Posted by: AC | July 6, 2009

GMAT Daily Question

Jeff Sackman, author of GMAT Hacks started a new website with a daily GMAT question, which I now enjoy with my morning coffee.

Here is today’s question:

Today’s Practice GMAT Question:

If the two-digit integers A and B are positive and have the same digits, but in reverse order, which of the following could be the sum of A and B ?
(A) 108
(B) 120
(C) 132
(D) 144
(E) 156

The best part about these questions are Jeff’s wonderful explanations.  Most GMAT books just give the mathematical explanation behind the answers, often not including strategies and helpful hints.

Here is Jeff’s helpful answer:

Answer: C

It might be tempting to try a series of numbers until you find something that works, but there must be a deeper pattern the GMAT is asking you to discover.

Let’s say the tens digit of A is x and the units of A is y. So if A is 73, x = 7 and y = 3. Algebraically, A = 10x + y. If the digits are reverse to create B, x is the units digit of B and y is the tens digit of B, meaning that B = 10y + x.

We can add those together:
A + B
= (10x + y) + (10y + x)
= 11x + 11y
= 11(x + y)

Since x and y are digits, they must be integers, so the sum of x and y must be an integer. 11 times any integer is a multiple of 11, so we’re looking for the choice that is a multiple of 11. You aren’t expected to know multiples of 11 off the top of your head, so start with an easy one, like 110. Add 11: 121. Add 11 again: 132. That’s choice (C), which is correct.

I am a big fan of GMAT Hacks and Jeff’s strategies, and I am really enjoying the Daily GMAT Questions!  Be sure and check out these sites.

34 days to GMAT TEST DAY!


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