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

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Difficulty:   25% (medium)

Question Stats: 72% (01:10) correct 28% (01:14) wrong based on 1647 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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Joined: 12 Sep 2015
Posts: 4064
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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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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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?
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Joined: 02 Sep 2009
Posts: 59095
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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E-mail : kinshook.chaturvedi@gmail.com Re: If 2^(x + y) = 4^8, what is the value of y?   [#permalink] 10 Jul 2019, 22:11
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