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Senior SC Moderator V
Joined: 14 Nov 2016
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If a, b, and c are integers. Is abc+ab+c an odd? 1) ac=odd 2) ab=odd  [#permalink]

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1 00:00

Difficulty:   75% (hard)

Question Stats: 54% (01:58) correct 46% (02:12) wrong based on 157 sessions

### HideShow timer Statistics If a, b, and c are integers. Is abc+ab+c an odd?

1) ac=odd
2) ab=odd

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If a, b, and c are integers. Is abc+ab+c an odd? 1) ac=odd 2) ab=odd  [#permalink]

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D
1)ac is odd
2cases : b is even
Then even +even + odd -> odd
When b is odd then too the Sun is odd

2 ) ab is odd
cases when c is odd .
Then the entire Sun is odd
When c is even then too the sum is odd

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Manager  S
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Re: If a, b, and c are integers. Is abc+ab+c an odd? 1) ac=odd 2) ab=odd  [#permalink]

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If a, b, and c are integers. Is abc+ab+c an odd?

1) ac=odd
2) ab=odd

ac=odd
i.e a and c both are odd
case 1 : when b is odd
abc=odd*odd=odd
ab=odd*odd
c=odd
so sum will also be odd

case 2: when b is even
abc=even
ab=even
c=odd
so sum will be odd
so Statement 1 is sufficient

same concept can be applied to statement 2 as well
so
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Re: If a, b, and c are integers. Is abc+ab+c an odd? 1) ac=odd 2) ab=odd  [#permalink]

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St 1: ac is odd. that means a is odd and c is odd. no idea about b. INSUFFICIENT
St 2: ab is odd. that means a is odd and b is odd. no idea about c. INSUFFICIENT

St 1 & St 2: a,b,c is odd. therefore abc is odd, ab is odd and c is odd
therefore abc +ab +c = odd +odd +odd = odd. ANSWER

Option C
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If a, b, and c are integers. Is abc+ab+c an odd? 1) ac=odd 2) ab=odd  [#permalink]

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If a, b, and c are integers. Is abc+ab+c an odd?

1) ac=odd

It means that both a & c are odd

Let a=c=1

abc+ab+c=b+b+1=2b+1=Even+ Odd=Odd

Sufficient

2) ab=odd

It means that both a & b are odd

Let a=b=1

abc+ab+c=c+1+c=2c+1=Even+odd=odd

Sufficient

Senior SC Moderator V
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Posts: 1329
Location: Malaysia
Re: If a, b, and c are integers. Is abc+ab+c an odd? 1) ac=odd 2) ab=odd  [#permalink]

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2
ziyuen wrote:
If a, b, and c are integers. Is $$abc+ab+c$$ an odd?

1) $$ac=odd$$
2) $$ab=odd$$

OFFICIAL SOLUTION

If you modify the original condition and the question, from abc+ab+c=odd?, ab(c+1)+c=odd?, you get the same result as c=odd?. This is because if c=odd, you get c+1=even, then ab(c+1)+c=ab(even)+odd=even+odd=odd, hence yes.

In the case of con 1), if ac=odd, the condition is yes and sufficient.

In the case of con 2), by the law of “CMT 4(B: if you get A or B too easily, consider D)”, when ab=odd,

① If c=odd, you get ab(c+1)+c=odd(odd+1)+odd=odd(even)+odd=odd, hence yes.

② If c=even, you get ab(c+1)+c=odd(even+1)=odd(odd)+even=odd, hence, in the case of ① and case of ②, it is always yes and sufficient. Therefore, the answer is D.
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Re: If a, b, and c are integers. Is abc+ab+c an odd? 1) ac=odd 2) ab=odd  [#permalink]

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If a, b, and c are integers. Is abc+ab+c an odd?

1) ac=odd
2) ab=odd

1... odd*b + odd*b + odd ( as odd * odd = odd so a and c will e odds)
if b is odd then odd + odd + odd = odd and if b is even then, even + even + odd = odd sufficient
2... odd *c +odd + c
if c is odd then, odd + odd + odd = odd and if c is even then, even + odd + even = odd sufficient
hence, d
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Re: If a, b, and c are integers. Is abc+ab+c an odd? 1) ac=odd 2) ab=odd  [#permalink]

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_________________ Re: If a, b, and c are integers. Is abc+ab+c an odd? 1) ac=odd 2) ab=odd   [#permalink] 12 Jul 2018, 05:25
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