Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 59229

If a and b are integers, is a + b + 3 an odd integer?
[#permalink]
Show Tags
26 Jun 2017, 02:51
Question Stats:
75% (01:18) correct 25% (01:20) wrong based on 1154 sessions
HideShow timer Statistics
If a and b are integers, is a + b + 3 an odd integer? (1) ab is an odd integer. (2) a − b is an even integer.
Official Answer and Stats are available only to registered users. Register/ Login.
_________________




Director
Joined: 04 Dec 2015
Posts: 736
Location: India
Concentration: Technology, Strategy
Schools: HEC Sept19 intake, ISB '19, Rotman '21, NUS '21, IIMA , IIMB, NTU '20, Bocconi '21, XLRI, Trinity MBA '20, Smurfit "21
WE: Information Technology (Consulting)

If a and b are integers, is a + b + 3 an odd integer?
[#permalink]
Show Tags
26 Jun 2017, 03:20
Bunuel wrote: If a and b are integers, is a + b + 3 an odd integer?
(1) ab is an odd integer. (2) a − b is an even integer. (1) \(ab\) is an odd integer.
\(Odd * Odd = Odd\)
Therefore \(a\) and \(b\) should be Odd integers.
(\(Odd + Odd = Even\) ) and (\(Even + Odd = Odd\)) \(a + b = Even\)
\(a + b + 3 = Even + 3\) = Odd integer.
Hence I is Sufficient.
(2) \(a − b\) is an even integer.
\(Odd  Odd = Even\)
\(Even  Even = Even.\)
Therefore \(a\) and \(b\) could both either be Even or both be Odd.
If \(a\) and \(b\) are Odd. (\(Odd + Odd = Even\)) and (\(Even + Odd = Odd\))
\(a + b + 3 = Odd + Odd + 3 = Even + 3 = Odd\)  True.
If \(a\) and \(b\) are Even. (\(Even + Even = Even\)) and (\(Even + Odd = Odd\))
\(a + b + 3 = Even + Even + 3 = Even + 3 = Odd\)  True.
Hence II is Sufficient. Answer (D)...




Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3307
Location: India
GPA: 3.12

If a and b are integers, is a + b + 3 an odd integer?
[#permalink]
Show Tags
26 Jun 2017, 03:23
Given : a and b are integers We need to find out if a + b + 3 is an odd integer (1) ab is an odd integer. This is possible only when both a and b are odd. Hence sum of a and b will be even, making the sum(a + b + 3) an odd integer(Sufficient) (2) a − b is an even integer.This is possible when both a and b is even or odd. In either case, the sum of a and b is even. Thus, a+b+3 is odd (Sufficient) (Option D)
_________________
You've got what it takes, but it will take everything you've got



Retired Moderator
Joined: 19 Mar 2014
Posts: 917
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5

Re: If a and b are integers, is a + b + 3 an odd integer?
[#permalink]
Show Tags
26 Jun 2017, 03:32
If a and b are integers, is \(a + b + 3\) an odd integer? In order to find \(a + b + 3\) is ODD, we need to find. ODD + ODD + 3 = ODD
EVEN + EVEN + 3 = ODDWhich means, if we are able to confirm if a & b both are ODD or if a & b both are EVEN we should be able to answer the question. (1) ab is an odd integerab = ODD This means that a & b both are ODD As per above this information should be sufficient to prove \(a + b + 3\) is ODD as ODD + ODD + 3 = ODDHence, Eq. (1) =====> is SUFFICIENT(2) a − b is an even integera  b is EVEN This is only possible if a & b are both ODD a & b are both EVEN As this is sufficient to answer the question \(a + b + 3\) is ODDHence, Eq. (2) =====> is SUFFICIENTHence, Answer is D
_________________
"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent."
Best AWA Template: https://gmatclub.com/forum/howtoget60awamyguide64327.html#p470475



Retired Moderator
Joined: 22 Aug 2013
Posts: 1416
Location: India

Re: If a and b are integers, is a + b + 3 an odd integer?
[#permalink]
Show Tags
03 Jul 2017, 01:27
Given that a and b are both integers, so each of them must be either even or odd. a+b+3 will be odd when (a+b) is even.
Statement 1. product of a & b is odd, which is only possible when both a & b are odd. And if both a & b are odd, then (a+b) is even. So we know. Sufficient.
Statement 2. ab is even, this will happen either when both a & b are even, in which case (a+b) will also be even or when both a & b are odd, in which case too (a+b) will be even.
a+b is even in any case, so we know. Sufficient.
Each statement alone is sufficient. Hence D answer



