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14 Jun 2021, 05:15
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
51% (02:13) correct
49%
(01:43)
wrong
based on 158
sessions
History
Date
Time
Result
Not Attempted Yet
Which of the following is a perfect square?
(A) 97,474
(B) 123,301
(C) 137,641
(D) 170,567
(E) 177,243
(A) 97,474
(B) 123,301
(C) 137,641
(D) 170,567
(E) 177,243
14 Jun 2021, 06:43
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Bunuel
I don’t believe GMAT would ever want you to calculate the square roots.
So we should be able to eliminate wrong choices by some trick.
Few of them are:
1) Units digit: The units digit of a perfect square will always be 0, 1, 4, 5, 6, or 9. Any number having a units digit of 2, 3, 7 or 8 will not be a perfect square.
2) Even number: If there is an even number, last two digits should be divisible by 4.
3) Multiple of 3: The sum of digits if divisible by 3 and not by 9 will not be a perfect square.
D and E cannot be perfect square as last digits are 7 and 3.
A cannot be a perfect square as last two digits 74 is not divisible by 4.
However, I cannot think immediately of some technique to eliminate one of B or C. It would require to be calculated.
1) Now B is not divisible by 2, 3, 5, or 11 by observation itself. so let us try with the prime 7, 13 and then 17. It is divisible by 17.
123,301=17*7253.
But 7253 is not divisible by 17.
2) Another method could be approximation.
90000<123301<160000, almost in middle of two perfect squares. So, it should be between 300^2 and 400^2, and closer to 350 and having 1 or 9 as units digit.
Let us try 351 => 351*351=123,201.
Hence 123,301 is not a perfect square.
C
14 Jun 2021, 08:24
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I agree with Chetan -- this is not a realistic GMAT question, for several reasons. The GMAT doesn't even expect test takers to know the term "perfect square", for one thing. And it is absolutely never true of GMAT Quant questions that the only practical way to pick the right answer is by eliminating wrong answers. There is always a way to prove the right answer is right in a reasonable amount of time. Here, to do that, you'd need to establish that 137,641 is a perfect square, and to do that, you either need to first estimate (its root would be between 300 and 400, at a very rough approximation), then try squaring plausible numbers with appropriate units digits (1 or 9). You never need to square numbers like 359 or 381 on the GMAT.
edit - accidentally clicked reply too soon! Or you might notice that 137,641 is divisible by 7, since it is 2,359 less than 140,000, and 2,359 is divisible by 7 (since it is 2100 + 210 + 49). So if that number is a perfect square, it would be divisible by 7^2, and if you divide 137,641 by 7^2, you get 2809. But the problem now is that this is 53^2, the square of a large prime, which is not a perfect square anyone could reasonably be expected to recognize. So I don't see any reasonable way to do this problem quickly, and it's not the kind of thing the GMAT would ever ask.
edit - accidentally clicked reply too soon! Or you might notice that 137,641 is divisible by 7, since it is 2,359 less than 140,000, and 2,359 is divisible by 7 (since it is 2100 + 210 + 49). So if that number is a perfect square, it would be divisible by 7^2, and if you divide 137,641 by 7^2, you get 2809. But the problem now is that this is 53^2, the square of a large prime, which is not a perfect square anyone could reasonably be expected to recognize. So I don't see any reasonable way to do this problem quickly, and it's not the kind of thing the GMAT would ever ask.
