MBApyq

Averages with Excluded Tests

CAT 2019 Slot 1 · Quantitative Ability · Easy · Averages

This is an easy Quantitative Ability question from the CAT 2019 Slot 1 paper. It tests Averages. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

All CAT 2019 Slot 1 questionsMore Averages questionsAll CAT QA

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.

Related Averages questions

Practise this under exam conditions

Sign in to solve it with a live timer, the on-screen CAT calculator, and streak and accuracy tracking across every question you attempt.

Solve in the workspace