Last visit was: 23 Apr 2026, 18:39 It is currently 23 Apr 2026, 18:39
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
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 23 Apr 2026
Posts: 109,785
Own Kudos:
810,873
 [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: 109,785
Kudos: 810,873
 [1]
If the product of two integers is an even number and the sum of the 12 Oct 2017, 23:47
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
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:

93% (00:44) correct 7% (01:05) wrong based on 153 sessions

History

Date
Time
Result
Not Attempted Yet
If the product of two integers is an even number and the sum of the same two integers is an odd number, which of the following must be true?

A. The two integers are both odd.
B. The two integers are both even.
C. One of the two integers is odd and the other is even.
D. One of the integers is 1.
E. The two integers are consecutive.
ShowHide Answer
Official Answer
C
User avatar
generis
User avatar
Senior SC Moderator
Joined: 22 May 2016
Last visit: 18 Jun 2022
Posts: 5,258
Own Kudos:
37,727
 [1]
Given Kudos: 9,464
Expert
Expert reply
Posts: 5,258
Kudos: 37,727
 [1]
If the product of two integers is an even number and the sum of the Updated on: 13 Oct 2017, 07:51
Originally posted by generis on 13 Oct 2017, 06:27.
Last edited by generis on 13 Oct 2017, 07:51, edited 1 time in total.
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
If the product of two integers is an even number and the sum of the same two integers is an odd number, which of the following must be true?

A. The two integers are both odd.
B. The two integers are both even.
C. One of the two integers is odd and the other is even.
D. One of the integers is 1.
E. The two integers are consecutive.
Show more
Options for two integers whose product is even:
E / E (2 * 2 = 4)
O / E (3 * 2 = 6)
E / O (4 * 5 = 20)

Options for two integers whose sum is odd:
E / O (2 + 1 = 3)
O / E (7 + 4 = 11)

The second case limits the first. For sum to be odd, E + E is not possible. (2 + 2 = 4). When you (must) remove E + E, you are left with two integers. One is odd. The other is even.

So, one of the two integers must be even, and the other integer must be odd.

That is Answer C.

a = 3, b = 4
Even product? Yes. (3*4) = 12
Odd sum? Yes. 3+4 = 7. CORRECT

You can disprove the others.

A. The two integers are both odd.
a = 3, b = 5
Even product? No. 3*5 = 15
Odd sum? No. 3 + 5 = 8
REJECT

B. The two integers are both even.
a = 2, b = 4
Even product? Yes. 2*4 = 8
Odd sum? No. 2 + 4 = 6
REJECT

D. One of the integers is 1. The other can be odd.
From above Answer A, if both are odd, incorrect.

True, if a = 1 and b = 2, the conditions are satisfied. But if the other number is odd, conditions are not satisfied. One contrary example means the answer does not HAVE to be true. REJECT

E. The two integers are consecutive.
IF the two integers are consecutive, then they are odd and even, or vice versa, and they satisfy the prompt's conditions.

But the prompt just says "two integers." Those two integers need only be odd and even, not necessarily consecutive. They could be 1 and 200.

Answer C

Edited to correct a mistaken assumption, with help from @jaissonespidey
avatar
jaissonespidey
avatar
Joined: 07 Aug 2011
Last visit: 09 Nov 2017
Posts: 1
Own Kudos:
2
 [2]
Given Kudos: 4
Posts: 1
Kudos: 2
 [2]
If the product of two integers is an even number and the sum of the 13 Oct 2017, 07:30
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
genxer123
Bunuel
If the product of two integers is an even number and the sum of the same two integers is an odd number, which of the following must be true?

A. The two integers are both odd.
B. The two integers are both even.
C. One of the two integers is odd and the other is even.
D. One of the integers is 1.
E. The two integers are consecutive.
Hmm. I get C AND E. I cannot figure out why they are not functionally equivalent.

