bySayantani Barman Experta en el extranjero
Question: The operation ⊙ is defined for all real numbers x and y by the equation x⊙y = \(x^2+y^2-xy\). Each of the following must be true EXCEPT
- x⊙x = \(x^2\)
- x⊙y = y⊙x
- x⊙1 =x
- x⊙0 =\(x^2\)
- x⊙y = (-x) ⊙(-y)
Answer:
Approach Solution (1):
It is an operation and what it means is given, so check all values by substituting the values
It is given that x⊙y= \(x^2+y^2-xy\)
- x⊙x =\(x^2\)… =\(x^2+x^2-xx=2x^2-x^2=x^2\)… True
- x⊙y = y⊙x… In x⊙y = \(x^2+y^2-xy\), x and y are interchangeable and still the equation remains the same. So true
- x⊙1 = x….\(x^2+1^2-x*1=x^2+1-x\) This is not equal to x. Hence false
- x⊙0 =\(x^2\)...=\(x^2+0^2-x*0=x^2\)… True
- x⊙y = (-x) ⊙(-y)… -x⊙y= \((-x)^2+(-y)^2-(-x)(-y)=x^2+y^2-xy\)
Correct Option: C
“The operation ⊙ is defined for all real numbers x and y by the equation x⊙y = \(x^2+y^2-xy\). Each of the following must be true EXCEPT?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.
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