
B) 26
C) 42
D) 64
E) 147

Solution: 112 ounces of a substance has a volume of 48 cubic inches   63 ounces of a substance has a volume of (48/114)*63 = 26 cubic inches   Answer 26
Answer: B
Rs. 9800 are invested partly in 9% stock at 75 and 10% stock at 80 to have equal amount of incomes. The investment in 9% stock is how much price? Choices
A) 2500
B) 2800
C) 3000
D) 5000
E) 4500

Solution: Assume that face value of both stocks are Rs.100 as it is not given.   Hence, dividend per share in 1st case is Rs.9   and dividend per share in 2nd case is Rs.10   Let investment in 9% stock = Rs.x   and investment in 10% stock = Rs.(9800-x)   Market value of a 9% stock= Rs.75   Number of 9% stocks he can purchase with Rs.x = x/75   Total dividend from 9% stocks = (x×9)/75   Market value of a 10% stock = Rs.80   Number of 10% stocks he can purchase with Rs.(9800-x) = (9800-x)/80   Total dividend from 10% stocks = (9800−x)×10/80   incomes fom both of the investments is same   (x×9)/75=(9800−x)×10/80   (x×3)/25=(9800−x)/8   24x=25×9800−25x   49x=25×9800   x=(25×9800)/49=25×200=5000   Answer is D.   ie, investment in 9% stock = Rs.5000
Answer: D
The roof of an apartment building is rectangular and its length is 4 times longer than its width. If the area of the roof is 784 feet squared, what is the difference between the length and the width of the roof?
Choose the correct choice from the following choices:	A) 38.	B) 40.	C) 42.	D) 44.	E) 46.

Solution: Let the width= x   x*4x=784   x^2= 196   x= 14   Length= 4*14= 
4*14 = 56
56   difference= 56-14= 
56-14 = 42
42   42. is the answer
Answer: C
In a test, 52% students failed in Hindi, 40% failed in English and 27% failed in both. What percentage of students passed in both the subjects? Choose the correct choice from the following answers
A) 25%  B) 48%  C) 35%  D) None of these  E) Cannot be determined

Solution: Explanation :   Percentage of passed students in both the subjects = 100-(52+40-27)= 
100-(52+40-27) = 35
35%   Answer : 35%
Answer: C
If n is a positive integer, write s(n) for the sum of the digits of n. What is
s(1) + s(2) + s(3) +...+ s(1000)?  Select the correct option.
A) 9991  B) 10000  C) 13501  D) 14999  E) 15000

Solution: We start by computing S := s(0) + s(1) + s(2) + s(3) + ...+ s(999). Each digit,   0 through 9, appears equally often: 100 times in the hundreds place, 100 times in the tens   place, and 100 times in the ones place. (Here we write, e.g., 3 as 003.) Therefore,   S = 300* 0 + 300 * 1 + + 300 * 9 = 300(0 + 1 +...+ 9) = 300 *45= 
300 *45 = 13_500
13500:   Since s(0)= 0 and s(1000) = 1 we obtain the answer.   correct answer 13501
Answer: C
A can run a kilometer race in 4 1/2 min while B can run same race in 5 min. How many meters start can A give B in a kilometer race, so that the race mat end in a dead heat?  Pick one:  A) 299  B) 278  C) 277  D) 100  E) 216

Solution: A can give B (5 min - 4 1/2 min) = 30 sec start.   The distance covered by B in 5 min = 1000 m.   Distance covered in 30 sec = (1000 * 30)/300= 
(1000 * 30)/300 = 100
100 m.   A can give B 100m start.   Answer: 100
Answer: D
Vijay bought 160 shirts at the rate of Rs. 225 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 20%? Choices.
A) 282 B) 229 C) 277 D) 285 E) 2812

Solution: Total CP per shirt = 225 + 1400/160 + 1.75 + 320/160 = Rs. 237.5   SP = CP[(100 + profit%)/100]   = 237.5 * [(100 + 20)/100] = Rs. 285.   Answer:285
Answer: D
If 1< x < 2, which of the following must be true?
I. x^3 < x^2
II. x^2 < 2 + x
III. x^2 < x^4	Select the correct option:
A) I only
B) I and II only
C) III only
D) I and III only
E) I, II and III

Solution: I. x^3 < x^2 --> for values greater than 1 x^3 > x^2, so this statement is false.   II. x^2 < 2 + x --> x(x-1) < 2 --> 2*(2-1)= 2 !< 2, so this statement is also false.   III. x^2 < x^4 --> for values of x between 1 and 2 x^2< x^4, so this statement is true.   Answer: III only.
Answer: C
John traveled 80% of the way from Yellow-town to Green-fields by train at an average speed of 80 miles per hour. The rest of the way John traveled by car at an average speed of v miles per hour. If the average speed for the entire trip was 65 miles per hour, what is v in miles per hour? Choose the correct choice from the following answers.
A) 30	B) 40	C) 50	D) 55	E) 70

