GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 03 Apr 2020, 04:15

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

For integers x and y, 2^x + 2^y =2^30. What is the value of x + y?

Author Message
TAGS:

Hide Tags

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9941
Location: United States (CA)
Re: For integers x and y, 2^x + 2^y =2^30. What is the value of x + y?  [#permalink]

Show Tags

12 Jun 2018, 10:09
1
Bunuel wrote:
For integers x and y, $$2^x + 2^y=2^{30}$$. What is the value of $$x + y$$?

A. 30
B. 32
C. 46
D. 58
E. 64

Dividing both sides by 2^x, we have:

1 + 2^(y - x) = 2^(30 - x)

We see that the right hand side is an integer power of 2. But the left hand side is 1 more than an integer power of 2, which can happen only if 2^(y - x) is also equal to 1. (When that happens, then the left side becomes 1 + 1 = 2, which is an integer power of 2.) (Also note that the only way in which 2^(y - x) can equal 1 is if (x - y) = 0.) Thus, the two sides of the equation can’t be equal unless y - x = 0, so that the left hand side is also an integer power of 2. So we have

1 + 2^0 = 2^(30 - x)

1 + 1 = 2^(30 - x)

2^1 = 2^(30 - x)

1 = 30 - x

x = 29

Since y - x = 0, so y = 29. Thus x + y = 29 + 29 = 58.

_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
197 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Director
Joined: 09 Mar 2018
Posts: 983
Location: India
Re: For integers x and y, 2^x + 2^y =2^30. What is the value of x + y?  [#permalink]

Show Tags

06 Feb 2019, 22:06
Bunuel wrote:
For integers x and y, $$2^x + 2^y=2^{30}$$. What is the value of $$x + y$$?

A. 30
B. 32
C. 46
D. 58
E. 64

Kudos for a correct solution.

keyword: test small numbers

$$2^4 = 2^x + 2^y$$

How is that possible, only when x = y = 3

$$2^5 = 2^x + 2^y$$, 32 = $$2^4 + 2^4$$, here as well x =y = 4

So to get $$2^30$$, x and y have to one less than 30 and x=y = 29

58

D
_________________
If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.
Manager
Joined: 04 Aug 2019
Posts: 54
Location: Viet Nam
Concentration: Organizational Behavior, Strategy
Schools: Desautels
WE: Research (Other)
Re: For integers x and y, 2^x + 2^y =2^30. What is the value of x + y?  [#permalink]

Show Tags

23 Feb 2020, 04:28
Bunuel wrote:
For integers x and y, $$2^x + 2^y=2^{30}$$. What is the value of $$x + y$$?

A. 30
B. 32
C. 46
D. 58
E. 64

Kudos for a correct solution.

2^x + 2^y = 2^30
(2^x+2^y)/2 = 2^29 (divide both sides by 2)
method 1: --> 2^29 is the average of 2^x and 2^y --> it is possible that 2^x = 2^y = 2^29 --> x = y = 29 --> x+ y = 29 + 29 = 58 (E)
method 2: --> 2^x + 2^y = 2.2^29 --> 2^x = 2^y = 2^29 --> x = y = 29 --> x + y = 29 + 29 = 58 (E)
_________________
"The devil is in the detail"
Intern
Joined: 03 Jul 2019
Posts: 8
Re: For integers x and y, 2^x + 2^y =2^30. What is the value of x + y?  [#permalink]

Show Tags

08 Mar 2020, 07:40
1
Bunuel wrote:
For integers x and y, $$2^x + 2^y=2^{30}$$. What is the value of $$x + y$$?

A. 30
B. 32
C. 46
D. 58
E. 64

Kudos for a correct solution.

2^10 = 1024 = 2^9 + 2^9 (512+512)
=>2^30= 2^29 + 2^29
=> x+y = 58
Intern
Joined: 30 Mar 2020
Posts: 5
Re: For integers x and y, 2^x + 2^y =2^30. What is the value of x + y?  [#permalink]

Show Tags

30 Mar 2020, 11:03
5
Can be solved by seeing a pattern in exponents
2^1 = 2^0 + 2^0
2^2 = 2^1 + 2^1
2^3 = 2^2 + 2^2
.
.
.
2^30 = 2^29 + 2^29

x + y = 58
Re: For integers x and y, 2^x + 2^y =2^30. What is the value of x + y?   [#permalink] 30 Mar 2020, 11:03

Go to page   Previous    1   2   [ 25 posts ]

Display posts from previous: Sort by