## If x is a positive number, is x an even integer?

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### If x is a positive number, is x an even integer?

by BTGmoderatorDC » Wed Sep 01, 2021 7:39 pm

00:00

A

B

C

D

E

## Global Stats

If x is a positive number, is x an even integer?

(1) 3x is an even integer.

(2) 5x is an even integer.

OA C

Source: Manhattan Prep

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### Re: If x is a positive number, is x an even integer?

by swerve » Fri Sep 03, 2021 3:24 am

00:00

A

B

C

D

E

## Global Stats

BTGmoderatorDC wrote:
Wed Sep 01, 2021 7:39 pm
If x is a positive number, is x an even integer?

(1) 3x is an even integer.

(2) 5x is an even integer.

OA C

Source: Manhattan Prep
$$x$$ is positive Integer means we need to think only in positive fractions and integers.

1) $$3x$$ is an even integer.

Let $$x= 2 \Rightarrow 3x=6 \Rightarrow x$$ is even integer

Let $$x=\dfrac{2}{3} \Rightarrow 3x=2 \Rightarrow x$$ is NOT even integer

Insufficient $$\Large{\color{red}\chi}$$

2) $$5x$$ is an even integer.

Let $$x= 2 \Rightarrow 5x=10 \Rightarrow x$$ is even integer

Let $$x=\dfrac{2}{5} \Rightarrow 5x=2 \Rightarrow x$$ is NOT even integer

Insufficient $$\Large{\color{red}\chi}$$

Combining 1 and 2, we have

There is no fraction could be multiplied simultaneously to $$3 \& 5$$ and give EVEN INTEGER. We left with that $$x=$$EVEN INTEGER to give make both $$3x \& 5x$$ even integers.

As $$3 \& 5$$ are odd numbers, then $$x$$ needs to be EVEN Integer to make both statements Even integers. $$\Large{\color{green}\checkmark}$$

Therefore, C

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