MU-NLPC/Calc-aqua_rat huggingface dataset:
At a certain resort, each of the 39 food service employees is trained to work in a minimum of 1 restaurant and a maximum of 3 restaurants. The 3 restaurants are the family buffet, the dining room, and the snack bar. Exactly 21 employees are trained to work in the family buffet, 18 are trained to work in the dining room, and 12 are trained to work in the snack bar. If 4 employees are trained to work in exactly 2 restaurants, how many employees are trained to work in all 3 restaurants?	Choices:  A) 2  B) 3  C) 4  D) 5  E) 6

Solution: 39 = 21 + 18 + 12 - 4 - 2x   2x = 21 + 18 + 12 - 4 - 39   = 47 - 39= 
47 - 39 = 8
8   x= 4   4
Answer: C
A sum of Rs. 2665 is lent into two parts so that the interest on the first part for 8 years at 3% per annum may be equal to the interest on the second part for 3 years at 5% per annum. Find the second sum?
Pick.
A) Rs.450  B) Rs. 1640  C) Rs.523  D) Rs.458  E) Rs.796

Solution: Explanation:   (x*8*3)/100 = ((2665 - x)*3*5)/100   24x/100 = 39975/100 - 15x/100   39x = 39975 => x = 1025   Second sum = 2665 – 1025 =Rs. 1640   Answer: Rs. 1640
Answer: B
Firm A's revenues are described by the equation Ra = 17.12x and its costs by Ca = 12.87x + 2200.
Firm B's revenues are described by the equation Rb = 13.27x and its costs by Cb = 8.77x + 1500.
(x denotes the quantity of sales).
If A's volume of sales increases from 1000 to 2000 over the same period that B's volume increases from 2000 to 3000, the percent increase in profits for the firm with the biggest dollar increase in profits is
Answers.
A) 20%  B) 30%  C) 60%  D) 50%  E) 33%

Solution: Ok, I do not know whether it is exactly what you want to hear but I did it that way: first look at difference between revenue and variable cost => take the bigger one (b) which gives you: 4.5x-1500 just plug in 2000 and 3000. you get 7500 and 12000 (difference 4500). 4500> 0.5*7500 so 33%   33%
Answer: E
If the selling price is doubled,the profit is tripled,what is the percentage of profit?? Options:
A) 50%  B) 100%  C) 150%  D) 200%  E) 250%

Solution: Let the profit be 10, then   SP-CP=10 and 2SP-CP=30   Solving the above equations we get SP=20 and CP=10, so CP=Profit   Hence the answer is 100% (100%)
Answer: B
What is the greatest prime factor of 4^17 - 2^26?	Choices:
A) 2  B) 3  C) 5  D) 127  E) 11

Solution: I'm happy to help with this.   We know 4 = 2^2, so 4^17 = (2^2)^17 = 2^(2*17) = 2^34   That takes advantage of a law of exponents that says (a^n)^m = a^(n*m)   So, 4^17 - 2^26 = 2^34 - 2^26 = 2^(26 + 8) - 2^26 = (2^26)*(2*8) - 2^26 = (2^8 - 1) *(2^26)   = (128 - 1)*(2^26) = 127*(2^26)   The prime factors of 63 are 127, so the largest prime factor is 127, 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.   127
Answer: D
Calculate the average of first 9 even numbers is?
Choose the correct choice from the following answers:	A) 10	B) 13	C) 12	D) 15	E) 17

Solution: Explanation:   Sum of 10 even numbers = 9 * 10= 
9 * 10 = 90
90   10verage= 90/9= 
90/9 = 10
10   10nswer: Option 10
Answer: A
There are 7 fictions and 6 non-fictions. How many cases are there such that 2 fictions and 2 non-fictions are selected from them?  Choose the correct choice from the following:
A) 90	B) 120	C) 315	D) 180	E) 200

