Nested proportion questions, a share of a share
A nested proportion question gives one percentage of the whole and a second percentage of only the group the first one picked out. Work out that group first, then take the second percentage of it. After you submit, each one shows the working and names the wrong turn behind every other option.
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One question of this type, worked in full
Work it out on paper, then open Check your answer to see the full solution.
A firm employs 3,200 people. 25% of the staff work in engineering, and 30% of the engineering staff are at senior grade. How many senior engineers does the firm employ?
Check your answer
- The senior share sits on the engineers, so find them first. 25% of 3,200 is 3,200 × 25 ÷ 100 = 800 engineers.
- Now take 30% of those 800 engineers rather than of all 3,200 staff, which is 800 × 30 ÷ 100 = 240 senior engineers.
Answer: 240 people. Testonome practice pace: 50 seconds for a question like this.
Four ways this question type goes wrong
Each question offers four wrong answers beside the right one, drawn from a longer list of mistakes. These four are among them, and the review names the one you took.
Whole staff base
Taking the senior share of all the staff, so the second percentage lands on the whole firm instead of on the engineers.
Engineering count only
Stopping once the engineers are counted, so the first step is given as the answer and the senior share is never applied.
Percentage as a count
Reading the senior percentage as a number of people, so the share is never applied to any group.
Engineers below senior
Counting the engineers who are not at senior grade, so the answer is the other side of the split from the one asked for.
What the review gives you after you submit
You get the working for every question, the answer you chose beside the right one, and the reason the option you picked is wrong. Nothing is sent anywhere while you work.
Other numerical skills you can drill
The nested proportion formula, beside the other numerical formulas