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# If xyz ≠ 0, is 3x/2 + y + 2z = 7x/2 + y?

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If xyz ≠ 0, is 3x/2 + y + 2z = 7x/2 + y?  [#permalink]

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Updated on: 13 May 2016, 07:12
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45% (medium)

Question Stats:

64% (01:21) correct 36% (01:48) wrong based on 107 sessions

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If xyz ≠ 0, is 3x/2 + y + 2z = 7x/2 + y?

(1) y = 3 and x = 2
(2) z = -x

Source: Manhattan Prep "Fractions, Decimals, Percents"

First they grouped all the "like" terns together and ended up with the equation z = x?
Answer: Only statement 2 is sufficient by itself. B

Why? I would have answered A because I plugged in the numbers given in statement 1 and solved for z. Then I came up with z = 2.
Then I plugged in the numbers for all 3 variables in the original equation (including z = 2) with the result of left side of equation = right side of equation so I can clearly answer the question with statement 1?

Originally posted by Silviax on 13 May 2016, 06:44.
Last edited by Bunuel on 13 May 2016, 07:12, edited 1 time in total.
Renamed the topic and edited the question.
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Joined: 02 Aug 2009
Posts: 7589
Re: If xyz ≠ 0, is 3x/2 + y + 2z = 7x/2 + y?  [#permalink]

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13 May 2016, 07:09
Silviax wrote:
Source: Manhattan Prep "Fractions, Decimals, Percents"

If xyz not equal 0, is 3x/2 + y + 2z = 7x/2 + y?

(1) y=3 and x = 2
(2) z = -x

First they grouped all the "like" terns together and ended up with the equation z = x?
Answer: Only statement 2 is sufficient by itself. B

Why? I would have answered A because I plugged in the numbers given in statement 1 and solved for z. Then I came up with z = 2.
Then I plugged in the numbers for all 3 variables in the original equation (including z = 2) with the result of left side of equation = right side of equation so I can clearly answer the question with statement 1?

Hi,

you have to find if $$\frac{3x}{2}+ y + 2z = \frac{7x}{2}+ y?$$...
But there are three variables and 'z' does not cancel out but remains till end..
so we cannot sove the equation.
we donot have to find z=2, we should be given z=2 for equation to be correct..
remember it is asking you IS A=B.. so you require both A and B
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If xyz ≠ 0, is 3x/2 + y + 2z = 7x/2 + y?  [#permalink]

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13 May 2016, 07:18
Silviax wrote:
If xyz ≠ 0, is 3x/2 + y + 2z = 7x/2 + y?

(1) y = 3 and x = 2
(2) z = -x

Source: Manhattan Prep "Fractions, Decimals, Percents"

First they grouped all the "like" terns together and ended up with the equation z = x?
Answer: Only statement 2 is sufficient by itself. B

Why? I would have answered A because I plugged in the numbers given in statement 1 and solved for z. Then I came up with z = 2.
Then I plugged in the numbers for all 3 variables in the original equation (including z = 2) with the result of left side of equation = right side of equation so I can clearly answer the question with statement 1?

Notice that the question asks is 3x/2 + y + 2z = 7x/2 + y? Which can be simplified to is z = x? We are NOT given that z = x, we are asked to find whether it's true.

(1) says that x = 2. So the question becomes is x = 2. We don't know that, thus the statement is not sufficient.

(2) says that z = -x. Now, if z = -x, then z = x can only be true when z = x = 0. Since we are told that xyz ≠ 0, then none of the variables is 0, therefore we can say that z ≠ x. Sufficient.

Hope it's clear.
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Re: If xyz ≠ 0, is 3x/2 + y + 2z = 7x/2 + y?  [#permalink]

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13 May 2016, 09:15
1
Information from the question:- xyz is not equal to 0

3x/2+y+2z= 7x/2+y?
3x/2+2z= 7x/2?
2z=4x/2?
2z=2x?
z=x?

So basically, the question is weather z=x?
Only statement 2 talks about both z and x. B is the answer
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If xyz ≠ 0, is 3x/2 + y + 2z = 7x/2 + y?  [#permalink]

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13 May 2016, 09:24
No I still don't get it because statement 1 gives us two values for two variables. So if plug in these values in my equation I get:

3(2)/2 + 3 + 2z = 7(2)/2 + 3
6/2 + 3 + 2z = 14/2 + 3
3 + 3 + 2z = 7 + 3
6 + 2z = 10
2z = 4
z = 2

So z = 2 results from the equation with the provided values for x and y and if I plug in all 3 values now I can see that both equation are the same so z = 2 and x = 2 thus z = x

Where is my thinking error here?

chetan2u wrote:
Silviax wrote:
Source: Manhattan Prep "Fractions, Decimals, Percents"

If xyz not equal 0, is 3x/2 + y + 2z = 7x/2 + y?

