It is currently 26 Jun 2017, 10:35

### 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

# Events & Promotions

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

# If i and j are integers, is i + j an even integer?

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

### Hide Tags

Intern
Joined: 30 Apr 2008
Posts: 4
If i and j are integers, is i + j an even integer? [#permalink]

### Show Tags

19 Jan 2009, 01:15
00:00

Difficulty:

5% (low)

Question Stats:

87% (01:21) correct 13% (00:15) wrong based on 196 sessions

### HideShow timer Statistics

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

If i and j are integers, is i + j an even integer?

(1) i < 10
(2) i = j

Official Guide 12 Question

 Question: 12 Page: 273 Difficulty: 600

Find All Official Guide Questions

Video Explanations:
[Reveal] Spoiler: OA
SVP
Joined: 04 May 2006
Posts: 1892
Schools: CBS, Kellogg
Re: OG pg.279 D/S No.25 [#permalink]

### Show Tags

19 Jan 2009, 02:10
sirrock wrote:
If i and j are integers, is i+j an even integer?
(1) i < 10
(2) i = j

OA is B

but what if i = j = 0?

Is 0 an even integer?

OG says 0 is an even integer.
_________________
SVP
Joined: 07 Nov 2007
Posts: 1799
Location: New York
Re: OG pg.279 D/S No.25 [#permalink]

### Show Tags

19 Jan 2009, 04:18
sirrock wrote:
If i and j are integers, is i+j an even integer?
(1) i < 10
(2) i = j

OA is B

but what if i = j = 0?

Is 0 an even integer?

yes zero is even integer.
_________________

Your attitude determines your altitude
Smiling wins more friends than frowning

Manager
Joined: 27 May 2008
Posts: 199
Re: OG pg.279 D/S No.25 [#permalink]

### Show Tags

19 Jan 2009, 08:19
0 is even

0 + 1 = 1

(even) + (odd) = (odd)

0 + 2 = 2

(even) + (even) = (even)
Senior Manager
Joined: 30 Nov 2008
Posts: 489
Schools: Fuqua
Re: OG pg.279 D/S No.25 [#permalink]

### Show Tags

19 Jan 2009, 09:06
selvae wrote:
0 is even

0 + 1 = 1

(even) + (odd) = (odd)

0 + 2 = 2

(even) + (even) = (even)

But what is the confusion here.

Second stmt says that i = j. If i, j = 0, then i + j = 0 + 0 = 0 which is even.
Intern
Joined: 16 Jan 2009
Posts: 14
Re: OG pg.279 D/S No.25 [#permalink]

### Show Tags

19 Jan 2009, 09:56
If i and j are integers, is i+j an even integer?
(1) i < 10
(2) i = j

OA is B

but what if i = j = 0?

Is 0 an even integer?

i and j either both should be even to get a even sum or both should be odd to get a even sum.
stmnt 1 : i < 10 which has no information abt j ..so its insufficient.

stmnt 2: i = j which means either i = j = even or i = j = odd which gives a even sum

yes 0 is an even integer.

i = j = 0 also gives a even sum. so its sufficient.

answer is B.

www.graduatetutor.com
Manager
Joined: 04 Jan 2009
Posts: 238
Re: OG pg.279 D/S No.25 [#permalink]

### Show Tags

19 Jan 2009, 10:01
yes; sum of two odds or two evens is even. Hence, 2 is enough.

sirrock wrote:
If i and j are integers, is i+j an even integer?
(1) i < 10
(2) i = j

OA is B

but what if i = j = 0?

Is 0 an even integer?

_________________

-----------------------
tusharvk

Intern
Joined: 02 May 2012
Posts: 3
Re: If i and j are integers, is i + j an even integer? [#permalink]

### Show Tags

02 May 2012, 22:16
what if i and j are negative.
Its mentioned that i and j are integers but its not mentioned that i and j are positive integers.
what if i = j = -3 then i+j = -6 which is not even integer.
it should be 6 to be even integer ie i = j = 3
Please clarify where am i wrong
Math Expert
Joined: 02 Sep 2009
Posts: 39698
Re: If i and j are integers, is i + j an even integer? [#permalink]

### Show Tags

03 May 2012, 00:28
apoorvpan wrote:
what if i and j are negative.
Its mentioned that i and j are integers but its not mentioned that i and j are positive integers.
what if i = j = -3 then i+j = -6 which is not even integer.
it should be 6 to be even integer ie i = j = 3
Please clarify where am i wrong

Negative integers can also be even or dd, for example -6 is an even integer. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and since -6/2=-3=integer then -6 is an even integer.

If i and j are integers, is i + j an even integer?

(1) i < 10 --> no info about j. Not sufficient.
(2) i = j --> $$i+j=j+j=2j$$, as $$j$$ is an integer then $$2j$$ is an even number. Sufficient.

Answer: B.

As for zero:

The same way as above: 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).

Or in another way: an even number is an integer of the form $$n=2k$$, where $$k$$ is an integer. So for $$k=0$$ --> $$n=2*0=0$$.

Also note that if we were not told that $$i$$ and $$j$$ are integers then this statement would not be sufficient as in this case $$j$$ could be for example 1.5, so $$i+j=j+j=2j=3=odd$$ or $$j$$ could be for example 1.1, so $$i+j=j+j=2j=2.2\neq{integer}$$.

For more on Number Properties check: math-number-theory-88376.html

Hope it helps.
_________________
Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1069
Re: If i and j are integers, is i + j an even integer? [#permalink]

### Show Tags

30 Jul 2016, 08:34
sirrock wrote:
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

If i and j are integers, is i + j an even integer?

(1) i < 10
(2) i = j

We need to determine whether i + j is an even integer. Remember:

even + even = even

odd + odd = even

Thus, if we can determine that i and j are either both even or both odd, we will be able to answer the question.

Statement One Alone:

i < 10

Knowing that i is less than 10 is not enough to determine whether i + j is an even integer. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

i = j

Since we know i = j, we know that i and j are both even or both odd. Following our addition rules for even and odd numbers, we see that i + j must be even.

Statement two alone is sufficient to answer the question.

The answer is B.
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: If i and j are integers, is i + j an even integer?   [#permalink] 30 Jul 2016, 08:34
Similar topics Replies Last post
Similar
Topics:
If p and j are positive integers, is p + j even? 1 02 Dec 2016, 07:51
5 If i and j are integers, is i + j an even integer? 12 02 Apr 2017, 22:46
If i and j are integers, is i + j an even integer? 1 20 Jan 2012, 13:55
10 Are i, j, k consecutive integers? 5 29 Dec 2016, 01:46
1 If i and j are integers, is i + j an even integer? 2 16 Oct 2010, 08:33
Display posts from previous: Sort by

# If i and j are integers, is i + j an even integer?

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

 Powered by phpBB © phpBB Group and phpBB SEO 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®.