Is xy an integer?

Question

Is xy an integer?

(1) x is the ratio of the area of a square to the area of the largest possible circle inscribed within that square.

(2) y is the ratio of the area of a circle to the area of the largest possible square inscribed within that circle.

Kudos for a correct  solution .

Celerma · Answer

I believe that the answer is E.

First statement is not sufficient as it does not give us any information about y.

Similarly, Second statement is not sufficient because it does not give any information about x.

Now, combing the two statements, we may or may not get integer, depending on values of x and y. x and y can be integer or non integer.

So IMO the answer is E.

HieuNguyenVN · Answer

Question.png My answer is C.

Celerma · Answer

Looks like you have got the right answer

SKMishra · Answer

Answer should be (C).

Statement 1: INSUFFICIENT. As no information about y is given, therefore no matter what is the value of x, the product xy can have any value.

Statement 2: INSUFFICIENT. Same reasoning as above.

Both Statements: SUFFICIENT
Statement 1 gives: The largest circle that can be inscribed in a square will have diameter equal to the side of the square (2r = A). Hence, x =  \frac{A^2}{\pi r^2} = \frac{4}{\pi}  (substituting A = 2r).
Statement 2 gives: The largest square that can be inscribed in a circle will have diagonal equal to the diameter (2r =  \sqrt{2} a). Hence, y =  \frac{\pi r^2}{a^2} = \frac{\pi}{2}  (substituting a =  \sqrt{2} r).

Hence, xy = 2 = integer.

Hemavakade · Answer

Answer = C

mvictor · Answer

clearly 1 and 2 alone are not sufficient.
A, D, and B are out.

we are left with C and E - 50% chance of getting the right answer.

since we have square/circle (something with Pi) * circle (something with pi)/square => we get an integer.
C is my best guess

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Is xy an integer?

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