Gmat Problem Solving 1000 - Section 2

Aim of this part is to put all the 1000 questions solved called to be must do 1000 sums for Problem Solving section of GMAT.

Section 1          Section 2             Section 3              Section 4               Section 5

Section 6          Section 7             Section 8              Section 9               Section 10

Section 11        Section 12           Section 13            Section 14             Section 15 

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1. The market value of a certain machine decreased by 30 percent of its purchase price each year. If the machine was purchased in 1982 for its market value of $8,000, what was its market value two years later?
(A) $8,000
(B) $5,600
(C) $3,200
(D) $2,400
(E) $800

Solution:
Price decreased every year = 30% of $8000 = $2400
Price after 2 years = $8000 - $2400 * 2 = $3200 

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2. What percent of 50 is 15?

(A) 30%

(B) 35%

(C) 70%

(D) 300%

(E) 333.33%

Solution:
Its 30%. I don’t think this needs explanation. 

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3. In a certain diving competition, 5 judges score each dive on a scale from 1 to 10. The point value of the dive is obtained by dropping the highest score and the lowest score and multiplying the sum of the remaining scores by the degree of difficulty. If a dive with a degree of difficulty of 3.2 received scores of 7.5, 8.0, 9.0, 6.0, and 8.5, what was the point value of the dive?

(A) 68.8

(B) 73.6

(C) 75.2

(D) 76.8

(E) 81.6

Solution:
Dropped scores = 9.0 and 6.0
Point value of dive = 3.2(7.5+8.5+8.0)
= 3.2 * 24
= 76.8 

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4. If 2x = 3y = 10, then 12xy =

(A) 1,200

(B) 200

(C) 120

(D) 40

(E) 20

Solution:
2x = 10 then x = 5
3y = 10 then y = 10/3

so 12xy = 12 * 5 * 10 / 3 = 200  

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5. If Jack walked 5 miles in 1 hour and 15 minutes, what was his rate of walking in miles per hour?

(A) 4

(B) 4.5

(C) 6

(D) 6.25

(E) 15

Solution:
I don’t think one needs explanation for this. Answer is 4 miles per hour.  

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6. Of a certain high school graduating class, 75 percent of the students continued their formal education, and 80 percent of those who continued their formal education went to four-year colleges. If 300 students in the class went to four-year colleges, how many students were in the graduating class?

(A) 500

(B) 375

(C) 240

(D) 225

(E) 180

Solution:
Let the number of students in graduating class be x
Then number of students continued their formal education = 0.75x
And number of students went got four year course = 0.80 * .075x =0 .6x
i.e. 0.6x = 300
x = 500  

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7. What is the least integer greater than –2+0.5?

(A) –2

(B) –1

(C) 0

(D) 1

(E) 2

Solution:
-1 is least integer greater than -1.5
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8. Which of the following is equivalent to (2x + 4) / (2x^2 + 8x+ 8) for all values of x for which both expressions are defined?

(A) 1/(2x^2 + 6)

(B) 1/(9x + 2)

(C) 2 / (x+6)

(D) 1 / (x+4)

(E) 1 / (x+2)

Solution:
(2x + 4) / (2x^2 + 8x+ 8)
= 2(x+2) / 2(x+2)^2
= 1/(x+2)  

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9. A certain business printer can print 40 characters per second, which is 4 times as fast as an average printer. If an average printer can print 5 times as fast as an electric typewriter, how many characters per minute can an electric typewriter print?

(A) 2

(B) 32

(C) 50

(D) 120

(E) 600

Solution:
Let the speed of electric typewrite be x
Then speed of average printer will be 5x
Then speed of business printer will be 20 x
i.e. 20 x = 40
x = 2 characters per second. i.e. 120 characters per minute.  

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10. When ticket sales began, Pat was the nth customer in line for a ticket, and customers purchased their tickets at the rate of x customers per minute. Of the following, which best approximates the time, in minutes, that Pat had to wait in line from the moment ticket sales began?

(A) (n - 1) x

(B) n + x –1

(C) (n - 1) /x

(D) x/ (n - 1)

(E) n / (x - 1)

Solution:
Pat is nth customer. So pat has to wait for n-1 customer to go.
Time taken will be (n-1) / x 

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11. If 6 gallons of gasoline are added to a tank that is already filled to 3/4 of its capacity, the tank is then filled to 9/10 of its capacity. How many gallons does the tank hold?

