Hi kdatt1991,

The key to this question is in finding a quick way to figure out how many multiples of 7 you're dealing with. If you're comfortable doing basic division by hand, the "math" required isn't too bad.

I'm going to start by figuring out how many TOTAL multiples of 7 we're dealing with:

250/7 = 35 remainder 5, so we know that there are 35 multiples of 7 in total. NOW we have to figure out how many of those multiples are in the first group of 100 cards...

100/7 = 14 remainder 2, so we know....

35 TOTAL multiples:

There are 14 multiples of 7 in the first deck.

There are 21 multiples of 7 in the second deck.

Pulling 1 card from both decks, the probability of pulling two multiples of 7 is:

(14/100)(21/150)

While this might look "scary", you can reduce BOTH fractions before you multiply. The answer choices hint that the product will reduce anyway...

(14/100) = 7/50

(21/150) = 7/50

(7/50)(7/50) = (7^2)/2500

Final Answer:

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Rich

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