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PRINCETON REVIEW TEST DS

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PRINCETON REVIEW TEST DS

by RAGS » Thu May 10, 2007 9:56 am
In a class of 30 students, 17 students study Chinese, and r students study Japanese. Every student studies either Chinese, Japanese, or both. How many students study both Chinese and Japanese?
(1) r = 14
(2) Thirteen students take only Japanese.



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by mschling52 » Thu May 10, 2007 11:52 am
Let C = # studying Chinese, r = # studying Japanese, and B = # studying both. From the stem, C+r-B = 30 (subtract B b/c those students are counted twice since they are in C and r). We are also given that C=17.

(1) Knowing r=14, we now have that 17+14-B=30 so that B=1. Sufficient.

(2) This gives us r-B=13, and we know that C=17 and C+r-B=30. However, we don't know anything about the value of B itself, just r-B. For example, there could be 7 only Chinese, 10 both, and 13 only Japanese. Or, there could be 12 only Chinese, 5 both, and 13 only Japanese. Not Sufficient
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