CAT Exam Model Paper 4 with solutions for free online practice

Question : 4 of 60

Marks: +1, -0

‘M’ and ‘N’ are natural numbers such that by M = (5N - 4) (5N + 1). If 1 ≤ N ≤ 200, what is the harmonic mean of all the possible values of M?

Solution:

When N = 1 M = 1 x 6
N = 2 M = 6 x 11
N = 200 M = 996 x 1001
Harmonic mean

= { 200 }/ { { 1 } /{ 1 ×6 } + { 1 } /{ 6 × 11 } + ... 1/ {996 ×1001}

=200/{1/5[1-1/6]+1/5[1/6-1/11]+...1/5[1/996-1/1001]}

= { 200 } /{ 1 [ 1 - { 1 }/{ 1001 }] } = { 200 }/ {1/ 5×1000/1001 } = 1001

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