It is currently 23 Jun 2017, 15:18

### 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? (1) 3a + 4b is even. (2)

Author Message
Manager
Joined: 10 Dec 2005
Posts: 95
If a and b are integers, is b even? (1) 3a + 4b is even. (2) [#permalink]

### Show Tags

24 Dec 2005, 22:43
00:00

Difficulty:

(N/A)

Question Stats:

67% (00:00) correct 33% (00:06) wrong based on 27 sessions

### HideShow timer Statistics

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

If a and b are integers, is b even?
(1) 3a + 4b is even.
(2) 3a + 5b is even.

I got the answer, but it took some time working out! Wanted to check any shorter methods!
_________________

JAI HIND!

VP
Joined: 06 Jun 2004
Posts: 1053
Location: CA

### Show Tags

24 Dec 2005, 23:51
1
This post was
BOOKMARKED
JAI HIND wrote:
If a and b are integers, is b even?
(1) 3a + 4b is even.
(2) 3a + 5b is even.

I got the answer, but it took some time working out! Wanted to check any shorter methods!

For a sum of two numbers to be even..two numbers can either

EVEN + EVEN
ODD + ODD

(1) 3a + 4b is even ==> 4b cannot be odd so it must be the even + even combination. B could be odd or even ==> Insufficient

(2) 3a + 5b is even ==> Could be EVEn + EVEN, ODD + ODD combo. Insufficient

(1) + (2) ==> From (1), we know that 3a must be even...so in (2) 5b must be even as well ==> b = even
_________________

Don't be afraid to take a flying leap of faith.. If you risk nothing, than you gain nothing...

CEO
Joined: 20 Nov 2005
Posts: 2894
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008

### Show Tags

25 Dec 2005, 01:14
TeHCM wrote:
JAI HIND wrote:
If a and b are integers, is b even?
(1) 3a + 4b is even.
(2) 3a + 5b is even.

I got the answer, but it took some time working out! Wanted to check any shorter methods!

For a sum of two numbers to be even..two numbers can either

EVEN + EVEN
ODD + ODD

(1) 3a + 4b is even ==> 4b cannot be odd so it must be the even + even combination. B could be odd or even ==> Insufficient

(2) 3a + 5b is even ==> Could be EVEn + EVEN, ODD + ODD combo. Insufficient

(1) + (2) ==> From (1), we know that 3a must be even...so in (2) 5b must be even as well ==> b = even

I got C. I did the same way as done by TeHCM
_________________

SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

Senior Manager
Joined: 15 Apr 2005
Posts: 415
Location: India, Chennai

### Show Tags

25 Dec 2005, 23:50
JAI HIND wrote:
If a and b are integers, is b even?
(1) 3a + 4b is even.
(2) 3a + 5b is even.

I got the answer, but it took some time working out! Wanted to check any shorter methods!

From 1 we get 3a+4b = 0 mod 2
From 2 we get 3a+5b = 0 mod 2

Subtracting 2 from 1 we get b = 0 mod 2 hence C.
Re: DS: Even integer   [#permalink] 25 Dec 2005, 23:50
Display posts from previous: Sort by