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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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New post 15 Sep 2019, 21:12
1
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A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

68% (01:01) correct 32% (00:52) wrong based on 62 sessions

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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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New post 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

Final answer is (A)
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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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New post 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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New post 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!

IMO answer is option A

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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New post 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

A is the correct answer
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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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New post 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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New post 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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New post 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.

Answer (A)
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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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New post 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.

Answer (A).
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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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New post 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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Given 3x + 4y = 18, what is x? (1) 5x + 2y = 16 (2) 3/2*x = 9 – 2y

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