It is currently 13 Dec 2017, 11:00

# Decision(s) Day!:

CHAT Rooms | Ross R1 | Kellogg R1 | Darden R1 | Tepper R1

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If a and b are integers, is b even?

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

### Hide Tags

Manager
Joined: 16 Apr 2010
Posts: 212

Kudos [?]: 147 [0], given: 12

If a and b are integers, is b even? [#permalink]

### Show Tags

16 Aug 2010, 05:57
4
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

62% (01:07) correct 38% (01:07) wrong based on 273 sessions

### HideShow timer Statistics

If a and b are integers, is b even?

(1) 3a + 4b is even
(2) 3a + 5b is even
[Reveal] Spoiler: OA

Kudos [?]: 147 [0], given: 12

Math Expert
Joined: 02 Sep 2009
Posts: 42583

Kudos [?]: 135518 [3], given: 12697

Re: Number Properties Problem [#permalink]

### Show Tags

16 Aug 2010, 06:05
3
KUDOS
Expert's post
3
This post was
BOOKMARKED
jakolik wrote:
If a and b are integers, is b even?
(1) 3a + 4b is even
(2) 3a + 5b is even

(1) 3a + 4b is even --> if $$a$$ is even, then it's not necessary for $$b$$ to be even, may be even or odd. Not sufficient.
(2) 3a + 5b is even --> if $$a$$ is even, then $$b$$ is even too, but if $$a$$ is odd, then $$b$$ is odd too. Not sufficient.

(1)+(2) Subtract (1) from (2) --> $$(3a+ 5b)-(3a + 4b)=even_2-even_1$$ --> $$b=even_2-even_1=even$$. Sufficient.

_________________

Kudos [?]: 135518 [3], given: 12697

Manager
Joined: 07 Oct 2006
Posts: 70

Kudos [?]: 9 [0], given: 3

Location: India
Re: Number Properties Problem [#permalink]

### Show Tags

16 Aug 2010, 06:07
IMO C.
Let me try to explain my approach for this one.
Addition of 2 numbers will be even when both of them are either even or odd.
Now lets check option 1.
3a + 4b is even. 3a can be either even or odd depending value of a. 4b will be even irrespective b being even or odd. Hence, 3a should be even if the sum has to be even. But, we cannot confirm whether b is odd or even with this statement.
Now lets check option 2.
3a + 5b is even. 3a can be either even or odd depending value of a. 5b can be either even or odd depending value of a. Hence, a and b can be either even or odd. This also not sufficient to conclude whether b is even or off.
Combing these 2 statements.
Both 3a + 4b and 3a + 5b are even.
Then as per first statement 3a should be even.
Then 4b and 5b should be even if the sum has to be even in both the cases.
Then b should be even. Hence, C is the answer.
Please let us know the OA and explanation if I am wrong or ambiguous.
_________________

-------------------------------------
Please give kudos, if my post is helpful.

For English Grammar tips, consider visiting http://www.grammar-quizzes.com/index.html.

Kudos [?]: 9 [0], given: 3

Intern
Joined: 24 Jun 2010
Posts: 41

Kudos [?]: 7 [0], given: 3

Location: Toronto
Schools: Berkeley Haas, UCLA Anderson, NYU Stern
Re: Number Properties Problem [#permalink]

### Show Tags

17 Aug 2010, 09:13
Statement 1: Not Sufficient
- A must be even
- B can be even or odd

Statement 2: Not sufficient
- Either A & B are both odd OR A & B are both even

Both: Sufficient
- A is even
- When A is even B is also even

Kudos [?]: 7 [0], given: 3

Current Student
Status: Three Down.
Joined: 09 Jun 2010
Posts: 1914

Kudos [?]: 2239 [1], given: 210

Concentration: General Management, Nonprofit
Re: If a & b are integers.... [#permalink]

### Show Tags

28 Oct 2010, 21:19
1
KUDOS
monirjewel wrote:
If a and b are integers, is b even?
(1) 3a + 4b is even
(2) 3a + 5b is even

If a sum is even, then both numbers are even or both numbers are odd.

Statement 1: 4b is even, and 3a + 4b is even, which means 3a is even and hence it tells us a is even. This is insufficient.

