Kurt T. answered • 02/02/18
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Math Tutoring and Test Prep
I am assuming that (e.g.) the number who own laptops includes those who also own a tablet, gaming system, or both. It makes a difference. Did 365 students own ONLY a tablet or a tablet and possibly something else as well?
Draw three interlocking circles. Label them L (laptop), T (tablet), and G (gaming system).
We know 67 students own all three devices. Write 67 in the center of the diagram, where all three circles overlap.
We know 193 students own as tablet and a laptop, of whom 67 also own a gaming system. Write 126 (193 - 67) in the section where tablet and laptop intersect but do not intersect with gaming system.
Do the same with the other two overlapping sections. 131 own a tablet and gaming system, and 71 own a laptop and gaming system.
We know 365 students own a tablet, but we have to subtract out the number who own at least one other device. 365 - 126 - 131 - 67 = 41. Write this number in the "tablet only" section of the diagram.
Do the same with the remaining sections. 29 own only a laptop and 13 own only a gaming system.
Now add up the seven numbers inside the diagram. There are 478 students who own at least one device.
Don't forget the 28 students who own none of the three devices. There are 506 students in all.
a. 506
b. 131
c. 29
d. 126 + 131 + 71 = 328
e. 478
