## Question 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

A) 30
B) 28
C) 32
D) 26

Option (C)

## Solution

From CAT 2017 – Quantitative Aptitude – Arithmetic – Averages, we can see that,
Average of 22 people = a/22
Let sum of heights of two people who left = x
From the question,
(a-x)/20 = a/22 + 2
On solving, we get x=a/33
Putting value of x in a, we get the value of a as 660
x=20
Average height of remaining 20 toddlers = (a-x)/20 = 32

## CAT 2017 Questions from Quantitative Aptitude – Arithmetic

Quantitative Aptitude – Arithmetic – Averages – Ques: A class consists of 20 boys and 30 girls. In the mid-semester examination, the average score of the girls was 5 higher than that of the boys.
Quantitative Aptitude – Arithmetic – Mixtures – Q1 : Consider three mixtures – the first having water and liquid A in the ratio 1 : 2, the second having water and liquid B in the ratio 1 : 3, and the third having water and liquid C in the ratio 1 : 4.
Quantitative Aptitude – Arithmetic – Mixtures – Q2: Bottle 1 contains a mixture of milk and water in 7 : 2 ratio and Bottle 2 contains a mixture of milk and water in 9 : 4 ratio.
Quantitative Aptitude – Arithmetic – Time and Work – Q1: Amal can complete a job in 10 days and Bimal can complete it in 8 days. Amal, Bimal and Kamal together complete the job in 4 days and are paid a total amount of Rs 1000 as remuneration.
Quantitative Aptitude – Arithmetic – Time and Work – Q2: A person can complete a job in 120 days. He works alone on Day 1. On Day 2, he is joined by another person who also can complete the job in exactly 120 days.
Quantitative Aptitude – Arithmetic – Time, Speed and Distance
Quantitative Aptitude – Arithmetic – Percentages
Quantitative Aptitude – Arithmetic – Profit and Loss
Quantitative Aptitude – Arithmetic – Pipes and Cisterns: A tank has an inlet pipe and an outlet pipe. If the outlet pipe is closed then the inlet pipe fills the empty tank in 8 hours.
Quantitative Aptitude – Arithmetic – Ratios

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a) 750+ Videos covering entire CAT syllabus
b) 2 Live Classes (online) every week for doubt clarification
c) Study Material & PDFs for practice and understanding
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## Question A class consists of 20 boys and 30 girls. In the mid-semester examination, the average score of the girls was 5 higher than that of the boys. In the final exam, however, the average score of the girls dropped by 3 while the average score of the entire class increased by 2. The increase in the average score of the boys is

A) 9.5
B) 10
C) 4.5
D) 6

Option (A)

## Solution

As per CAT 2017 – Quantitative Aptitude – Arithmetic – Averages, we can see that
Score of girls = x
Score of boys = y
As per the question, x/30 = y/20 + 5
Average of class = (x + y)/ 50
New score of girls = x’
New score of boys = y’
x/30 – 3 = x’/30
(x’ + y’)/50 = (x + y)/50 + 2
x’ = x – 90
On solving we get, y’ = y + 190
New average of boys = (y + 190)/20 = y/20 + 9.5
So, average of boys increases by 9.5
Option (A)

## CAT 2017 Questions from Quantitative Aptitude – Arithmetic

Quantitative Aptitude – Arithmetic – Averages – Ques: The average height of 22 toddlers increases by 2 inches when two of them leave this group.
Quantitative Aptitude – Arithmetic – Mixtures – Q1 : Consider three mixtures – the first having water and liquid A in the ratio 1 : 2, the second having water and liquid B in the ratio 1 : 3, and the third having water and liquid C in the ratio 1 : 4.
Quantitative Aptitude – Arithmetic – Mixtures – Q2: Bottle 1 contains a mixture of milk and water in 7 : 2 ratio and Bottle 2 contains a mixture of milk and water in 9 : 4 ratio.
Quantitative Aptitude – Arithmetic – Time and Work – Q1: Amal can complete a job in 10 days and Bimal can complete it in 8 days. Amal, Bimal and Kamal together complete the job in 4 days and are paid a total amount of Rs 1000 as remuneration.
Quantitative Aptitude – Arithmetic – Time and Work – Q2: A person can complete a job in 120 days. He works alone on Day 1. On Day 2, he is joined by another person who also can complete the job in exactly 120 days.
Quantitative Aptitude – Arithmetic – Time, Speed and Distance
Quantitative Aptitude – Arithmetic – Percentages
Quantitative Aptitude – Arithmetic – Profit and Loss
Quantitative Aptitude – Arithmetic – Pipes and Cisterns: A tank has an inlet pipe and an outlet pipe. If the outlet pipe is closed then the inlet pipe fills the empty tank in 8 hours.
Quantitative Aptitude – Arithmetic – Ratios

## Online Coaching Course for CAT Exam Preparation

a) 750+ Videos covering entire CAT syllabus
b) 2 Live Classes (online) every week for doubt clarification
c) Study Material & PDFs for practice and understanding
d) 10 Mock Tests in the latest pattern
e) Previous Year Questions solved on video