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The following questions are accompanied by three statements (I), (II), and (III). You have to determine which statements(s) is/are sufficient/necessary to answer the questions. What is the average height of a group of five persons P, Q, R, S and T? I. Average height of P, Q and R is 155 cm and average height of R, S and T is 167 cm. II. Height of R is 2 more than the overall average. III. Height of P and S together is 500 cm

The following questions are accompanied by three statements (I), (II), and (III). You have to determine which statements(s) is/are sufficient/necessary to answer the questions. What is the average height of a group of five persons P, Q, R, S and T? I. Average height of P, Q and R is 155 cm and average height of R, S and T is 167 cm. II. Height of R is 2 more than the overall average. III. Height of P and S together is 500 cm Correct Answer Both I and II

From statement I:

(P + Q + R)/3 = 155

P + Q + R = 155 × 3 = 465      ----(1)

(R + S + T)/3 = 167

R + S + T = 167 × 3 = 501

S + T = 501 - R

Let average of all the persons = A

A = (P + Q + R + S + T)/5        ----(2)

From equations (1) and (2)

A = (465 + 501 – R)/5

5A = 966 – R      ----(3)

From statement II:

R = 2 + A

Replacing R in equation (3), we get

5A = 966 - 2 - A

From here A can be calculated

∴ Statements I and II are required.

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