Manager
Joined: 30 Apr 2016
Posts: 71
Location: India
GPA: 4

Re: If a and b are integers, is a + b + 3 an odd integer?
[#permalink]
Show Tags
03 Jul 2017, 23:49
Bunuel wrote: If a and b are integers, is a + b + 3 an odd integer?
(1) ab is an odd integer. (2) a − b is an even integer. for a+b+3 to be odd a+b should be even 1) if ab is an odd integer then a and b are individually odd, so a+b= odd+odd=Even : sufficient . 2)a b is an even integer, so a and b are both even or both odd. In either cases the sum a+b is even : sufficient.



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8453
Location: United States (CA)

Re: If a and b are integers, is a + b + 3 an odd integer?
[#permalink]
Show Tags
17 Nov 2017, 12:31
Bunuel wrote: If a and b are integers, is a + b + 3 an odd integer?
(1) ab is an odd integer. (2) a − b is an even integer. We need to determine whether a + b + 3 is odd, or in other words, whether a + b is even. Statement One Alone: ab is an odd integer. Because ab is odd, we know that a and b must both be odd, and since odd + odd = even, a + b is even. Statement one alone is sufficient to answer the question. Statement Two Alone: a  b is an even integer. Since a  b is even, a + b is also even. Statement two alone is sufficient. Answer: D
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button.



Intern
Joined: 10 Dec 2017
Posts: 2

Re: If a and b are integers, is a + b + 3 an odd integer?
[#permalink]
Show Tags
10 Jan 2018, 12:37
While I am clear on the even and odd concept ,for this question given that they are integers do we ignore about them being positive or negative integers?



Math Expert
Joined: 02 Sep 2009
Posts: 59229

Re: If a and b are integers, is a + b + 3 an odd integer?
[#permalink]
Show Tags
10 Jan 2018, 13:28
deeptijp wrote: While I am clear on the even and odd concept ,for this question given that they are integers do we ignore about them being positive or negative integers? a and b could be negative even/odd integers but this does not change the answer. Is it what you were asking?
_________________



Intern
Joined: 10 Dec 2017
Posts: 2

Re: If a and b are integers, is a + b + 3 an odd integer?
[#permalink]
Show Tags
10 Jan 2018, 14:32
Bunuel wrote: deeptijp wrote: While I am clear on the even and odd concept ,for this question given that they are integers do we ignore about them being positive or negative integers? a and b could be negative even/odd integers but this does not change the answer. Is it what you were asking? yes,as I was a bit doubtful when solving the question that when do we consider the signs as no one posted solution considering signs.



IIMA, IIMC School Moderator
Joined: 04 Sep 2016
Posts: 1371
Location: India
WE: Engineering (Other)

Re: If a and b are integers, is a + b + 3 an odd integer?
[#permalink]
Show Tags
23 Jan 2018, 18:56
amanvermagmat niks18Quote: Given that a and b are both integers, so each of them must be either even or odd. a+b+3 will be odd when (a+b) is even.
Statement 1. product of a & b is odd, which is only possible when both a & b are odd. And if both a & b are odd, then (a+b) is even. So we know. Sufficient.
Statement 2. ab is even, this will happen either when both a & b are even, in which case (a+b) will also be even or when both a & b are odd, in which case too (a+b) will be even.
a+b is even in any case, so we know. Sufficient.
Each statement alone is sufficient. Hence D answer I landed with same ans using identical approach of dissecting Q stem before moving to ans choices. I just took few additional secs for checking for St 2 by taking random nos. Did you carry above step mentally?
_________________
It's the journey that brings us happiness not the destination. Feeling stressed, you are not alone!!



