GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 23 Oct 2019, 01:25

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58449
If 2^(x + y) = 4^8, what is the value of y?  [#permalink]

### Show Tags

26 Oct 2015, 09:51
4
30
00:00

Difficulty:

25% (medium)

Question Stats:

72% (01:10) correct 28% (01:14) wrong based on 1600 sessions

### HideShow timer Statistics

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.

_________________
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 4018
Re: If 2^(x + y) = 4^8, what is the value of y?  [#permalink]

### Show Tags

26 Oct 2015, 09:59
6
6
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
_________________
Test confidently with gmatprepnow.com
##### General Discussion
Senior Manager
Joined: 10 Mar 2013
Posts: 465
Location: Germany
Concentration: Finance, Entrepreneurship
Schools: WHU MBA"20 (A)
GMAT 1: 580 Q46 V24
GPA: 3.88
WE: Information Technology (Consulting)
Re: If 2^(x + y) = 4^8, what is the value of y?  [#permalink]

### Show Tags

26 Oct 2015, 10:06
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

_________________
When you’re up, your friends know who you are. When you’re down, you know who your friends are.

800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50
GMAT PREP 670
MGMAT CAT 630
KAPLAN CAT 660
Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4771
Location: India
GPA: 3.5
Re: If 2^(x + y) = 4^8, what is the value of y?  [#permalink]

### Show Tags

30 Nov 2016, 12:57
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)
_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Intern
Joined: 17 Nov 2016
Posts: 24
Re: If 2^(x + y) = 4^8, what is the value of y?  [#permalink]

### Show Tags

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?
Math Expert
Joined: 02 Sep 2009
Posts: 58449
Re: If 2^(x + y) = 4^8, what is the value of y?  [#permalink]

### Show Tags

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.
_________________
Manager
Joined: 19 Jul 2017
Posts: 82
Location: India
Concentration: General Management, Strategy
GPA: 3.5
Re: If 2^(x + y) = 4^8, what is the value of y?  [#permalink]

### Show Tags

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
Intern
Joined: 29 Aug 2016
Posts: 2
Re: If 2^(x + y) = 4^8, what is the value of y?  [#permalink]

### Show Tags

31 Mar 2018, 14:51
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!
SVP
Joined: 03 Jun 2019
Posts: 1746
Location: India
Re: If 2^(x + y) = 4^8, what is the value of y?  [#permalink]

### Show Tags

10 Jul 2019, 22:11
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
_________________
"Success is not final; failure is not fatal: It is the courage to continue that counts."

Please provide kudos if you like my post. Kudos encourage active discussions.

My GMAT Resources: -

Efficient Learning
All you need to know about GMAT quant

Tele: +91-11-40396815
Mobile : +91-9910661622
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
Display posts from previous: Sort by