Solution: HiBunuel   THe question seems incorrect. it should not be 80% at the speed of 80. However if it's 20% at the speed of 80, Answer comes out 55.   The question is correct. Here's the explanation:   Let distance be D. We can find the total timeequate it, which comes as:   0.855 / 80 + 0.255 / v = 55 / 65 => v = 55 (Option 55).
Answer: D
The product of all the prime numbers less than 10 is closest to which of the following powers of 10 ?
Choose the correct option:
A) 10^9
B) 10^8
C) 10^7
D) 5*10^6
E) 10^5

Solution: 2*3*5*7*11*13*17*19   2*19*3*17*5*13*7*11   38*51*65*77   By approximation   40*50*70*70   2000*4900   By approximation   1000*5000   5,000,000   5*10^6
Answer: D
Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. In how much time will the trains cross each other? Options.
A) 87/7 sec  B) 80/7 sec  C) 80/9 sec  D) 80/5 sec  E) 20/7 sec

Solution: Relative speed = (54 + 72)* 5/18 = 7 * 5= 
7 * 5 = 35
35 mps.   The time required= d/s = (100 + 100 + 200)/35   = 400/35 = 80/7 sec.   Answer: 80/7 sec
Answer: B
After a storm deposits 110 billion gallons of water into the city reservoir, the reservoir is 60% full. If the original contents of the reservoir totaled 220 billion gallons, the reservoir was approximately what percentage full before the storm? Choose the correct choice from the following options
A) 40%
B) 48%
C) 54%
D) 58%
E) 65%

Solution: When the storm deposited 110 billion gallons, volume of water in the reservoir = 220 + 110 = 360 billion gallons   If this is only 60% of the capacity of the reservoir, the total capacity of the reservoir = 330/0.6= 
330/0.6 = 550
550 billion gallons   Therefore percentage of reservoir that was full before the storm= (220/550)*100= 
(220/550)*100 = 40
40%   Option 40%
Answer: A
if the ratio of two number is 5:7 and LCM of the number is 320 then what is the number.	Answers:  A) 15  B) 9  C) 10  D) 11  E) 35

Solution: product of two no = lcm *hcf   5x*7x=320*x   x=9   ANSWER:9
Answer: B
Krishan and Nandan jointly started a business. Krishan invested three times as Nandan did and invested his money for fourtime as compared to Nandan. Nandan earned Rs. 4000. If the gain is proportional to the money invested and the time for which the money is invested and the total gain was  Choose the correct option:  A) Rs.32000  B) Rs.62000  C) Rs.42000  D) Rs.52000  E) Rs.22000

Solution: 3:1   4:1   ------   12:1   1 ----- 4000   13 ----- ? => Rs.52,000   Answer: Rs.52000
Answer: D
Randy'sbar serves customers every weeknight from 5 pm to 1 am. In Randy's bar,Silvermoonbeer is sold at a constant rate except during happy hour, from 8:30 to 7:30 pm, when the rate triples.
If a keg of Silvermoon beer is half empty at 5pm on Monday, and two-thirds empty at the beginning of the happy hour, when will it be completely empty? Choices:
A) Monday, 7:30 pm
B) Monday, 9 pm
C) Monday, 7 pm
D) Monday, 6:45 pm
E) Monday, 9:30 pm

Solution: Let the keg be a 150 Litre keg   At 5 pm.. There are 75 litres   At 6:30 pm there are 50 litres.   So, consumption rate is 25 litres per 1.5 hours.   So it will take 3 hours to finish 50 litres at this rate.   During happy hour it sells 3 times faster. So, rate = 1 hour per 50 litres.   So, keg becomes empty at 6:30 + 1 hour = 6:45 pm   Answer is Monday, 6:45 pm.
Answer: D
In a hostel there were 100 students. To accommodate 25 more students the average is decreased by rupees 5. But total expenditure increased by Rs.400. Find the total expenditure of the hostel now?	Options
A) A)Rs.5800	B) B)Rs.5480	C) C)Rs.5400	D) D)Rs.4500	E) E)Rs.5430

Solution: 100x + 400   = 125(x – 5)   x = 41   100 * 41 + 400= 
100 * 41 + 400 = 4_500
4500   Answer:Rs.4500
Answer: D
What is the smallest five digit number that is divisible by 16, 36, 45, and 54?  Choices:
A) 10200	B) 10400	C) 10600	D) 10800	E) 11200

Solution: 16 = 2^4   36 = 2^2 * 3^2   45 = 3^2 * 5   54 = 2 * 3^3   LCM = 2^4 * 3^3 * 5 = 2160   The smallest five-digit number that is a multiple of 2160 is 5*2160 = 10,800   The answer is 10800.
Answer: D
3 pumps,working 8 hours a day,can empty a tank in 2 days.How many hours a day must 4 pumps work to empty the tank in 1 day ?
Choose one:
A) 9
B) 10
C) 11
D) 12
E) 13

Solution: Solution   Let the required number of working hours per day be x.   More pumps,Less working hours per day (Indirect Proportion)   Less days,More working hours per day (Indirect Proportion)   ∴ 4 × 1 × x = 3 × 2 × 8 ⇔ x = 3x2x8/4 = x= 12, Answer 12
Answer: D
A train 110 m long is running with a speed of 30 km/h. In how many seconds will the train pass a man who is running at 3 km/h in the direction opposite to that in which the train is going?
Choose the correct choice.
A) 6  B) 8  C) 10  D) 12  E) 14

