Bunuel wrote:
What is the square root of 239,121?
(A) 476
(B) 489
(C) 497
(D) 511
(E) 524
Kudos for a correct solution.
VERITAS PREP OFFICIAL SOLUTIONThe square root of 239,121 represents the number that, squared, will give you 239,121. With a calculator this problem is plug-and-play, and at most it will take 45 seconds to try all five combinations and see which answer is correct. Without a calculator to do all the heavy lifting, we have to get a little smarter.
The brute force approach will still work. Simply multiply 476 by 476 and find the product. If it is not 239,121, we rinse and repeat for all five numbers. This technique does work, but it will take a significant amount of time as it ignores the hints the exam is giving you to solve the question quickly.
A great concept to utilize here is the idea of the unit digit. If I multiply any two numbers, the unit digit will simply be the product of the unit digits of the two numbers. This is because there is no carry over from other positions possible. Hence, here we need a number that gives a unit digit of 1 when we multiply it by itself. Going through each option, we can eliminate A (6×6), C (7×7) and E (4×4). This should make a lot of intuitive sense because any even number multiplied by itself will give you another even number, so answers A and E were never in the running. Answer choice C could have worked, but 7×7 must yield a unit digit of 9, so it cannot possibly work.
Only two answer choices remain: 489 and 511. Unfortunately, they both give unit digits of 1, so we need a different strategy to determine which answer is correct. This is where the concept of order of magnitude can save us the trouble of actually having to calculate the numbers. It’s worth noting that at this point multiplying one of the numbers will either give the correct answer or the incorrect answer. Either option solves the question, and is a legitimate way of getting the correct answer. However, knowing that 5 x 5 gives 25 means that 500 x 500 must give 25 followed by four 0’s, or 250,000. Since our number is a little below that, we know the answer must be smaller than 500, but not by very much. Answer choice D is thus too big to be the correct answer, and answer choice B must be correct.
There are many questions like this one that can be solved without having to do any math whatsoever, simply by knowing how to apply mathematical properties. This is what makes the GMAT tricky. The questions will not ask for very difficult math to be executed, but figuring out the correct way to get the correct answer is never a question of blindly attacking the problem with a brute force approach. This is why there is a timing component on the GMAT: To avoid reliance on brute forcing the answer (also to allow multiple tests to be scheduled in the same day). Focusing your study approach on the how, rather than the what, will help you maximize your score.
An apropos comparison is to think of the GMAT as an industrial strength lock. If you try to force your way in, the resistance will be significant. However if you know the combination to the lock, it will open easily. The key (pun intended) is to ascertain how to approach each question and work on the skillful approach instead of the forceful approach. Best of all, inside the safe is a ticket to the business school of your choice. Your job is to find the best way inside the safe. The lock mechanism is designed to keep you out, but like a password that is just “password”, it only appears difficult until you crack the safe.
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