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If x is a positive integer, is x^2 + 6x +10 odd? [#permalink]
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23 Jun 2015, 01:52
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67% (01:26) correct 33% (01:19) wrong based on 133 sessions
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Re: If x is a positive integer, is x^2 + 6x +10 odd? [#permalink]
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23 Jun 2015, 03:34
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This post received KUDOS
If x is a positive integer, is x^2 + 6x +10 odd?
In the expression x^2 + 6x + 10, 6x + 10 is always even. So we need to check whether x^2 is either even or odd to decide if the expression x^2 + 6x +10 is odd. We have 2 conditions: 1)If x^2 is even then x^2 + 6x +10 is even 2)If x^2 is odd then x^2 + 6x +10 is odd
(1) x^2 + 4x + 5 is odd
In the above expression 4x + 5 is always odd. Since the expression x^2 + 4x + 5 is odd, x^2 has to be even. As x^2 is even, x is also even. Referring to the above 2 conditions we can say x^2 + 6x +10 is even.
Sufficient
(2) x^2 + 3x + 4 is even
For the above expression to be even then x^2 + 3x has to be even. If x is odd then x^2 + 3x is even If x is even then x^2 + 3x is even
So the expression x^2 + 6x +10 can be either odd or even.
Insufficient
Ans:A



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Re: If x is a positive integer, is x^2 + 6x +10 odd? [#permalink]
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23 Jun 2015, 08:46
Bunuel wrote: If x is a positive integer, is x^2 + 6x +10 odd?
(1) x^2 + 4x + 5 is odd (2) x^2 + 3x + 4 is even
Kudos for a correct solution. Statement 1: x^2 + 4x + 5 is odd: 4x is even, 5 is odd, therefore, x^2 is even and x is even. Now, x^2+6x+10 is even. Sufficient Statement 2: x^2 + 3x + 4 is even: 4 is even, 3x+x^2 can be ODD or 3x+x^2 can be EVEN. Insufficient Answer A



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Re: If x is a positive integer, is x^2 + 6x +10 odd? [#permalink]
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23 Jun 2015, 09:25
Bunuel wrote: If x is a positive integer, is x^2 + 6x +10 odd?
(1) x^2 + 4x + 5 is odd (2) x^2 + 3x + 4 is even
Kudos for a correct solution. Question : Is x^2 + 6x +10 odd?Since x is a Positive Integer therefore 6x+10 will always be even so for x^2 + 6x +10 to be odd, x^2 MUST be odd i.e. the question is asking whether x is an odd integer or not QUESTION REDEFINED: is x an odd Integer?Statement 1: x^2 + 4x + 5 is oddSince 4x is even therefore we infer that, x^2 + 5 is odd But Since EVEN + ODD = ODD therefore, x^2 must be even for x^2+5 to be odd i.e. x is certainly ODD Hence, SUFFICIENTStatement 2: x^2 + 3x + 4 is evenEVE + EVE = EVEN Since, 4 is even, therefore x^2 + 3x MUST be even as well but, ODD + ODD = EVEN also, EVEN + EVEN = EVEN therefore x may be odd or even Hence, NOT SUFFICIENTAnswer: Option
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Re: If x is a positive integer, is x^2 + 6x +10 odd? [#permalink]
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23 Jun 2015, 09:41
Bunuel wrote: If x is a positive integer, is x^2 + 6x +10 odd?
(1) x^2 + 4x + 5 is odd (2) x^2 + 3x + 4 is even
Kudos for a correct solution. the Q basically asks us "is x odd?"(as all terms except x^2 are even).. 1) stat 1 tells us that x^2 + 4x + 5 is odd... here x^2 has to be even... suff 2) stat 2 tells us that x^2 + 3x + 4 is even... here x can take even or odd value to satisfy the eq... insuff ans A
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Re: If x is a positive integer, is x^2 + 6x +10 odd? [#permalink]
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29 Jun 2015, 05:50
Bunuel wrote: If x is a positive integer, is x^2 + 6x +10 odd?
(1) x^2 + 4x + 5 is odd (2) x^2 + 3x + 4 is even
Kudos for a correct solution. MANHATTAN GMAT OFFICIAL SOLUTION:The question can first be simplified by noting that, if x is even, x^2 + 6x + 10 will be even, and if x is odd, x^2 + 6x+ 10 will be odd. Thus, you can simplify this question: “Is x odd or even?” (A couple of shortcuts to save time in reaching that conclusion: the exponent on the first term can be ignored, since an even squared is still even and an odd squared is still odd. 6x will be even no matter what, since 6 is even, and obviously 10 is even no matter what. So, an even plus two evens is even, and an odd plus two evens is odd.) (1) SUFFICIENT: You can plug in numbers or simply use number theory. If x is even, you get even + even + odd = odd, and if x is odd, you get odd + even + odd = even. Thus, since x^2 + 4x + 5 is odd, x is even. (2) INSUFFICIENT: x^2 + 3x + 4 is actually even regardless of what integer is plugged in for x. If x is even, you get even + even + even = even, and if x is odd, you get odd + odd + even = even. Thus, x could be odd or even. Plugging in numbers will yield the same conclusion  x could be any integer. Note that you should not factor any of the expressions above. If you wasted time factoring, remember: factoring is meaningless if you don’t have an equation set equal to zero! This problem was about number theory (or number testing), not factoring. The correct answer is (A).
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Re: If x is a positive integer, is x^2 + 6x +10 odd? [#permalink]
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25 Sep 2017, 19:53
Bunuel wrote: If x is a positive integer, is x^2 + 6x +10 odd?
(1) x^2 + 4x + 5 is odd (2) x^2 + 3x + 4 is even
Kudos for a correct solution. The question is merely "is X odd?" Statement 1 This basically tells us the expression must be odd + odd + odd =odd suff Statement 2 An odd OR even could satisfy this condition such as 1 or 2 insuff A




Re: If x is a positive integer, is x^2 + 6x +10 odd?
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