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02 Sep 2015, 22:54
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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:
65%
(hard)
Question Stats:
64% (02:19) correct
36%
(02:20)
wrong
based on 630
sessions
History
Date
Time
Result
Not Attempted Yet
Which of the following is two more than the square of an odd integer?
(A) 14,173
(B) 14,361
(C) 14,643
(D) 14,737
(E) 14,981
(A) 14,173
(B) 14,361
(C) 14,643
(D) 14,737
(E) 14,981
06 Sep 2015, 05:42
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Bunuel
MANHATTAN GMAT OFFICIAL SOLUTION:
From the size of the answer choices, we should recognize that there must be some trick – a way to find the answer quickly within 2 minutes, since theoretically, every GMAT problem must be solvable that way.
Let’s start from first principles. We can represent a general odd integer as 2k + 1, where k is an integer. So the square of an odd integer can be written this way:
(2k + 1)^2
= 4k^2 + 4k + 1
Since the first two terms (4k^2 and 4k) contain 4 as a factor, we can see that they are both multiples of 4, and thus their sum is also a multiple of 4. This means that the square of any odd integer is 1 more than a multiple of 4. Thus, the number we are looking for (“two more than the square…”) is 3 more than a multiple of 4.
To quickly determine whether a number is a multiple of 4, we can just examine the last 2 digits. The reason is that 100 is divisible by 4, so only the tens and the ones digit matter. The hundreds digit, the thousands digit, etc. will never affect divisibility by 4.
Looking at the answer choices and cutting off everything but the last 2 digits, we are left with 73, 61, 43, 37, and 81. Of these, only 43 is 3 more than a multiple of 4 (40). Thus, C is the right answer. (Incidentally, 14,643 is 2 + 121^2.)
The correct answer is (C).
03 Sep 2015, 08:02
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Bunuel
one of the given options should be a square if 2 is subtracted from it.
the options would be
(A) 14,171
(B) 14,359
(C) 14,641
(D) 14,735
(E) 14,979
We can solve this question with many approaches. Here are the 2 easiest methods.
Method 1:-
If a square has odd unit's digit, then it's ten's digit will always be even.
Only 14,641 satisfies this condition.
Method 2:-
If you know about palindromic numbers,
then you can clearly see that 14,641 is a palindromic square.
Answer:- C
