Rephrase this inequality when used together...?

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benjiboo: Senior | Next Rank: 100 Posts; Posts: 60; Joined: Thu Sep 24, 2009 2:38 pm; Location: NYC; Thanked: 33 times; Followed by:9 members; GMAT Score:710

Rephrase this inequality when used together...?

by benjiboo » Fri Sep 14, 2012 7:09 pm

Is x < z?

(1) x = (1/2)y

(2) y = 0.5z

Is it proper to say: (answer and question below, incase you wanted to try it out first)

[spoiler]2x=y
2y=z
so therefore...
4x=z

And the answer is E because if x=1, z=4, but x and z could both be zero... Or is this not what is actually being tested?[/spoiler]

Quote

Source: Beat The GMAT — Data Sufficiency | Fri Sep 14, 2012 7:09 pm

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Sat Sep 15, 2012 7:54 am

benjiboo wrote:Is x < z?

(1) x = (1/2)y

(2) y = 0.5z

Is it proper to say: (answer and question below, incase you wanted to try it out first)

[spoiler]2x=y
2y=z
so therefore...
4x=z

And the answer is E because if x=1, z=4, but x and z could both be zero... Or is this not what is actually being tested?[/spoiler]

Your answer of E is correct, but you do need to determine the sufficiency of each statement alone before combining them to get 4x = z

My solution.

Target question: Is x < z?

Statement 1: x = (1/2)y
This tells us the relationship between x and y, but since there is no mention of z, there is no way to tell whether or not x is less than z.
INSUFFICIENT

Statement 2: y = 0.5z
This tells us the relationship between y and z, but since there is no mention of x, there is no way to tell whether or not x is less than z.
INSUFFICIENT

Statements 1 & 2:
If y = 0.5z and x = (1/2)y then we can conclude (as you have done) that 4x = z
Is this sufficient to answer the target question with certainty? No.
If 4x = z, there are several possible cases to consider. Here are two:
case a: x=1 and z=4, in which case x is less than z.
case b: x= -1 and z= -4, in which case x is not less than z.
INSUFFICIENT

Answer = E

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com