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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If p, q, r are a series of three consecutive positive integers, is the

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Math Expert V
Joined: 02 Sep 2009
Posts: 59200
If p, q, r are a series of three consecutive positive integers, is the  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 76% (01:30) correct 24% (01:46) wrong based on 133 sessions

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Tough and Tricky questions: Number Properties.

If p, q, r are a series of three consecutive positive integers, is the sum of all the integers odd?

(1) Two of the three numbers p, q, r are odd numbers.
(2) (p + q + r)/3 is an even integer.

Kudos for a correct solution.

Source: Chili Hot GMAT

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Current Student B
Joined: 12 Aug 2014
Posts: 147
Location: United States (AZ)
Concentration: Finance, Strategy
GMAT 1: 700 Q47 V39 Re: If p, q, r are a series of three consecutive positive integers, is the  [#permalink]

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1
If p, q, r are a series of three consecutive positive integers, is the sum of all the integers odd?

(1) Two of the three numbers p, q, r are odd numbers.

Pick numbers (realize you have to start with an odd integer since you need two odd):

p = 1, q = 2, r = 3; sum = 1 + 2 + 3 = 6 (even) NO

odd + even + odd = always even

Statement 1 is sufficient to answer the question alone.

(2) (p + q + r)/3 is an even integer.

Realize that you need the numerator to be even since only even/odd = even; odd/odd = odd. Therefore, p + q + r = even.

Statement 2 is sufficient to answer the question alone.

Intern  Joined: 25 May 2014
Posts: 46
Re: If p, q, r are a series of three consecutive positive integers, is the  [#permalink]

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1
(1) Two of the three numbers p, q, r are odd numbers.
sum of 3 consecutive numbers in which 2 are even will always be even [ coz odd+even+odd = even]
sufficient

(2) (p + q + r)/3 is an even integer.
let p = n-1
q = n
r = n+1
then p+q+r = 3n
(p + q + r)/3 = n= even then 3n will always be even
sufficient

in both the options the answer to the question is that sum of all the integers is not odd
[D]
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Manager  Joined: 12 Sep 2014
Posts: 142
GMAT 1: 740 Q49 V41 GPA: 3.94
Re: If p, q, r are a series of three consecutive positive integers, is the  [#permalink]

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1
From the premise, we're trying to determine if we have o, e, o or e, o, e for the three integers. If the first integer is even, the sum is odd and if the first integer is odd, the sum is even.

From statement 1: two are odd, meaning we have odd, even, odd--sum = even. Sufficient.
From statement 2: basically the same thing, sum/3 = even, so sum must be even. Sufficient.

Choose D
Manager  Joined: 22 Sep 2012
Posts: 122
Concentration: Strategy, Technology
WE: Information Technology (Computer Software)
Re: If p, q, r are a series of three consecutive positive integers, is the  [#permalink]

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1
Statement 1: two of the three numbers p, q, r are odd numbers.

The series can be represented as : 2n+1, 2n+2, 2n+3 [where n is an integer, greater than equal to 0]

Sum = 6n + 6 = 2*(n+3) . Sufficient, since any integer multiplied by 2 yields an even integer.

Statement 2: (p + q + r)/3 is an even integer.

therefore, p + q + r = 3*2*n [n is an integer]

Sufficient, since any integer multiplied by 2 yields an even integer.

Current Student B
Joined: 02 Sep 2014
Posts: 86
Location: United States
GMAT 1: 770 Q50 V44 GPA: 3.97
Re: If p, q, r are a series of three consecutive positive integers, is the  [#permalink]

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1
Bunuel wrote:

Tough and Tricky questions: Number Properties.

If p, q, r are a series of three consecutive positive integers, is the sum of all the integers odd?

(1) Two of the three numbers p, q, r are odd numbers.
(2) (p + q + r)/3 is an even integer.

Kudos for a correct solution.

Source: Chili Hot GMAT

1) IF 2 integers are odd, then third is even, so sum is even. SUFFICIENT.
2) If average is even, then 2 integers are odd, so sum is even. SUFFICIENT.

Math Expert V
Joined: 02 Sep 2009
Posts: 59200
Re: If p, q, r are a series of three consecutive positive integers, is the  [#permalink]

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Bunuel wrote:

Tough and Tricky questions: Number Properties.

If p, q, r are a series of three consecutive positive integers, is the sum of all the integers odd?

(1) Two of the three numbers p, q, r are odd numbers.
(2) (p + q + r)/3 is an even integer.

Kudos for a correct solution.

Source: Chili Hot GMAT

Yes, the correct answer is D.
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Re: If p, q, r are a series of three consecutive positive integers, is the  [#permalink]

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_________________ Re: If p, q, r are a series of three consecutive positive integers, is the   [#permalink] 24 Jan 2019, 08:08
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