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If a , b , and c are consecutive odd integers, which express
[#permalink]
09 Nov 2017, 07:16

Expert Reply

Question Stats:

If a, b, and c are consecutive odd integers, which expression must be odd?

Choose \(all\) that apply.

❑ \(a*(b+c)\)

❑ \((a+b) - c\)

❑ \(a*b*c\)

❑ \(2*(c-a) + b\)

❑ \(a + b + c\)

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Re: If a , b , and c are consecutive odd integers, which express
[#permalink]
09 Nov 2017, 08:30

1

Let's check them one by one

❑ \(a*(b+c)\) -> odd+odd = even, odd*even = even, so it must be even

❑ \((a+b) - c\) -> odd+odd = odd, odd-odd = odd, so it must be odd

❑ \(a*b*c\) -> odd*odd = odd, so it must be odd

❑ \(2*(c-a) + b\) -> odd-odd = odd, even*odd = even, even+odd = odd, so it must be odd

❑ \(a + b + c\) -> odd+odd = even, even+odd = odd, so it must be odd

Then, the answers are B, C, D, E.

❑ \(a*(b+c)\) -> odd+odd = even, odd*even = even, so it must be even

❑ \((a+b) - c\) -> odd+odd = odd, odd-odd = odd, so it must be odd

❑ \(a*b*c\) -> odd*odd = odd, so it must be odd

❑ \(2*(c-a) + b\) -> odd-odd = odd, even*odd = even, even+odd = odd, so it must be odd

❑ \(a + b + c\) -> odd+odd = even, even+odd = odd, so it must be odd

Then, the answers are B, C, D, E.

Re: If a , b , and c are consecutive odd integers, which express
[#permalink]
22 Jan 2019, 07:13

1

Expert Reply

Carcass wrote:

If a, b, and c are consecutive odd integers, which expression must be odd?

Choose \(all\) that apply.

A) \(a*(b+c)\)

B) \((a+b) - c\)

C) \(a*b*c\)

D) \(2*(c-a) + b\)

E) \(a + b + c\)

To solve this question, we can EITHER apply the rules for ODDS and EVENS (as IlCreatore has done) or we can plug in 3 consecutive ODD integers for a, b and c

How about a = 1, b = 3 and c = 3

We get:

A) \(1*(3+5) = 8\), which is EVEN. ELIMINATE.

B) \((1+3) - 5 = -1\), which is ODD. KEEP!

C) \(1*3*5 = 15\), which is ODD. KEEP!

D) \(2*(5-1) + 3 = 11\), which is ODD. KEEP!

E) \(1 + 3 + 5 = 9\), which is ODD. KEEP!

Answer: B, C, D, E

Cheers,

Brent

_________________

Re: If a , b , and c are consecutive odd integers, which express
[#permalink]
27 Sep 2021, 01:34

1

Logic behind that question:

ODD-EVEN RULE:

ODD ± EVEN = ODD and ODD * ODD = ODD ; and Even otherwise.

There are 3 consecutive odd integers as: 1, 3, 5 i.e ODD, ODD, ODD integers.

Here ODD is denoted as O and Even is denoted by E.

Let's start manipulation.

A. ax(b+c) = Ox(O+O) = O x E = E (NOT!)

B. (a+b)-c = (O+O)-O = E-O = O (Yes!)

C. axbxc = OxOxO = OxO = O (Yes!)

D. 2x(c-a)+b = Ex(O-O)+O = ExE + O = E + O = O (Yes!)

E. a+b+c = O + O + O = E + O = O (Yes!)

Answer is : B, C, D, E

Cheers,

If you like the answer give the kudos!

ODD-EVEN RULE:

ODD ± EVEN = ODD and ODD * ODD = ODD ; and Even otherwise.

There are 3 consecutive odd integers as: 1, 3, 5 i.e ODD, ODD, ODD integers.

Here ODD is denoted as O and Even is denoted by E.

Let's start manipulation.

A. ax(b+c) = Ox(O+O) = O x E = E (NOT!)

B. (a+b)-c = (O+O)-O = E-O = O (Yes!)

C. axbxc = OxOxO = OxO = O (Yes!)

D. 2x(c-a)+b = Ex(O-O)+O = ExE + O = E + O = O (Yes!)

E. a+b+c = O + O + O = E + O = O (Yes!)

Answer is : B, C, D, E

Cheers,

If you like the answer give the kudos!

gmatclubot

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