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Which of the following cannot yield an odd integer when divided by 5?

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Which of the following cannot yield an odd integer when divided by 5?  [#permalink]

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New post Updated on: 05 Jul 2017, 08:27
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Which of the following cannot yield an odd integer when divided by 5?

A. an odd integer squared
B. an integer less than 5
C. the product of an odd integer and an even integer
D. the sum of three consecutive integers
E. an even integer minus an odd integer

What is wrong with B??

Originally posted by Viserion99 on 05 Jul 2017, 07:56.
Last edited by Bunuel on 05 Jul 2017, 08:27, edited 1 time in total.
Edited the question.
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Re: Which of the following cannot yield an odd integer when divided by 5?  [#permalink]

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New post 05 Jul 2017, 08:28
1
Viserion99 wrote:
Which of the following cannot yield an odd integer when divided by 5?

A. an odd integer squared
B. an integer less than 5
C. the product of an odd integer and an even integer
D. the sum of three consecutive integers
E. an even integer minus an odd integer

What is wrong with B??



simply consider -5 as an example....

-5 / 5 = -1.....

hope it helps
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Re: Which of the following cannot yield an odd integer when divided by 5?  [#permalink]

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New post 05 Jul 2017, 08:31
1
1
Which of the following cannot yield an odd integer when divided by 5?

A. an odd integer squared: 5^2/5 = 5 = odd. Possible.

B. an integer less than 5: (-5)/5 = -1 = odd. Possible.

C. the product of an odd integer and an even integer: If even*odd/5 = odd , then we'd get even*odd = odd*5, which cannot be true: LHS is even, while RHS is odd.

D. the sum of three consecutive integers: (4 + 5 + 6)/5 = 3 = odd. Possible.

E. an even integer minus an odd integer: (6 - 1)/5 = 1 = odd. Possible.

Answer: C.
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Re: Which of the following cannot yield an odd integer when divided by 5?  [#permalink]

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New post 05 Jul 2017, 08:41
Bunuel wrote:
Which of the following cannot yield an odd integer when divided by 5?

A. an odd integer squared: 5^2/5 = 5 = odd. Possible.

B. an integer less than 5: (-5)/5 = -1 = odd. Possible.

C. the product of an odd integer and an even integer: If even*odd/5 = odd , then we'd get even*odd = odd*5, which cannot be true: LHS is even, while RHS is odd.

D. the sum of three consecutive integers: (4 + 5 + 6)/5 = 3 = odd. Possible.

E. an even integer minus an odd integer: (6 - 1)/5 = 1 = odd. Possible.

Answer: C.



Thanks.
I thought negative numbers cannot be classified as odd/even.
Remember reading it somewhere.
So, I was confused.
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Re: Which of the following cannot yield an odd integer when divided by 5?  [#permalink]

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New post 05 Jul 2017, 08:46
1
Viserion99 wrote:
Bunuel wrote:
Which of the following cannot yield an odd integer when divided by 5?

A. an odd integer squared: 5^2/5 = 5 = odd. Possible.

B. an integer less than 5: (-5)/5 = -1 = odd. Possible.

C. the product of an odd integer and an even integer: If even*odd/5 = odd , then we'd get even*odd = odd*5, which cannot be true: LHS is even, while RHS is odd.

D. the sum of three consecutive integers: (4 + 5 + 6)/5 = 3 = odd. Possible.

E. an even integer minus an odd integer: (6 - 1)/5 = 1 = odd. Possible.

Answer: C.



Thanks.
I thought negative numbers cannot be classified as odd/even.
Remember reading it somewhere.
So, I was confused.


An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder. So, ..., -4, -2, 0, 2, 4, ... are all even integers.

An odd number is an integer that is not evenly divisible by 2. So, ..., -3, -1, 1, 3, 5, ... are all odd integers.
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Re: Which of the following cannot yield an odd integer when divided by 5?  [#permalink]

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New post 14 Jul 2017, 10:47
Viserion99 wrote:
Which of the following cannot yield an odd integer when divided by 5?

A. an odd integer squared
B. an integer less than 5
C. the product of an odd integer and an even integer
D. the sum of three consecutive integers
E. an even integer minus an odd integer

What is wrong with B??


Let’s test each answer choice:

A) an odd integer squared

Since 5^2 = 25 and 25/5 = 5, an odd integer squared can yield an odd integer when divided by 5.

B) an integer less than 5

Since -5/5 = -1, an integer less than 5 can yield an odd integer when divided by 5.

C) the product of an odd integer and an even integer

The product of an odd and even integer will always produce an even integer.

Any even integer (such as 10, 20, 30, etc.) that is divisible by 5 will always yield an even number.

Answer: C
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Re: Which of the following cannot yield an odd integer when divided by 5?  [#permalink]

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