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Roger wants to buy a television and DVD player. There are 9 available models of televisions and 6 available models of DVD players, but 3 of these television sets are not compatible with 2 of the DVD players. In how many ways can he buy a television and a compatible DVD player?

a. 48
b. 54
c. 62
d. 70
e. 72

If you are in time crunch then we know that there are 54 total ways and there is just one option which is less than 54. So that has to be the answer.
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Nixondutta
Roger wants to buy a television and DVD player. There are 9 available models of televisions and 6 available models of DVD players, but 3 of these television sets are not compatible with 2 of the DVD players. In how many ways can he buy a television and a compatible DVD player?

a. 48
b. 54
c. 62
d. 70
e. 72

If all 9 models of televisions and 6 models of DVD players are compatible with one another, then there are 9 x 6 = 54 ways to purchase them. However, since 3 models of televisions and 2 models of DVD players are not compatible, we need to remove 3 x 2 = 6 ways from the above mentioned 54 ways, leaving us with 54 - 6 = 48 ways to purchase a TV and a DVD player.

Answer: A
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Hello from the GMAT Club BumpBot!

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