x is a positive integer. Is x even? (1) 9x^2 is divisible by 4 (2) 3x

1 stm. tells us that \(9x^2\) is even. We know that neither square root, nor multiplication by odd number change the +- nature of x, so x is even --> suff.
2 stm. tells that \(3x+2\) is even. We know that neither adding even number, nor multiplication by odd number change the +- nature of x, so x is even --> suff.

In My Opinion
Ans: D

Given x > 0

Statement 1: 9x^2 = 4k, hence 9x^2 = even. x = even, since Odd * Even = Even. Statement 1 is Sufficient.

Statement 2: 3x + 2 = 8k, hence 3x + 2 = even. x = even, since Even + Even = Even. Statement 2 is Sufficient.


Answer D.



Thanks,
GyM
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Hi gym,
In st2, at x= 4,8 etc. 3x+2 is not divisible by 8.
But st2 is valid for some of the even integers(2,10 etc) not all.
In this case Is x even? Yes or No.
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In DS questions, we need to consider the given statements are True. Consider them as constraints for us to solve the question.

The task at hand is to determine is X = even?

In statement 2 it is given 3x + 2 is divisible by 8, our job is to determine which value of x can satisfy this condition.

As rightly identified by you, the condition is satisfied by x = 2, 10, etc. our task at hand is to determine whether these values which satisfy (3x + 2) = 8k are even or not.

Using statement 2, we can answer the question as YES, x = even.

However, If we were to find values of x as odd as well as even & satisfying statement 2, then statement 2 would not be sufficient. Since we will get answer for X = even? as YES & NO.



Hope that answers your query.


Thanks,
GyM
_________________

In DS questions, we need to consider the given statements are True. Consider them as constraints for us to solve the question.

The task at hand is to determine is X = even?

In statement 2 it is given 3x + 2 is divisible by 8, our job is to determine which value of x can satisfy this condition.

As rightly identified by you, the condition is satisfied by x = 2, 10, etc. our task at hand is to determine whether these values which satisfy (3x + 2) = 8k are even or not.

Using statement 2, we can answer the question as YES, x = even.

However, If we were to find values of x as odd as well as even & satisfying statement 2, then statement 2 would not be sufficient. Since we will get answer for X = even? as YES & NO.



Hope that answers your query.


Thanks,
GyM[/quote]

Thanks gym,
My point was:- Although 3x+2 is even as mentioned in your explanation, it is not divisible by 8.
Now you have made it clear.
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No problem. My fault I wasn't clear enough, thankfully GMAT is an objective test.

Cheers!
GyM
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Statement 1 :

9\(x^2\) is divisible by 4.

9 is not divisible by 4. So, \(x^2\)has to be divisible by 4. It means\(x^2\) is a multiple of 4 . even times even yields even all time. So, Sufficient.

Statement 2 :

3x + 2 is divisible by 8. As 3x + 2 is divisible by 8 , 3x + 2 must be the multiple of 8 . It means 3x + 2 is even. Thus x is even. Sufficient.


So both of the statements are sufficient. The best answer is D.

Solution

Given:

• x is a positive integer

To find:

• Is x even?

Analysing Statement 1
“\(9x^2\) is divisible by 4”

• Implies, \(9x^2 = 4k\) .................. (1), where k is a positive integer
• The right-hand side of equation (1) is even, which implies that the left-hand side should be even
• Thus, x is even (since 9 is odd)

Therefore, Statement (1) ALONE is sufficient to answer this question

Analysing Statement 2
“3x + 2 is divisible by 8”

• Implies, 3x + 2 = 8k, where k is a positive integer

o 3x + 2 = 8k
o 3x = 8k -2
o 3x = 2*(4k -1) ............................. (2)

• The right-hand side of equation (2) is even, which implies that the left-hand side should be even
• For 3x to be even, x should be even

Thus, Statement (2) ALONE is sufficient to answer this question

Therefore, EACH Statement ALONE is sufficient to answer this question

Hence, the correct answer is option D.

Answer: D
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