Last visit was: 23 Apr 2026, 06:56 It is currently 23 Apr 2026, 06:56
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
User avatar
nades09
User avatar
Joined: 18 Feb 2010
Last visit: 24 Feb 2014
Posts: 21
Own Kudos:
617
 [20]
Given Kudos: 5
Posts: 21
Kudos: 617
 [20]
If x and y are distinct prime numbers, each greater than 2, Updated on: 02 Sep 2025, 06:00
Originally posted by nades09 on 13 Nov 2010, 11:09.
Last edited by Bunuel on 02 Sep 2025, 06:00, edited 1 time in total.
3
Kudos
Add Kudos
17
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:

75% (hard)

Question Stats:

51% (01:53) correct 49% (01:57) wrong based on 448 sessions

History

Date
Time
Result
Not Attempted Yet
If x and y are distinct prime numbers, each greater than 2, which of the following must be true?

(I) x + y is divisible by 4
(II) x*y has even number of factors
(III) x + y has an even number of factors

A. I only
B. II only
C. I and III only
D. II and III only
E. I and II only

Show Spoiler

I plugged in numbers for each option, but it took me more than 2 mins to get to the right answer -OA is B.

I had to consider x=13 and y=23 for ruling out (III), since x+y in this case =36 which has odd no. of factors.

PLease explain if there is any other method for solving this under 2 mins

Thanks
NAD
ShowHide Answer
Official Answer
B
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 23 Apr 2026
Posts: 109,778
Own Kudos:
810,779
 [5]
Given Kudos: 105,853
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: 109,778
Kudos: 810,779
 [5]
If x and y are distinct prime numbers, each greater than 2, 13 Nov 2010, 11:48
2
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
nades09
Source: 4Gmat
Q. If x and y are distinct prime numbers, each greater than 2, which of the following must be true?

(I) x+y is divisible by 4
(II)x * y has even number of factors
(III)x+y has an even number of factors

A. I only
B. II only
C. I and III only
D. II and III only
E. I and II only

I plugged in numbers for each option, but it took me more than 2 mins to get to the right answer -OA is B.

I had to consider x=13 and y=23 for ruling out (III), since x+y in this case =36 which has odd no. of factors.

PLease explain if there is any other method for solving this under 2 mins

Thanks
NAD
Show more

First of all we are asked "which of the following MUST be true" not COULD be true.

"MUST BE TRUE" questions:
These questions ask which of the following MUST be true, or which of the following is ALWAYS true no matter what set of numbers you choose. Generally for such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.

As for "COULD BE TRUE" questions:
The questions asking which of the following COULD be true are different: if you can prove that a statement is true for one particular set of numbers, it will mean that this statement could be true and hence is a correct answer.

I. x+y is divisible by 4 --> if \(x=3\) and \(y=7\) then \(x+y=10\), which is not divisible by 4. So this statement is not always true;

II. xy has even number of factors --> only perfect squares have an odd number of factors (check this: a-perfect-square-79108.html?hilit=perfect%20square%20reverse#p791479), as \(x\) and \(y\) are distinct prime numbers then \(xy\) cannot be a perfect square and thus cannot have an odd number of factors, so \(xy\) must have an even number of factors. This statement is always true;

III. x+y has an even number of factors --> now, \(x+y\) can be a perfect square, for example if \(x=3\) and \(y=13\) then \(x+y=16=perfect \ square\), so \(x+y\) can have an odd number of factors. So this statement is not always true;

Answer: B (II only).

Hope it's clear.
General Discussion
User avatar
nades09
User avatar
Joined: 18 Feb 2010
Last visit: 24 Feb 2014
Posts: 21
Own Kudos:
617
Given Kudos: 5
Posts: 21
Kudos: 617
If x and y are distinct prime numbers, each greater than 2, 13 Nov 2010, 12:51
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Yes, Thank you very much. You rock!
User avatar
medanova
User avatar
Joined: 19 Aug 2010
Last visit: 15 Feb 2012
Posts: 51
Own Kudos:
112
Given Kudos: 2
Posts: 51
Kudos: 112
If x and y are distinct prime numbers, each greater than 2, 13 Nov 2010, 13:10
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel,

Does that mean that me never count 1 as a factor?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 23 Apr 2026
Posts: 109,778
Own Kudos:
810,779
 [1]
Given Kudos: 105,853
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: 109,778
Kudos: 810,779
 [1]
If x and y are distinct prime numbers, each greater than 2, 13 Nov 2010, 13:17
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
medanova
Bunuel,

