E.
I am not sure of this.
let me attempt. Pls jump in and correct me.

stmt 1: y = x +1
stmt 2: y = x^2 +1

It is clear that each stmt independently is insufficient.

lets try to combine them.
I can see that x = 0 and x = 1 satisfies both the stmts.

So it is insufficinet. Ans is E

Alternately, one can try to add or subtract stmts 1 and 2 to get x and y.


Ht Helps
-V

xy = ?

Take stmt 1)

y = x + 1
multiply by x
xy = x^2 + x
Insuffcient since we dont know x

Take stmt 2)

y = x^2 + 1
multiply by x
xy = x^3 + x
Insufficient

Taking both together we can equate
x^2 + x = x^3 + x
solving gives
x = 0 or 1
hence, xy = 0 or xy = 2
so C) insufficient

Hence E)

Solving by forming equations gives sure shot answer and sometimes, according to me, faster.

Any other better methods ?

syr wrote:xy = ?

Take stmt 1)

y = x + 1
multiply by x
xy = x^2 + x
Insuffcient since we dont know x

Take stmt 2)

y = x^2 + 1
multiply by x
xy = x^3 + x
Insufficient

Taking both together we can equate
x^2 + x = x^3 + x
solving gives
x = 0 or 1
hence, xy = 0 or xy = 2
so C) insufficient

Hence E)

Solving by forming equations gives sure shot answer and sometimes, according to me, faster.

Any other better methods ?

Thanks Syr,
Ur soln is better.

Nice solutions.

y= x+1
y = x^2+1

x+1 = x^2+1

x^2-x = 0
x ( x-1) = 0

x=0 x=1

Two possible solutions that change xy.

INSUFF
Regards,
CR