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21 Dec 2023, 07:00
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12 Days of Christmas 🎅 GMAT Competition with Lots of Questions & Fun
George is at a location between his house and the concert hall. To reach the concert hall, he has two options, both taking the same amount of time: he can either walk directly there, or he can walk back to his house and then drive to the concert hall. If George drives 12 times as fast as he walks, what is the ratio of George's distance from his house to his distance from the concert hall?
A. 1:11
B. 11:12
C. 11:13
D. 13:11
E. 11:1
George is at a location between his house and the concert hall. To reach the concert hall, he has two options, both taking the same amount of time: he can either walk directly there, or he can walk back to his house and then drive to the concert hall. If George drives 12 times as fast as he walks, what is the ratio of George's distance from his house to his distance from the concert hall?
A. 1:11
B. 11:12
C. 11:13
D. 13:11
E. 11:1
|
22 Dec 2023, 06:36
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GMAT Club Official Explanation:
George is at a location between his house and the concert hall. To reach the concert hall, he has two options, both taking the same amount of time: he can either walk directly there, or he can walk back to his house and then drive to the concert hall. If George drives 12 times as fast as he walks, what is the ratio of George's distance from his house to his distance from the concert hall?
A. 1:11
B. 11:12
C. 11:13
D. 13:11
E. 11:1
Let's assume George's distance from his house is x, and his distance from the concert hall is y. The question is asking us to find the ratio x/y.
If we assume his walking speed is v, then walking directly to the concert hall (the first option) would take a time of y/v.
The second option, walking back to his house and then driving to the concert hall, would take a time of x/v + (x + y)/(12v).
Since both options take the same amount of time, we have y/v = x/v + (x + y)/(12v).
Multiplying everything by v to eliminate it, we get: y = x + (x + y)/12. Simplifying this, we find 11y = 13x, leading to the ratio x/y = 11/13.
Answer: C.
General Discussion
21 Dec 2023, 07:35
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Given: George is at a location between his house and the concert hall. To reach the concert hall, he has two options, both taking the same amount of time: he can either walk directly there, or he can walk back to his house and then drive to the concert hall.
Asked: If George drives 12 times as fast as he walks, what is the ratio of George's distance from his house to his distance from the concert hall?
House-------------d1----------George -------------d2--------Concert Hall
Let the walking speed be v
Driving speed = 12v
Time taken to walk to concert hall = d2/v
Time taken to walk to home and then drive to concert hall = d1/v + (d1+d2)/12v
Since Time taken to walk to concert hall = Time taken to walk to home and then drive to concert hall
d2/v = d1/v + (d1+d2)/12v
1 = d1/d2 + (d1/d2 + 1)/12
Let d1/d2 = the ratio of George's distance from his house to his distance from the concert hall = k
12 = 12k + (k+1) = 13k + 1
k = 11/13
IMO C
Asked: If George drives 12 times as fast as he walks, what is the ratio of George's distance from his house to his distance from the concert hall?
House-------------d1----------George -------------d2--------Concert Hall
Let the walking speed be v
Driving speed = 12v
Time taken to walk to concert hall = d2/v
Time taken to walk to home and then drive to concert hall = d1/v + (d1+d2)/12v
Since Time taken to walk to concert hall = Time taken to walk to home and then drive to concert hall
d2/v = d1/v + (d1+d2)/12v
1 = d1/d2 + (d1/d2 + 1)/12
Let d1/d2 = the ratio of George's distance from his house to his distance from the concert hall = k
12 = 12k + (k+1) = 13k + 1
k = 11/13
IMO C
22 Dec 2023, 05:10
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Bunuel
Let the distance from George's location to his home be 'd1'
Let the distance from George's location to the concert be 'd2'
Let his walking speed be 'm'
Let his driving speed be '12m'
The required ratio = d1/d2
As per the question
Time for George to walk to the concert = Time taken to walk back to his house and then drive to the concert hall
=> d2/m = d1/m + (d1 + d2)/12m
=> 12(d2 - d1) = d1 + d2
=> 12(d2) - d2 = d1 + 12(d1)
=> 11(d2) = 13(d1)
=> d1/d2 = 11/13
Option C
