GMAT Official Guide 2019 If x is a positive integer

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Fri Jun 29, 2018 10:04 pm

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If x is a positive integer and $$4^x$$-3=y, which of the following CANNOT be a value of y ?

A. 1

B. 7

C. 13

D. 61

E. 253

Source: Beat The GMAT — Problem Solving | Fri Jun 29, 2018 10:04 pm

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sat Jun 30, 2018 1:19 am

BTGmoderatorDC wrote:If x is a positive integer and $$4^x$$-3=y, which of the following CANNOT be a value of y ?

A. 1

B. 7

C. 13

D. 61

E. 253

Subtract 3 from increasing powers of 4:
4Â¹ - 3 = 1
4Â² - 3 = 13
The results above indicate that the following case is not possible:
$$4^x - 3 = 7$$

The correct answer is B.

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Mon Jul 30, 2018 10:30 am

BTGmoderatorDC wrote:If x is a positive integer and $$4^x$$-3=y, which of the following CANNOT be a value of y ?

A. 1

B. 7

C. 13

D. 61

E. 253

Since 4^1 - 3 = 1 and 4^2 - 3 = 13, we see that y can't be 7.

Answer: B

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Head of GMAT Instruction
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