Does that mean that me never count 1 as a factor?
Show more

No. 1 is a factor of every positive integer. Also 1 is a perfect square (1=1^2) and it has 1 (so odd) factor - itself.
User avatar
EMPOWERgmatRichC
User avatar
Major Poster
Joined: 19 Dec 2014
Last visit: 31 Dec 2023
Posts: 21,777
Own Kudos:
13,047
 [1]
Given Kudos: 450
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Expert
Expert reply
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Posts: 21,777
Kudos: 13,047
 [1]
If x and y are distinct prime numbers, each greater than 2, 29 Jan 2015, 13:38
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi All,

Roman Numeral questions on the GMAT often come with a "design shortcut", meaning that you probably WON'T have to think about all 3 Roman Numerals (IF you pay attention to how the answer choices are designed).

Here, we're told that X and Y are DISTINCT (meaning "different") PRIME numbers that are each greater than 2. We're asked which of the following Roman Numerals MUST be true (which really means "which of these is ALWAYS TRUE no matter how many different examples you can come up with). It's often easier to try to prove that something is NOT true, so that should be our goal here - try to come up with a way to disprove a Roman Numeral so that we can ELIMINATE it.

TESTing VALUES will work perfectly here.

I. (X+Y) is divisible by 4

3+5 = 8 which is divisible by 4
3+7 = 10 which is NOT divisible by 4
Roman Numeral 1 is NOT always true, so we can ELIMINATE IT.

**NOTE: Look at the answers. Since Roman Numeral 1 has been eliminated, we can....
1) Eliminate answers A, C and E.
2) Notice that the two remaining answers both have Roman Numeral II in them, so that Roman Numeral MUST be TRUE. As such, we don't even have to deal with it!!!!!

III. (X+Y) has an even number of factors

3+5 = 8 which has 4 factors
3+7 = 10 which has 4 factors
3+11 = 14 which has 4 factors
3+13 = 16 which has 5 factors
Roman Numeral 3 is NOT always true, so we can ELIMINATE IT.
Eliminate Answer D.

Final Answer:
Show Spoiler
B

GMAT assassins aren't born, they're made,
Rich
User avatar
stonecold
User avatar
Joined: 12 Aug 2015
Last visit: 09 Apr 2024
Posts: 2,231
Own Kudos:
3,643
Given Kudos: 893
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Posts: 2,231
Kudos: 3,643
If x and y are distinct prime numbers, each greater than 2, 14 Mar 2016, 05:42
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
nades09
Source: 4Gmat
Q. If x and y are distinct prime numbers, each greater than 2, which of the following must be true?

(I) x+y is divisible by 4
(II)x * y has even number of factors
(III)x+y has an even number of factors

A. I only
B. II only
C. I and III only
D. II and III only
E. I and II only

I plugged in numbers for each option, but it took me more than 2 mins to get to the right answer -OA is B.

I had to consider x=13 and y=23 for ruling out (III), since x+y in this case =36 which has odd no. of factors.

PLease explain if there is any other method for solving this under 2 mins

Thanks
NAD

First of all we are asked "which of the following MUST be true" not COULD be true.

"MUST BE TRUE" questions:
These questions ask which of the following MUST be true, or which of the following is ALWAYS true no matter what set of numbers you choose. Generally for such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.

As for "COULD BE TRUE" questions:
The questions asking which of the following COULD be true are different: if you can prove that a statement is true for one particular set of numbers, it will mean that this statement could be true and hence is a correct answer.

I. x+y is divisible by 4 --> if \(x=3\) and \(y=7\) then \(x+y=10\), which is not divisible by 4. So this statement is not always true;

II. xy has even number of factors --> only perfect squares have an odd number of factors (check this: a-perfect-square-79108.html?hilit=perfect%20square%20reverse#p791479), as \(x\) and \(y\) are distinct prime numbers then \(xy\) cannot be a perfect square and thus cannot have an odd number of factors, so \(xy\) must have an even number of factors. This statement is always true;

III. x+y has an even number of factors --> now, \(x+y\) can be a perfect square, for example if \(x=3\) and \(y=13\) then \(x+y=16=perfect \ square\), so \(x+y\) can have an odd number of factors. So this statement is not always true;

Answer: B (II only).

