Last visit was: 24 Apr 2026, 00:18 It is currently 24 Apr 2026, 00:18
Home
Messages
Tests
Schools
Events
Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
Sub 505 (Easy)|   Algebra|   Exponents|                     
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 23 Apr 2026
Posts: 109,802
Own Kudos:
810,906
 [56]
Given Kudos: 105,868
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,802
Kudos: 810,906
 [56]
If x is a positive integer and 4^x 3 = y, which of the following CAN 22 Jun 2018, 00:14
6
Kudos
Add Kudos
50
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

5% (low)

Question Stats:

96% (00:56) correct 4% (01:07) wrong based on 4278 sessions

History

Date
Time
Result
Not Attempted Yet
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


(PS04797)
ShowHide Answer
Official Answer
B
Need more similar questions? Run a 5 to 10 question quiz in GMAT Club Forum Quiz →
Most Helpful Reply
User avatar
EgmatQuantExpert
User avatar
e-GMAT Representative
Joined: 04 Jan 2015
Last visit: 02 Apr 2024
Posts: 3,657
Own Kudos:
20,872
 [49]
Given Kudos: 165
Expert
Expert reply
Posts: 3,657
Kudos: 20,872
 [49]
If x is a positive integer and 4^x 3 = y, which of the following CAN 22 Jun 2018, 03:31
33
Kudos
Add Kudos
16
Bookmarks
Bookmark this Post

Solution



Given:
    • x is a positive integer
    • \(4^x – 3 = y\)

To find:
    • From the given options, which one cannot be the value of y

Approach and Working:

Apart from checking with the options, there is one more way of figuring out the correct answer
From the given expression \(4^x – 3 = y\),
    • \(4^x = y + 3\)

Now, for any value of x, \(4^x\) will always end with either 4 of 6
    • Hence, y must be ending with either 1 or 3

From the given options, only option B is not ending with either 1 or 3

Hence, the correct answer is option B.

Answer: B
avatar
Mega1234
avatar
Joined: 03 Aug 2014
Last visit: 02 May 2019
Posts: 17
Own Kudos:
17
 [6]
Given Kudos: 31
Schools: Kellogg '21 (A)
Schools: Kellogg '21 (A)
Posts: 17
Kudos: 17
 [6]
If x is a positive integer and 4^x 3 = y, which of the following CAN 22 Jun 2018, 02:15
4
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
4x-3 = y => 4x = y+3

This implies that y+3 should be a multiple of 4. Quickly scanning the options reveal that for option B, 7+3 = 10 is not a multiple of 4.

Sent from my Pixel using GMAT Club Forum mobile app
General Discussion
avatar
Iakovos1995
avatar
Joined: 08 Jul 2017
Last visit: 01 Dec 2018
Posts: 13
Own Kudos:
36
 [1]
Given Kudos: 222
Location: Greece
GPA: 3.31
Posts: 13
Kudos: 36
 [1]
If x is a positive integer and 4^x 3 = y, which of the following CAN 22 Jun 2018, 00:26
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
If x=1: 4^1 - 3 = 1
If x=2: 4^2 - 3 = 13
If x=3: 4^3 - 3 = 61
If x=4: 4^4 - 3 = 253

The only value that y cannot take is 7.

The correct answer is B.
User avatar
LevanKhukhunashvili
User avatar
Joined: 13 Feb 2018
Last visit: 23 Jan 2021
Posts: 369
Own Kudos:
457
 [1]
Given Kudos: 50
GMAT 1: 640 Q48 V28
GMAT 1: 640 Q48 V28
Posts: 369
Kudos: 457
 [1]
If x is a positive integer and 4^x 3 = y, which of the following CAN 22 Jun 2018, 01:29
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
OG 2019? very interesting
Has "bb" already made an excel spreadsheet about it?
If yes, please give me the link
User avatar
KSBGC
User avatar
Joined: 31 Oct 2013
Last visit: 10 Mar 2022
Posts: 1,240
Own Kudos:
1,509
 [1]
Given Kudos: 635
Concentration: Accounting, Finance
GPA: 3.68
WE:Analyst (Accounting)
Posts: 1,240
Kudos: 1,509
 [1]
If x is a positive integer and 4^x 3 = y, which of the following CAN 22 Jun 2018, 02:16
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
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



NEW question from GMAT® Official Guide 2019


(PS04797)
Show more


Note:

x = positive integer

Given,

\(4^x\)-3=y

we are asked to find out which can't be the value of y. No specific value of x is given.

Trail and error is the way to get the correct answer. Assume the value of x = 1 , 2 , 3 , 4. All the option matches except B.

