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Numbers and Operations

SAT Numbers

If \(x\) and \(y\) are integers, for which of the following ordered pairs \((x,y)\) is \(x-2y\) an odd number?

(A) \(\ \ (32,1)\)
(B) \(\ \ (16, 1)\)
(C) \(\ \ (6, 17)\)
(D) \(\ \ (0, -19)\)
(E) \(\ \ (-15, -10)\)

If \(x\) and \(y\) are integers, and \(x^{6}y^{9}\) is odd, which of the following must be true?

I. \(xy\) is odd.
II. \(x^{6}y\) is even.
III. \(y^{9}\) is odd.

(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) I, II, and III

If \(x\) represents a positive even integer, which of the following represents the even integer that immediately precedes \(x\)?

(A) \(\ \ x-1\)
(B) \(\ \ x-2\)
(C) \(\ \ x+2\)
(D) \(\ \ 2x\)
(E) \(\ \ 2x+2\)

How many integers between \(100\) and \(1000\) contain exactly one zero?

(A) \(\ \ 9\)
(B) \(\ \ 81\)
(C) \(\ \ 162\)
(D) \(\ \ 170\)
(E) \(\ \ 200\)

If \(n\) is an odd integer, all of the following must be odd integers EXCEPT:

(A) \(\ \ n^{11}\)
(B) \(\ \ n^{11}+10\)
(C) \(\ \ n^{11} + 11n +11\)
(D) \(\ \ n^{10}\)
(E) \(\ \ n^{10}+ 10n + 11\)

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