# In an apartment complex, the number | Quantitative Aptitude - Arithmetic – Averages

### CAT Verbal Ability

CAT 2018 – The CAT QA section has grown increasingly difficult since 2015. In order to tackle the tougher CAT Level QA questions for the CAT Exam, it is important to understand the basics of CAT. To obtain a great CAT score, make use of MBAP Free Study material with detailed solutions and video explanations. Check out MBAP free Mock test to take these questions in a test format for free.

## CAT 2018 - Slot-1 - Arithmetic - Question- 4 - In an apartment complex, the number

Q. 4: In an apartment complex, the number of people aged 51 years and above is 30 and there are at most 39 people whose ages are below 51 years. The average age of all the people in the apartment complex is 38 years. What is the largest possible average age, in years, of the people whose ages are below 51 years?
1. 27
2. 28
3. 26
4. 25

Correct Answer: 2. 28

Let the average age of people aged 51 years and above be x years. Let the average age of people aged below 51 years be y years.

Let the number of people aged below 51 years be N.

Given, the average age of all the people in the apartment complex is 38 years.

Therefore,

(x*30+y*N) / 30+N = 38 ……(1)

We want to maximize y, which occurs when x is minimum i.e. for x=51. Substituting the value of x in (1) we get

390=N×(38-y)

Again, when y is maximum, N is also maximum i.e. 39 Therefore maximum value of y = 28.

### Past Year Question Paper & Solutions

Counselling Session
By IIM Mentor