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23 Dec 2015, 14:17
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
79% (02:10) correct
21%
(02:12)
wrong
based on 466
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John would have reduced the time it took him to drive from his home to a certain store by 1/3 if he had increased his average speed by 15 miles per hour. What was John's actual average speed, in miles per hour, when he drove from his home to the store?
(A) 25
(B) 30
(C) 40
(D) 45
(E) 50
Source: GMAT Focus
(A) 25
(B) 30
(C) 40
(D) 45
(E) 50
Source: GMAT Focus
27 Dec 2015, 08:48
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Hi All,
This question is based on a math 'truism' that many Test Takers don't know: Increasing your speed by 50% decreases the amount of travel time by 1/3. Here's why:
Distance = (Rate)(Time)
D = (R)(T)
Since the distance remains the same (you're just changing the rate and time), any increase in rate or time is met with a change in the other term. Increasing the rate by 50% would give us...
D = (3/2)(R)(?)
The change in time has to 'offset' the (3/2) that is now part of the calculation. The fraction (2/3) creates that 'offset', which gives us....
D = (3/2)(R)(2/3)(T)
D = (6/6)(R)(T)
In this prompt, we're told that the time is decreased by 1/3 after the 15 miles/hour increase in speed. We're asked for the ORIGINAL speed, which means that the 15 miles/hour represents the 50% increase. Thus, the original speed must be 30 miles/hour.
Final Answer:
GMAT assassins aren't born, they're made,
Rich
This question is based on a math 'truism' that many Test Takers don't know: Increasing your speed by 50% decreases the amount of travel time by 1/3. Here's why:
Distance = (Rate)(Time)
D = (R)(T)
Since the distance remains the same (you're just changing the rate and time), any increase in rate or time is met with a change in the other term. Increasing the rate by 50% would give us...
D = (3/2)(R)(?)
The change in time has to 'offset' the (3/2) that is now part of the calculation. The fraction (2/3) creates that 'offset', which gives us....
D = (3/2)(R)(2/3)(T)
D = (6/6)(R)(T)
In this prompt, we're told that the time is decreased by 1/3 after the 15 miles/hour increase in speed. We're asked for the ORIGINAL speed, which means that the 15 miles/hour represents the 50% increase. Thus, the original speed must be 30 miles/hour.
Final Answer:
GMAT assassins aren't born, they're made,
Rich
Updated on: 29 Apr 2021, 13:47
Originally posted by BrentGMATPrepNow on 02 Mar 2018, 07:49.
Last edited by BrentGMATPrepNow on 29 Apr 2021, 13:47, edited 1 time in total.
Last edited by BrentGMATPrepNow on 29 Apr 2021, 13:47, edited 1 time in total.
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RSOHAL
John would have reduced the time it took him to drive from his home to a certain store by 1/3 if he had increased his average speed by 15 miles per hour. What was John's actual average speed, in miles per hour, when he drove from his home to the store?
(A) 25
(B) 30
(C) 40
(D) 45
(E) 50
Source: GMAT Focus
(A) 25
(B) 30
(C) 40
(D) 45
(E) 50
Source: GMAT Focus
Let's start with a word equation:
(John's travel time at faster speed) = 2/3(John's regular travel time)
Let r = John's regular speed
So, r+15 = John's faster speed
Let d = the distance traveled at regular speed
So d = the distance traveled at regular speed
time = distance/speed
So, we get: d/(r + 15) = (2/3)(d/r)
Rewrite as: d/(r + 15)= 2d/3r
Cross multiply: (d)(3r) = 2d(r + 15)
Expand: 3rd = 2rd + 30d
Rearrange to get: rd = 30d
Divide both sides by d to get: r = 30
Answer: B
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