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# Is the product of a and b odd?

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Math Expert
Joined: 02 Sep 2009
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Is the product of a and b odd?  [#permalink]

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11 Nov 2014, 05:47
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Difficulty:

15% (low)

Question Stats:

80% (01:02) correct 20% (00:59) wrong based on 178 sessions

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Tough and Tricky questions: Number Properties.

Is the product of a and b odd?

(1) a has only 2 factors
(2) b = 2x + 1, where x is an integer

Kudos for a correct solution.

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Re: Is the product of a and b odd?  [#permalink]

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11 Nov 2014, 08:06
1
(1) a has only 2 factors => a is a prime number. It could be 2 (even) or 3 (odd). +No information about b.
Insufficient
(2) b = 2x + 1, where x is an integer => b=even+odd => b=odd. No information about a
Insufficient

Together: b is odd, and a can be either odd or even
(odd)(even)=even
(odd)(odd)=odd
Insufficient

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Re: Is the product of a and b odd?  [#permalink]

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11 Nov 2014, 10:59
1

Statement 1: not sufficient
A could be 2 (even) or other prime # (odd). We would need to know if B is even or odd to answer the question.

Statement 2: not sufficient
This tells us that B is odd since 2 times any number (even or odd) will be even. Add +1 to an even # and it will always be odd. We need to know if A is even or odd to answer the question.

Down to answer choices C and E.

When combined, we know that A is even or odd and that B is odd. If A is even, A*B would be even. If A is odd, A*B would be odd. Combined, the statements are not sufficient.

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Re: Is the product of a and b odd?  [#permalink]

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11 Nov 2014, 12:25
1
Bunuel wrote:

Tough and Tricky questions: Number Properties.

Is the product of a and b odd?

(1) a has only 2 factors
(2) b = 2x + 1, where x is an integer

Kudos for a correct solution.

The product will be odd if both a and b are odd
1. a has two factors so a is prime...now if a=2,b=odd number then product is not even but if a=any other prime and b=odd number than product is odd...clearly we dont have enough information.. Option A and D ruled out

b=2x+1 so possible values for b=1,3,5,7...b= odd number...B ruled out

Combining both statements we can still have product even or odd..

ans E
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Re: Is the product of a and b odd?  [#permalink]

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11 Nov 2014, 19:41
1
From 1, we can say a can be 2, 3, 5, 7 ... any prime number. Donot know the value of b. Therefore, insufficient

From 2, we can say b is odd. But we don't know a. Therefore, insufficient.

Combining a) and b), we can't say whether the product of a and b is odd or even, since it depends on the value of "a" which can either be even (value = 2) or odd (primes other than 2).

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Re: Is the product of a and b odd?  [#permalink]

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14 Oct 2016, 06:10
Here we need to prove that A*B is odd
Note => It is not specified whether they are integers or not.
Statement 1 => A = prime => No clue of B
A=2 B=3 => A*B=even
A=3 B=5 => A*b= odd
Not suff
Statement 2 => B must be odd
no clue of A
not suff
combining them we can say if A is 2 then AB is even else Ab will be odd
since no boundary condition on A is given => not suff

Hence E
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Is the product of a and b odd?  [#permalink]

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15 Oct 2016, 08:05
Bunuel wrote:

Tough and Tricky questions: Number Properties.

Is the product of a and b odd?

(1) a has only 2 factors
(2) b = 2x + 1, where x is an integer

Kudos for a correct solution.

FROM STATEMENT - I INSUFFICIENT

a can be both Odd / Even ; further we have no knowledge of b so, we can not find ab

FROM STATEMENT - II INSUFFICIENT

If x = odd , 2x + 1 will be even
If x = even , 2x + 1 will be odd

Since a consistent value of b can not be determined we can not find the value of ab...

Thus, Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed, answer will be (E)

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Re: Is the product of a and b odd?  [#permalink]

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17 Jul 2017, 17:17
Bunuel wrote:

Tough and Tricky questions: Number Properties.

Is the product of a and b odd?

(1) a has only 2 factors
(2) b = 2x + 1, where x is an integer

Kudos for a correct solution.

This question is just asking- is "a" an even number - simple even and odd properties

Statement 1

This just means "a" is prime; but 2 is an even prime number

Statement 2
This just mean B must be odd because any number multiplied by an even number is even and the sum of an even and odd number is odd. But even if this statement forces B to be odd, we still cannot say what A is.

E
Re: Is the product of a and b odd?   [#permalink] 17 Jul 2017, 17:17
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