Solution: Number of ways of selecting 2 fiction books = 73152   Number of ways of selecting 2 non fiction books = 63152   73152 * 63152 = 21 * 15= 
21 * 15 = 315
315   Answer: 315
Answer: C
Find the average of all the numbers between 6 and 34 which are divisible by 7.	Choose the correct choice from the following options.
A) 18
B) 20
C) 17.5
D) 30
E) 32

Solution: Solution   Average	= (7+14+21+28)/4)   = 70 / 4   = 17.5.   Answer 17.5
Answer: C
The radius of a wheel is 20.4 cm. What is the distance covered by the wheel in making 400 resolutions? Choose the correct choice from the following choices: A) 512.448 m B) 704 m C) 510.448 m D) 706 m E) 204 m

Solution: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 400 resolutions.   = 400 * 2 * 22/7 * 20.4 = 51244.8 cm   = 512.448 m   512.448 mnswer:512.448 m
Answer: A
If 5a = 6b and ab ≠0, what is the ratio of a/6 to b/5?	Choices:
A) 36/25
B) 10/12
C) 1
D) 1/5
E) 25/36

Solution: A nice fast approach is the first find a pair of numbers that satisfy the given equation: 5a = 6b   Here's one pair: a =6and b =5   What is the ratio of a/6 to b/5?   In other words, what is the value of (a/6)/(b/5)?   Plug in values to get: (a/6)/(b/5) = (6/6)/(5/5)= 
(6/6)/(5/5) = 1
1/1= 
1/1 = 1
1   1
Answer: C
In what time will a train 140 m long cross an electric pole, it its speed be 190 km/hr?
Choose the correct choice from the following options:	A) 2.6 sec	B) 2.9 sec	C) 2.7 sec	D) 8.7 sec	E) 8.5 sec

Solution: Speed = 190 * 5/18 = 53 m/sec   Time taken = 140/53 = 2.6 sec.   2.6 secnswer: 2.6 sec
Answer: A
Jim is twice as old as Stephanie, who, four years ago, was three times as old as Kate. If, five years from now, the sum G of their ages will be 51, how old is Stephanie ?  Options:
A) 6  B) 10  C) 14  D) 20  E) 24

Solution: 1) take C (14y.o.), so mean that S=14, J=28, their sum itself is 42+10 years from now is 52, it is over the 51,   so eliminate C,D,E   2) take B (10y.o.),G= meaning S=10,J=20, so  20+10+10= 
 20+10+10 = 40
40 and for K=10-4/3=2+9= 
2+9 = 11
11, finally 40+11= 
40+11 = 51
51. It is correct   10
Answer: B
In order to fulfill a local school’s request for x cakes, y parents agreed to each bake an equal number of cakes. If z of the parents did not bake any cakes, which of the following represents the additional number of cakes that each of the other parents had to bake in order for the school’s request for x cakes to be fulfilled?  Choose the correct choice from the following options
A) xy
B) xyz
C) xy/z
D) zx/(y(y - z))
E) zy/x

Solution: No of cakes each parent has to bake : x/y   No of parents did not bake cake = z   No of cakes that were not baked by p parents = z*x/y   No of parents has to bake additional cakes = y-z   additional number of cakes that each of the other parents had to bake in order for the school’s request for x cakes = zx/(y(y - z))   Answer zx/(y(y - z))
Answer: D
Simplify: 200 x 200 - 150 x 150  Choose one
A) 761200	B) 761400	C) 761800	D) 17500	E) None of them

Solution: (200)^2 - (150)^2 = (200 + 150) (200 - 150) = 350 x 50 = 17500.   Answer is 17500
Answer: D
Walking 7/6 of his usual rate, a boy reaches his school 4 min early. Find his usual time to reach the school? Pick one:  A) 21  B) 16  C) 16  D) 28  E) 12

