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# Plane X flies at r miles per hour from A to B. Plane Y flies at S mile

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Math Expert
Joined: 02 Sep 2009
Posts: 50583
Plane X flies at r miles per hour from A to B. Plane Y flies at S mile  [#permalink]

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05 Nov 2017, 01:14
00:00

Difficulty:

15% (low)

Question Stats:

82% (01:25) correct 18% (01:01) wrong based on 156 sessions

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Plane X flies at r miles per hour from A to B. Plane Y flies at S miles per hour from B to A. Both planes take off at the same time. Which plane flies at a faster rate? Town C is between A and B.

(1) C is closer to A than it is to B.
(2) Plane X flies over C before plane Y

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Joined: 22 May 2017
Posts: 88
GMAT 1: 580 Q41 V29
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Re: Plane X flies at r miles per hour from A to B. Plane Y flies at S mile  [#permalink]

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06 Nov 2017, 09:50
Bunuel wrote:
Plane X flies at r miles per hour from A to B. Plane Y flies at S miles per hour from B to A. Both planes take off at the same time. Which plane flies at a faster rate? Town C is between A and B.

(1) C is closer to A than it is to B.
(2) Plane X flies over C before plane Y

AS INDIVIDUAL STATEMENT DOES NOT GIVE ANYTHING.
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Joined: 28 Dec 2010
Posts: 49
Re: Plane X flies at r miles per hour from A to B. Plane Y flies at S mile  [#permalink]

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06 Nov 2017, 20:48
1
1. You don't know anything about planes reaching Town C.
Insufficient.

2. You don't know where is Town C.
Insufficient.

Both. These conditions still don't give us which is faster.
When Plane Y is faster, but Town C is very close to Town A. (Conditions satisfy)
When Plane X is faster, and Town C is closer to Town A (Conditions satisfy)

E.
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Re: Plane X flies at r miles per hour from A to B. Plane Y flies at S mile  [#permalink]

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09 Nov 2017, 07:40
Bunuel wrote:
Plane X flies at r miles per hour from A to B. Plane Y flies at S miles per hour from B to A. Both planes take off at the same time. Which plane flies at a faster rate? Town C is between A and B.

(1) C is closer to A than it is to B.
(2) Plane X flies over C before plane Y

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

. <-- a --> <-- b -->
|---------|---------|
A--------C---------B

..| t1 | t2
-------------------------
v | r | 5
-------------------------
d | a | b

Question asks if r < 5 or r > 5.

Since we have 3 variables and 0 equation, E is most likely to be the answer.
If E is most likely to be the answer, we need to check both conditions 1) & 2) together first by VA method.

Condition 1) & 2)
We have conditions a < b and a/r < b/5 from 1) and 2).

a = 1, b = 2, r = 6 ==> r > 5
a = 20, b = 30, r = 4 ==> r < 5

For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80 % chance that E is the answer, while C has 15% chance and A, B or D has 5% chance. Since E is most likely to be the answer using 1) and 2) together according to DS definition. Obviously there may be cases where the answer is A, B, C or D.
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Plane X flies at r miles per hour from A to B. Plane Y flies at S mile  [#permalink]

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11 Nov 2017, 07:14
I. C is closer to A than to B. Cannot tell about speed
II. X reaches C before does Y. Obviously, as C is closer to X, X is bound to reach C faster than does Y.
Hence E

eg. Now, Say, C is just 100 km from X while it is 10000km from Y. So, even at a crawling speed. X would reach C before does Y. Or may be C is 100 km from X and 300km from Y. But Y at 290km/hr almost reaches C in 1 hour (within 10kms), while X at 100km/hr reaches C before does Y. X is still slow.
eg. C is 500kms from X while 501 kms from Y. X reaches C in 1 hour @ 500km/hr while Y reaches only 30kms at 30km/hr. X is lightning fast.
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Re: Plane X flies at r miles per hour from A to B. Plane Y flies at S mile  [#permalink]

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13 Feb 2018, 07:02
Why is the correct option C?
https://gmatclub.com/forum/train-t-leav ... 51615.html
This question is identical and the answer is E!
Re: Plane X flies at r miles per hour from A to B. Plane Y flies at S mile &nbs [#permalink] 13 Feb 2018, 07:02
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