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

Question

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

Source:   Nova GMAT  
Difficulty Level:   500

sashiim20 · Answer

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...

Abhishek009 · Answer

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...

pushpitkc · Answer

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.

hdwnkr · Answer

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

sonikavadhera · Answer

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>

JeffTargetTestPrep · Answer

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.

Answer: D

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

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