Solution: Speed Ratio = 1:7/6 = 6:7   Time Ratio = 7:6   1 -------- 7   4 --------- ? è 28 m   Answer: 28
Answer: D
You need to unlock a secret code using following clues,
Can you?
Here you have the clues:
Clue-1 : 0 7 9 (One of the numbers is correct and is placed in its correct position)
Clue-2 : 0 3 2 (Nothing is correct)
Clue-3 : 1 0 8 (Two numbers are correct but not placed at its correct position.)
Clue-4 : 9 2 6 (One number is correct but not placed at its correct position.)
Clue-5 : 6 7 8 (One number is correct but not placed at its correct position.)  Pick.
A) 819
B) 918
C) 198
D) 189
E) 891

Solution: 0 7 9 : 9 is placed correctly   * 0 3 2 : None of the numbers is in the code   * 1 0 8 : 1 and 8 are correct number of code but placed at wrong position   * 9 2 6 : Number 9 is there but placed at wrong position   * 6 7 8 : Number 8 is there but placed at wrong position   correct answer is 819)819
Answer: A
On a map, 1 inch represents 28 miles. How many V inches would be necessary to represent a distance of 383.6 miles?
Select:	A) 5.2	B) 7.4	C) 13.7	D) 21.2	E) 28.7

Solution: V inches necessary to represent a distance of 383.6 miles = 383.6/28= 
383.6/28 = 13.7
13.7   Answer 13.7
Answer: C
In a particular state, 60% of the counties received some rain on Monday, and 55% of the counties received some rain on Tuesday. No rain fell either day in 25% of the counties in the state. What percent of the counties received some rain on Monday and Tuesday? Choose one
A) 12.5%  B) 40%  C) 50%  D) 60%  E) 67.5%

Solution: 60 + 55 + 25= 
60 + 55 + 25 = 140
140%   The number is 40% above 100% because 40% of the counties were counted twice.   The answer is 40%.
Answer: B
A Washing machine is available for $39000 cash or $17000 as down payment followed by five equal monthly instalments of $4800 each. The simple rate of interest per annum under the instalment plan would be
Choose the correct answer
A) 18%
B) 19%
C) 21.2%
D) 21.81%
E) 22.07%

Solution: Simple interest SI = (P*R*T)/100   where P is the principal amount   R is the rate of interest   and T is time in years   the way I see it:Washing machine on down payment of 17,000, customer is not paying any interest. it is the remaining sum which will be paid for 5 months that will bear an interest. Therefore, the principal amount for which interest is being charged is 39,000 - 17,000 = 22,000   For this 22,000 a total sum of 5*4800 = 24,000 was pain. (Time is five months, so T = 5/12, as T is in years.)   thus, SI = 2000 or   2000 = (P*R*T)/100   2000 = (22,000*R*5)/(100*12)   R = (2,000*12*100)/22,000*5   R = 21.81%   Therefore answer is 21.81%
Answer: D
Certain stocks in January were 30% greater than they were in February and 20% lesser than they were in March. What was the percentage decrease in the stocks from February to March?
Choose the correct choice from the following answers:
A) 44%	B) 30%	C) 40%	D) 47.5%	E) 50%

Solution: Let stocks value in Feb = 100 => In Jan = 70 and March = 70 * 80/100= 
70 * 80/100 = 56
56   Thus, percent decrease in stocks from Feb to March= 100 - 56= 
100 - 56 = 44
44%   Hence 44%nswer is 44%
Answer: A
A solid yellow stripe is to be painted in the middle of a certain highway. If 1 gallon of paint covers an area of e square feet of highway, how many gallons of paint will be needed to paint a stripe of t inches wide on a stretch of highway m miles long? (1 mile = 5,280 feet and 1 foot = 12 inches)  Choose the correct choice:
A) (5,280 mt) / 12 e
B) (5,280 pt) / 12m
C) (5,280 pmt) /12
D) (5,280)(12m) / pt
E) (5,280)(12p) / mt

