GMAT prep question

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zozo123: Senior | Next Rank: 100 Posts; Posts: 56; Joined: Tue Feb 13, 2007 6:19 am

by zozo123 » Tue Jun 12, 2007 6:32 am

If x, y, and k are positive numbers such that (x/(x+y))(10) + (y/(x+y))(20) = k and if x < y, which of the following could be the value of k?

A. 10
B. 12
C. 15
D. 18
E. 30

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Source: Beat The GMAT — Problem Solving | Tue Jun 12, 2007 6:32 am

f2001290: Master | Next Rank: 500 Posts; Posts: 400; Joined: Sat Mar 10, 2007 4:04 amFollowed by: 1 member; Thanked: 1 times

by f2001290 » Tue Jun 12, 2007 6:48 am

Is it D.

Given equation can be reduced to (10-k)x = (k-20)y

From here, I used back-solving. Only D satisfies the condition X<Y

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jayhawk2001: Community Manager; Posts: 789; Joined: Sun Jan 28, 2007 3:51 pmFollowed by: 1 member; Location: Silicon valley, California; Thanked: 30 times

Re: GMAT prep question

by jayhawk2001 » Tue Jun 12, 2007 8:48 pm

zozo123 wrote:If x, y, and k are positive numbers such that (x/(x+y))(10) + (y/(x+y))(20) = k and if x < y, which of the following could be the value of k?

A. 10
B. 12
C. 15
D. 18
E. 30

The eqn can be reduced to

(10x + 20y) / (x+y) = k

10 + 10y/(x+y) = k

y / (x+y) will be > 0 and < 1 as we know x and y are positive. So,
discard A and E.

When x = y, y/(x+y) = 1/2 and when x = 0, y/(x+y) = 1. So, value of
y/(x+y) will vary between 1/2 and 1. So, discard B and C.

Only D remains.

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