If x, y, and z are consecutive odd integers, with x < y < z, then which of the following must be true?
x + y is even
is an integer
xz is even
I only
II only
III only
I and II only
I, II, and III
I eliminated option D as I considered 1,1,3 as one of the possibilities and hence 1+1 = 0 which is neutral.Please suggest if we should consider this possibility.
consecutive odd integers
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 prachi18oct
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 Brent@GMATPrepNow
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You're missing part of the question (see above)prachi18oct wrote:If x, y, and z are consecutive odd integers, with x < y < z, then which of the following must be true?
x + y is even
is an integer
xz is even
I only
II only
III only
I and II only
I, II, and III
I eliminated option D as I considered 1,1,3 as one of the possibilities and hence 1+1 = 0 which is neutral.Please suggest if we should consider this possibility.
Cheers,
Brent
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I found the original question. It reads as follows:
I. x + y is even
Since x and y are both ODD, x + y = ODD + ODD = EVEN
So, statement I is true
II. (x + z)/y is an integer
Must this be true?
Since x, y and z are consecutive odd integers, we know that y is 2 greater than x, and z is 4 greater than x.
So, we can write the following:
x = x
y = x + 2
z = x + 4
This means that (x + z)/y = (x + x + 4)/(x + 2)
= (2x + 4)/(x + 2)
= 2
Aha, so (x + z)/y will ALWAYS equal 2 (an integer)
So, statement II is true
III. xz is even
Since x and z are both ODD, xz = (ODD)(ODD) = ODD
So, statement III is NOT true
Answer: D
Cheers,
Brent
The key word here is MUSTIf x, y, and z are consecutive odd integers, with x < y < z, then which of the following MUST be true?
I. x + y is even
II. (x + z)/y is an integer
III. xz is even
A) I only
B) II only
C) III only
D) I and II only
E) I, II, and III
I. x + y is even
Since x and y are both ODD, x + y = ODD + ODD = EVEN
So, statement I is true
II. (x + z)/y is an integer
Must this be true?
Since x, y and z are consecutive odd integers, we know that y is 2 greater than x, and z is 4 greater than x.
So, we can write the following:
x = x
y = x + 2
z = x + 4
This means that (x + z)/y = (x + x + 4)/(x + 2)
= (2x + 4)/(x + 2)
= 2
Aha, so (x + z)/y will ALWAYS equal 2 (an integer)
So, statement II is true
III. xz is even
Since x and z are both ODD, xz = (ODD)(ODD) = ODD
So, statement III is NOT true
Answer: D
Cheers,
Brent
Brent Hanneson  Creator of GMATPrepNow.com
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 Brent@GMATPrepNow
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Your mistake is highlighted above.prachi18oct wrote:If x, y, and z are consecutive odd integers, with x < y < z, then which of the following must be true?
I. x + y is even
II. (x + z)/y is an integer
III. xz is even
A) I only
B) II only
C) III only
D) I and II only
E) I, II, and III
I eliminated option D as I considered 1,1,3 as one of the possibilities and hence 1+1 = 0 which is neutral.Please suggest if we should consider this possibility.
I believe you are confusing even/odd with positive/negative.
0 is neither positive nor negative.
But 0 is definitely even.
A number is "even" if that number can be written as the product of 2 and some integer.
Since we can write 0 as (2)(0), 0 is even.
Cheers,
Brent
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 prachi18oct
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 Rich.C@EMPOWERgmat.com
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Hi prachi18oct,
Roman Numeral questions are sometimes "built" to take longer to solve than typical Quant questions. However, they almost always involve Number Properties, which can be used to save time (if you know your Number Property rules).
From the onset of the question, we're told that X, Y and Z are CONSECUTIVE ODD INTEGERS. That type of vocabulary is a HUGE clue to think about Number Properties (re "patterns" in numbers). As Brent has shown in his explanation, you can quickly prove that Roman Numeral I is true and Roman Numeral III is false.
Be on the lookout for these patterns. Number Properties tend to show up all over the Quant section (especially in DS); knowing them will give you a great way to save time and pick up points.
GMAT assassins aren't born, they're made,
Rich
Roman Numeral questions are sometimes "built" to take longer to solve than typical Quant questions. However, they almost always involve Number Properties, which can be used to save time (if you know your Number Property rules).
From the onset of the question, we're told that X, Y and Z are CONSECUTIVE ODD INTEGERS. That type of vocabulary is a HUGE clue to think about Number Properties (re "patterns" in numbers). As Brent has shown in his explanation, you can quickly prove that Roman Numeral I is true and Roman Numeral III is false.
Be on the lookout for these patterns. Number Properties tend to show up all over the Quant section (especially in DS); knowing them will give you a great way to save time and pick up points.
GMAT assassins aren't born, they're made,
Rich

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Hi Brent ,
Can you pls explain why did you take y=x+2 if x=x it must be consecutive. I am bit confused in this.
Thanks
Shreyans
Can you pls explain why did you take y=x+2 if x=x it must be consecutive. I am bit confused in this.
Thanks
Shreyans
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Not to step on Brent's toes, but he did this because the numbers are consecutive ODD integers, which must differ by 2 (e.g. 1 and 3 or 3 and 5).j_shreyans wrote:Hi Brent ,
Can you pls explain why did you take y=x+2 if x=x it must be consecutive. I am bit confused in this.
Thanks
Shreyans
GMAT/MBA Expert
 Brent@GMATPrepNow
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Let's examine some consecutive ODD integers: 7, 9, 11j_shreyans wrote:Hi Brent ,
Can you pls explain why did you take y=x+2 if x=x it must be consecutive. I am bit confused in this.
Thanks
Shreyans
Notice that each integer is 2 greater than the one before it.
So, for example, 9 is 2 greater than 7, and 11 is 4 greater than 7
We can write:
7 = 7
9 = 7 + 2
11 = 7 + 4
Likewise, if x, y and z are consecutive ODD integers, then:
x = x
y = x + 2
z = x + 4
Once we know this, we can take (x + z)/y and replace y with x + 2 and replace z with x + 4 to get (x + x + 4)/(x + 2), which simplifies to (2x + 4)/(x + 2), which simplifies to 2
Cheers,
Brent
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(Note that 0 is an even integer, so D can not be eliminated based on your statement.)prachi18oct wrote: ↑Wed Aug 20, 2014 6:41 amIf x, y, and z are consecutive odd integers, with x < y < z, then which of the following must be true?
x + y is even
is an integer
xz is even
I only
II only
III only
I and II only
I, II, and III
I eliminated option D as I considered 1,1,3 as one of the possibilities and hence 1+1 = 0 which is neutral.Please suggest if we should consider this possibility.
Since x, y, and z are consecutive odd integers, x + y = odd + odd = even, and xz = (odd)(odd) = odd. So statement I is true, and statement III is false.
Since x = y  2 and z = y + 2, then (x + z)/y = (y  2 + y + 2)/y = 2y/y = 2 is an integer. So statement II is true also.
Answer: D
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