Solution: Given that: 1 gallon of paint covers an area ofesquare feet. Question:how many gallonsof paint will be needed ...   In any case you will have:(total area in square feet)/(gallons per feet)=(total area in square feet)/e, so e must be in the denominator: eliminate all but A and D.   Now, lets see where should be t: (area in square feet)=(width in feet)*(length in feet) --> width=tinchesas1 feet=12 inchesthent inches=t/12 feet, so (area in square feet)=(t/12) * (length in feet), so t must be in the nominator: only A is left.   (5,280 mt) / 12 enswer: (5,280 mt) / 12 e.
Answer: A
In a certain book club, the members are voting between two books – a mystery novel and a biography – to decide which book the group will read next. There are 4 times as many votes for the mystery novel as there are votes for the biography. The ratio of biography votes to the total number of votes is
Choose the correct answer:
A) 1 to 2 B) 1 to 3 C) 1 to 4 D) 1 to 5 E) 3 to 4

Solution: IMO : Answer 1 to 5 1 to 5
Answer: D
A student committee that must consists of 3 members is to be formed from a pool of 8 candidates. How many different committees are possible Pick one:
A) 5 B) 8 C) 40 D) 56 E) 336

Solution: I think the answer is 56.   Out of 8 people, any 3 can be selected for a committee. So 8c3 is the answer.   56
Answer: D
A cement block balances evenly on the scales with 3 quarters of a pound and 3 quarters of a block. What is the weight of the whole block?	Pick
A) 1 pounds  B) 2 pounds  C) 3 pounds  D) 4 pounds  E) 5 pounds

Solution: x= 3/4 +x*3/4   x/4 = 3/4   x= 3 pounds   ANSWER:3 pounds
Answer: C
How many different sets of positive square integers P, each greater than 1, add up to 75? Choose the correct choice from the following choices:
A) 1  B) 4  C) 7  D) 11  E) 13

Solution: 13= 13 is the correct answer.
Answer: E
Of the three-digit integers greater than 800, how many have two digits that are equal to each other and the remaining digit different from the other two?  Choices.
A) 90  B) 82  C) 43  D) 45  E) 36

Solution: Three digit number can have only following 3 patterns:   A. all digits are distinct;   B. two digits are alike and third is different;   C. all three digits are alike.   We need to calculate B. B=Total - A - C   Total numbers from 800 to 999 = 199 (3-digit numbers greater than 800);   A. all digits are distinct = 2*9*8= 
2*9*8 = 144
144 (first digit can have only three values 7, 8, or 9);   C. all three are alike= 2(, 888, 999).   So, 199-144-2=43   Answer: 43.
Answer: C
HCF and LCM two numbers are 12 and 396 respectively. If one of the numbers is 24, then the other number is?	Choose the correct choice from the following answers:
A) 36 B) 198 C) 132 D) 264 E) 364

Solution: 12 * 396 = 24 * x   x = 198   ANSWER:198
Answer: B
If a man walks at a rate of 10kmph, he misses a train by 14minutes. However, if he walks at the rate of 12kmph, he reaches the station 10minutes before the arrival of the train. Find the distance covered by him to reach the station.	Choose the most appropriate option.
A) 6 KM
B) 15
C) 12
D) 4
E) 8

Solution: Let the required distance x km   difference in the times taken at two speeds = 12min = 1/5 hr   (x/10)-(x/12) = 1/10   x = 6   the required distance is 6 km   6 KMnswer is 6 KM
Answer: A
Today is Saturday. The day after 59 days will be  Choose the correct choice from the following: A) Monday B) Tuesday C) Saturday D) Sunday E) None of these

Solution: Explanation :   59 days = 8 weeks 3 days = 3 odd days   Hence if today is Saturday, After 59 days, it will be = (Saturday + 3 odd days)   = Tuesday. Answer : Option Tuesday
Answer: B
In a class of 10 students, the teacher writes a number on the board. The first student tells that number is divisible by 1, the second student tells that the number is divisible by 2, the third by 3, the forth by 4 and so on till 10. If the statement of one of the students is wrong then what is the least number possible.
Choose one:  A) 320  B) 340  C) 360  D) 380  E) 400

