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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, 08:51
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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, 08:59
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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 30 Nov 2016, 11:57
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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 26 Oct 2015, 09:06
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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.


\(2^(x+y)=2^16\), 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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New post 10 Sep 2017, 11:00
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, 20:31
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 10 Sep 2017, 23:04
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]

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New post 31 Mar 2018, 13:51
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.


On the OG2018, 6.3 Practice Questions, Prob. 350. It appears as follows:

2^x +y = 4^8

But in the 6.5 Answer explanations, Prob 350. It appears as follows:

2^(x+y) = 4^8

The correct statement is the second one! I hope this helps someone!

Kudos +1 if it helps you!
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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 Jul 2019, 21:11
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 = (2^2)^8 = 2^16
=> x+y = 16

Q y = ?

S1:
x^2 = 81
x = +/- 9
If x = 9, y = 7
If x = -9 y = 25
NOT SUFFICIENT.

S2:
x-y=2
x = y+2
2y +2 = 16
y = 7
SUFFICIENT.

IMO 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 03 Mar 2020, 10:55
If 2^(x + y) = 4^8, what is the value of y?

(1) x^2 = 81
(2) x − y = 2


The question asks if we can find Y or not. Immediately, before we start testing each statement, let's see if we can simplify this problem to make it easier on ourselves. 2^(x+y) = 4^8. Wouldn't it be easier if we could compare the two sides of the equation if they had the same base? Adjust accordingly. The given information turns into 2(x+y) = 2(^2^8) = 2^16. So we have this information: 2(x+y) = 2^16. But wait, we can go even further with the simplification. We know we are looking for Y. Each side has the same base (2), so we can simplify this into x+y=16. Now this is much more manageable.

Statement 1) x^2 = 81
We know that x can be either 9 or -9.
Let's plug each into our equation x+y=16, or y=16-x

X=9: y=16-(9)=7
X=-9: y=16-(-9)=25.

We get two different answers for y: 7 and 25, so this is an insufficient statement to determine what the value of y is.

Statement 2) x-y=2
We know that x+y=16 and x-y=2. We have two different 2-variable equations that aren't the same, so we can use whatever method we want (combination, substitution, case testing) to solve. I think combinations is the easiest, so let's solve:

x+y=16
+(x-y=2)
:2x=18, so we know that x=9. Plug this back into any of the two equations to find y. 9+y=16. y=7 This is sufficient, there is only one answer for y.
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Re: If 2^(x + y) = 4^8, what is the value of y?  [#permalink]

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New post 25 Jun 2020, 11:14
FYI - the 2020 GMAT official prep book has a typo in this problem, #406. The problem is shown as 2^(x)+y=4^8. I was so annoyed when I looked at the solution and the equation was supposed to be written 2^(x+y)=4^8.
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Re: If 2^(x + y) = 4^8, what is the value of y?   [#permalink] 25 Jun 2020, 11:14

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

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