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

[BTGmoderatorDC]

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

[swerve]

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