Statement 2: 3a + 5b is even, this means that either both a and b are even or both a and b are odd, since either way the sum will be even. But that is insufficient too.

Combining both statements, we know that a is even, which means for the second statement to be valid, b also has to be even.

Hence the answer is C.

Kudos [?]: 2239 [1], given: 210

Intern
Joined: 19 Jul 2010
Posts: 11

Kudos [?]: 2 [0], given: 3

Re: Number Properties Problem [#permalink]

### Show Tags

02 Jan 2013, 04:22
Bunuel wrote:
jakolik wrote:
If a and b are integers, is b even?
(1) 3a + 4b is even
(2) 3a + 5b is even

(1) 3a + 4b is even --> if $$a$$ is even, then it's not necessary for $$b$$ to be even, may be even or odd. Not sufficient.
(2) 3a + 5b is even --> if $$a$$ is even, then $$b$$ is even too, but if $$a$$ is odd, then $$b$$ is odd too. Not sufficient.

(1)+(2) Subtract (1) from (2) --> $$(3a+ 5b)-(3a + 4b)=even_2-even_1$$ --> $$b=even_2-even_1=even$$. Sufficient.

Hi Just a small doubt, can we consider b to be zero.
Is zero treated as an even integer.
Thx

Kudos [?]: 2 [0], given: 3

Math Expert
Joined: 02 Sep 2009
Posts: 42583

Kudos [?]: 135518 [0], given: 12697

Re: Number Properties Problem [#permalink]

### Show Tags

02 Jan 2013, 04:29
tarunjagtap wrote:
Bunuel wrote:
jakolik wrote:
If a and b are integers, is b even?
(1) 3a + 4b is even
(2) 3a + 5b is even

(1) 3a + 4b is even --> if $$a$$ is even, then it's not necessary for $$b$$ to be even, may be even or odd. Not sufficient.
(2) 3a + 5b is even --> if $$a$$ is even, then $$b$$ is even too, but if $$a$$ is odd, then $$b$$ is odd too. Not sufficient.

(1)+(2) Subtract (1) from (2) --> $$(3a+ 5b)-(3a + 4b)=even_2-even_1$$ --> $$b=even_2-even_1=even$$. Sufficient.

Hi Just a small doubt, can we consider b to be zero.
Is zero treated as an even integer.
Thx

Zero is an even integer. Zero is nether positive nor negative, but zero is definitely an even number.

An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even (in fact zero is divisible by every integer except zero itself).

For more check Number Theory chapter of Math Book: math-number-theory-88376.html

Hope it helps.
_________________

Kudos [?]: 135518 [0], given: 12697

Non-Human User
Joined: 09 Sep 2013
Posts: 14868

Kudos [?]: 287 [0], given: 0

Re: If a and b are integers, is b even? [#permalink]

### Show Tags

16 Dec 2014, 18:43
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 287 [0], given: 0

EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 10378

Kudos [?]: 3685 [0], given: 173

Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Re: If a and b are integers, is b even? [#permalink]

### Show Tags

24 Dec 2014, 09:32
Hi All,

This question can be solved by TESTing VALUES.

We're told that A and B are integers. We're asked if B is even. This is a YES/NO question.

Fact 1: 3A + 4B is even

IF...
A = 0
B = 0
The answer to the question is YES.

A = 0
B = 1
The answer to the question is NO.
Fact 1 is INSUFFICIENT

Fact 2: 3A + 5B is even

IF...
A = 0
B = 0
The answer to the question is YES.

A = 1
B = 1
The answer to the question is NO.

Combined, we know...
3A + 5B = Even
3A + 4B = Even

We can actually do algebra here and subtract one equation from another...

(3A + 5B) - (3A + 4B) = B
(Even) - (Even) = Even

B = Even, so the answer to the question is ALWAYS YES.

[Reveal] Spoiler:
C

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save \$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Kudos [?]: 3685 [0], given: 173

Non-Human User
Joined: 09 Sep 2013
Posts: 14868

Kudos [?]: 287 [0], given: 0

Re: If a and b are integers, is b even? [#permalink]

### Show Tags

23 Jun 2016, 00:50
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 287 [0], given: 0

Re: If a and b are integers, is b even?   [#permalink] 23 Jun 2016, 00:50
Display posts from previous: Sort by

# If a and b are integers, is b even?

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

 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®.