It is currently 22 Nov 2017, 17:28

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If the product of two integers is an even number and the sum of the

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42305

Kudos [?]: 133072 [0], given: 12403

If the product of two integers is an even number and the sum of the [#permalink]

Show Tags

New post 12 Oct 2017, 23:47
Expert's post
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

93% (00:42) correct 7% (01:05) wrong based on 46 sessions

HideShow timer Statistics

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.
[Reveal] Spoiler: OA

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 133072 [0], given: 12403

1 KUDOS received
Director
Director
avatar
P
Joined: 22 May 2016
Posts: 998

Kudos [?]: 347 [1], given: 594

If the product of two integers is an even number and the sum of the [#permalink]

Show Tags

New post 13 Oct 2017, 06:27
1
This post received
KUDOS
Bunuel wrote:
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.

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

Last edited by genxer123 on 13 Oct 2017, 07:51, edited 1 time in total.

Kudos [?]: 347 [1], given: 594

2 KUDOS received
Intern
Intern
avatar
B
Joined: 07 Aug 2011
Posts: 1

Kudos [?]: 2 [2], given: 4

CAT Tests
Re: If the product of two integers is an even number and the sum of the [#permalink]

Show Tags

New post 13 Oct 2017, 07:30
2
This post received
KUDOS
genxer123 wrote:
Bunuel wrote:
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?



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.

Kudos [?]: 2 [2], given: 4

2 KUDOS received
Director
Director
avatar
P
Joined: 22 May 2016
Posts: 998

Kudos [?]: 347 [2], given: 594

If the product of two integers is an even number and the sum of the [#permalink]

Show Tags

New post 13 Oct 2017, 07:37
2
This post received
KUDOS
jaissonespidey wrote:
genxer123 wrote:
Bunuel wrote:
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.

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.

Kudos [?]: 347 [2], given: 594

If the product of two integers is an even number and the sum of the   [#permalink] 13 Oct 2017, 07:37
Display posts from previous: Sort by

If the product of two integers is an even number and the sum of the

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.