Retired Moderator
Joined: 25 Feb 2013
Posts: 1162
Location: India
GPA: 3.82

Re: If a and b are integers, is a + b + 3 an odd integer?
[#permalink]
Show Tags
23 Jan 2018, 19:40
adkikani wrote: amanvermagmat niks18Quote: Given that a and b are both integers, so each of them must be either even or odd. a+b+3 will be odd when (a+b) is even.
Statement 1. product of a & b is odd, which is only possible when both a & b are odd. And if both a & b are odd, then (a+b) is even. So we know. Sufficient.
Statement 2. ab is even, this will happen either when both a & b are even, in which case (a+b) will also be even or when both a & b are odd, in which case too (a+b) will be even.
a+b is even in any case, so we know. Sufficient.
Each statement alone is sufficient. Hence D answer I landed with same ans using identical approach of dissecting Q stem before moving to ans choices. I just took few additional secs for checking for St 2 by taking random nos. Did you carry above step mentally? On adding or subtracting two integers, the nature of resulting value will not change I.e if on subtracting two integers the resulting value is Even then on adding the same numbers the resulting value will be Even. If you thought about this then the question is very simple and you might not need to test values. So if a=5 and b=3, then ab=2 and a+b=8 both are Even Similarly if both are Even then result will obviously be Even Posted from my mobile device



Retired Moderator
Joined: 22 Aug 2013
Posts: 1416
Location: India

If a and b are integers, is a + b + 3 an odd integer?
[#permalink]
Show Tags
23 Jan 2018, 22:38
adkikani wrote: amanvermagmat niks18Quote: Given that a and b are both integers, so each of them must be either even or odd. a+b+3 will be odd when (a+b) is even.
Statement 1. product of a & b is odd, which is only possible when both a & b are odd. And if both a & b are odd, then (a+b) is even. So we know. Sufficient.
Statement 2. ab is even, this will happen either when both a & b are even, in which case (a+b) will also be even or when both a & b are odd, in which case too (a+b) will be even.
a+b is even in any case, so we know. Sufficient.
Each statement alone is sufficient. Hence D answer I landed with same ans using identical approach of dissecting Q stem before moving to ans choices. I just took few additional secs for checking for St 2 by taking random nos. Did you carry above step mentally? Hi Yes, now I dont need to do any calculation mentally regarding even/odd in these kind of questions  because the basic rules regarding addition/subtraction/multiplication of even/odd are drilled in my head. I suggest that you too look at these rules again (from number theory) here (in case you think you need to improve on this): https://gmatclub.com/forum/mathnumber ... 88376.htmlAnd then practice with as many values as you can, till it becomes easy and natural to you. Good luck!



Senior Manager
Joined: 22 Feb 2018
Posts: 260
Location: India
Concentration: Entrepreneurship, Healthcare

If a and b are integers, is a + b + 3 an odd integer?
[#permalink]
Show Tags
17 Aug 2019, 19:52
Hi, Bunuel/scotttargettestprep/Veritaskarishma/chetan2u/Empowergmatrich Statement 1 indicates both are odd whereas statement 2 indicates both are even. Is it possible that a and b both are of different type of no. (odd and even) together to satisfy the single condition, I.e, a+b+3=odd. Kindly throw some lights. Regards, Raxit T. Bunuel wrote: deeptijp wrote: While I am clear on the even and odd concept ,for this question given that they are integers do we ignore about them being positive or negative integers? a and b could be negative even/odd integers but this does not change the answer. Is it what you were asking?
_________________
Thanks in the forum can be expressed by hitting Kudos!!!



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8453
Location: United States (CA)

Re: If a and b are integers, is a + b + 3 an odd integer?
[#permalink]
Show Tags
21 Aug 2019, 09:56
Raxit85 wrote: Hi, Bunuel/scotttargettestprep/Veritaskarishma/chetan2u/Empowergmatrich
Statement 1 indicates both are odd whereas statement 2 indicates both are even.
Is it possible that a and b both are of different type of no. (odd and even) together to satisfy the single condition, I.e, a+b+3=odd.
Kindly throw some lights.
In statement two both, a and b can also be odd since odd  odd = even
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button.



Intern
Joined: 22 Aug 2019
Posts: 1

Re: If a and b are integers, is a + b + 3 an odd integer?
[#permalink]
Show Tags
22 Aug 2019, 02:41
We need to determine whether a + b + 3 is odd or, in other words, whether a + b is even.
Statement One Alone:
ab is an odd integer.
Thus, a and b are both odd, and since odd + odd = even, a + b is even. Statement one alone is sufficient to answer the question.
Statement Two Alone:
a  b is an even integer.
Since a  b is even, a + b is also even. Statement two alone is sufficient.




Re: If a and b are integers, is a + b + 3 an odd integer?
[#permalink]
22 Aug 2019, 02:41






