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# What is the value of x?

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Math Expert
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What is the value of x? [#permalink]

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10 Nov 2014, 08:29
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Tough and Tricky questions: Sequences.

What is the value of x?

(1) 2x - 5y + 6 = 12

(2) 8x - (4x + 10y) + 27 = 39

Kudos for a correct solution.
[Reveal] Spoiler: OA

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Re: What is the value of x? [#permalink]

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10 Nov 2014, 08:47
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Both equations are of the same line...So we can't make out the value of x..it can be anywhere over the line 2x-5y-6=0

So it should be E..??
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Re: What is the value of x? [#permalink]

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10 Nov 2014, 11:37
I see that people are posting E so maybe I am missing something but I liked option C. Since we need a value for X, each statement alone will be insufficient since they each have 2 variables and you cannot get 1 of them to a single value. Since each statement only has 2 variables and they are x and y, we can combine them to get a value for x. Answer C!

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Re: What is the value of x? [#permalink]

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11 Nov 2014, 02:08
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Eq 1 and 2 are insuff alone as they inclide two variables and its impossible to solve for one variable i.e x. Combined they provide the same info, so nothing new. Answer should be E.

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Re: What is the value of x? [#permalink]

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11 Nov 2014, 05:13
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(1) 2x - 5y + 6 = 12 => 2x - 5y = 6

(2) 8x - (4x + 10y) + 27 = 39 => 4x - 10y = 12 or 2 (2x -5y ) = 2* 6

Since both equation are same, x can not be determined, hence E

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Re: What is the value of x? [#permalink]

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14 Nov 2014, 00:40
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Bunuel wrote:

Tough and Tricky questions: Sequences.

What is the value of x?

(1) 2x - 5y + 6 = 12

(2) 8x - (4x + 10y) + 27 = 39

Kudos for a correct solution.

S1 : 2x-5y = 6....can have many different values of x & Y e.g. X=8, Y=2 is one solution ; x=13, Y=4 is another one. Hence S1 is insufficient.

S2 : 4x-10y = 12 ....the equation is the same as S1 [multiplied by 2]. Hence S2 is insufficient.

Since both equations are same, we can't solve for X & Y using these two equations. Hence taking S1 & S2 together is also insufficient.

Hence Answer E.

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Re: What is the value of x? [#permalink]

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14 Nov 2014, 00:48
Bunuel wrote:

Tough and Tricky questions: Sequences.

What is the value of x?

(1) 2x - 5y + 6 = 12

(2) 8x - (4x + 10y) + 27 = 39

Kudos for a correct solution.

I agree it is E as well. Both equations are same so x cannot be solved.

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Re: What is the value of x? [#permalink]

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14 Nov 2014, 00:54
IMO E

both are same equations when simplified

OA?
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Re: What is the value of x? [#permalink]

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14 Nov 2014, 02:17
Bunuel wrote:

Tough and Tricky questions: Sequences.

What is the value of x?

(1) 2x - 5y + 6 = 12

(2) 8x - (4x + 10y) + 27 = 39

Kudos for a correct solution.

The correct answer is E.
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Re: What is the value of x? [#permalink]

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08 Sep 2017, 18:39
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Bunuel wrote:

Tough and Tricky questions: Sequences.

What is the value of x?

(1) 2x - 5y + 6 = 12

(2) 8x - (4x + 10y) + 27 = 39

Kudos for a correct solution.

The parentheses is just here to confuse you

8x-4x +10y= 12
4x-2x =10y =6
2x -5y =6

redundant info

E

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Director
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Re: What is the value of x? [#permalink]

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10 Sep 2017, 13:03
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Bunuel wrote:

Tough and Tricky questions: Sequences.

What is the value of x?

(1) 2x - 5y + 6 = 12

(2) 8x - (4x + 10y) + 27 = 39

Kudos for a correct solution.

The subtle trick played here is redundant information- the questions asks for the value of X, specifically.

St 1

2x-5y= 6

insuff

St 2

8x-4x-10y =12
4x- 10y= 12
2(2x-5y) =12
(2x-5y) =6

No better than st 1

insuff

St 1 & 2

Insuff because both statements give us the same thing

E

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Re: What is the value of x? [#permalink]

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11 Sep 2017, 14:12
Expert's post
Top Contributor
Bunuel wrote:

Tough and Tricky questions: Sequences.

What is the value of x?

(1) 2x - 5y + 6 = 12

(2) 8x - (4x + 10y) + 27 = 39

Kudos for a correct solution.

Target question: What is the value of x?

Statement 1: 2x - 5y + 6 = 12
Subtract 6 from both sides to get: 2x - 5y = 6
Since we have one equation with 2 variables, there are infinitely many solutions.
In other words, x can have infinitely many values, which means statement 1 is NOT SUFFICIENT.

ASIDE: If you're not 100% convinced that there are infinitely many solutions, you can always test some values
There are several values of x and y that satisfy the equation 2x - 5y = 6. Here are two:
Case a: x = 3 and y = 0, in which case x = 3
Case b: x = 8 and y = 2, in which case x = 8

Statement 2: 8x - (4x + 10y) + 27 = 39
Subtract 27 from both sides to get: 8x - (4x + 10y) = 12
Expand: 8x - 4x - 10y = 12
Simplify: 4x - 10y = 12
Here we have another equation with 2 variables, which means there are infinitely many solutions.
In other words, x can have infinitely many values, which means statement 2 is NOT SUFFICIENT.

Statements 1 and 2 combined
Statement 1 tells us that 2x - 5y = 6
Statement 2 tells us that 4x - 10y = 12
IMPORTANT: the two equations above are EQUIVALENT equations.
If we take the equation 4x - 10y = 12 and divide both sides by 2 we get the EQUIVALENT equation 2x - 5y = 6
Since the two statements provide the same information, and since each statement alone is NOT SUFFICIENT, we can conclude that the COMBIEND statements are NOT SUFFICIENT

Answer:
[Reveal] Spoiler:
E

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Re: What is the value of x?   [#permalink] 11 Sep 2017, 14:12
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# What is the value of x?

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