Solution: The speed of the train relative to the man = 30 + 3= 
30 + 3 = 33
33 km/h.   33000 m/h * 1h/3600 s= (330/36) m/s   (110 m) / (330/36 m/s) = (110 * 36) / 330 = 36/3= 
36/3 = 12
12 seconds   The answer is 12.
Answer: D
Tough and Tricky questions: Word Problems.
AM Car Company wants to manufacture a new car known as Model X, and it is trying to determine how many cars it needs to sell in order to make an annual profit of $30,500,000. The annual fixed costs for Model X total $50,200,000. In addition, each Model X car has an average cost of $5,000 per vehicle to manufacture. If the Company forecasts it will sell 20,000 Model X cars this year, at what price must the Company sell the car to achieve the desired annual profit?
Choose the correct choice from the following answers.
A) $4,035	B) $4,036	C) $9,035	D) $16,140	E) $36,140

Solution: The AM company plans to make a profit of $30,500,000 and it needs to earn the fixed costs of $50,200,000, so it needs to earn $80,700,000 on top of the costs for the production of the 20,000 cars.   Therefore, price of each car needs to be the unit costs plus $80,700,000/20,000. After removing the 0's, we end with the unit costs plus $8,070/2, which is $5,000 plus $4,035. Therefore, Answer $9,035 is correct.
Answer: C
A box contains 4 red chips and 2 blue chips. If two chips are selected at random without replacement, what is the probability that the chips are different colors? Choose the correct choice from the following choices.
A) 1/2 B) 8/15 C) 7/12 D) 2/3 E) 7/10

Solution: Total selection ways: 6C2=6!/2!4!=15   Selecting one blue chip out of two: 2C1=2!/1!1!=2   Selecting one red chip out of four: 4C1=4!/1!3!=4   Thus, (2C1*4C1)/6C2=(2*4)/15=8/15   ANSWER:8/15
Answer: B
When positive integer x is divided by positive integer y, the remainder is 5. If x/y = 96.2, what is the value of y?
Select: A) 96 B) 75 C) 48 D) 25 E) 12

Solution: Guys, one more simple funda.   5/2= 
5/2 = 5/2 = around 2.5
2.5   now .5 x2=1 is the remainder     25/4= 
  25/4 = 25/4 = around 6.25
6.25   now .25x4=1 is the remainder     32/5= 
  32/5 = 32/5 = around 6.4
6.4   now.4x5= 2 is the remainder   given x/y = 96.2 and remainder is 5   So .2 X y = 5   hence y= 25   Ans 25
Answer: D
If 7 and 9 are factors of 60n, what is the minimum value of n?  Choices
A) 2 B) 3 C) 7 D) 14 E) 21

Solution: 60n/7*9 should be integer => 2*2*3*5*n/7*3*3 = 2*2*5*n/21 must be an integer   for this to be true n must multiple of 21, thus min of n = 21   hence 21
Answer: E
How many alphabets need to be there in a language if one were to make 1 million distinct 3 digit initials using the alphabets of the language?  Choose the correct choice from the following options:  A) 26  B) 50  C) 1000  D) 100  E) 90

Solution: 1 million distinct 3 digit initials are needed.   Let the number of required alphabets in the language be ‘n’.   Therefore, using ‘n’ alphabets we can form n * n * n = n3 distinct 3 digit initials.   Note distinct initials is different from initials where the digits are different.   For instance, AAA and BBB are acceptable combinations in the case of distinct initials while they are not permitted when the digits of the initials need to be different.   This n3 different initials = 1 million   i.e. n3 = 106 (1 million = 106)   => n3 = (102)3 => n = 102 = 100   Hence, the language needs to have a minimum of 100 alphabets to achieve the objective.   ANSWER 100
Answer: D
A train starts full of passengers at the first station it drops 1/3 of the passengers and takes 280more at the second station it drops one half the new total and takes twelve more .on arriving at the third station it is found to have 248 passengers. Find the no of passengers in the beginning? Choose the correct choice from the following answers.
A) 288 B) 388 C) 188 D) 258 E) None of them

Solution: Let no of passengers in the beginning be x   288fter first station no passengers=(x-x/3)+280=2x/3 +280   288fter second station no passengers =1/2(2x/3+280)+12   ½(2x/3+280)+12=248   2x/3+280=2*236   2x/3=192   x=288   288nswer is 288.
Answer: A
Ten years ago, P was half of Q in age. If the ratio of their present ages is 3:4, what will be the total of their present ages  Choose the correct choice.
A) 5 B) 6 C) 7 D) 8 E) 9

Solution: Let the present age of P and Q be 3x and 4x respectively.   Ten years ago, P was half of Q in age   => 2(3x – 10) = (4x – 10)   => 6x – 20 = 4x – 10   => 2x = 10   => x = 5   5nswer: 5
Answer: A