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

Question

(1) x^2 = 81
(2) x − y = 2

BrentGMATPrepNow · Accepted Answer

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

Cheers,
Brent

BrainLab · Answer

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)

Abhishek009 · Answer

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)

Zoser · Answer

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

Bunuel · Answer

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.

Arsh4MBA · Answer

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

RodolfoPozo · Answer

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!

Kinshook · Answer

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

DSBlender · Answer

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.

sydlyisaacs · Answer

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.

CrackverbalGMAT · Answer

Solution:

2x+y = (2^2)^8 = 2^16

=> x + y = 16

St (1)

x2 = 81 and thus

x = 9, - 9

Hence y = 7, 25

No unique value of y is obtained. Insufficient

St (2)

x-y =2

Along with x + y =16 (given) a unique value of y = 7 can be obtained.
Thus sufficient.

Hence option (b)

Hope this helps

Devmitra Sen (GMAT Expert-Quants)

KellyL · Answer

2^(x+y) = 4^8 
2^(x+y) = 2^2(8)
2^(x+y) = 2^16 
x+y = 16

Statement 1
X^2+81 
x= -9 or 9 
x=-9 y=25
x=9 y=7

*Whenever you see a variable raised to an even exponent remember that that variable could be negative or positive. 
Don't fall for the trap by assuming that x is positive.

Insufficient

Statement 2 
x= 2+y 
2+2y +16 
y=7 
Sufficient

ScottTargetTestPrep · Answer

Solution:

Question Stem Analysis:

We need to determine the value of y, given that 2^(x + y) = 4^8. Notice that 4^8 = 2^16. Therefore, x + y = 16. In other words, y = 16 - x.

Statement One Alone:
 
We see that x is either 9 or -9. If x = 9, then y = 16 - 9 = 7. However, if x = -9, then y = 16 - (-9) = 25. Since we can’t determine a unique value for y, statement one alone is not sufficient.

Statement Two Alone:
 
We see that x = y + 2. Since y = 16 - x, we have:

y = 16 - (y + 2)

y = 14 - y

2y = 14

y = 7

We see that y = 7. Statement two alone is sufficient.

Answer: B

GMATinsight · Answer

Answer: Option B

Video solution by  GMATinsight

https://www.youtube.com/watch?v=gT0AJyTsw9w

avigutman · Answer

Video solution from Quant Reasoning: Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=zdXg7YiDzPk

Kimberly77 · Answer

Great explantion BrentGMATPrepNow . One confusion why is it possible to use the derived info x + y = 16 with St 2 here but not possible in below question? Thanks Brent https://gmatclub.com/forum/is-4-x-y-8-1 ... 39120.html

BrentGMATPrepNow · Answer

In the question above, we are GIVEN the information that 2^(x + y) = 4^8. In other words, this information is not provided in the statements. From this given information, we are able to conclude that x + y = 16 In general, we can apply any given information to each of the statements. In this question, https://gmatclub.com/forum/is-4-x-y-8-1 ... 39120.html, we are not GIVEN any information. Here the question simply asks us "Is 4^(x+y) = 8^10?"

Kimberly77 · Answer

Hi Brent @BrentGMATPrepNow, thanks for your reply. still a bit confused...so basically.... GIVEN the information that 2^(x + y) = 4^8. , conclude x + y = 16 , and use this to apply to the statement. In this question, https://gmatclub.com/forum/is-4-x-y-8-1 ... 39120.html, given "Is 4^(x+y) = 8^10?" , conclude x+y=15 , but we can't use this to apply to statement? I'm not able to see any difference between the two questions here. Not sure what did I miss? Thanks Brent

BrentGMATPrepNow · Answer

, conclude x+y=15 , but we can't use this to apply to statement? I'm not able to see any difference between the two questions here. Not sure what did I miss? Thanks Brent

The question above reads "If 2^(x + y) = 4^8 , what is the value of y?" Of the target question is: What is the value of y? The underlined part, 2^(x + y) = 4^8 , is given information that we can use to help determine whether each statement is sufficient to answer the target question. In the question here, https://gmatclub.com/forum/is-4-x-y-8-1 ... 39120.html, we aren't given any information. Instead we have the target question "Is 4^(x+y) = 8^10?" So, without any extra information, there is no way to determine whether 4^(x+y) = 8^10 It COULD be the case that 4^(x+y) = 8^10, or it COULD be the case that 4^(x+y) ≠ 8^10 Since we don't know whether or not 4^(x+y) = 8^10, we can't then apply this information to each statement.

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

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