DS question

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magical cook: Master | Next Rank: 500 Posts; Posts: 484; Joined: Sun Jul 30, 2006 7:01 pmFollowed by: 1 member; Thanked: 2 times

by magical cook » Mon Feb 12, 2007 10:27 am

Hi,

The attached question answer is C but I thought was A because X is absolute value in question, so 1) X=z-y is same as lxl=y-z ? (whether answer for A is minus or plus, as long as value is the same, it should be ok...)

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Source: Beat The GMAT — Data Sufficiency | Mon Feb 12, 2007 10:27 am

amitamit2020: Junior | Next Rank: 30 Posts; Posts: 17; Joined: Wed Jan 24, 2007 3:35 am

definition of mode

by amitamit2020 » Mon Feb 12, 2007 11:33 am

Let us revisit the definition of mode. It goes like ...

mode (p) = p , if p > = zero
= - p , if p < zero.

Now let us take the question here,

Is mode (x) = y - z?

(A) says, x = z - y, thus by definition
mode (x) = z - y, if x = z - y > = zero
= y - z, if X = z - y < zero

Thus (A) is not enough to surely answer the question.

Let us look at (B), it says x > zero, (B) alone clearly does not suffice for the answer of the question.

Let's combine both (A) and (B) ; -- it clearly says that as X > zero;
mode (x) = y - z.

Thus [C] is the correct answer.

I hope it clears the doubt.

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magical cook: Master | Next Rank: 500 Posts; Posts: 484; Joined: Sun Jul 30, 2006 7:01 pmFollowed by: 1 member; Thanked: 2 times

Thanks!

by magical cook » Tue Feb 13, 2007 6:21 am

Hi amit,

I think I got it.... I was trying to figoure out the result of lXl = y- z (for example, if y=3, z=1, the result is x=2. With the same numbers for x = z - y, the result will be x=-2 ) So, whether the answer is 2 or -2, X is absolute value, so it dose not matter..

But I just realize the question is NOT asking the value of lXl but simply asking whether lXl is y-z (and not z=y).

Thanks again for your help.
Rina

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sanju438: Newbie | Next Rank: 10 Posts; Posts: 5; Joined: Tue Sep 05, 2006 9:33 pm

by sanju438 » Wed Sep 24, 2008 12:56 pm

Let x = 5, y = -8
Condition 1) z = x + y . Hence z = -3
(y-z) = -5. clearly |x| = 5 is not equal to (y-z)

As per condition (2) x < 0.
Let x = -3, y = -8. Hence according to condition (1) z = -11.
|x| = 3.
(y-z) = 3

Hence both conditions are required.

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