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10 May 2018, 01:43
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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If x and y are integers, then \(\frac{x(x + 1)(x + 2)}{2*3*5^y}\) must be an integer if which of the following is true ?
A. x is even.
B. x is odd.
C. x is divisible by three.
D. y is even.
E. y is equal to zero.
A. x is even.
B. x is odd.
C. x is divisible by three.
D. y is even.
E. y is equal to zero.
Updated on: 10 May 2018, 02:17
Originally posted by DavidTutorexamPAL on 10 May 2018, 02:02.
Last edited by DavidTutorexamPAL on 10 May 2018, 02:17, edited 1 time in total.
Last edited by DavidTutorexamPAL on 10 May 2018, 02:17, edited 1 time in total.
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Bunuel
If x and y are integers, then \(\frac{x(x + 1)(x + 2)}{2*3*5^y}\) must be an integer if which of the following is true ?
A. x is even.
B. x is odd.
C. x is divisible by three.
D. y is even.
E. y is equal to zero.
A. x is even.
B. x is odd.
C. x is divisible by three.
D. y is even.
E. y is equal to zero.
Questions dealing with number properties can often be solved with logic and very little calculation.
We'll look for such a solution, a Logical approach.
A fraction is an integer if its numerator is divisible by its denominator.
So, our correct answer must either say that the numerator is 0 (as 0 divided by any number is 0) or have some information about the denominator, that is about y. (Otherwise y could be any number, and specifically one that is not a factor of the numerator)
(A), (B), (C) are eliminated.
(D) is also insufficient as we can just increase y until we find a power of 5 that is not a factor of x(x+1)(x+2).
(E) must be our answer.
We can mark it, if we have the time we'll also see why it is true: x(x+1)(x+2) are 3 consecutive numbers and therefore at least one of them is even and one must be divisible by 3. So they are definitely divisible by 2*3 and since y = 0 means 5^y = 1, (E) is correct.
10 May 2018, 02:14
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Bunuel
If x and y are integers, then \(\frac{x(x + 1)(x + 2)}{2*3*5^y}\) must be an integer if which of the following is true ?
A. x is even.
B. x is odd.
C. x is divisible by three.
D. y is even.
E. y is equal to zero.
A. x is even.
B. x is odd.
C. x is divisible by three.
D. y is even.
E. y is equal to zero.
nice question.
first we must pay attention to x, x+1, x+2..............3 consecutive integers. Any 3 consecutive integers must be divisible by 6. Look at the denominator. we 2*3 but \(5^y\) is problematic here. Option E tell us that Y is equal to 0. \(5^0\) = 1. thus, regardless of the value of x ultimate product will be divisible by 2*3*1.
Therefore the best answer is E.
