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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If 2^(x + y) = 4^8, what is the value of y?

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Math Expert V
Joined: 02 Sep 2009
Posts: 64891
If 2^(x + y) = 4^8, what is the value of y?  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 74% (01:10) correct 26% (01:16) wrong based on 1963 sessions

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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.

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GMAT Club Legend  V
Joined: 11 Sep 2015
Posts: 4947
GMAT 1: 770 Q49 V46
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

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

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1
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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1
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

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

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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?
Math Expert V
Joined: 02 Sep 2009
Posts: 64891
Re: If 2^(x + y) = 4^8, what is the value of y?  [#permalink]

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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 $$\sqrt{x}$$, 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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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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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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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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Intern  B
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Re: If 2^(x + y) = 4^8, what is the value of y?  [#permalink]

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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.
Intern  Joined: 05 Apr 2020
Posts: 2
Re: If 2^(x + y) = 4^8, what is the value of y?  [#permalink]

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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. 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?  