153 persons bought three different kinds of cellular phones namely Nokia, Sony Ericsson and Motorola. The number of people who bought both Nokia and Sony Ericsson is 30. The number of people who bought both Nokia and Motorola and the number of people who bought both Sony Ericsson and Motorola is 20 and 25 respectively. The ratio of the difference between the people who bought only Nokia and only Sony Ericsson to the difference between the number of people who bought only Nokia and only Motorola is 2 : 3. For every one person who bought only Sony Ericsson, there are two persons who bought only Nokia. Among the persons who bought only one kind of mobile phone, the number of persons buying Nokia was the highest.Find the minimum possible number of persons who bought all three kinds of cellular phones.a)0b)1c)2d)3Correct answer is option 'D'. Can you explain this answer?

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153 persons bought three different kinds of cellular phones namely Nokia, Sony Ericsson and Motorola. The number of people who bought both Nokia and Sony Ericsson is 30. The number of people who bought both Nokia and Motorola and the number of people who bought both Sony Ericsson and Motorola is 20 and 25 respectively. The ratio of the difference between the people who bought only Nokia and only Sony Ericsson to the difference between the number of people who bought only Nokia and only Motorola is 2 : 3. For every one person who bought only Sony Ericsson, there are two persons who bought only Nokia. Among the persons who bought only one kind of mobile phone, the number of persons buying Nokia was the highest.

Find the minimum possible number of persons who bought all three kinds of cellular phones.

a)
0
b)
1
c)
2
d)
3

Correct answer is option 'D'. Can you explain this answer?

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Most Upvoted Answer

153 persons bought three different kinds of cellular phones namely No...

To find the minimum possible number of persons who bought all three kinds of cellular phones, let's analyze the given information step by step.

Step 1: Understanding the given information

- Total number of persons = 153
- Three types of cellular phones: Nokia, Sony Ericsson, and Motorola
- Number of people who bought both Nokia and Sony Ericsson = 30
- Number of people who bought both Nokia and Motorola = 20
- Number of people who bought both Sony Ericsson and Motorola = 25
- Ratio of the difference between people who bought only Nokia and only Sony Ericsson to the difference between people who bought only Nokia and only Motorola = 2:3
- For every one person who bought only Sony Ericsson, there are two persons who bought only Nokia

Step 2: Setting up equations

Let's assume the number of people who bought all three types of phones as 'x'.

- Number of people who bought only Nokia = N
- Number of people who bought only Sony Ericsson = S
- Number of people who bought only Motorola = M

Based on the given information, we can set up the following equations:

1. N + S + M + 30 + 20 + 25 + x = 153 (Total number of persons)
2. N - 30 = 2(S - 30) (Ratio between people who bought only Nokia and only Sony Ericsson)
3. N - 20 = 3(M - 20) (Ratio between people who bought only Nokia and only Motorola)
4. S = 2N (For every one person who bought only Sony Ericsson, there are two persons who bought only Nokia)

Step 3: Solving the equations

Let's solve these equations simultaneously to find the values of N, S, and M.

From equation 4, we can substitute S as 2N in equation 2:

N - 30 = 2(2N - 30)
N - 30 = 4N - 60
3N = 30
N = 10

Substituting N = 10 in equation 4, we get:

S = 2(10)
S = 20

Substituting N = 10 in equation 3, we get:

10 - 20 = 3(M - 20)
-10 = 3M - 60
3M = 50
M = 16.67 (Approx.)

Since the number of persons buying the phones should be a whole number, we can assume M = 17.

Step 4: Finding the minimum possible number of persons who bought all three kinds of cellular phones

Substituting the values of N, S, and M in equation 1:

10 + 20 + 17 + 30 + 20 + 25 + x = 153
122 + x = 153
x = 31

Therefore, the minimum possible number of persons who bought all three kinds of cellular phones is 31.

Conclusion:

The correct answer is option D) 3.

Answered by Wizius Careers · View profile

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Community Answer

153 persons bought three different kinds of cellular phones namely No...

In the following venn diagram N, S and M stands for Nokia, Sony Ericsson and Motorola respectively.

Given that (a − c) : (a − b) = 2 : 3 and a : c = 2 : 1. Let us assume that a = 4K, b = K and c = 2K where K is a constant

Now, 4K + 50 − x + 2K + 25 − x + K = 153 Or. 7K = 78 + 2x

The following are the possible values of K and x that satisfy the above equation:

(K = 12, x = 3) ; (K = 14, x = 10) and (K = 16 and x = 17)

Minimum possible number of persons who bought all three kinds of cellular phones is 3.

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153 persons bought three different kinds of cellular phones namely Nokia, Sony Ericsson and Motorola. The number of people who bought both Nokia and Sony Ericsson is 30. The number of people who bought both Nokia and Motorola and the number of people who bought both Sony Ericsson and Motorola is 20 and 25 respectively. The ratio of the difference between the people who bought only Nokia and only Sony Ericsson to the difference between the number of people who bought only Nokia and only Motorola is 2 : 3. For every one person who bought only Sony Ericsson, there are two persons who bought only Nokia. Among the persons who bought only one kind of mobile phone, the number of persons buying Nokia was the highest.Find the minimum possible number of persons who bought all three kinds of cellular phones.a)0b)1c)2d)3Correct answer is option 'D'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about 153 persons bought three different kinds of cellular phones namely Nokia, Sony Ericsson and Motorola. The number of people who bought both Nokia and Sony Ericsson is 30. The number of people who bought both Nokia and Motorola and the number of people who bought both Sony Ericsson and Motorola is 20 and 25 respectively. The ratio of the difference between the people who bought only Nokia and only Sony Ericsson to the difference between the number of people who bought only Nokia and only Motorola is 2 : 3. For every one person who bought only Sony Ericsson, there are two persons who bought only Nokia. Among the persons who bought only one kind of mobile phone, the number of persons buying Nokia was the highest.Find the minimum possible number of persons who bought all three kinds of cellular phones.a)0b)1c)2d)3Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 153 persons bought three different kinds of cellular phones namely Nokia, Sony Ericsson and Motorola. The number of people who bought both Nokia and Sony Ericsson is 30. The number of people who bought both Nokia and Motorola and the number of people who bought both Sony Ericsson and Motorola is 20 and 25 respectively. The ratio of the difference between the people who bought only Nokia and only Sony Ericsson to the difference between the number of people who bought only Nokia and only Motorola is 2 : 3. For every one person who bought only Sony Ericsson, there are two persons who bought only Nokia. Among the persons who bought only one kind of mobile phone, the number of persons buying Nokia was the highest.Find the minimum possible number of persons who bought all three kinds of cellular phones.a)0b)1c)2d)3Correct answer is option 'D'. Can you explain this answer?.

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