Solution: Statement of 7th student was wrong.   No is not divisible by 7.   L360M of 2,3,4,5,6,8,9,10 = 360   ANSWER:360
Answer: C
A box contains 3 blue marbles, 3 red, 6 green marbles and 2 yellow marbles. If three marbles are picked at random, what is the probability that they are all blue?
Answers:
A) 1/364 B) 2/455 C) 1/91 D) 4/455 E) None of these

Solution: Given that there are three blue marbles, three red marbles, six green marbles and two yellow marbles.   Probability that all the three marbles picked at random are blue = 3C₃/14C₃ = (1 * 3 * 2 * 1)/(14 * 13 * 12) = 1/364   1/364NSWER:1/364
Answer: A
A shopkeeper purchased 90 kg of potatoes for Rs. 540 and sold the whole lot at the rate of Rs. 8 per kg. What will be his gain percent? Pick one:	A) 38 1/9 %	B) 38 9/3 %	C) 38 1/3 %	D) 32 1/3 %	E) 33 2/6 %

Solution: C.P. of 1 kg = 540/90 = Rs. 6S.P. of 1 kg = Rs. 8Gain % = 2/6 * 100 = 200/6 = 33 2/6 %Answer: 33 2/6 %
Answer: E
Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagar's age at present?  Select
A) 16 years B) 18 years C) 20 years D) 22 years E) 24 years

Solution: Explanation:   Let the ages of Kunal and Sagar 6 years ago be 6x and 5x years respectively.   Then,   (6x + 6) + 4	=11   (5x + 6) + 4	=10   ⇒ 10(6x + 10) = 11(5x + 10)   ⇒ 5x = 10   ⇒ x = 2.   Sagar's present age = (5x + 6) = 16 years.   16 yearsnswer: 16 years
Answer: A
Two employees X and Y are paid a total of Rs. 616 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week? Pick
A) s.250	B) s.280	C) s.290	D) s.299	E) s.300

Solution: Let the amount paid to X per week = x   and the amount paid to Y per week = y   Then x + y = 616   s.280ut x = 120% of y = 120y/100 = 12y/10   ∴12y/10 + y = 616   ⇒ y[12/10 + 1] = 616   ⇒ 22y/10 = 616   ⇒ 22y = 6160   ⇒ y = 6160/22 = 560/2 = Rs.280   s.280
Answer: B
A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B's share?	Choose the correct option
A) Rs. 500 B) Rs. 1500 C) Rs. 2000 D) Rs. 2500 E) None of these

Solution: Let the shares of A, B, C and D be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x respectively.   Then, 4x - 3x = 1000   x = 1000.   B's share = Rs. 2x = Rs. (2 x 1000) = Rs. 2000.   Answer: Option Rs. 2000
Answer: C
In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr?	Options
A) 2.5	B) 7.3	C) 2.3	D) 1.4	E) 1.1

Solution: Speed = 144 * 5/18= 
144 * 5/18 = 40
40 m/sec   Time taken= 100/40= 
100/40 = 5/2 = around 2.5
2.5 sec.   2.5nswer: 2.5
Answer: A
A cylindrical tank of diameter 35 cm is full of water. If 11 litres of water is drawn off, the water level in the tank will drop by:  Pick one
A) 11 3/7cm	B) 11 2/7cm	C) 11 1/7cm	D) 11cm	E) None of these

Solution: Explanation:   Let the drop in the water level be h cm, then,   Volume of cylinder= πr2h   =>22/7∗35/2∗35/2∗h=11000   =>h=11000∗7∗4/ 22∗35∗35cm=80/7cm=11 3/7cm   Option 11 3/7cm
Answer: A
If the area of a circle is 144pi square feet, find its circumference.
Select the correct option.
A) 65 pi feet	B) 24 pi feet	C) 42 pi feet	D) 18 pi feet	E) 64 pi feet

