Private GMAT Tutoring in NYC & Online

GMAT Question of the Day - Data Sufficiency - Number Properties/Odds and Evens

Is (a^2 - b^2)/2 an odd integer?

(1) a-b is odd

(2) a^2 + b^2 is odd

Answer Show

GMAT Question of the Day Solution

For this question of the day it's important to remember one thing: a and b don't have to be integers. With GMAT tutoring students I often see this idea of integer v. non-integer overlooked, especially in the Data Sufficiency. Remember special numbers: 1, 0, Negative, Positive, Integer, Decimal.

Let's simplify this question a bit more. What is it really asking? What type of number when divided by two becomes an odd integer? Certainly not an odd number and certainly not a decimal. So what's left? Even. But not any even. For instance, 4/2 is even. But 6/2 is odd. So we're wondering whether the numerator (a^2 - b^2) is an even number with only one 2.

If a and b are integers then statement (1) tells us that the expression will yield a decimal. So the answer would be No. However, a and b could be decimals. (1.5+.5)(1.5-5) = 2. 2/2 = Odd. This is a Yes. Yes/No means insufficient. With statement (2) you also have two options. Both number could be odd integers in which case the answer is No. However, a could be √2.5 and b could be √.5 so that a^2 - b^2 yields an even number with only one 2. This would be a Yes. So statement (2) is insufficient. Putting them both together the square roots are not possible because they will not work with statement (1). So the answer is a definitive No.

GMAT Question of the Day Number Properties Solution Diagram

 

Sorry, comments are closed for this post.

GMAT Classes New York

GMAT ARTICLES

CONTACT


Atlantic GMAT

451 East 51st St.

NY, NY 10022

(347) 669-3545

info@AtlanticGMAT.com