Is yz x? (1) y x/z (2) z

Question

Is yz > x?

(1) y > x/z
(2) z < 0

Source: self-made

funkyleaf · Answer

The question stem poses us with a yes or no question so the information we need to provide sufficiency does not need to make the statement yz>x true.

1) not sufficient - gives us no numerical basis to determine a definite yes or a definite no to the question posed.
2) not sufficient - we have a numerical basis for z but have no idea how this will relate to the values of x and y giving us no definite answer once again.

Looking at it together we see that z must be negative   and when applying that to (1) we can divide z (a negative) across the inequality causing a switch in the sign of the inequality giving us yz < x telling us a DEFINITE NO to the question stem thus providing sufficiency.

This gives us answer choice C - together the information in the statements provided is sufficient.

I think this is pretty close to the reasoning required here please let me know if I am wrong, thanks!

EMPOWERgmatRichC · Answer

Hi Harley1980,

This question can be solved by TESTing VALUES (knowing inequality 'rules' would help here too).

We're asked if YZ > X. This is a YES/NO question. Notice how we are not told ANYTHING about the 3 variables - they could be any type of number (positive, negative, 0, fractions, etc.), so we have to consider more than just the obvious possibilities (re: positive integers).

Fact 1: Y > X/Z

While it might be tempting to "multiply both sides by Z" and get YZ > X, this is NOT allowed since we don't know what type of number Z is. IF Z is positive, then this math is acceptable, but if Z is negative, then you have to "flip" the inequality (which would give you YZ < X). The following examples prove that the answer to the question changes depending on what the variables are....

IF....
Y = 1
X = 0
Z = 1
1 > 0/1
(1)(1) > 0, so the answer to the question is YES

IF....
Y = 1
X = 0
Z = -1
1 > 0/-1
(1)(-1) is NOT > 0, so the answer to the question is NO
Fact 1 is INSUFFICIENT

Fact 2: Z < 0

This tells us nothing about X and Y, so we cannot answer the question.
Fact 2 is INSUFFICIENT

Combined, we know....
Y > X/Z
Z < 0

Now that we know that Z is negative, we can 'modify' the first inequality by multiplying both sides by Z. We have to remember to "flip" the inequality though (since Z is NEGATIVE). This gives us.....

YZ < X.

With this information, the answer to the question is ALWAYS NO.
Combined, SUFFICIENT.

Final Answer:

Show Spoiler

C

GMAT assassins aren't born, they're made,
Rich

CrazyIvan · Answer

Is yz > x? (1) y > x/z (2) z < 0 (1) y > x/z y-x/z > 0 (yz-x)/z > 0 2 cases: a) yz-x>0 and z>0 in which case YES yz>x. b) yz-x < 0 and z<0 in which case yz

Kinshook · Answer

Asked: Is yz > x? (1) y > x/z yz >x if z<>0 NOT SUFFICIENT (2) z < 0 y & x are unknown NOT SUFFICIENT (1) + (2) (1) y > x/z yz >x if z<>0 (2) z < 0 Since z<>0 y>x/z SUFFICIENT IMO C

MHIKER · Answer

(1) Depends on the sign of the z. If z is negative then yz<x but if z is positive then yz>x. INSUFFICIENT.

(2) z<0, No information about y and x. INSUFFICIENT.

Considering both information. 
z<0, then y<x. Sufficient.

Ans. C

bumpbot · Answer

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Is yz > x? (1) y > x/z (2) z < 0

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