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If x is an integer, is 3x + 7 even?

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If x is an integer, is 3x + 7 even?  [#permalink]

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New post 15 Nov 2017, 08:44
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A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

86% (01:16) correct 14% (01:48) wrong based on 75 sessions

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Re: If x is an integer, is 3x + 7 even?  [#permalink]

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New post 15 Nov 2017, 08:50
Bunuel wrote:
If x is an integer, is 3x + 7 even?

Question is essentially asking if x is odd?

Quote:
(1) (x – 5)(x + 1) = 0


x = -1,5
in both cases x is odd => 3x + 7 is even. Sufficient.

Quote:
(2) x is a factor of 105.

x = 1,3,5,7,21,105
in all these cases x is odd => 3x + 7 is even. Sufficient.

D is the answer.
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Re: If x is an integer, is 3x + 7 even?  [#permalink]

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New post 15 Nov 2017, 10:06
We are given that x is an integer. So if x is odd, 3x will be odd and hence 3x+7 will be even. And if x is even, 3x will be even and hence 3x+7 will be odd. So we just need to know whether x is odd or even.

(1) (x-5)(x+1) = 0
this tells us that either x=5 or x=-1. Both these values are odd. So 3x+7 will be even in either case. Sufficient.

(2) x is a factor of 105. Since 105 is an odd number, ALL its factors have to be odd. So no matter which of its factors x is, x will be odd. So 3x+7 will be even in either case. Sufficient.

Hence D answer
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Re: If x is an integer, is 3x + 7 even?  [#permalink]

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New post 15 Nov 2017, 19:14
I would say D. If we know that x= odd integer, then we are good to go.
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Re: If x is an integer, is 3x + 7 even?  [#permalink]

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New post 15 Nov 2017, 20:06
Basic Properties :
odd X odd = odd
odd + odd = even
Number of factors : if N = a^p X b^q X c^ r (where a,b and c are prime factors) then no. of factors = (p+1)(q+1)(r+1)
From statement 1 :
(x – 5)(x + 1) = 0
=> x can be either 5 or -1
either case are odd (-1 is an odd number)( All negative integers can either be odd or even)
Thus substituting these values will give 3x+7 as even.
hence Sufficient
From statement 2 :
X is a factor of 105.
the factors of 105 are : 1,3,5,7,15,21,35,105 (there are 8 factors of 105.)
since all these factors are odd, the expression 3x+7 will be even.
Hence sufficient.
As both the options are sufficient the answer should be D
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Re: If x is an integer, is 3x + 7 even?  [#permalink]

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New post 16 Nov 2017, 22:18
Bunuel wrote:
If x is an integer, is 3x + 7 even?

(1) (x – 5)(x + 1) = 0

(2) x is a factor of 105.



Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question, and then recheck the numbers of variables and equations.

The question that \(3x + 7\) is even is equivalent to the statement that \(x\) is odd, because if \(x\) is odd, \(3x + 7\) is even and if \(x\) is even, \(3x + 7\) is odd.

Condition 1)
\((x-5)(x+1)=0\) is equivalent to \(x = 5\) or \(x = -1\).
Both of them are odd.
Thus this is sufficient.

Condition 2)
The condition 2) that \(x\) is a factor of \(105\) means all factors are odd since \(105\) doesn't have a factor \(2\).
Thus \(x\) must be odd.
Thus this is sufficient, too.

Therefore, the answer is D.

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59 % chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
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Re: If x is an integer, is 3x + 7 even? &nbs [#permalink] 16 Nov 2017, 22:18
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