Math Gurus: can you please check what is wrong with my approach.

Statement 2: if x=y+a
then y=x-a
That makes the original statement: Does (x + a)^2 = (x-a)^2? for any value of x and a, can it be true?

Does (x + a)^2 = y^2?
(1) x = y - a
(2) x = y + a

the original question may ask whether a=0 or not? It may also ask given x=-7,a=2 is y=5? (or x=7,a=-2, y=-5, even we can apply modes here ... restatements could be various)
with statement (1) we cannot answer if a=0 or not; also not clear if 7=! -5+2 neither -7=! 5-2 This is Not Sufficient and the answer cannot be A.

statement (2) does not provide any useful information either, as we don't know if a=0 or not; neither we know if -7=! 5+2 nor 7=! -5-2 Not Sufficient.

combined st(1&2): y-a=y+a must be Sufficient, as we know for sure that a=0 and then can answer the question as Yes, (x + a)^2 = y^2

p.s. I am surprised throughout the year NR's post could not find the right click for this question, even experts gave this two tries

the terrible mistake of most posters here including Fabio's was using original statement from question (x + a)^2 = y^2 for plugging in statement (1) and statement (2) expressions.

when we rewrite statement (1) from x+a=y into (x+a)^2=y^2 we should not forget that this is an arbitrary way of squaring both sides, we don't know the signs of (x+a) and y

the same rule of thumb is noticed for many prior solutions concerning statement (2)

zooki wrote:Math Gurus: can you please check what is wrong with my approach.


Statement 2: if x=y+a
then y=x-a
That makes the original statement: Does (x + a)^2 = (x-a)^2? for any value of x and a, can it be true?

answer A

straight

(A)
QED

Answer -> A

Don't noe if this approach is good but i picked numbers for this problem where x=2,a=3 so (x+a)^2=y^2
which is (2^2+2(6)+3^2)=25, so y= 5,so seeing the statements only statement (A) satisfies the condition where x= 5-3, which gives us 2 so it is sufficient whereas statement 2 gives us x= 5+3, which is insufficient.

Plz correct me if this approach is correct !!

A for Answer.

if a =0

then, x=y+a
=y+0

x+a=y

here (x+a)^2=y^2

OA is A
since x=y-a
therefor we get y^2=y^2
However for statement 2 we get
y+2a^2=y^2
now if a=0
then we get y^2=y^2
if a is any other number they arent equal
therefore OA is A

obviously A

Night reader wrote:Does (x + a)^2 = y^2?

(1) x = y - a

(2) x = y + a

Direct substitution
(1) (y - a + a)^2 = (y)^2 = y^2
SUFFICIENT

(2) (y + a + a)^2 = (y + 2a) = y^2
INSUFFICIENT because we don't know what "a" is

Does (x + a)^2 = y^2?

(1) x = y - a

(2) x = y + a

(1) (y-a+a)^2 =y^2 Sufficient
(2) (y+a+a)^2 = (y+2a)^2 Not sufficient

Ans: A

answer is A, we don't know value of a for statement II to be valid.