Data Sufficiency

Gurpinder wrote:

3,4,5 and 5,12,13 are two Pythagorean Triple relevant here.

13^2 = 5^2 + 12^2

statement (1) If x<12, then diagonal < 13 (A clear YES) Hence, SUFFICIENT

statement (2) diagonal of the rectangle>10 doesn't tell us if it is greater than or lesser than 13.

Therefore answer is option (A), statement (1) alone is sufficient.

Can somebody confirm?

Even i was looking for numbers to use the statement but was not success full in it.
for me its A now but i will be very pleased if anybody can give the proper reasoning i know its related to the theory that sum of two sides should always be greater than third side.
But looking for better explanations.

You are right, Goyalsau, to be thinking about the relationship between
the lengths of the sides, but because the triangles are parts of a
rectangle, they are right triangles so we can use a more specific rule
than the sum of two sides being greater than the third side. We can
use the Pythagorean theorem, as Euro does, to relate the sides
directly.

From the diagram, we can see a right triangle whose hypotenuse is the
diagonal of the rectangle; let's call that d. The legs of the triangle
are of length 5 and x, so the Pythagorean theorem states 5^2 + x^2 =
d^2. That means d = sqrt(5^2 + x^2). Next, recall that 5, 12, 13 is a
Pythagorean triple-this can help us avoid some nasty computations.
Since 5-12-13 is a Pythagorean triple, in order for d to EQUAL 13, x
will have to be equal to 12. So for d to be less than 13, x will have
to be less than 12.

Statement 1 says that x < 12, so 5^2 + x^2 < 5^2 + 12^2 = 13^2, so the
diagonal must be less than 13. Statement 1 is sufficient.

Statement 2 only says the diagonal of the rectangle is greater than
10. It could be 10.5 or 11, which are less than 13, but it could also
be 14 or 15. Since we can't know whether the diagonal is less than 13,
the statement is insufficient.

Choice A is correct.

Gurpinder wrote:

Statement 1:
The length < 12
Given one side is 5
If the diagnol were to be 13 , then by pythogoras theorem , X = 12
But the statement 1 says that X< 12 ...hence the diagnol will surely be lesser than 13
So sufficient

Statement 2 :
Says diagnol is > 10
Take x= 12 ... then diagnol = 13 (same as above by Pythogoras theorem)... That means for 10<X<12 the diagnol is less than 13
Now since X > 10..X can be say 15 ..In that case diagnol = square root of ( 15^2 + 5 ^2) ...Surely in this case, the diagnol > 13 ....Hence this statement is not sufficient

So answer = A