(1) y=3 and x = 2
(2) z = -x

First they grouped all the "like" terns together and ended up with the equation z = x?
Answer: Only statement 2 is sufficient by itself. B

Why? I would have answered A because I plugged in the numbers given in statement 1 and solved for z. Then I came up with z = 2.
Then I plugged in the numbers for all 3 variables in the original equation (including z = 2) with the result of left side of equation = right side of equation so I can clearly answer the question with statement 1?

Hi,

you have to find if $$\frac{3x}{2}+ y + 2z = \frac{7x}{2}+ y?$$...
But there are three variables and 'z' does not cancel out but remains till end..
so we cannot sove the equation.
we donot have to find z=2, we should be given z=2 for equation to be correct..
remember it is asking you IS A=B.. so you require both A and B
Math Expert
Joined: 02 Sep 2009
Posts: 54544
Re: If xyz ≠ 0, is 3x/2 + y + 2z = 7x/2 + y?  [#permalink]

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13 May 2016, 09:29
Silviax wrote:
No I still don't get it because statement 1 gives us two values for two variables. So if plug in these values in my equation I get:

3(2)/2 + 3 + 2z = 7(2)/2 + 3
6/2 + 3 + 2z = 14/2 + 3
3 + 3 + 2z = 7 + 3
6 + 2z = 10
2z = 4
z = 2

So z = 2 results from the equation with the provided values for x and y and if I plug in all 3 values now I can see that both equation are the same so z = 2 and x = 2 thus z = x

Where is my thinking error here?

chetan2u wrote:
Silviax wrote:
Source: Manhattan Prep "Fractions, Decimals, Percents"

If xyz not equal 0, is 3x/2 + y + 2z = 7x/2 + y?

(1) y=3 and x = 2
(2) z = -x

First they grouped all the "like" terns together and ended up with the equation z = x?
Answer: Only statement 2 is sufficient by itself. B

Why? I would have answered A because I plugged in the numbers given in statement 1 and solved for z. Then I came up with z = 2.
Then I plugged in the numbers for all 3 variables in the original equation (including z = 2) with the result of left side of equation = right side of equation so I can clearly answer the question with statement 1?

Hi,

you have to find if $$\frac{3x}{2}+ y + 2z = \frac{7x}{2}+ y?$$...
But there are three variables and 'z' does not cancel out but remains till end..
so we cannot sove the equation.
we donot have to find z=2, we should be given z=2 for equation to be correct..
remember it is asking you IS A=B.. so you require both A and B

We don't know whether 3x/2 + y + 2z = 7x/2 + y. We are asked to find out whether 3x/2 + y + 2z = 7x/2 + y. Please read my reply above.
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Re: If xyz ≠ 0, is 3x/2 + y + 2z = 7x/2 + y?  [#permalink]

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13 May 2016, 09:52
The question asked is effectively, as Divya pointed out is if x=y which is the simplified version of the equations in questions. only statement 2 answers this.
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Re: If xyz ≠ 0, is 3x/2 + y + 2z = 7x/2 + y?  [#permalink]

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08 Sep 2017, 20:26
Silviax wrote:
If xyz ≠ 0, is 3x/2 + y + 2z = 7x/2 + y?

(1) y = 3 and x = 2
(2) z = -x

Source: Manhattan Prep "Fractions, Decimals, Percents"

First they grouped all the "like" terns together and ended up with the equation z = x?
Answer: Only statement 2 is sufficient by itself. B

Why? I would have answered A because I plugged in the numbers given in statement 1 and solved for z. Then I came up with z = 2.
Then I plugged in the numbers for all 3 variables in the original equation (including z = 2) with the result of left side of equation = right side of equation so I can clearly answer the question with statement 1?

Rewrite and see the pattern here

Essentially 3x/2 +2x + y = 7x/2 + Y

This would mean that X would have to be equal to Y, x=y beccause

3x/2 +4x/2 + y = 7x/2 + Y

St 1

Clearly Insuff because we know nothing about Z

St 2

-x/2 + y 7x/2 +y = this could only be true if X were 0 but neither x nor y nor z can be 0

Suff
Re: If xyz ≠ 0, is 3x/2 + y + 2z = 7x/2 + y?   [#permalink] 08 Sep 2017, 20:26
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