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If 2^(x + y) = 4^8, what is the value of y?

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If 2^(x + y) = 4^8, what is the value of y? [#permalink]

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New post 26 Oct 2015, 09:51
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Re: If 2^(x + y) = 4^8, what is the value of y? [#permalink]

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Bunuel wrote:
If 2^(x + y) = 4^8, what is the value of y?

(1) x^2 = 81
(2) x − y = 2

Kudos for a correct solution.


Target question: What is the value of y?

Given: 2^(x + y) = 4^8
Notice that 4^8 = (2^2)^8 = 2^16
In other words, 2^(x + y) = 2^16, which means x + y = 16

Statement 1: x^2 = 81
This tells us that x = 9 OR x = -9
Let's examine each possible case
Case a: x = 9. If x + y = 16, then we can conclude that y = 7
Case b: x = -9. If x + y = 16, then we can conclude that y = 25
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x − y = 2
When we combine this information with x + y = 16, we see that we have TWO different equations and TWO variables.
So, we COULD solve this system to find one unique value of y (incidentally, we get y = 7)
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

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Re: If 2^(x + y) = 4^8, what is the value of y? [#permalink]

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New post 26 Oct 2015, 10:06
Bunuel wrote:
If 2^(x + y) = 4^8, what is the value of y?

(1) x^2 = 81
(2) x − y = 2

Kudos for a correct solution.


\(2^(x+y)=2^16\), x+y=16
(1) x=+/- 9 different values of y possible NOT SUFFICIENT
(2) x=2+y -> 2+2y=16 -> y=7 Sufficient

Answer (B)
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Re: If 2^(x + y) = 4^8, what is the value of y? [#permalink]

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Re: If 2^(x + y) = 4^8, what is the value of y? [#permalink]

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New post 30 Nov 2016, 12:57
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Bunuel wrote:
If 2^(x + y) = 4^8, what is the value of y?

(1) x^2 = 81
(2) x − y = 2

Kudos for a correct solution.


\(2^{(x + y)} = 4^8\)

Or, \(2^{(x + y)} = 2^{16}\)

So, \(x + y = 16\)

FROM STATEMENT - I ( INSUFFICIENT )

\(x^2 = 81\)

So, x = + 9

If x = +9 ; y = 7 & If x = - 9 ; y = 25

We do not have a unique value of y

FROM STATEMENT - II ( SUFFICIENT )

Given, \(x − y = 2\) and we know \(x + y = 16\) thus \(x = 9\) & \(y = 7\)

Thus, Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked, answer will be (B)
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Re: If 2^(x + y) = 4^8, what is the value of y? [#permalink]

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New post 10 Sep 2017, 12:00
Quote:
Statement 1: x^2 = 81
This tells us that x = 9 OR x = -9
Let's examine each possible case
Case a: x = 9. If x + y = 16, then we can conclude that y = 7
Case b: x = -9. If x + y = 16, then we can conclude that y = 25
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT


To my understanding, a sqrt of a number can never be negative. How come the sqyt of 81 is 9 or -9?

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Re: If 2^(x + y) = 4^8, what is the value of y? [#permalink]

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New post 10 Sep 2017, 21:31
Zoser wrote:
Quote:
Statement 1: x^2 = 81
This tells us that x = 9 OR x = -9
Let's examine each possible case
Case a: x = 9. If x + y = 16, then we can conclude that y = 7
Case b: x = -9. If x + y = 16, then we can conclude that y = 25
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT


To my understanding, a sqrt of a number can never be negative. How come the sqyt of 81 is 9 or -9?


Yes, when the GMAT provides the square root sign for an even root, such as \(\sqrt{x}\) or \(\sqrt[4]{x}\), then the only accepted answer is the positive root. That is, \(\sqrt{81}=9\), NOT +9 or -9. Even roots have only a positive value on the GMAT.

In contrast, the equation \(x^2=81\) has TWO solutions, +9 and -9.
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Re: If 2^(x + y) = 4^8, what is the value of y? [#permalink]

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New post 11 Sep 2017, 00:04
Bunuel wrote:
If 2^(x + y) = 4^8, what is the value of y?

(1) x^2 = 81
(2) x − y = 2

Kudos for a correct solution.


Given 2^(x+y)= 2^16;
so we have x+y=16 from q.
With x^2=81 we have 2 values for x +9 or -9. So y would also have 2 values.
So S1 is not sufficient.

From S2 given x-y=2; Solving for 2y=14; so y=2; Sufficient.

Ans:B

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Re: If 2^(x + y) = 4^8, what is the value of y?   [#permalink] 11 Sep 2017, 00:04
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