If x is an even number, which of the following must be odd?

Question

I. 3x + 1

II. (5x)^2 + 2

III. (x + 1)^2

(A) I only

(B) III only

(C) I and II only

(D) I and III only

(E) I, II, and III

DavidTutorexamPAL · Answer

Even/Odd questions are usually solvable without explicit calculations, using basic properties.
We'll look for such an answer, a Logical approach.

I. x is even --> 3x is odd*even=even --> 3x+1 is even + odd= odd
II. x is even --> 5x is odd*even=even --> (5x)^2 is even*even=even --> (5x)^2 + 2 is even+even=even
III. x is even --> x+1 is even+odd=odd --> (x+1)^2 is odd*odd=odd

(D) is our answer.

wishalsp333 · Answer

If x is an even number, which of the following must be odd?

I. 3x + 1

II. (5x)^2 + 2

III. (x + 1)^2

(A) I only

(B) III only

(C) I and II only

(D) I and III only

(E) I, II, and III

Lets substitute x=2,
1) 3(2) + 1 = 7 (ODD)
2) (5(2))^2 + 2 = 102 (Even)
3) (2+1)^2 = 9 (ODD)

So the option id D

JeffTargetTestPrep · Answer

We may recall that even + odd = odd and odd + even = odd.

I. 3x + 1

Since x is even, 3*(even) + 1 = even + odd = odd.

I is true.

II. (5x)^2 + 2

(5*(even))^2 + 2 = even + even = even

II is not true.

III. (x + 1)^2

(even + 1)^2 = (odd)^2 = odd

III is true.

Answer: D

Manasvi1 · Answer

I. 3x + 1 
 x is even so 3*x will be even 
And, any even no. +1 gives odd no. 
therefore, In this expression the resulting no. will be odd

II. (5x)^2 + 2
 x is even so 5*x will be even 
And, Square of any even no. will be even
And, any even no. +2 gives an even no.
therefore, In this expression the resulting no. will be even

III. (x+1)^2
 x is even so X+1 will be odd
And, square of any odd no. is odd
therefore, In this expression the resulting no. will be odd

So, in expressions I. and III. the resulting no. must be odd

Hence OA (D)

Abhishek009 · Answer

BY USING PROPERTIES

(I) Odd*Even = Even & Even + Even = Odd
(II) (Odd*Even)^2 = Even , Even + Even = Even
(III) (Even + Odd)^2 = Odd

Answer must be (D)

PLUG IN AND CHECK

Let x = 2

I.  3x + 1 = 3*2 + 1 = 7

II.  (5x)^2 + 2 = (5*2)^2 = 102

III.  (x + 1)^2 = (2+1)^2 = 9

Answer must be (D)

If x is an even number, which of the following must be odd?

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GMAT Problem Solving (PS) Questions

If x is an even number, which of the following must be odd?

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