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# Given 3x + 4y = 18, what is x? (1) 5x + 2y = 16 (2) 3/2*x = 9 – 2y

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Given 3x + 4y = 18, what is x? (1) 5x + 2y = 16 (2) 3/2*x = 9 – 2y  [#permalink]

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15 Sep 2019, 21:12
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68% (01:01) correct 32% (00:52) wrong based on 62 sessions

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Given $$3x + 4y = 18$$, what is x?

(1) $$5x + 2y = 16$$

(2) $$\frac{3}{2}*x = 9 – 2y$$

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Re: Given 3x + 4y = 18, what is x? (1) 5x + 2y = 16 (2) 3/2*x = 9 – 2y  [#permalink]

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15 Sep 2019, 21:29
1
Given Eq(1) $$3x+4y=18$$,
Q.what is x?

(1) $$5x+2y=16$$
Multiplying both sides by 2, we get $$10x+4y=32$$ --> $$4y=32-10x$$. Substituting 4y in Eq(1), $$3x+(32-10x)=18$$ --> $$x=2.$$
SUFFICIENT

(2) $$(3x)/2=9–2y$$
Multiplying both sides by 2, we get $$3x=18-4y$$ --> $$3x+4y=18$$, which is identical with Eq(1). Thus, we cannot determine value of $$x$$.
NOT SUFFICIENT

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Re: Given 3x + 4y = 18, what is x? (1) 5x + 2y = 16 (2) 3/2*x = 9 – 2y  [#permalink]

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15 Sep 2019, 21:44
1
Given 3x+4y=18, we are to find x.

From 1, we know 5x+2y=16 ......(2)
(2)*2 yields 10x+4y=32 .....(3)
(3)-(1) yields 7x=14 hence x=2. Sufficient.

From 2, 1.5x+2y=9 .....(4)
(4)*2 yields 3x+4y=18 ......(5)
We can see that information provided by statement 2 is the same as the the one provided in the question stem. Hence 2 is not sufficient.

The answer is A in my opinion.

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Re: Given 3x + 4y = 18, what is x? (1) 5x + 2y = 16 (2) 3/2*x = 9 – 2y  [#permalink]

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Updated on: 16 Sep 2019, 21:29
Given 3x+4y=18, what is x?

(1) 5x+2y=16
Two equation, two variable. Can calculate x and y. Hence sufficient.

(2) 3/2∗x=9–2y
After expansion, you get 3x+4y=18, which is the question itself. INSUFFICIENT!

P.S: in such questions, you know it is possible to answer the question, so no need to answer waste time finding the answer since t is a DS question.
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Originally posted by EncounterGMAT on 15 Sep 2019, 21:49.
Last edited by EncounterGMAT on 16 Sep 2019, 21:29, edited 1 time in total.
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Re: Given 3x + 4y = 18, what is x? (1) 5x + 2y = 16 (2) 3/2*x = 9 – 2y  [#permalink]

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15 Sep 2019, 23:18
Given 3x + 4y = 18 what is x?

STATEMENT (1)--5x + 2y = 16
and 3x + 4y = 18

solving both equation we get x = 2

SUFFICIENT

STATEMENT (2)--$$\frac{3}{2}$$*x = 9 - 2y

rearranging the above equation we get
3x = 18 - 4y
3x+4y = 18 (same as given)
we need one more equation to solve for x
so INSUFFICIENT

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Re: Given 3x + 4y = 18, what is x? (1) 5x + 2y = 16 (2) 3/2*x = 9 – 2y  [#permalink]

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Updated on: 16 Sep 2019, 21:25
equate given eqn to y=(16-5x)/2
so #1
y=16-5x/2
solve for x we get x=2
sufficient
#2
equate given eqn we get ; 18-3x/4=y
solve for x not one value
Insufficient
IMO A

Given 3x+4y=18, what is x?

(1) 5x+2y=16

(2) 3∗x/2=9–2y

Originally posted by Archit3110 on 16 Sep 2019, 01:07.
Last edited by Archit3110 on 16 Sep 2019, 21:25, edited 1 time in total.
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Re: Given 3x + 4y = 18, what is x? (1) 5x + 2y = 16 (2) 3/2*x = 9 – 2y  [#permalink]

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16 Sep 2019, 01:20
Each alone is sufficient. x=2
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Re: Given 3x + 4y = 18, what is x? (1) 5x + 2y = 16 (2) 3/2*x = 9 – 2y  [#permalink]

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16 Sep 2019, 05:35
Quote:
Given $$3x+4y=18$$, what is x?

(1) $$5x+2y=16$$
(2) $$3/2∗x=9–2y$$

(1) $$5x+2y=16-(3x+4y=18)…2x-2y=-2…x-y=-1…y=x+1…3x+4(x+1)=18…x=2$$: sufic.
(2) $$3/2∗x=9–2y…3x=18-4y…3x+4y=18$$: same as given info, insufic.

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Re: Given 3x + 4y = 18, what is x? (1) 5x + 2y = 16 (2) 3/2*x = 9 – 2y  [#permalink]

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16 Sep 2019, 06:02
Given $$3x + 4y = 18$$, what is x?

(1) $$5x + 2y = 16$$
Two equations and two variables thus sufficient to find them.
SUFFICIENT.

(2) $$\frac{3}{2}*x = 9 – 2y$$
$$3x = 18 – 4y$$

So same equation as given thus not enough information to solve for variables.
INSUFFICIENT.

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Re: Given 3x + 4y = 18, what is x? (1) 5x + 2y = 16 (2) 3/2*x = 9 – 2y  [#permalink]

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16 Sep 2019, 08:51
I think statement 1 alone is sufficient as we will then have two equations for two variables.
Statement 2 does not give us any new information.

Given 3x+4y=18, what is x?

(1) 5x+2y=16
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Re: Given 3x + 4y = 18, what is x? (1) 5x + 2y = 16 (2) 3/2*x = 9 – 2y   [#permalink] 16 Sep 2019, 08:51
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