GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 Nov 2018, 03:43

### 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 November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
• ### All GMAT Club Tests are Free and open on November 22nd in celebration of Thanksgiving Day!

November 22, 2018

November 22, 2018

10:00 PM PST

11:00 PM PST

Mark your calendars - All GMAT Club Tests are free and open November 22nd to celebrate Thanksgiving Day! Access will be available from 0:01 AM to 11:59 PM, Pacific Time (USA)
• ### Free lesson on number properties

November 23, 2018

November 23, 2018

10:00 PM PST

11:00 PM PST

Practice the one most important Quant section - Integer properties, and rapidly improve your skills.

# If a^5+7a+2b+b^2 is even and a and b are integers, is

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Aug 2009
Posts: 7038
If a^5+7a+2b+b^2 is even and a and b are integers, is  [#permalink]

### Show Tags

08 Feb 2018, 18:28
00:00

Difficulty:

55% (hard)

Question Stats:

56% (01:55) correct 44% (02:40) wrong based on 57 sessions

### HideShow timer Statistics

If a^5 + 7a + 2b + b^2 is even and a and b are integers, is a even integer?

(1) a + 2b is even.
(2) a + b is even.

_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Senior Manager
Joined: 31 Jul 2017
Posts: 494
Location: Malaysia
GMAT 1: 700 Q50 V33
GPA: 3.95
WE: Consulting (Energy and Utilities)
Re: If a^5+7a+2b+b^2 is even and a and b are integers, is  [#permalink]

### Show Tags

08 Feb 2018, 18:56
chetan2u wrote:
If a^5+7a+2b+b^2 is even and a and b are integers, is a even integer?
(1) a+2b is even.
(2) a+b is even.

From Statement 1: We have $$a + 2b = Even,$$ 2b will be always even irrespective of b = odd/even. Hence, a = Even.
From Statement 2: We have $$a + b = Even.$$
I. a= Odd, b = Odd
$$a^5 + 7a + 2b + b^2 = Even$$---> b = Even(But as per our assumption b has to be Odd). So, this is ruled out.

II. a = Even, b = Even
$$a^5 + 7a + 2b + b^2 = Even$$
The only case possible is a = Even.

Hence, D.
_________________

If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!

DS Forum Moderator
Joined: 21 Aug 2013
Posts: 1371
Location: India
Re: If a^5+7a+2b+b^2 is even and a and b are integers, is  [#permalink]

### Show Tags

08 Feb 2018, 21:50
1
chetan2u wrote:
If a^5 + 7a + 2b + b^2 is even and a and b are integers, is a even integer?

(1) a + 2b is even.
(2) a + b is even.

In a^5 + 7a + 2b + b^2, since a & b are integers:
2b is always going to be even.
a^5 + 7a will also always be even (if a is odd, we get odd+odd = even; and if a is even, we get even+even = even)
Since a^5 + 7a + 2b is always even, for entire sum to be even, b^2 also must be even. This means b is even.
Thus we know that 'b' is even for sure, we need to establish whether 'a' is even or not.

Statement 1

a+2b is even, 2b is anyway even; so for this sum to be even, 'a' also must be even. Sufficient.

Statement 2

a+b is even. We have already established that 'b' is even, so for this sum to be even, 'a' also must be even. Sufficient.

Re: If a^5+7a+2b+b^2 is even and a and b are integers, is &nbs [#permalink] 08 Feb 2018, 21:50
Display posts from previous: Sort by