Is y a positive integer? (1) y^2 - 1 = 0 (2) y

Question

Is y a positive integer?

(1) y^2 - 1 = 0

(2) y < 1

chetan2u · Answer

Is y a positive integer?

(1)  y^2 - 1 = 0.........|y|=1 
So, y can be 1 or -1.
Insuff

(2) y < 1
y can be anything below 1,  but the least value of a positive INTEGER is 1. 
 So, y can be positive but not a positive integer. 
Sufficient

B

Showmeyaa · Answer

1) y^2 = 1 |y| = 1 y = +1, -1 - Insufficient! 2)y < 1 The least integer that satisfies the above condition is 0. But 0 is non-negative! So, the answer is NO, y is not a positive integer! (B) IMO! Great question

Sanya15 · Answer

Thank you!

My doubt here was in Statement (2) -- y <1, y=0, so, since 0 is a neither a positive nor a negative number, stmt (2) becomes sufficient.

shivani1351 · Answer

Using the Difference of Squares identity:
a^2 - b^2 = (a+b)(a-b)

1. (y+1)(y-1) = 0
So y can either be -1 or 1, negative or positive respectively.
Hence, we cannot ascertain the nature of y from the 1st option.

2. y < 1
As it is directly stated that y < 1, y can either be 0 or a negative integer, but  it is definitely not positive !
 
Hence, using the 2nd option alone, we can deduce that y is not a positive integer, so option (B) is the correct answer.

Is y a positive integer? (1) y^2 - 1 = 0 (2) y < 1

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