Answer
MRI
Work Step by Step
An MRI would be the best choice for localizing the tumor in the man's brain. Dense structures (such as bone) do not show up in an MRI, making it easy to look into the skull and allowing imaging of brain matter.
A PET would not be the best option because it is mainly used to observe metabolic processes and here, you are trying to locate a tumor in the brain. Sonography would also not work as it has very low penetrating power and produce only vague outlines of organs.
Although X-rays can be used to identify tumors in the lungs, it would not be best to use an X-ray to locate a brain tumor; X-rays are best at imaging hard, bony structures and if used to locate a brain tumor, would produce an image of the skull and not the brain matter that you would wish to see.
