AAPL wrote:Economist GMAT

If \(a\) and \(b\) are positive integers, which of the following cannot be odd?

A. \(\frac{2+4a}{4+4b}\)

B. \(\frac{4a}{b}\)

C. \(\frac{a}{b}\)

D. \(\frac{4+a}{2+4b}\)

E. \(\frac{4+a}{1+4b}\)

OA A

First, read the question carefully. The question asks, "which of the following cannot be odd?" it does not mean, "which of the following is even? The correct answer could be an expression that is either even or fraction.

Let's take each option one by one.

A. \(\frac{2+4a}{4+4b}\): \(\frac{2(1+2a)}{2(2+2b)}\) = \(\frac{1+2a}{2+2b}\) = Odd / Even = Fraction ≠ Odd: Correct answer

whether a is even or odd, the numerator (1 + 2a) is odd; similarly, whether b is even or odd, the numerator (2 + 2b) is even

Though we go the correct answer, let's discuss other options, too.

B. \(\frac{4a}{b}\): Say b = 4 and a = 1, then \(\frac{4a}{b}\) is odd.

C. \(\frac{a}{b}\): Say b = 6 and a = 2, then \(\frac{a}{b}\) is odd.

D. \(\frac{4+a}{2+4b}\): Say b = 1 and a = 2, then \(\frac{4+a}{2+4b}\) is odd.

E. \(\frac{4+a}{1+4b}\): Say b = 1 and a = 1, then \(\frac{4+a}{1+4b}\) is odd.

The correct answer: A

Hope this helps!

-Jay
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AAPL wrote:Economist GMAT

If \(a\) and \(b\) are positive integers, which of the following cannot be odd?

A. \(\frac{2+4a}{4+4b}\)

B. \(\frac{4a}{b}\)

C. \(\frac{a}{b}\)

D. \(\frac{4+a}{2+4b}\)

E. \(\frac{4+a}{1+4b}\)

OA A

In answer choice A, notice that 2 + 4a = 2(1 + 2a) and 4 + 4b = 4(1 + b). So

(2+4a)/(4+4b)

= 2(1+2a)/[4(1+b)]

= (1+2a)/[2(1+b)]

We see that (1 + 2a) is an odd number and 2(1 + b) is an even number, regardless of what a and b are, so the quotient can't be an odd number since it's not even an integer.

Answer: A