Simplifying algebraic expressions

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jeffedwards: Master | Next Rank: 500 Posts; Posts: 109; Joined: Mon Oct 12, 2009 4:58 amFollowed by: 1 member; Thanked: 12 times; GMAT Score:720

by jeffedwards » Wed Nov 11, 2009 6:57 pm

Is there a better way to solve it than what the book says? It makes sense, but I doubt I could duplicate that on the test. Any tips?

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

1
10
12
15
18
30

OA: D
Source: OG 12th E; PS #148

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Source: Beat The GMAT — Problem Solving | Wed Nov 11, 2009 6:57 pm

gmatv09: Master | Next Rank: 500 Posts; Posts: 256; Joined: Mon Aug 10, 2009 6:31 pm; Thanked: 3 times

by gmatv09 » Wed Nov 11, 2009 8:48 pm

Is there a mistake in the problem...
there eqn should be [x/(x+y)]10+[y/(x+y)]20=k

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palvarez: Master | Next Rank: 500 Posts; Posts: 199; Joined: Sat Oct 24, 2009 4:43 pm; Thanked: 22 times; GMAT Score:710

by palvarez » Wed Nov 11, 2009 11:12 pm

(10x+20y)/(x+y) = k, which is an integer

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

k > 10

10y/(x+y) = 10/(1+(y/x))

y/x's max value 1.

10/(1+(y/x))'s min value = 5

therefore, k > 15

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

here, k < 20

We got one value in that range. 18

10y = 8x+8y
y = 4x, which is consistent with x < y.

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KICKGMATASS123: Master | Next Rank: 500 Posts; Posts: 113; Joined: Thu Feb 26, 2009 8:13 am; Location: New Jersey; GMAT Score:650

by KICKGMATASS123 » Thu Nov 12, 2009 4:43 pm

palvarez wrote:(10x+20y)/(x+y) = k, which is an integer

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

k > 10

10y/(x+y) = 10/(1+(y/x))

y/x's max value 1.

10/(1+(y/x))'s min value = 5

therefore, k > 15

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

here, k < 20

We got one value in that range. 18

10y = 8x+8y
y = 4x, which is consistent with x < y.

dont get 10 + (10y/(x+y)) = k step!

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palvarez: Master | Next Rank: 500 Posts; Posts: 199; Joined: Sat Oct 24, 2009 4:43 pm; Thanked: 22 times; GMAT Score:710

by palvarez » Thu Nov 12, 2009 5:33 pm

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

divide by (x+y), you are left with 10 + 10y/(x+y)

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okigbo: Master | Next Rank: 500 Posts; Posts: 177; Joined: Sun Aug 02, 2009 9:39 pm; Thanked: 6 times

by okigbo » Thu Nov 12, 2009 11:31 pm

This is just a weighted average problem. No need to do calculations - average of 10 and 20 is 15 - equation is weigthed on the 20 side so must be greater than 15 - pick 18 and move on.

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