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If p, q, r are a series of three consecutive positive integers, is the
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25 Nov 2014, 08:19
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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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Re: If p, q, r are a series of three consecutive positive integers, is the
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25 Nov 2014, 08:30
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.
Answer is D.



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Re: If p, q, r are a series of three consecutive positive integers, is the
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25 Nov 2014, 10:20
(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 = n1 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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Re: If p, q, r are a series of three consecutive positive integers, is the
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25 Nov 2014, 17:47
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, oddsum = even. Sufficient. From statement 2: basically the same thing, sum/3 = even, so sum must be even. Sufficient.
Choose D



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Re: If p, q, r are a series of three consecutive positive integers, is the
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25 Nov 2014, 20:36
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.
Answer should be D)



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Re: If p, q, r are a series of three consecutive positive integers, is the
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26 Nov 2014, 01:11
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 Answer D. 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. Answer = D.



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Re: If p, q, r are a series of three consecutive positive integers, is the
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26 Nov 2014, 07:19
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
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