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If 3x – 3y = 12z, what is the value of x?

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If 3x – 3y = 12z, what is the value of x?

by BSSMN » Tue Jan 11, 2011 3:38 pm
If 3x - 3y = 12z, what is the value of x?

(1) 4z = 2 + y
(2) 4z = 6 - y

Answer is B

But i said D bc , thru elimination, i was able to get a value for x from stmnt (1). Maybe my use of elimination was incorrect, however, this is what i did:

From (1) 2 + y = 4z --> multiply both sides by 3 --> (1) becomes 6 + 3y = 12z
Now using elimination (by adding)

Q/S 3x - 3y = 12z
(1) + 6 + 3y = 12z

--> 3x + 6 = 0
--> x = -2

Is my use of elimination incorrect?

Thnks!
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by Night reader » Tue Jan 11, 2011 3:46 pm
BSSMN wrote:If 3x - 3y = 12z, what is the value of x?

(1) 4z = 2 + y
(2) 4z = 6 - y
simplifying question stem x-y=4z, find x-?

st(1) 4z=2+y and x-y=2+y <=> x=2+2y where y is unknown, Not Sufficient.
st(2) 4z=6-y and x-y=6-y <=> x=6 Sufficient.

Answer B
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by Night reader » Tue Jan 11, 2011 3:51 pm
BSSMN wrote:If 3x - 3y = 12z, what is the value of x?

(1) 4z = 2 + y
(2) 4z = 6 - y

Answer is B

But i said D bc , thru elimination, i was able to get a value for x from stmnt (1). Maybe my use of elimination was incorrect, however, this is what i did:

From (1) 2 + y = 4z --> multiply both sides by 3 --> (1) becomes 6 + 3y = 12z
Now using elimination (by adding)

Q/S 3x - 3y = 12z
(1) + 6 + 3y = 12z

--> 3x + 6 = 0
--> x = -2[/b]

Is my use of elimination incorrect?

Thnks!
3x+ 6 = 12z + 12z (not 0)
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by Adam@Knewton » Tue Jan 11, 2011 3:57 pm
It's actually a silly little math mistake. When you add:

3x - 3y = 12z
6 + 3y = 12z

You will get:

3x + 6 = 24z

This is a two-variable linear equation that is clearly Insufficient to solve for x. Your error was that you added on the left side (-3y + 3y = 0) and then subtracted on the right side (12z - 12z = 0). It seems silly but it's an error we are very likely to make when under test-day pressure. The way to avoid it is to be more proactive about what we're looking for. First, solve the given equation for x, since that's what we're asked about:

3x - 3y = 12z
3x = 12z + 3y
x = 4z + y

Now, realize that they're "really" asking you this: "What is 4z + y?"

Don't bother with any substitution or combination. The GMAT is predictable -- that is its greatest strength (because it maintains scoring consistency) AND its greatest weakness (that you can exploit to Beat it!). You know now that you've seen through their clever ways and you've done the hard part. Statement (1) cannot give us 4z+y, because it gives us 4z-y instead. Statement (2) gives us 4z+y=6 and is exactly what we're looking for.

On test day, trust your strategies and trust the questions you've seen before in preparation. If you get out ahead of the test and know what they're looking for, then this kind of question becomes a 40-second one, and you don't even give yourself the opportunity to make silly math mistakes :)
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by BSSMN » Tue Jan 11, 2011 4:00 pm
Wow, thanks guys.

I must say, my little math mistake was from time pressure!

I will try to put more emphasis on rephrasing the DS QSs before proceeding to the statements.

Thanks again

B.
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by GMATGuruNY » Tue Jan 11, 2011 11:03 pm
BSSMN wrote:If 3x - 3y = 12z, what is the value of x?

(1) 4z = 2 + y
(2) 4z = 6 - y

Answer is B

But i said D bc , thru elimination, i was able to get a value for x from stmnt (1). Maybe my use of elimination was incorrect, however, this is what i did:

From (1) 2 + y = 4z --> multiply both sides by 3 --> (1) becomes 6 + 3y = 12z
Now using elimination (by adding)

Q/S 3x - 3y = 12z
(1) + 6 + 3y = 12z

--> 3x + 6 = 0
--> x = -2

Is my use of elimination incorrect?

Thnks!
If you're prone to making algebraic errors, a safer approach would be to test the 2 statements by plugging in values:

Since we're looking for x, we should rewrite the given equation:
3x - 3y = 12z
3x = 3y + 12z
x = y + 4z

Statement 1: 4z = 2 + y
If z=1, y=2, so x = y+4z = 2 + 4*1 = 6.
If z=2, y=6, so x = y+4z = 6 + 4*2 = 14.
Since the value of x changes, insufficient.

Statement 1: 4z = 6 - y
If z=2, y= -2, so x = y+4z = -2 + 4*2 = 6.
If z=3, y= -6, so x = y+4z = -6 + 4*3 = 6.
Since the value of x stays the same, sufficient.

The correct answer is B.

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