\(4^1\)-3=1
\(4^2\)-3=13
\(4^3\)-3=61
\(4^4\)-3=253

Thus , B is the correct answer.
User avatar
Abhishek009
User avatar
Board of Directors
Joined: 11 Jun 2011
Last visit: 17 Dec 2025
Posts: 5,903
Own Kudos:
5,452
 [1]
Given Kudos: 463
Status:QA & VA Forum Moderator
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Posts: 5,903
Kudos: 5,452
 [1]
If x is a positive integer and 4^x 3 = y, which of the following CAN 20 Aug 2019, 07:52
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel
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



NEW question from GMAT® Official Guide 2019


(PS04797)
Show more

(A) \(4^1 - 3 = 1\) ; Possible
(C) \(4^2 - 3 = 13\) ; Possible
(D) \(4^3 - 3 = 61\) ; Possible
(E) \(4^4 - 3 = 253\) ; Possible

Thus, Answer must be (B) 7
User avatar
Kinshook
User avatar
Major Poster
Joined: 03 Jun 2019
Last visit: 24 Apr 2026
Posts: 5,987
Own Kudos:
5,858
 [1]
Given Kudos: 163
Location: India
Schools: HBS '26 CBS '26 Wharton '26
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Products:
My Reviews
Schools: HBS '26 CBS '26 Wharton '26
GMAT 1: 690 Q50 V34
Posts: 5,987
Kudos: 5,858
 [1]
If x is a positive integer and 4^x 3 = y, which of the following CAN 15 Sep 2019, 03:08
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
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



NEW question from GMAT® Official Guide 2019


(PS04797)
Show more

Given: x is a positive integer and \(4^x – 3 = y\)

Asked: Which of the following CANNOT be a value of y ?

\(4^x – 3 = y\)

A. 1
4^x - 3 = 1
4^x = 4
x =1

B. 7
4^x - 3 = 7
4^x = 10
x is not an integer

C. 13
4^x - 3 = 13
4^x = 16
x = 2

D. 61
4^x = 61+3 = 64
x = 3

E. 253
4^x = 253+3 = 256
x = 4

IMO B
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 23 Apr 2026
Posts: 22,283
Own Kudos:
26,531
Given Kudos: 302
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 22,283
Kudos: 26,531
If x is a positive integer and 4^x 3 = y, which of the following CAN 08 Sep 2020, 10:27
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
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



NEW question from GMAT® Official Guide 2019


(PS04797)
Show more

Solution:

If x = 1, y = 4^1 - 3 = 1.

If x = 2, y = 4^2 - 3 = 13.

If x = 3, y = 4^3 - 3 = 61.

If x = 4, y = 4^4 - 3 = 253.

We see that y can’t be 7 if x is a positive integer.

Answer: B
avatar
clover1987
avatar
Joined: 06 Apr 2020
Last visit: 05 May 2022
Posts: 7
Own Kudos:
3
 [2]
Given Kudos: 7
Posts: 7
Kudos: 3
 [2]
If x is a positive integer and 4^x 3 = y, which of the following CAN 30 Oct 2020, 12:07
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
The simple method I used:

Q: 4^x - 3 = y

All units digit of power of 4's follow this pattern: 4, 6, 4, 6
(For example: 4^1 = 4 or 4^2 = 16 or 4^3 = 64)

Therefore the units digit of the answer can only be:
i) 4 - 3 = 1
ii) 6 - 3 = 3

Therefore, out of the answer choices ANS B ends with 7 and is the only that does not end with 1 or 3.

ANS B is correct
User avatar
GMATinsight
User avatar
Major Poster
Joined: 08 Jul 2010
Last visit: 24 Apr 2026
Posts: 6,976
Own Kudos:
16,909
 [1]
Given Kudos: 128
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Products:
My Reviews
Expert
Expert reply
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
Posts: 6,976
Kudos: 16,909
 [1]
If x is a positive integer and 4^x 3 = y, which of the following CAN 06 May 2021, 23:51
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
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



NEW question from GMAT® Official Guide 2019


(PS04797)
Show more


Answer: Option B

Video solution by GMATinsight

User avatar
avigutman
User avatar
Joined: 17 Jul 2019
Last visit: 30 Sep 2025
Posts: 1,285
Own Kudos:
1,908
Given Kudos: 66
Location: Canada
Schools: NYU Stern (WA)
GMAT 1: 780 Q51 V45
GMAT 2: 780 Q50 V47
GMAT 3: 770 Q50 V45
Expert
Expert reply
Schools: NYU Stern (WA)
GMAT 3: 770 Q50 V45
Posts: 1,285
Kudos: 1,908
If x is a positive integer and 4^x 3 = y, which of the following CAN 19 Sep 2022, 15:28
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Video solution from Quant Reasoning:
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1
User avatar
Rohanx9
User avatar
Joined: 15 Jul 2024
Last visit: 16 Apr 2026
Posts: 49
Own Kudos:
48
Given Kudos: 5
Location: Australia
Schools: Anderson (UCLA) (WD)
GPA: 6.188
Schools: Anderson (UCLA) (WD)
Posts: 49
Kudos: 48
If x is a positive integer and 4^x 3 = y, which of the following CAN 19 Jul 2025, 23:24
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Another way of figuring it out without calculating.
4^x - 4 should be a multiple of 4. Therefore any answer term minus -1 (as 4^x -3 - 1 = 4^x-4) should be a multiple of 4.

Only 7 is not, as 7-1 = 6. Not a multiple of 4.
User avatar
totaltestprepNick
User avatar
Joined: 25 Aug 2014
Last visit: 23 Apr 2026
Posts: 469
Own Kudos:
4
Given Kudos: 2
GMAT 1: 750 Q49 V42
GMAT 1: 750 Q49 V42
Posts: 469
Kudos: 4
If x is a positive integer and 4^x 3 = y, which of the following CAN 23 Feb 2026, 16:07
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
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


(PS04797)
Show more

Show Spoiler
B




Nick Slavkovich, GMAT/GRE tutor with 20+ years of experience

[email protected]
Moderators:
Bunuel
Math Expert
109802 posts
Krunaal
Tuck School Moderator
853 posts