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Math Expert V
Joined: 02 Sep 2009
Posts: 59587
If a and b are integers and ab − a is odd, which of the following must  [#permalink]

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4 00:00

Difficulty:   45% (medium)

Question Stats: 73% (01:37) correct 27% (01:34) wrong based on 180 sessions

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If a and b are integers and ab − a is odd, which of the following must be odd?

(A) b^2
(B) b
(C) a^2 + b
(D) ab
(E) ab + b

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Manager  B
Status: Preparing
Joined: 05 May 2016
Posts: 51
Location: India
Re: If a and b are integers and ab − a is odd, which of the following must  [#permalink]

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Bunuel wrote:
If a and b are integers and ab − a is odd, which of the following must be odd?

(A) b^2
(B) b
(C) a^2 + b
(D) ab
(E) ab + b

b has to even for ab-a to be odd.
Intern  B
Joined: 11 Oct 2016
Posts: 14
Location: Mexico
Schools: Jones '21 (A\$)
GMAT 1: 710 Q48 V40 GPA: 3
Re: If a and b are integers and ab − a is odd, which of the following must  [#permalink]

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2
If a and b are integers and ab − a is odd...

then a(b-1) is odd

then a and (b-1) are odds

then b= (b-1)+1 is even

so we have
i) a odd
ii) b even

which of the following must be odd?

(A) b^2 evenxeven=even NOT
(B) b even NOT
(C) a^2 + b = oddxpdd + even = odd + even = odd YES
(D) ab = oddxeven = even NOT
(E) ab + b oddxeven + even = even + even = even NOT
Senior Manager  S
Joined: 21 Mar 2016
Posts: 494
Re: If a and b are integers and ab − a is odd, which of the following must  [#permalink]

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there can be two scenarios,,
if a is odd, b is even,,,or vice versa...

hece C fits in,,,,ans C
Director  D
Joined: 13 Mar 2017
Posts: 730
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: If a and b are integers and ab − a is odd, which of the following must  [#permalink]

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1
1
Bunuel wrote:
If a and b are integers and ab − a is odd, which of the following must be odd?

(A) b^2
(B) b
(C) a^2 + b
(D) ab
(E) ab + b

a,b E Integer
ab-a is odd.

Now ab - a can be odd - even or even - odd for the total value to be odd.

Case 1 : a is odd
To make ab even, b must be even. so {a= odd, b = even}.

Case 2 : a is even
But in this case ab can't be odd. so this case is not possible.

So overall a = odd, b = even.

(A) b^2 = even
(B) b = even
(C) a^2 + b = odd
(D) ab = even
(E) ab + b = even

Senior Manager  G
Joined: 02 Mar 2017
Posts: 252
Location: India
Concentration: Finance, Marketing
Re: If a and b are integers and ab − a is odd, which of the following must  [#permalink]

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mohshu wrote:
there can be two scenarios,,
if a is odd, b is even,,,or vice versa...

hece C fits in,,,,ans C

Only one scenario is there right??

Given a and b are integers.

For ab − a to be odd
a--->odd
b--->even
square of an odd integer is odd ,adding an even number will give odd number
hence C

if b is odd and a is even then ab-a will be even.
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9850
Location: Pune, India
Re: If a and b are integers and ab − a is odd, which of the following must  [#permalink]

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1
VyshakhR1995 wrote:
mohshu wrote:
there can be two scenarios,,
if a is odd, b is even,,,or vice versa...

hece C fits in,,,,ans C

Only one scenario is there right??

Given a and b are integers.

For ab − a to be odd
a--->odd
b--->even
square of an odd integer is odd ,adding an even number will give odd number
hence C

if b is odd and a is even then ab-a will be even.

Yes, if ab - a is odd, one of ab and a must be odd and the other even.
If a is even, then ab must be even too. Hence a must be odd only. To make ab even, then b must be even.

There is only one scenario: a odd and b even
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Karishma
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Target Test Prep Representative G
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2809
Re: If a and b are integers and ab − a is odd, which of the following must  [#permalink]

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Bunuel wrote:
If a and b are integers and ab − a is odd, which of the following must be odd?

(A) b^2
(B) b
(C) a^2 + b
(D) ab
(E) ab + b

We can simplify the given expression:

a(b - 1) = odd

Since odd x odd = odd, we see that a has to be odd and b - 1 has to be odd, which means b must be even.

Since even + odd (or odd + even) = odd, we see that a^2 + b must be odd:

a^2 = odd^2 = odd number

b = even number

Thus, odd + even = odd.

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Manager  B
Joined: 16 Jan 2018
Posts: 58
Concentration: Finance, Technology
GMAT 1: 600 Q40 V33 Re: If a and b are integers and ab − a is odd, which of the following must  [#permalink]

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If a and b are integers and ab − a is odd, which of the following must be odd?

(A) b^2
(B) b
(C) a^2 + b
(D) ab
(E) ab + b

ab-a is O

O*O=O
O+/-E = O

so, either ab = even and a is odd. In that case b is even
or ab = odd and a is even. Not possible (if a is even ab has to be even)

only, C a^2+b is O+O = O
Manager  S
Joined: 20 Jul 2018
Posts: 87
GPA: 2.87
Re: If a and b are integers and ab − a is odd, which of the following must  [#permalink]

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As ab-a is odd
It means either ab is odd or a is odd. Both can’t be even or odd.
If a is odd and b is even then ab is even and whole expression will be odd.
If b is odd and a is even then ab will be even and whole expression will be even which is not true according to statement.

So a must be odd and b must be even.

A) B^2 even
B) b even
C) a^2 + b odd + even = odd
D) ab even
E) ab + b even

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Hasnain Afzal

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Re: If a and b are integers and ab − a is odd, which of the following must  [#permalink]

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_________________ Re: If a and b are integers and ab − a is odd, which of the following must   [#permalink] 30 Nov 2019, 08:31
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