Problem Solving

[email protected] wrote:Hi Sri,

This is more of a "concept" question that a "calculation" question, although you do have to do some calculations to find the correct answer.

The way that you "saw" how E wasn't a perfect square is likely the same way that you knock out other answers. Here's how...

Consider answer D: 2509....

50 x 50 = 2500

51 x 51 would, at the very least, add ANOTHER 51 to the total, which would put that total past 2551. So there's no way to that 2509 would be a perfect square. This logic can be used to eliminate the other wrong answers as well (with varying degrees of "necessary" math).

GMAT assassins aren't born, they're made,
Rich

[email protected] wrote:Hi Sri,

The question that you linked (below), uses a different set of Number Properties and can be solved with a bit of brute-force calculations. My approach follows the question:

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Which of the following numbers is a perfect square?

A) 1266

B) 1444

C) 2022

D) 4034

E) 8122

OA: B
--------------

The first Number Property is that "perfect" squares can only end in certain digits: 1, 4, 5, 6, or 9. So the answers that end in "2" are not possible. Eliminate C and E.

From here, we just have to find the ONE ANSWER that's a perfect square. I'm going to focus on the first 2 answers, since they're "relatively close" to one another. If neither of them are perfect squares, then the answer would have to be D.

30^2 = 900
40^2 = 1600

Both A and are in that range (between 30 and 40), so we just need to narrow down the options a bit more...

The only possible perfect squares that could end in a 4 or a 6 (in this range) are...

32, 34, 36, 38

By starting with one of the "middle" options, I might be able to save some time/work...

34^2 = 1156 .....this is too small to be either answer A or B. I can now eliminate "32" as a possibility as well.

36^2 = 1296 .....not a match for either A or B.

38^2 = 1444 .....this IS a match!!!

Final Answer: B

While there are other high-concept approaches to answering this question, the GMAT does not require you to know them. I ultimately answered this question by thinking a bit about how multiplication "works" and then multiplying a couple of 2-digit numbers together. There are certain questions in which "brute force" is a great way to get the job done (and I consider this to be one of them); look at all the information that you're given though - there might be a way to avoid some of the work. In this question, I didn't have to check every number between 30 and 40, I only needed to check 3 of them.

GMAT assassins aren't born, they're made,
Rich