For integers a, x, and y, a = x^2 + 2x + y. Is a even?

Question

For integers a, x, and y,  a = x^2 + 2x + y . Is a even?

(1) y = x + 4

(2) x + 4 = 15

sidsst · Accepted Answer

a = x^2 + 2x + y

From statement 1 :

y= x+4.

a = x^2+2x+x+4
a = (x^2+x) + (2x+4) .
 a = x(x+1) + 2(x+2)  Now 2(x+2)is an even entity thus we just need to concentrate on the x(x+1) part.
Of any two consecutive integers, one of them is even. Thus the entity x(x+1) is also even.
We know that even + even = even.

Therefore a = even.

This statement is sufficient to answer the question.

Statement 2 :

x +4 = 15; x = 11;
Thus a = 121+22+y
a = 143 +y

if y is odd a is even. If y is even a is odd.
This statement is not sufficient.

Therefore Answer = A

rohit8865 · Answer

(1)  Case 1:- 
when x is odd then y =odd

let x= 1 then y = 5
then a = 1+2+5= 8---even

Case 2:- 
when x =even then y = even
let x=2 then y =6
substituting a = 4+4+6 =even

both cases a= even

Case 3:- 
but if x =1/2 then y = 9/2
substituting 
a= 1/4 + 1 + 9/2 =23/4 ---fraction -----not even

(2) no information of y 
but x is integer
insuff

combining both from (2) as x= integer
thus a must be even (from first 2 cases in (1) )

Ans C

amanvermagmat · Answer

a = x^2 + 2x + y
We don't know whether x and y are integers: and if they are, whether even or odd integers.

Statement 1. y= x+4. So a becomes:
a = x^2 + 2x + x + 4 = x^2 + 3x + 4
But we don't know if x is an integer or if it is, then even/odd integer? So  Insufficient .

Statement 2. x+4=15, so x = 15-4 = 11. But we don't know about y. So  Insufficient .

Combining the two statements: x = 11, y = x+4 = 15. Now we can easily check whether a is even or not.  Sufficient .

Hence  C answer

sasidharrs · Answer

Given
1. y= x+4 => y = x+even=> x even -> Y even; x odd-> Y odd
substituting in the equation for x both even and odd, we get y as even only. Sufficient
2. It doesn't give anything about Y. So, not sufficient
Ans : A

ps: please correct me if I am wrong..

amanvermagmat · Answer

Hi

You are assuming that x will be either even or odd. But its not given that x is an integer. Its possible that x is a number like 1.33. Then y becomes 5.33
In this case 'a' will turn out to be a decimal number, so neither even nor odd.

Hero8888 · Answer

Hi  Bunuel

You know better than anyone on this forum that in GMAT world statement 1 is insufficient until we get information regarding to property of x. What if I tell you that x=1/2?

a = {1/2}^2 + 2*1/2 + 1/2 +4 
 a = 5 + 3/4  - fraction

In case if x = 0, then a = 4 - indeed even

Clearly, the question stem or OA should be modified. Thanks.

Mo2men · Answer

Hi Hero8888 You were faster than in posting same examples

Bunuel Can you please confirm what we all miss here? Does the questions miss that x & y are integers?

Arro44 · Answer

It seems I got the right answer by overlooking the fact that the numbers are not integers.

Bunuel · Answer

You are all right. Veritas Prep modified the question and added the part saying that a, x, and y are integers.

Bismarck · Answer

OA: A

(1)  y= x + 4  
  a= x^2 + 2x + y 
  a=x^2 + 2x +(x+4) 
  a = x^2 +x+ (2x +4) 
  a = x(x+1) + (2x +4) 
  Case   1  : if  x  is odd, then  x+1  will be even.
  a = odd(even) + (even)=even+even 
  a  will be even
  Case   2  : if  x  is even, then  x+1  will be odd.
  a = even(odd) + (even)=even+even 
  a  will be even 
 So Statement  1  alone is sufficient to answer whether  a  is even or not.

(2) x + 4 = 15 , 
  x=11 , putting  x=11  in question stem
  a = x^2 + 2x + y 
  a = 121 + 2*11 + y 
  a = 143+y 
  Case  1  : when y is odd
  a= odd+ odd =even 
  Case  2  : when y is even
  a= odd + even= odd 
 So Statement  2  alone is not sufficient to answer whether  a  is even or not.

Mo2men · Answer

Solve the question conceptually without plugging numbers

a = x^2 + 2x + y

Since 2x is even.......the question will boil down to:

Is  a = x^2 + y  even? (Note:  x^2  does not change the nature of a number)

(2) x + 4 = 15

No info about y

Insufficient

(1) y = x + 4

y - x= 4

This mean that either both are odd or both are even....In whichever case, the answer is YES

Sufficient

Answer: A

dagrawal · Answer

From Question: a=x^2 + 2x + y
a=x(x+2)+y

Now Statement 1: y=x+4
=> a=x(x+2)+x+4
a=x(x+2)+(x+2)+2
a=(x+2)(x+1)+2

Hence if x is even or odd a is even
Sufficient

Statement 2: x+4=15 => x=11
a=121+22+y
a=143+y

Hence if y is even a is odd and if y is odd a is even
Insufficient

IMO A

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For integers a, x, and y, a = x^2 + 2x + y. Is a even?

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For integers a, x, and y, a = x^2 + 2x + y. Is a even?

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