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# If a, b and c are consecutive positive integers and a < b < c, which

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Math Expert
Joined: 02 Sep 2009
Posts: 52161
If a, b and c are consecutive positive integers and a < b < c, which  [#permalink]

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10 May 2018, 01:14
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Difficulty:

25% (medium)

Question Stats:

73% (01:41) correct 27% (01:25) wrong based on 78 sessions

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If a, b and c are consecutive positive integers and a < b < c, which of the following must be an odd integer?

A. abc
B. a + b + c
C. a + bc
D. a(b + c)
E. (a + b)(b + c)

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Posts: 951
Concentration: Accounting, Finance
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Re: If a, b and c are consecutive positive integers and a < b < c, which  [#permalink]

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10 May 2018, 01:21
Bunuel wrote:
If a, b and c are consecutive positive integers and a < b < c, which of the following must be an odd integer?

A. abc
B. a + b + c
C. a + bc
D. a(b + c)
E. (a + b)(b + c)

let's assume the value of a, b , c

2<3<4
1<2<3

E. (2+3) (3+4) =35
(1+2) (2+3) =15

Thus E is the best answer.
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Re: If a, b and c are consecutive positive integers and a < b < c, which  [#permalink]

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10 May 2018, 03:21
Bunuel wrote:
If a, b and c are consecutive positive integers and a < b < c, which of the following must be an odd integer?

A. abc
B. a + b + c
C. a + bc
D. a(b + c)
E. (a + b)(b + c)

Your consecutive integers will either be odd+even+odd or even+odd+even

A. Anything that is multiplied by an even will be even. Eliminate answer A.
B. odd+even+odd= even. Eliminate answer B.
C. a can be odd or even. bc has to be even. even+even=odd. Eliminate answer C.
D. Anything that is multiplied by an even will be even. If a is even, we will have (even+even)=even. Eliminate D.
E. even+odd=odd. So a+b=odd and b+c=odd. --> Odd x odd = Odd. Answer E MUST be odd.
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Re: If a, b and c are consecutive positive integers and a < b < c, which  [#permalink]

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13 May 2018, 16:56
Bunuel wrote:
If a, b and c are consecutive positive integers and a < b < c, which of the following must be an odd integer?

A. abc
B. a + b + c
C. a + bc
D. a(b + c)
E. (a + b)(b + c)

Since a, b, and c are consecutive integers, we see that a and c could both be even while b is odd, OR a and c could both be odd while b is even.

Since even + odd = odd, we see that a + b will always be odd, and b + c will always be odd; and, since odd x odd = odd we see that , (a + b)(b + c) will always be odd.

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Re: If a, b and c are consecutive positive integers and a < b < c, which &nbs [#permalink] 13 May 2018, 16:56
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