CAT 2017 Question Paper | Quants Slot 2

CAT Questions

Online prepration for CAT encompasses going through the very basics and building your way upwards to enable yourself to tackle the CAT Question Paper. Solving CAT previous year paperis the right step that'll advance you in this direction. Ace your CAT Exam Preparation by going through the repository of questions curated by 2IIM by visit 2IIM's Question Bank. Start your CAT Online Preparation right away with a question from a simple yet important topic of Arithmetic, i.e. Averages. See if you can solve the question correctly without the help of the text and video solutions provided.

Question 6 : 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

1. 30
2. 28
3. 32
4. 26

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Video Explanation

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Explanatory Answer

Method of solving this CAT Question from Averages

From the given data let us assume the average height of 22 toddlers to be a
If two of them leaves this group then average height of 20 toddlers increases by 2 so a + 2
If the average height of two toddlers who leaves the group is one third the average height of the original 22
No.of toddlers × average = Total
Hence we can write the equation in such a way that,
22a = 20(a + 2) + \\frac{2a}{3})
2a – \\frac{2a}{3}) = 40
⟹ \\frac{4a}{3}) = 40
a = 30
We need to find the average of remaining 20 toddlers.
⟹ a + 2 = 30 + 2 = 32

The question is "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"

Hence, the answer is 32

Choice C is the correct answer