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If x is an integer, which of the following must be an even i

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If x is an integer, which of the following must be an even i [#permalink] New post 17 Feb 2017, 02:27
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If x is an integer, which of the following must be an even integer?

A) \(x^2\) — x — 1

B) \(x^2\) — 4x + 6

C) \(x^2\) — 5x + 5

D) \(x^2\) + 3x + 8

E) \(x^2\) + 2x + 10
[Reveal] Spoiler: OA

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Re: If x is an integer, which of the following must be an even i [#permalink] New post 21 Feb 2017, 16:45
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Explanation

Again the best strategy is plugging values. Take an odd integer say 1. For simplicity and put the values


A) \(x^2\) — x — 1 = 1 - 1 -1 = -1

B) \(x^2\) — 4x + 6 = 1 -4 + 6 = 3

C) \(x^2\) — 5x + 5 = 1 -5 +5 = 1

D) \(x^2\) + 3x + 8 = 1 + 3 + 8 = 12

E) \(x^2\) + 2x + 10 = Don't need to evaluate this. You already have your answer.


Hence D is correct.


Note: During plugging values if you have found an answer the do not continue plugging in other options. This is very important time saving tactic.
Also keep in mind when a question has very generic statements like all integers satisfy "Expression..." It is highlly likely that plugging values is the best strategy.
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Re: If x is an integer, which of the following must be an even i [#permalink] New post 12 Aug 2018, 04:26
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sandy wrote:
Explanation

Again the best strategy is plugging values. Take an odd integer say 1. For simplicity and put the values


A) \(x^2\) — x — 1 = 1 - 1 -1 = -1

B) \(x^2\) — 4x + 6 = 1 -4 + 6 = 3

C) \(x^2\) — 5x + 5 = 1 -5 +5 = 1

D) \(x^2\) + 3x + 8 = 1 + 3 + 8 = 12

E) \(x^2\) + 2x + 10 = Don't need to evaluate this. You already have your answer.


Hence D is correct.


Note: During plugging values if you have found an answer the do not continue plugging in other options. This is very important time saving tactic.
Also keep in mind when a question has very generic statements like all integers satisfy "Expression..." It is highlly likely that plugging values is the best strategy.


X can be any integer (i.e. either odd or even) so even though your answer is correct the procedure is incomplete. You would have to check:

1) if D) fits for X as an even integer and than you are finished.

OR

2) if E) fits for x = 1, which it does not [so D) is the only possible option].
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Re: If x is an integer, which of the following must be an even i [#permalink] New post 12 Aug 2018, 13:24
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NewBorn wrote:

X can be any integer (i.e. either odd or even) so even though your answer is correct the procedure is incomplete. You would have to check:

1) if D) fits for X as an even integer and than you are finished.

OR

2) if E) fits for x = 1, which it does not [so D) is the only possible option].



You are correct I should have plugged an even and an odd integer!
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Re: If x is an integer, which of the following must be an even i [#permalink] New post 12 Aug 2018, 20:39
sandy wrote:
Explanation

Again the best strategy is plugging values. Take an odd integer say 1. For simplicity and put the values


A) \(x^2\) — x — 1 = 1 - 1 -1 = -1

B) \(x^2\) — 4x + 6 = 1 -4 + 6 = 3

C) \(x^2\) — 5x + 5 = 1 -5 +5 = 1

D) \(x^2\) + 3x + 8 = 1 + 3 + 8 = 12

E) \(x^2\) + 2x + 10 = Don't need to evaluate this. You already have your answer.


Hence D is correct.


Note: During plugging values if you have found an answer the do not continue plugging in other options. This is very important time saving tactic.
Also keep in mind when a question has very generic statements like all integers satisfy "Expression..." It is highlly likely that plugging values is the best strategy.

The question isn't mine but thanks!
Re: If x is an integer, which of the following must be an even i   [#permalink] 12 Aug 2018, 20:39
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