Solution: The area is given by pi * r * r. Hence   pi * r *r = 144 pi   r *r = 81 ; hence r = 12 feet   The circumference is given by   2 *pi *r = 2 * pi * 12 = 24 pi feet   correct answer 24 pi feet
Answer: B
In how many ways can the six letters of the word "mammal" be arranged in a row?	Choose the correct choice from the following options.
A) 20	B) 40	C) 31	D) 60	E) 64

Solution: Since there are 3 "m"s , 2 "a"s and 1 "l" in the word "mammal", we have:   (3+2+1)! / (3! * 2! * 1!)=60   ​Ans-60
Answer: D
a light flashes every 6 seconds, how many times will it flash in ? of an hour? Select
A) 550  B) 600  C) 650  D) 700  E) 750

Solution: 1flash=6sec   for 1 min=10flashes   so for 1 hour=10*60= 
10*60 = 600
600 flashes.   ANSWER:600
Answer: B
Suppose a game is played between two players A and B. On each turn of the game, exactly
one of A or B gets a point. Suppose A is better than B and has a probability of 2/3 of getting
a point on each turn of the game. The first person to get two points ahead in the game is the
winner. What is the probability that A wins the game?
Choices
A) 5/9 B) 4/7 C) 2/3 D) 4/5 E) 8/9

Solution: Let W0 be the event that Player A wins the game. The goal is to compute P(W0).   Let W1 be the event that Player A wins the game given that she is ahead by one point. Let   W-1 be the event Player A wins the game given that she is behind by one point. Then, the   probability that Player A wins the game is   P(W0) = P(A is ahead by 1 point)P(W1) + P(A is behind by 1 point)P(W-1)   = (2/3)P(W1) + (1/3)P(W-1): (1)   Now,   P(W1) = P(Player A gets a point on the next turn) + P(Player B gets a point on the next turn)P(W0)   = (2/3) + (1/3)P(W0);   and   P(W-1) = P(Player A gets a point on the next turn)P(W0) = (2/3)P(W0):   Substituting these equations into (1) we have   P(W0) = (2/3)[(2/3) + (1/3)P(W0)] + (1/3)(2/3)P(W0) = 4/9 + (4/9)P(W0):   Therefore, P(W0) = (4/9)(9/5) = 4/5   correct answer 4/5
Answer: D
If the ratio of apples to bananas is 5 to 2 and the ratio of bananas to cucumbers is 1 to 3, what is the ratio of apples to cucumbers? Choose the correct option
A) 2:3  B) 5:3  C) 5:6  D) 1:4  E) 3:4

Solution: The ratio of bananas to cucumbers is 1 to 3 which equals 2 to 6.   The ratio of apples to bananas to cucumbers is 5 to 2 to 6.   The ratio of apples to cucumbers is 5 to 6.   The answer is 5:6.
Answer: C
A man's speed with the current is 20 kmph and speed of the current is 3 kmph. The Man's speed
against the current will be  Choices:	A) 11 kmph	B) 12 kmph	C) 14 kmph	D) 17 kmph	E) None of these

Solution: Explanation:   Speed with current is 20,   speed of the man + It is speed of the current   Speed in sƟll water = 20 - 3= 
20 - 3 = 17
17   Now speed against the current will be   speed of the man - speed of the current= 17 - 3= 
17 - 3 = 14
14 kmph   Answer: 14 kmph
Answer: C
Jake, Lena, Fred, John and Inna need to drive home from a corporate reception in an SUV that can seat 7 people. If only Inna or Jake can drive, how many seat allocations are possible?
Choose the correct option
A) 30
B) 42
C) 120
D) 360
E) 720

Solution: 5 people ,7 seats, only 2 can drive   if inna is in one seat remaining, 4 people can be arranged in 4p4 i.e 4! =24 ways   since any one can drive total ways = 24 *2= 
24 *2 = 48
48 ways   4 seats can be chosen out of remaining 6 seats in 6c4 ways= 6!/(4!*2!)= 15 ways     48*15= 
  48*15 = 720
720   ANSW720R:720
Answer: E
A certain sum amounts to Rs.1725 in 3 years and Rs.1875 in 5 years. Find the rate % per annum?	Choose the correct choice from the following options:
A) 2 B) 5 C) 6 D) 7 E) 8

