The average height of 22 toddlers increases by 2 inches when two of them leave this group. If the average height of these two toddlers is one-third the average height of the original 22, then the average height, in inches, of the remaining 20 toddlers is

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32 — Easy Conserve total height. Let the original average be $x$; express the two leavers' total and the remaining $20$ toddlers' total, then equate to $22x$ and solve. 1 Set up the totals. Original average $x$, so total $=22x$. The two who leave average $	frac{x}{3}$, and the remaining $20$ average $x+2$. $$\begin{aligned} &22x=2\cdot\frac{x}{3}+20\,(x+2) \end{aligned}$$ 2 Solve for $x$. Clear the fraction and collect terms. $$\begin{aligned} &22x=\frac{2x}{3}+20x+40\ &\Rightarrow\ 66x=2x+60x+120

CAT 2017 Slot 2 — QA Question 6

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