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

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

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New post 10 May 2017, 12:08
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A
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C
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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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New post 10 May 2017, 12:36
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.
Answer is C
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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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New post 10 May 2017, 18:54
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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
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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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New post 11 May 2017, 04:59
there can be two scenarios,,
if a is odd, b is even,,,or vice versa...

hece C fits in,,,,ans C
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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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New post 11 May 2017, 05:19
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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


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

Answer C.

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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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New post 11 May 2017, 05:22
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.
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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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New post 11 May 2017, 09:08
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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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Re: If a and b are integers and ab − a is odd, which of the following must  [#permalink]

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New post 15 May 2017, 17:25
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.

Answer: C
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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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New post 17 Aug 2018, 18:24
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
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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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New post 17 Aug 2018, 18:39
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.

Now lets look at answers:
A) B^2 even
B) b even
C) a^2 + b odd + even = odd
D) ab even
E) ab + b even

So answer is (C)

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Re: If a and b are integers and ab − a is odd, which of the following must   [#permalink] 17 Aug 2018, 18:39
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