PS

[shikh]

If A@B=A^2+B^2 for all real numbers A and B. then (A@B)@C=
A. A^2+B^2+C^2 B. 2A^2+2B^2+C^2
C. A^4+B^4+C^2 D. A^4+B^4+2A^2B^2+C^2

OA aftr smtym

[shankar.ashwin]

(A @ B) = A^2 + B^2

(A^2 + B^2) @ C = (A^2 + B^2)^2 + C^2 -> D IMO

[Anurag@Gurome]

If A@B=A^2+B^2 for all real numbers A and B. then (A@B)@C=
A. A^2+B^2+C^2 B. 2A^2+2B^2+C^2
C. A^4+B^4+C^2 D. A^4+B^4+2A^2B^2+C^2

OA aftr smtym

A@B = A² + B²
(A@B)@C = (A² + B²) @ C = (A² + B²)² + C² = A^4 + B^4 + 2A²B² + C²

The correct answer is D.

[GMATGuruNY]

If A@B=A^2+B^2 for all real numbers A and B. then (A@B)@C=
A. A^2+B^2+C^2 B. 2A^2+2B^2+C^2
C. A^4+B^4+C^2 D. A^4+B^4+2A^2B^2+C^2

OA aftr smtym

Let A=2, B=1 and C=1.
A@B = 2²+1² = 5.
(A@B)@C = 5@1 = 5²+1² = 26. This is our target.

Now we plug A=2, B=1 and C=1 into the answers to see which yields our target of 26.

A quick scan of the answers reveals that only answer choice D works:
A^4 + B^4 + 2A²B² + C² = 2^4 + 1^4 + 2(2²)(1²) + 1² = 16+1+8+1 = 26.

The correct answer is D.

[shikh]

thanku all..