If x, y, and z are integers greater than 0 and x = y + z

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If x, y, and z are integers greater than 0 and x = y + z [#permalink]

11 Nov 2010, 02:55

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Question: If x, y, and z are integers greater than 0 and x = y + z, what is the value of ?

(1) (x-y)/y=4/5
(2) z/y=4/5

A)Statement (1) ALONE is sufficient, but statement (2) is not sufficient.
B)Statement (2) ALONE is sufficient, but statement (1) is not sufficient.
C)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D)EACH statement ALONE is sufficient.
E)Statements (1) and (2) TOGETHER are NOT sufficient.

[Reveal] Spoiler: OA

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Re: GOOD DS question [#permalink]

11 Nov 2010, 03:13

amirdubai1982 wrote:

Question: If x, y, and z are integers greater than 0 and x = y + z, what is the value of ?

(1) (x-y)/y=4/5
(2) z/y=4/5

Question should be: If x, y, and z are integers greater than 0 and x=y+z, what is the value of (y-z)/y?

\frac{y-z}{y}=1-\frac{z}{y}=? So, basically the question asks about the value of \frac{z}{y}.

(1) \frac{x-y}{y}=\frac{4}{5} --> cross multiply --> 5x-5y=4y --> 5x=9y --> as x=y+z (or as 5x=5y+5z) then 9y=5y+5z --> 4y=5z --> \frac{z}{y}=\frac{4}{5}. Sufficient.

(2) \frac{z}{y}=\frac{4}{5}, directly gives the value of the ratio we need. Sufficient.

Answer: D.
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Re: GOOD DS question [#permalink]

11 Nov 2010, 06:01

amirdubai1982 wrote:

Question: If x, y, and z are integers greater than 0 and x = y + z, what is the value of (y-z)/y?

(1) (x-y)/y=4/5
(2) z/y=4/5

A)Statement (1) ALONE is sufficient, but statement (2) is not sufficient.
B)Statement (2) ALONE is sufficient, but statement (1) is not sufficient.
C)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D)EACH statement ALONE is sufficient.
E)Statements (1) and (2) TOGETHER are NOT sufficient.

Data from question stem: x = y + z. Since we need the value of 1 - \frac{z}{y}, let us divide this equation by y. We get \frac{x}{y} = 1 + \frac{z}{y}

Question: What is \frac{(y-z)}{y} = 1 - \frac{z}{y}
To get z/y, we should either have x/y (as seen above) or z/y

1.\frac{(x - y)}{y} = \frac{4}{5}
or \frac{x}{y} - 1 = \frac{4}{5}
From here, we get the value of x/y. Sufficient.

2. This directly gives us the value of z/y. Sufficient.
Answer (D)
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Re: GOOD DS question [#permalink] 11 Nov 2010, 06:01

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If x, y, and z are integers greater than 0 and x = y + z

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