(A) 20
(B) 24
(C) 36
(D) 40
(E) 60

Solution:
When 6 gallons of gasoline was added, then gasoline in tank increased to 90% of its capacity from 75%.
Capacity of tank = 6 / 15 * 100 = 40 gallons.
Currently tank is filled up to 90%.
Hence currently tank hold 0.9 * 40 = 36 gallons
Maximu tank can hold =40gallons
gallons of gasoline. 

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12. A bus trip of 450 miles would have taken 1 hour less if the average speed S for the trip had been greater by 5 miles per hour. What was the average speed S, in miles per hour, for the trip?(A) 10
(B) 40
(C) 45
(D) 50
(E) 55

Solution:
(450 / S) – (450 /(S+5)) = 1 Hr
450 ((S + 5 – S) / S(S+5)) = 1
2250 = S^2 + 5S
S^2 + 5S – 2250 = 0
(S-45) (S+50) = 0
S = 45 miles per hour or S = -50 miles per hour
S can’t be negative as they are in same direction.
Hence S = 45. 

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13. 103 is how many times (0.01)3?
(A) 106
(B) 108
(C) 109
(D) 1012
(E) 1018

Solution:
(0.01)3= 10-6
hence 103 is 109 times the (0.01)3.  

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14. Which of the following groups of numbers could be the lengths of the sides of a right triangle?

Ⅰ. 1, 4, √(17)
Ⅱ. 4, 7, √(11)
Ⅲ. 4, 9, 6

(A) Ⅰonly
(B) Ⅰand Ⅱ only
(C) Ⅰand Ⅲ only
(D) Ⅱand Ⅲ only
(E) Ⅰ,Ⅱ, and Ⅲ

Solution:
To be sides of right angle triangle it has to follow the law of Pythagoras.
Ie.e sum of squares of 2 smaller sides should be equal to square of biggest side. This is followed by only case I. 

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15. When the stock market opened yesterday, the price of a share of stock X was 10.5. When the market closed, the price was 11.25. Of the following, which is closest to the percent increase in the price of stock X?

(A) 0.5%

(B) 1.0%

(C) 6.7%

(D) 7.1%

(E) 7.5%

Solution:

Price increased = 11.25 – 10.50 = 0.75
Hence percent increase in share price = 0.75 * 100 / 10.50 = 7.143 % = 7.1%  

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16. xy^2 is a positive odd integer, which of the following must be true?

Ⅰ. xy is positive.

Ⅱ. xy is odd.

Ⅲ. x + y is even.

(A) Ⅰ only

(B) Ⅱ only

(C) Ⅲ only

(D) Ⅰ and Ⅱ

(E) Ⅱ and Ⅲ

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  17. The figure above shows the dimensions of a rectangular box that is to be completely wrapped with paper. If a single sheet of paper is to be used without patching, then the dimensions of the paper could be
(A) 17 in by 25 in
(B) 21 in by 24 in
(C) 24 in by 12 in
(D) 24 in by 14 in
(E) 26 in by 14 in

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18. x - y = 3

2x = 2y + 6
The system of equations above has how many
solutions?

(A) None
(B) Exactly one
(C) Exactly two
(D) Exactly three
(E) Infinitely many

Solution:
Equation 1 is x - y = 3
x = y + 3
Multiply by 2 on both the sides
2x = 2y + 6
which is nothing but equation 2, hence we can not have an unique solution.This will have infinite solutions.  

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19. If M and N are positive integers that have remainders of 1 and 3, respectively, when divided by 6, which of the following could NOT be a possible value of M+N?
(A) 86
(B) 52
(C) 34
(D) 28
(E) 10

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20. The R students in a class agree to contribute equally to buy their teacher a birthday present that costs y dollars. If x of the students later fail to contribute their share, which of the following represents the additional number of dollars that each of the remaining students must contribute in order to pay for the present?
(A) y/R
(B) y/(R - x)
(C) xy / (R – x)
(D) xy / R(R – x)
(E) y / R(R – x)

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