If x is an integer, is (x + p)(x + q) an even integer? (1) q is an eve

Question

If x is an integer, is (x + p)(x + q) an even integer?

(1) q is an even integer.
(2) p is an odd integer.

chetan2u · Answer

We surely require to know what each of p and q are. They can be fractions too.

Combined
Whatever x be, one of x+p or x+q will surely be even and other odd, as p and q are of opposite type. 
Product of even and odd is even. 
Sufficient

C

mdsaddamforgmat · Answer

IMO: C
Given: x is an integer
Need to evaluate: (x + p)(x + q) an even integer
Pre-thinking: X can be Odd, Even or Zero &
P,Q can be odd,Even, Zero or Fraction

St. 1: q is an even integer
We need to have both p & Q designations in order to evaluate the given equation

St. 2 : p is an odd integer.
Again, designation of Q is missing

Combining both Statements, we can arrive that X is even (here, by putting both X an odd & even we will get final result as even)

carouselambra · Answer

Basics :e*e = even / o*e = even
We need to check if (x + p)(x + q) is an even integer - so we must be know that either of the number HAS to be even.

(1) q is an even integer.
We do not know the value of 'x' or 'p' here.
Example : (3+1)(3+2) = even
 (7+0)(7+2) = odd

A is not sufficient.

(2) p is an odd integer.
Same logic can be applied as above.

Combining, we will know that (x +  odd )(x +  even ) 
We can know for sure that the overall value is even because :
(2+3)(2+2) = even
(3+5)(3+6) = even

IMO C

Pankaj0901 · Answer

IMO C

Each of the statements alone is not sufficient, because we don't x,p or q can take any values (odd/even).

If both statements are considered together: (x + odd)(x + even), whatever the value of x is, one pair would be EVEN and would the product be also EVEN.

daniformic · Answer

(1) q = even integer.
If x=even and p=odd -> (2+1)(2+2)=even
If x=odd and p=even -> (1+2)(1+2)=odd
NS

(2) p=odd integer
Same logic above
NS

(1&2)
If x=even -> (2+1)(2+2)=even
If x=odd -> (1+3)(1+2)=even

Answer C

akadiyan · Answer

If x is an integer, is (x + p)(x + q) an even integer?

Given :
X is an Integer

Not Known :
P and Q is an Integer or Not

(1) q is an even integer.
Q is an even integer. But we do not have any information on P. P can be E/O - Integer, Zero or decimal. 
We cannot say whether (x+p) (x+q) an even integer.

Insufficient.

(2) p is an odd integer.
Same reasoning as option 1. But we do not have any information on P. P can be E/O - Integer, Zero or decimal. 
We cannot say whether (x+p) (x+q) an even integer.

Insufficient.

Now considering both (1) + (2) together

Q is an even integer & P is an odd integer

(x + p)(x + q)

If x is odd , then (x+p)(x+q) is Even
If x is even, then (x+p)(x+q) is Even

In both the cases, X is Even

Ans:   C

GCMEMBER · Answer

If x is an integer, is (x + p)(x + q) an even integer?

(1) q is an even integer.
Nothing is known about p. 
Not sufficient

(2) p is an odd integer.
Nothing is known about q.
Not sufficient

(1) + (2) 
If x is odd (x + p) will be even and (x + p)(x + q) will become even.

If x is even (x + q) will be even and (x + p)(x + q) will become even.

Sufficient

Option C

Posted from my mobile device

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If x is an integer, is (x + p)(x + q) an even integer? (1) q is an eve

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If x is an integer, is (x + p)(x + q) an even integer? (1) q is an eve

Prep Toolkit

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