Options for two integers whose product is even:
E / E (2 * 2 = 4)
O / E (3 * 2 = 6)
E / O (4 * 5 = 20)

For the sum of two integers to be odd, options are
E / O (2 + 1 = 3)
O / E (7 + 4 = 11)

The second case limits the first. For sum to be odd, E + E is not possible. (2 + 2 = 4). When you (must) remove E + E, you are left with two integers. One is odd. The other is even.

So, one of the two integers must be even, and the other integer must be odd. That is Answer C.

But by definition, consecutive integers are odd and even, or vice versa. That is Answer E

You can disprove the others.

A, B, and D are incorrect
A. The two integers are both odd.
a = 3, b = 5
Even product? No. 3*5 = 15
Odd sum? No. 3 + 5 = 8
REJECT

B. The two integers are both even.
a = 2, b = 4
Even product? Yes. 2*4 = 8
Odd sum? No. 2 + 4 = 6
REJECT

D. One of the integers is 1. The other can be odd.
From above Answer A, if both are odd, incorrect.

True, if a = 1 and b = 2, the conditions are satisfied. But if the other number is odd, conditions are not satisfied. One contrary example means the answer does not HAVE to be true. REJECT

C and E?
As far as I can tell, C and E are both true. (By definition, if integers are consecutive, one is even and one is odd. That seems to me to be the same as answer C.)

C. One of the two integers is odd and the other is even.
See analysis of E, below

E. The two integers are consecutive.
If a = 1 and b = 2
Even product? Yes. 1 * 2 = 2
Odd sum? Yes. 1 + 2 = 3

Try a = -1, b = 0
Even product? Yes. 0 * -1 = 0
Odd sum? Yes. 0 + (-1) = -1

Am I missing something?
Bunuel , are the answer choices correct?
Show more


The prompt asks which answer MUST BE TRUE. While consecutive integers will result in the stated conditions, the integers don't HAVE to be consecutive in order to obtain that result. Any odd/even combination will suffice.
User avatar
generis
User avatar
Senior SC Moderator
Joined: 22 May 2016
Last visit: 18 Jun 2022
Posts: 5,258
Own Kudos:
37,727
 [2]
Given Kudos: 9,464
Expert
Expert reply
Posts: 5,258
Kudos: 37,727
 [2]
If the product of two integers is an even number and the sum of the 13 Oct 2017, 07:37
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
jaissonespidey
genxer123
Bunuel
If the product of two integers is an even number and the sum of the same two integers is an odd number, which of the following must be true?

A. The two integers are both odd.
B. The two integers are both even.
C. One of the two integers is odd and the other is even.
D. One of the integers is 1.
E. The two integers are consecutive.
Hmm. I get C AND E. I cannot figure out why they are not functionally equivalent.

Am I missing something?
The prompt asks which answer MUST BE TRUE. While consecutive integers will result in the stated conditions, the integers don't HAVE to be consecutive in order to obtain that result. Any odd/even combination will suffice.
Show more
jaissonespidey : Got it. I assumed the wrong thing, exactly backwards. That is, I assumed the truth of the answer choice. I'll edit. Thanks! And kudos.
User avatar
JeffTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 04 Mar 2011
Last visit: 05 Jan 2024
Posts: 2,974
Own Kudos:
8,710
Given Kudos: 1,646
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Expert
Expert reply
Posts: 2,974
Kudos: 8,710
If the product of two integers is an even number and the sum of the 27 Nov 2017, 19:11
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
If the product of two integers is an even number and the sum of the same two integers is an odd number, which of the following must be true?

A. The two integers are both odd.
B. The two integers are both even.
C. One of the two integers is odd and the other is even.
D. One of the integers is 1.
E. The two integers are consecutive.
Show more

The only way for the product of two numbers to be even and the sum to be odd is if we have one even and one odd number.

Answer: C
Moderators:
Bunuel
Math Expert
109785 posts
Krunaal
Tuck School Moderator
853 posts