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

 It is currently 15 Oct 2019, 19:44

### 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 n is a positive integer and x + 3 = 4^n, which of the following cou

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58340
If n is a positive integer and x + 3 = 4^n, which of the following cou  [#permalink]

### Show Tags

12 Feb 2019, 00:59
00:00

Difficulty:

15% (low)

Question Stats:

88% (01:02) correct 13% (00:57) wrong based on 40 sessions

### HideShow timer Statistics

If n is a positive integer and x + 3 = 4^n, which of the following could not be a value of x?

(A) 1
(B) 13
(C) 45
(D) 61
(E) 253

_________________
VP
Joined: 31 Oct 2013
Posts: 1471
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
If n is a positive integer and x + 3 = 4^n, which of the following cou  [#permalink]

### Show Tags

Updated on: 12 Feb 2019, 01:51
Bunuel wrote:
If n is a positive integer and x + 3 = 4^n, which of the following could not be a value of x?

(A) 1
(B) 13
(C) 45
(D) 61
(E) 253

x + 3 must not be expressed as the base of 4.

Option C) 45

45 + 3 = 48

48 can't be written as the base of 4.

Thus , the correct answer is C.

Originally posted by KSBGC on 12 Feb 2019, 01:04.
Last edited by KSBGC on 12 Feb 2019, 01:51, edited 3 times in total.
Manager
Joined: 13 Oct 2018
Posts: 85
Location: India
GPA: 3.1
WE: Information Technology (Computer Software)
Re: If n is a positive integer and x + 3 = 4^n, which of the following cou  [#permalink]

### Show Tags

12 Feb 2019, 01:05
n = 1
x = 1

n= 2
x = 13

so 4 will not have any power which can give 45

please award kudos if this is right

Posted from my mobile device
_________________
Ankit
GMAT is tough so I am ...
Giving Kudos is the best way to encourage and appreciate people
Director
Joined: 09 Mar 2018
Posts: 996
Location: India
Re: If n is a positive integer and x + 3 = 4^n, which of the following cou  [#permalink]

### Show Tags

12 Feb 2019, 01:37
1
Bunuel wrote:
If n is a positive integer and x + 3 = 4^n, which of the following could not be a value of x?

(A) 1
(B) 13
(C) 45
(D) 61
(E) 253

$$x = 4^n - 3$$

Now if that is the case, n cannot be 0

cyclicity of unit digit of 4 is 4,6,4,6

Now we will be always subtracting 3 out of it, new cyclicity becomes 1,3,1,3

Key word: could not be a value of x

It will be C
_________________
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: 19 Jan 2019
Posts: 88
Re: If n is a positive integer and x + 3 = 4^n, which of the following cou  [#permalink]

### Show Tags

12 Feb 2019, 01:46
Plug in the values of X in answer choices. All the option except c will give a value of 4^n...

Posted from my mobile device
Intern
Joined: 11 Dec 2018
Posts: 10
Re: If n is a positive integer and x + 3 = 4^n, which of the following cou  [#permalink]

### Show Tags

12 Feb 2019, 01:55
Bunuel wrote:
If n is a positive integer and x + 3 = 4^n, which of the following could not be a value of x?

(A) 1
(B) 13
(C) 45
(D) 61
(E) 253

The best way to answer this question is working backward.

Plug-in the answer choices in X and try to solve the equation:

X= 4^n - 3

1) 1= 4^1 - 3 = 1 OK!

2)13 = 4^2 - 3 = 13 OK!

3)45 = 4^3 - 3= 61 NO!

So the correct answer is C. We don't need to check the other two options.
Re: If n is a positive integer and x + 3 = 4^n, which of the following cou   [#permalink] 12 Feb 2019, 01:55
Display posts from previous: Sort by

# If n is a positive integer and x + 3 = 4^n, which of the following cou

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne