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# If x, y, and z are consecutive integers in increasing order, which of

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If x, y, and z are consecutive integers in increasing order, which of  [#permalink]

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15 Jun 2017, 07:31
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If x, y, and z are consecutive integers in increasing order, which of the following must be true?

I. xy is even.
II. x – z is even.
III. xz is even.

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

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If x, y, and z are consecutive integers in increasing order, which of  [#permalink]

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15 Jun 2017, 07:37
Bunuel wrote:
If x, y, and z are consecutive integers in increasing order, which of the following must be true?

I. xy is even.
II. x – z is even.
III. xz is even.

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

Let x, y and z = 1,2,3

I. xy is even. = $$1*2 = 2$$ (even) -------- True
II. x – z is even. = $$1 - 3 = -2$$ (even) -------- True
III. xz is even. = $$1*3 = 3$$ (odd) --------- Not true

Lets x, y and z = 2, 3, 4

I. xy is even. = $$2 *3 = 6$$ (even) --------- True
II. x – z is even. = $$(2 - 4) = -2$$ (even) --------- True
III. xz is even. = $$2 * 4 = 8$$ (even) --------- True

From both cases we get I and II must be true. Answer D...
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Re: If x, y, and z are consecutive integers in increasing order, which of  [#permalink]

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15 Jun 2017, 08:40
Bunuel wrote:
If x, y, and z are consecutive integers in increasing order, which of the following must be true?

I. xy is even.
II. x – z is even.
III. xz is even.

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

Let x = 2 , y = 3 and z = 4

I. xy = 2*3 = 6 is even.
II. x – z = 2 - 4 = -2 is even.
III. xz = 2*4 = 8 is even.

Let x = 3 , y = 4 and z = 5

I. xy = 3*4 = 12 is even.
II. x – z = 3 - 5 = -2 is even.

III. xz = 3*5 = 15 is odd.

Thus, answer will be (D) as found out from the above...
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Re: If x, y, and z are consecutive integers in increasing order, which of  [#permalink]

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15 Jun 2017, 12:22
Since x,y and z are consecutive integers
If x is odd, y is even, and z is odd OR if x is even, y is odd, and z is even
1.So whatever happens xy will always be EVEN.
2.Also x-z is even always because ODD - ODD/EVEN - EVEN is always EVEN.
3.However xz could be ODD/EVEN (which is incorrect)

Hence, Option D(I and II) is always true whatever the case.
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Re: If x, y, and z are consecutive integers in increasing order, which of  [#permalink]

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18 Jun 2017, 03:53
E,O,E

or O,E,O

These are the two combinations of consecutive integers.

Properties put to test:
1. Sum of two even numbers is even
2. Sum/Difference of two odd numbers is Even
3. Difference of two even numbers is Even
4. Even multiplied to anything gives even

The third statement in the question is not true. This eliminates two options that has III in it.

Ans. D
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Re: If x, y, and z are consecutive integers in increasing order, which of  [#permalink]

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21 Jun 2017, 01:15
three consecutive integers can have two possibilities for x,y,z
possibility 1: even, odd, even
possibility 2: odd, even, odd

Statement I : true for both possibilities
Statement II: true for both possibilities
Statement III: true in possibility I and false in possibility II

hence answer: I & II - Option D>
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Re: If x, y, and z are consecutive integers in increasing order, which of  [#permalink]

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06 Jul 2017, 17:25
Bunuel wrote:
If x, y, and z are consecutive integers in increasing order, which of the following must be true?

I. xy is even.
II. x – z is even.
III. xz is even.

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

Since x, y, and z are consecutive integers, those integers consists of either 2 even and 1 odd or 2 odd and 1 even number. Let’s now analyze our Roman numerals:

I. xy is even.

Since x and y are consecutive integers, one will be even and one will be odd. The product even x odd = even holds for all integers. Roman numeral I must be true.

II. x – z is even.

Since x and z are either both odd or both even, and since odd - odd = even and even - even = even, the difference of x and z will always be even. Roman numeral II is true.

III. xz is even.

Recall that x and z are either both odd or both even. If x and z are both even, the product is even.
However, if x and z are both odd, the product is odd. Thus, xz is not necessarily even. Roman numeral III is not true.

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Re: If x, y, and z are consecutive integers in increasing order, which of   [#permalink] 06 Jul 2017, 17:25
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