Solution: 3 --- 1725   5 --- 1875   --------------   2 --- 150   N = 1 I = 75 R = ?   P = 1725 - 225= 
1725 - 225 = 1_500
1500   75= (1500*1*R)/100   R = 5%.Answer: 5
Answer: B
Jaclyn buys $20 000 worth of debentures in a company. She earns 9.5% p.a. simple interest, paid to her quarterly (that is, every 3 months). If the agreed period of the debenture was 18 months: calculate the amount of interest Jaclyn will earn for each quarter	Choose one.
A) 475
B) 234
C) 289
D) 345
E) None of these

Solution: Explanation:   I=(p x r x t)/100   = 30000*9.5/100*(18/12)^1/6 = 475   475nswer: 475
Answer: A
A train 280m long is running at 70kmph. In how much time will it pass a platform 210m long? Answers
A) 1.5 seconds
B) 9.56 seconds
C) 28.56 seconds
D) 30.56 seconds
E) 3.5 seconds

Solution: Distance travelled = 280 + 210= 
280 + 210 = 490
490mSpeed= 70 * 5/8 = 205/4mTime = 490 * 4/205 = 9.56 SecondsAnswer : 9.56 seconds.
Answer: B
A person purchases 90 shirts and sells 40 shirts at a gain of 10% and 50 shirts at a gain of 20%. If he sold all of them at a uniform profit of 15%, then he would have got $40 less. The cost price of each shirt is:	Choices.
A) 10  B) 30  C) 80  D) 40  E) 90

Solution: C   80   Let C.P. of shirt be $x.   Then, C.P. of 90 shirts = $90x.   [(110% of 40x) + (120% of 50x)] - (115% of 90x) = 40   44x + 60x - 103.5x = 40   0.5x = 40 => x = 80
Answer: C
A trained covered x km at 40 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 3x km.  Choose the correct option:
A) 12 kmph B) 88 kmph C) 24 kmph D) 17 kmph E) 19 kmph

Solution: Total time taken = x/40 + 2x/20 hours   = 5x/40 = x/8 hours   Average speed = 3x/(x/8) = 24 kmph   Answer: 24 kmph
Answer: C
If 20 shirts can be purchased for 5 dollars, how many shirts can be purchased for 10 dollars? Choose the correct choice from the following answers.
A) 10 B) 30 C) 60 D) 40 E) 20

Solution: 200/5= 
200/5 = 40
40   Ans= 40
Answer: D
How many seconds will a 500 meter 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 63 km/hr? Choose the correct choice:	A) 299 meters	B) 278 meters	C) 500 meters	D) 276 meters	E) 299 meters

Solution: Let length of tunnel is x meter   Distance = 800+x meter   Time = 1 minute = 60 seconds   Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s   Distance = Speed*Time   800+x = (65/3) * 60   800+x = 20 * 65= 
20 * 65 = 1_300
1300   x= 1300 - 800= 
1300 - 800 = 500
500 meters   Answer: 500 meters
Answer: C
ABCD is a parallelogram on xy rectangular coordinate plane, three of the four vertices of parallelogram are (5,15) , (5,20) and (-5,15). Which can be the coordinate of fourth vertex?	Select the correct option
A) (-5,-5) B) (5,15) C) (-5,-20) D) (-5,10) E) (15,20)

Solution: A(-5, 15)   B(5, 15)   C(5, 20)   X(-5, 20): Parallelogram=Square=AXCB, where AX||CB, AX=CB, XC||AB, XC=AB   Y(-5, 5): Parallelogram=AYBC, where AY||BC, AY=BC, AC||YB, AC=YB   Z(15, 20): Parallelogram=ACZB, where AC||ZB, AC=ZB, CZ||AB, CZ=AB   Ans:(15,20)
Answer: E