Averages with Excluded Tests

CAT 2019 Slot 1 · QA · Easy · Averages

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A CAT aspirant appears for a certain number of tests. His average score increases by 1 if the first 10 tests are not considered, and decreases by 1 if the last 10 tests are not considered. If his average scores for the first 10 and the last 10 tests are 20 and 30, respectively, then the total number of tests taken by him is

Answer

60

Explanation

Let nn be the total number of tests, AA be the overall average, and SS be the total score (S=nAS = nA). Sum of first 10 tests = 10×20=20010 \times 20 = 200. Sum of last 10 tests = 10×30=30010 \times 30 = 300.

When first 10 are excluded: S−200n−10=A+1⇒nA−200=(n−10)(A+1)=nA+n−10A−10⇒n−10A=−190\frac{S - 200}{n - 10} = A + 1 \Rightarrow nA - 200 = (n - 10)(A + 1) = nA + n - 10A - 10 \Rightarrow n - 10A = -190.

When last 10 are excluded: S−300n−10=A−1⇒nA−300=(n−10)(A−1)=nA−n−10A+10⇒n+10A=310\frac{S - 300}{n - 10} = A - 1 \Rightarrow nA - 300 = (n - 10)(A - 1) = nA - n - 10A + 10 \Rightarrow n + 10A = 310.

Adding the two equations: 2n=120⇒n=602n = 120 \Rightarrow n = 60.

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