Last visit was: 09 Jul 2025, 00:06 It is currently 09 Jul 2025, 00:06
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.
Close
Request Expert Reply
Confirm Cancel
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 9 July 2025
Posts: 102,597
Own Kudos:
739,645
 [2]
Given Kudos: 97,452
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,597
Kudos: 739,645
 [2]
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
User avatar
Skywalker18
User avatar
Retired Moderator
Joined: 08 Dec 2013
Last visit: 15 Nov 2023
Posts: 2,052
Own Kudos:
9,677
 [2]
Given Kudos: 171
Status:Greatness begins beyond your comfort zone
Location: India
Concentration: General Management, Strategy
GPA: 3.2
WE:Information Technology (Consulting)
Products:
Posts: 2,052
Kudos: 9,677
 [2]
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
User avatar
GMATinsight
User avatar
Major Poster
Joined: 08 Jul 2010
Last visit: 08 Jul 2025
Posts: 6,371
Own Kudos:
15,564
 [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:
Expert
Expert reply
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
Posts: 6,371
Kudos: 15,564
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
BrainLab
User avatar
Current Student
Joined: 10 Mar 2013
Last visit: 26 Jan 2025
Posts: 350
Own Kudos:
3,009
 [1]
Given Kudos: 200
Location: Germany
Concentration: Finance, Entrepreneurship
GMAT 1: 580 Q46 V24
GPA: 3.7
WE:Marketing (Telecommunications)
GMAT 1: 580 Q46 V24
Posts: 350
Kudos: 3,009
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
If y is an integer, is y^2 divisible by 4?

(1) y is even.
(2) y^3 is divisible by 4.


Kudos for a correct solution.


St1: y is even - Zero is also even so it could be 0 in this case 2,4 in any of those cases it's divisible by 4 SUFFICIENT
St2: y is an even integer in this case because if it were odd odd*odd*odd is odd and not divisible by 4 - SUFFICIEINT

Answer (D)
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 9 July 2025
Posts: 102,597
Own Kudos:
739,645
 [1]
Given Kudos: 97,452
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,597
Kudos: 739,645
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
If y is an integer, is y^2 divisible by 4?

(1) y is even.
(2) y^3 is divisible by 4.


Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

Question Type: Yes/No. This question asks: “Is y^2 divisible by 4.”

Given information in the question stem or diagram: y is an integer.

Statement 1: y is even. With a conceptual understanding of factors, you know that if y is an even number then y^2 will have to be a multiple of 4. If you want to quickly test this you can use some small even numbers. For example, if y = 2, then y^2=4; yes, that is divisible by 4. If y = 4, then y^2 = 16; this is also divisible by 4. Even 0, which is an even number, will work. 0^2 = 0; and yes, 0 is divisible by 4. This confirms what we already knew from our conceptual understanding: an even
number when squared is a multiple of 4. The answer is either A or D.

Statement 2: y^3 is divisible by 4. For some, this may not seem sufficient at first glance. y^3 might be divisible by 4 while y^2 is not. For example, y could be the cube root of 4. However, if you leverage properly the information in the question stem (always so important!) then you know that “y is an integer.” So y cannot be the cube root of 4; it must be an integer. Once you have established that y must be an integer then the only way for y^3 to be divisible by 4 is for y to be an even number. In other words, it gives you the same information that you already found sufficient in Statement 1. Thus, the correct answer is D.

Note: This is another good example of “When one statement is easy, the other is hard/counterintuitive.” The first statement is relatively simple so you should be extra careful analyzing the second statement. As is often the case, the key with Statement 2 is to make sure you properly leverage the given information.
User avatar
SaquibHGMATWhiz
User avatar
GMATWhiz Representative
Joined: 23 May 2022
Last visit: 12 Jun 2024
Posts: 623
Own Kudos:
Given Kudos: 6
Location: India
GMAT 1: 760 Q51 V40
Expert
Expert reply
GMAT 1: 760 Q51 V40
Posts: 623
Kudos: 653
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
If y is an integer, is y^2 divisible by 4?

(1) y is even.
(2) y^3 is divisible by 4.

Solution:
Pre Analysis:
  • y is an integer
  • We are asked if \(y^2\) is divisible by 4 or not

Statement 1: y is even
  • Since y is even, we can assume \(y=2k\) where k is a non-negative integer
  • So, \(y^2=(2k)^2=4k^2\)
  • This means \(y^2\) is a multiple of 4
  • Thus, statement 1 alone is sufficient and we can eliminate options B, C and E

Statement 2: \(y^3\) is divisible by 4
  • According to this statement, \(y^3=4k\) or \(y^3=2^2k\)
  • This means \(y^2\) at least has to be \(2^2\) or a multiple of 4
  • Thus, statement 2 alone is also sufficient

Hence the right answer is Option D
Moderator:
Math Expert
102597 posts