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05 Nov 2021, 06:45
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
84% (01:44) correct
16%
(01:32)
wrong
based on 70
sessions
History
Date
Time
Result
Not Attempted Yet
What is value of y, so that (40560)(y) is square of an integer?
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
05 Nov 2021, 06:56
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If 40560*y will be the square of an integer, then in the prime factorization of 40560*y, all of our exponents will need to be even. Since 40560 = 4056*10 = 4056*2*5, and since we clearly don't have any other 5's anywhere in 4056, we're going to need to multiply by at least one 5 to get an even power on the 5, and since only one answer, 15, is divisible by 5, it has to be right.
If you wanted to solve 'properly', you'd want to prime factorize 40560 = (10)(4056) = (2)(5)(8)(507) = (2^4)(5)(507), and now you might notice 507 is divisible by 3 (but not by 3^2, so at this point we can see our answer needs to be divisible by 3 also), and it turns out 507 = (3)(169) = (3)(13^2). So we've just found out that 40560 = (2^4)(3)(5)(13^2), and if we multiply this by 15 = (3)(5), we'll get (2^4)(3^2)(5^2)(13^2), which is the square of (2^2)(3)(5)(13).
This question is almost identical to a published official problem, but it's worthwhile seeing the official version, just to see how computationally intensive these questions tend to be (or really, tend not to be) on the GMAT. The GMAT used a much smaller number than the "40,560" used here.
If you wanted to solve 'properly', you'd want to prime factorize 40560 = (10)(4056) = (2)(5)(8)(507) = (2^4)(5)(507), and now you might notice 507 is divisible by 3 (but not by 3^2, so at this point we can see our answer needs to be divisible by 3 also), and it turns out 507 = (3)(169) = (3)(13^2). So we've just found out that 40560 = (2^4)(3)(5)(13^2), and if we multiply this by 15 = (3)(5), we'll get (2^4)(3^2)(5^2)(13^2), which is the square of (2^2)(3)(5)(13).
This question is almost identical to a published official problem, but it's worthwhile seeing the official version, just to see how computationally intensive these questions tend to be (or really, tend not to be) on the GMAT. The GMAT used a much smaller number than the "40,560" used here.
05 Nov 2021, 08:55
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Bunuel
Breaking Down the Info:
We will have to factor 40560 and complete the "missing" factors.
\(40560 = 10 * 4056 = 10 * 4 * 1014 = 10 * 8 * 507\). If we take a peek at the choices, they suggest 507 is not a prime so we can continue breaking this down. (507 is also a multiple of 3).
\(507 = 480 + 27 = 3*(160 + 9) = 3*13^2\), so putting all of this together, we have \(40560 = 5 * 2^4 * 3 * 13^2\).
By picking apart the factors, we can see 5 and 3 do not have even powers. This means we need to fill in a 5 and 3 from y, therefore y = 15 at least.
Answer: D
