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If a and b are integers, is a + b = 12?

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Joined: 02 Aug 2009
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If a and b are integers, is a + b = 12?  [#permalink]

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18 Oct 2019, 00:52
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75% (hard)

Question Stats:

43% (01:44) correct 57% (01:22) wrong based on 53 sessions

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If a and b are integers, is a + b = 12?

(1) $$a-b=7$$
(2) $$\frac{a}{b}=8$$

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Re: If a and b are integers, is a + b = 12?  [#permalink]

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Updated on: 20 Oct 2019, 22:49
1
chetan2u wrote:
If a and b are integers, is a + b = 12?

(1) $$a-b=7$$
(2) $$\frac{a}{b}=8$$

New question!!...

Asked: If a and b are integers, is a + b = 12?

(1) $$a-b=7$$
a - b = 7; (a,b) = {(even, odd),(odd,even)}
a + b = even + odd = odd
12 = even
a + b $$\neq$$ 12
SUFFICIENT

(2) $$\frac{a}{b}=8$$
a = 8b
a+b = 9b;
9b $$\neq$$ 12; since b is an integer
SUFFICIENT

IMO D
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Originally posted by Kinshook on 18 Oct 2019, 00:56.
Last edited by Kinshook on 20 Oct 2019, 22:49, edited 1 time in total.
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Re: If a and b are integers, is a + b = 12?  [#permalink]

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20 Oct 2019, 09:15
1
chetan2u wrote:
If a and b are integers, is a + b = 12?

(1) $$a-b=7$$
(2) $$\frac{a}{b}=8$$

New question!!...

(1) $$a-b=7$$
Let $$a + b = 12$$ and $$a-b = 7$$ on solving we see that $$a$$ and $$b$$ are not integers, So it is not possible that $$a-b =7$$ and $$a+b= 12$$ both be true and $$a$$and $$b$$ be integers. SUFF

(2) $$\frac{a}{b}=8$$
So question becomes is $$8b +b = 12$$ or is $$9b= 12$$ ? we know that $$b$$ is an integer hence $$9b$$ can never be equal to $$12$$, SUFF

Ans - D
chetan2u, please can you show how statement 2 is NOT SUFF. IMO ans should be D.
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Re: If a and b are integers, is a + b = 12?  [#permalink]

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20 Oct 2019, 09:45
stne wrote:
chetan2u wrote:
If a and b are integers, is a + b = 12?

(1) $$a-b=7$$
(2) $$\frac{a}{b}=8$$

New question!!...

(1) $$a-b=7$$
Let $$a + b = 12$$ and $$a-b = 7$$ on solving we see that $$a$$ and $$b$$ are not integers, So it is not possible that $$a-b =7$$ and $$a+b= 12$$ both be true and $$a$$and $$b$$ be integers. SUFF

(2) $$\frac{a}{b}=8$$
So question becomes is $$8b +b = 12$$ or is $$9b= 12$$ ? we know that $$b$$ is an integer hence $$9b$$ can never be equal to $$12$$, SUFF

Ans - D
chetan2u, please can you show how statement 2 is NOT SUFF. IMO ans should be D.

Yes, it is D.
Edited. Kudos for the solution.
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Posts: 8187
Re: If a and b are integers, is a + b = 12?  [#permalink]

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20 Oct 2019, 22:39
chetan2u wrote:
If a and b are integers, is a + b = 12?

(1) $$a-b=7$$
(2) $$\frac{a}{b}=8$$

New question!!...

Now a and b are integers, so a+b will be EVEN only when either BOTH rare even or BOTH are odd..

(1) $$a-b=7$$
a-b will be ODD only when one is odd and the other is even, so a+b will also be ODD and hence $$a+b\neq{12}$$

(2) $$\frac{a}{b}=8$$
a=8b... so a+b=8b+b=9b, and $$9b\neq{12}$$, as b is an integer

D
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Re: If a and b are integers, is a + b = 12?   [#permalink] 20 Oct 2019, 22:39
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