Practice GMAT Data Sufficiency Question
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x is a positive integer; is x + 17,283 odd?
 x  192,489,358,935 is odd
 x/4 is not an even integer
Correct Answer: A
 Before evaluating Statements (1) and (2), it is extremely helpful to keep in mind that an odd number is the result of a sum of numbers with unlike parity. In other words: even + odd = odd. Since 17,283 is odd, the only way x + 17,283 will be odd is if x is even. Consequently, the simplified version of the question is: is x even?

Evaluate Statement (1) alone.
 Statement (1) says that x  192,489,358,935 is odd. Since there is only one way for a difference to be odd (i.e., if the parity of the numbers is different), Statement (1) implies that x is even (otherwise, if x were odd, x  192,489,358,935 would be even). Since Statement (1) gives the parity of x, it is SUFFICIENT.
 Statement (1) alone is SUFFICIENT.

Evaluate Statement (2) alone.
 Statement (2) says that x/4 is not an even integer. It is important to note that this does not mean that x cannot be even (e.g., 6 is even yet 6/4 is not an even integer). Possible values of x include 2, 3, 6, 10, 11.
x Parity of x x/4 2 Even Not an even integer 3 Odd Not an even integer 6 Even Not an even integer 10 Even Not an even integer 11 Odd Not an even integer  As this list indicates, there is no definitive information about the parity of x (e.g., 11 is odd and 10 is even). Consequently, Statement (2) is NOT SUFFICIENT.
 Statement (2) alone is NOT SUFFICIENT.
 Statement (2) says that x/4 is not an even integer. It is important to note that this does not mean that x cannot be even (e.g., 6 is even yet 6/4 is not an even integer). Possible values of x include 2, 3, 6, 10, 11.
 Since Statement (1) alone is SUFFICIENT and Statement (2) alone is NOT SUFFICIENT, answer A is correct.
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