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

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Bunuel
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If a, b and c are consecutive positive integers and a < b < c, which [#permalink] New post   10 May 2018, 02:14
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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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E
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Re: If a, b and c are consecutive positive integers and a < b < c, which [#permalink] New post   10 May 2018, 02:21
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] New post   10 May 2018, 04:21
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] New post   13 May 2018, 17:56
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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.

Answer: E
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Re: If a, b and c are consecutive positive integers and a < b < c, which [#permalink] New post   26 Oct 2022, 11:13
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Given that a, b, and c are consecutive positive integers and a < b < c and we need to find which of the following must be an odd integer

As a, b and c are consecutive positive integers
=> b = a + 1
=> c = b + 1 = a + 2

Let's evaluate each option choice now

(A) abc
As we have three consecutive numbers => At least one of them will be even making the product of abc as Even => FALSE

(B) a + b + c
If both a and c are Odd and b is even then a + b + c = Odd + Even + Odd = Even => FALSE

(C) a + bc
If both a and c are Even and b is odd then a + bc = Even + Even = Even => FALSE

(D) a(b + c)
If a is even then a(b+c) = Even => FALSE

(E) (a + b)(b + c)
a + b is sum of two consecutive numbers => ALWAYS Odd
b + c is sum of two consecutive numbers => ALWAYS Odd
=> (a + b)(b + c) = Odd * Odd = Odd => TRUE

So, Answer will be E
Hope it helps!

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Re: If a, b and c are consecutive positive integers and a < b < c, which [#permalink]
26 Oct 2022, 11:13
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