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

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Intern
Joined: 02 Jun 2016
Posts: 1
If x is an integer, which of the following must be an even integer?  [#permalink]

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02 Jun 2016, 04:00
2
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Difficulty:

25% (medium)

Question Stats:

78% (01:39) correct 22% (01:36) wrong based on 95 sessions

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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

I assume that picking numbers is the best way to go around here. I'll let X be even and I'm going to start testing the third equation

e . e - o . e + o =
e - o + o =
Result: EVEN

my question is, when doing this number picking strategy and letting x always be even, you realize that the only equation that generates an odd result is D. But, do I need to test all equations again letting x be odd? Putting it another way, for this type of exercise, does the ODD/EVEN result change depending what you let the unknown be?

On a side note, you can see that B and E are similar so probably you dont need to test both.

thanks!!
Math Expert
Joined: 02 Aug 2009
Posts: 7036
Re: If x is an integer, which of the following must be an even integer?  [#permalink]

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02 Jun 2016, 08:38
1
2
rbtta23 wrote:
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

I assume that picking numbers is the best way to go around here. I'll let X be even and I'm going to start testing the third equation

e . e - o . e + o =
e - o + o =
Result: EVEN

my question is, when doing this number picking strategy and letting x always be even, you realize that the only equation that generates an odd result is D. But, do I need to test all equations again letting x be odd? Putting it another way, for this type of exercise, does the ODD/EVEN result change depending what you let the unknown be?

On a side note, you can see that B and E are similar so probably you dont need to test both.

thanks!!

Hi,

the point one should see is that the first two terms are in variable which can be converted into x*(x-some integer).....

1) if integer is EVEN, x*(x-integer) will depend on WHAT x is - even if x is even and odd if x is odd..
we can eliminate such choices as they depend on x and will not result in MUST..

2) If integer is ODD, x*(x-integer) will always be EVEN...
so the entire equation will depend on WHAT integer is added to x*(x-integer)..
If it is ODD, answer will be EVEN +-ODD = ODD

3) If integer is ODD, x*(x-integer) will always be EVEN...
so the entire equation will depend on WHAT integer is added to x*(x-integer)..
If it is EVEN, answer will be EVEN +-EVEN = EVEN

Lets check the choices-

A:$$x^2-x-1........x(x-1)-1....$$ type (2)... will be ODD
B:$$x^2-4x+6......x(x-4)+6...$$Type (1).... will depend on x
C: $$x^2-5x+5........x(x-5)+5....$$ type (2)... will be ODD
D: $$x^2+3x+8........x(x+3)+8....$$ type (3)... will be EVEN...answer
E:$$x^2+2x+10......x(x+2)+10...$$Type (1).... will depend on x

D
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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If x is an integer, which of the following must be an even integer?  [#permalink]

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02 Jun 2016, 09:50
2
rbtta23 wrote:
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

I assume that picking numbers is the best way to go around here. I'll let X be even and I'm going to start testing the third equation

e . e - o . e + o =
e - o + o =
Result: EVEN

my question is, when doing this number picking strategy and letting x always be even, you realize that the only equation that generates an odd result is D. But, do I need to test all equations again letting x be odd? Putting it another way, for this type of exercise, does the ODD/EVEN result change depending what you let the unknown be?

On a side note, you can see that B and E are similar so probably you dont need to test both.

thanks!!

ALTERNATE METHOD - USE OPTIONS

Check the options by plugging in some values ( Preferably smaller integers like 1 and 2 )

A: x^2-x-1 = -1 { If x = 1 }

B: x^2-4x+6 = 3 { If x = 1 }

C: x^2-5x+5 = 1 { If x = 1 }

D: x^2+3x+8 = 12 { If x = 1 } & x^2+3x+8 = 18 { If x = 2 }

E: x^2+2x+10 = 13 { If x = 1 }

Thus the only possible answer is (D)
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Abhishek....

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Manager
Joined: 18 Oct 2016
Posts: 139
Location: India
WE: Engineering (Energy and Utilities)
Re: If x is an integer, which of the following must be an even integer?  [#permalink]

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13 Apr 2017, 03:01
Option D

x is an integer. Odd: O, Even: E & Fraction: F

x = Odd or Even = O or E

A: x^2-x-1 = E^2 - E - 1 or O^2 - O - 1 = E - 1 or E - 1 = O
B: x^2-4x+6 = E^2 - 4E + 6 or O^2 - 4O + 6 = E or O + E = E or O
C: x^2-5x+5 = E^2 - 5E + 5 or O^2 - 5O + 5 = E + 5 or E + 5 = O
D: x^2+3x+8 = E^2 +3E + 8 or O^2 +3O + 8= E + 8 or E + 8 = E
E: x^2+2x+10 = E^2 + 2E + 10 or O^2 + 2O + 10= E + 10 or O + E = E or O
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Re: If x is an integer, which of the following must be an even integer?  [#permalink]

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09 Jul 2018, 06:50
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Re: If x is an integer, which of the following must be an even integer? &nbs [#permalink] 09 Jul 2018, 06:50
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