Hope it's clear.
Show more

Are there any other primes so that there sum yields a perfect square ?
what about x-y being a perfect square ?
is it possible too?
just curious as i got this question wrong ..
Did not think of 13 and 3
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 23 Apr 2026
Posts: 109,778
Own Kudos:
810,779
 [1]
Given Kudos: 105,853
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: 109,778
Kudos: 810,779
 [1]
If x and y are distinct prime numbers, each greater than 2, 14 Mar 2016, 07:06
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Chiragjordan
Bunuel
nades09
Source: 4Gmat
Q. If x and y are distinct prime numbers, each greater than 2, which of the following must be true?

(I) x+y is divisible by 4
(II)x * y has even number of factors
(III)x+y has an even number of factors

A. I only
B. II only
C. I and III only
D. II and III only
E. I and II only

I plugged in numbers for each option, but it took me more than 2 mins to get to the right answer -OA is B.

I had to consider x=13 and y=23 for ruling out (III), since x+y in this case =36 which has odd no. of factors.

PLease explain if there is any other method for solving this under 2 mins

Thanks
NAD

First of all we are asked "which of the following MUST be true" not COULD be true.

"MUST BE TRUE" questions:
These questions ask which of the following MUST be true, or which of the following is ALWAYS true no matter what set of numbers you choose. Generally for such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.

As for "COULD BE TRUE" questions:
The questions asking which of the following COULD be true are different: if you can prove that a statement is true for one particular set of numbers, it will mean that this statement could be true and hence is a correct answer.

I. x+y is divisible by 4 --> if \(x=3\) and \(y=7\) then \(x+y=10\), which is not divisible by 4. So this statement is not always true;

II. xy has even number of factors --> only perfect squares have an odd number of factors (check this: a-perfect-square-79108.html?hilit=perfect%20square%20reverse#p791479), as \(x\) and \(y\) are distinct prime numbers then \(xy\) cannot be a perfect square and thus cannot have an odd number of factors, so \(xy\) must have an even number of factors. This statement is always true;

III. x+y has an even number of factors --> now, \(x+y\) can be a perfect square, for example if \(x=3\) and \(y=13\) then \(x+y=16=perfect \ square\), so \(x+y\) can have an odd number of factors. So this statement is not always true;

Answer: B (II only).

Hope it's clear.

Are there any other primes so that there sum yields a perfect square ?
what about x-y being a perfect square ?
is it possible too?
just curious as i got this question wrong ..
Did not think of 13 and 3
Show more

2 + 7 = 9 = 3^2
3 + 13 = 16 = 4^2
2 + 23 = 25 = 5^2
5 + 31 = 36 = 6^2
2 + 47 = 49 = 7^2
3 + 61 = 64 = 8^2
...

3 - 2 = 1 = 1^2
7 - 3 = 4 = 2^2
11 - 2 = 9 = 3^2
19 - 3 = 16 = 4^2
...
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 22 Apr 2026
Posts: 22,281
Own Kudos:
26,529
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: 22,281
Kudos: 26,529
If x and y are distinct prime numbers, each greater than 2, 02 Nov 2017, 16:57
Kudos
Add Kudos
Bookmarks
Bookmark this Post
nades09
If x and y are distinct prime numbers, each greater than 2, which of the following must be true?

(I) x+y is divisible by 4
(II) x*y has even number of factors
(III) x+y has an even number of factors

A. I only
B. II only
C. I and III only
D. II and III only
E. I and II only
Show more

Since x and y are prime numbers greater than two, they are both odd prime numbers. Let’s analyze each answer choice:

I. x+y is divisible by 4

This is not true. If x = 11 and y = 7, then x + y = 18, which is not divisible by 4.

II. x*y has an even number of factors

The only numbers that have an odd number of factors are perfect squares. Since x and y are distinct primes, x*y can’t be a perfect square, and thus it must have an even number of factors. This statement is true.

III. x+y has an even number of factors

This is not true. If x = 3 and y = 13, then x + y = 16, which is a perfect square. Recall that in Roman numeral II, we’ve mentioned that a perfect square has an odd number of factors.

Answer: B
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,959
Own Kudos:
1,117
Posts: 38,959
Kudos: 1,117
If x and y are distinct prime numbers, each greater than 2, 13 Oct 2025, 07:48
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109778 posts
Krunaal
Tuck School Moderator
853 posts