samichange wrote:
If x and y are positive integers, is x^2 + x + y + 1 an even number?
1. x is equal to half the sum of the HCF of 12, 26, and 48 and LCM of 25, 35, and 50.
2. y^4/16 is an even number.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
X2 will be odd when x is odd , will be even when X is even .
4 possible scenarios for F(XY)=x^2 + x + y + 1
X=Odd , Y= Even , F(XY) = ODD
X=Even , Y= Even , F(XY) = ODD
X=Odd, Y=Odd, F(XY) = EVEN
X=Even, Y=Odd F(XY)=EVEN
1. x is equal to half the sum of the HCF of 12, 26, and 48 and LCM of 25, 35, and 50.
not sufficient as we do not know about Y (it may be odd or even) .
2. y^4/16 is an even number.
clearly Y is even , let look at above scenarios.
we see that whenever Y is EVEN F(XY) is ODD.
so this statement is sufficient.
not that hard question IMO.