Question

What is the average height of the class?
(I) Average height of the class decreases by 1 cm if we exclude the tallest person of the class whose height is 56 cm.
(II) Average height of the class increases by 1 cm if we exclude the shortest person of the class whose height is 42 cm.

• A. Data in Statement I alone is sufficient to answer the question but the data in Statement II alone is not sufficient to answer the question.
• B. Data in Statement II alone is sufficient to answer the question but the data in Statement I alone is not sufficient to answer the question.
• C. Data in statements I and II together are necessary to answer the question.
• D. Data in statements I and II together is not sufficient to answer the question.

Answer 1

The Correct Option is C

We want to determine the average height of the class. Let's analyze the given statements:

Statement I: Average height of the class decreases by 1 cm if we exclude the tallest person whose height is 56 cm.

Let the total number of students be \( n \) and the average height be \( A \). Therefore, the total height is \( n \times A \). When the tallest person (56 cm) is excluded, the new average becomes \( A - 1 \), and the total height becomes \((n-1)(A-1)\).

Equating the total heights:

\( nA - 56 = (n-1)(A-1) \)

Expanding and simplifying:

\( nA - 56 = nA - n - A + 1 \)

\( 56 = n + A - 1 \)

\( A = 57 - n \)

Without \( n \), we can't find a specific value for \( A \).

Statement II: Average height increases by 1 cm if we exclude the shortest person whose height is 42 cm.

The similar approach as Statement I gives:

Total height excluding shortest person: \((n-1)(A+1)\)

Equating total heights, we get:

\( nA - 42 = (n-1)(A+1) \)

Expanding and simplifying:

\( nA - 42 = nA + n - A - 1 \)

\( 42 = n - A - 1 \)

\( A = n - 43 \)

Without \( n \), we can't find a specific value for \( A \).

Now consider Statements I and II together:

From Statement I: \( A = 57 - n \)

From Statement II: \( A = n - 43 \)

Equating the two expressions for \( A \):

\( 57 - n = n - 43 \)

\( 100 = 2n \)

\( n = 50 \)

Substitute \( n = 50 \) in \( A = 57 - n \): \( A = 57 - 50 = 7 \)

Thus, the average height of the class is 7 cm.

Therefore, data in Statements I and II together are necessary to answer the question.