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If x > y, is zx > yx?

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If x > y, is zx > yx? [#permalink]

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New post 30 Jul 2012, 18:13
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If x > y, is zx > yx?

(1) z > 0

(2) y < 0
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Re: If x > y, is zx > yx? [#permalink]

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If x > y, is zx > yx?

Is \(zx > yx\)? --> is \(zx-yx>0\)? --> is \(x(z-y) >0\)?

(1) z > 0. Clearly insufficient.

(2) y < 0. Clearly insufficient.

(1)+(2) Now, remember that we can subtract inequalities with the signs in opposite direction --> subtract (2) from (1): \(z-y>0\). So, we know that the second multiply in \(x(z-y)\) is positive, but we still don't know the sign of \(x\): from the stem (\(x>y\)) and the second statement (\(y<0\)) the only thing we can deduce is that \(x\) is greater than negative number \(y\), hence \(x\) could be negative, positive or zero. Not sufficient.

Answer: E.

Hope it's clear.
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New post 31 Jul 2012, 01:03
Its E.. bt i got c ..then i realized we must knw what wud be the value of x ..and value of x is not given ...so its E..
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New post 23 Dec 2013, 18:57
Does anyone have advice on how to tackle these problems faster? I always end up resorting to plugging in numbers and various conditions and even though that helps me ensure more accuracy, it usually takes me about 3 min. per such problem (inequalities with only variables).

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New post 15 Sep 2015, 01:23
x>y and Is zx>yx? Y/N question

The question: Is z>x and x,y,z>0?

St.1 z>0. INSUFF (we do not know whether x,y>0)
St.2 y<0. INSUFF (we do not need other variables because if one is negative we cannot answer definitely)
St.1+St.2. Still y<0, so INSUFF

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New post 24 Sep 2015, 10:19
just to make sure i understood it:
zx > yx --> we cannot simplify to z > y because we don't know if x is positive or negative, right?

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New post 24 Sep 2015, 10:43
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nicksson wrote:
just to make sure i understood it:
zx > yx --> we cannot simplify to z > y because we don't know if x is positive or negative, right?


Yes exactly. In inequalities be very careful with cancelling variables without knowing for sure what signs are they.

In the current question, zx>xy --> x(z-y)>0

After combining the 2 statements, you do know that -y>0 and z>0 ---> z-y>0 but without knowing the sign of 'x', you will not be able to answer yes or no for the question asked.

Hope this helps.

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New post 20 Oct 2016, 03:19
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Re: If x > y, is zx > yx?   [#permalink] 20 Oct 2016, 03:19
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