Latest self Aptitude Question SOLUTION: The sum of N real numbers (not necessarily unique) is 20. The sum of the 3 smallest of these numbers is 5. The sum of the 3 largest is 7. What is N?

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The sum of N real numbers (not necessarily unique) is 20. The sum of the 3 smallest of these numbers is 5. The sum of the 3 largest is 7. What is N?

jyotish r (11 years ago)

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chaitanya  (11 years ago)

N = 10

The whole set:
{1, 2, 2, 2, 2, 2, 2, 2, 2, 3} has 10 members

subset of the three smallest:
{1 + 2 + 2} sum to 5

subset of the three largest:
{2 + 2 + 3} sum to 7

remaining memebers of the set:
{2 + 2 + 2 + 2} sum to 8

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Aman  (11 years ago)

N= 10
each of smallest 3 = 5/3 = 1.66666.... or numbers are 1.7,1.7 and (1.6 say)
each of largest 3 = 7/3 = 2.33333.... or 2.3,2.3 and 2.4
so other numbers lie between 1.7 and 2.3
say these numbers are 2,2,2,... only.
number of 2s = (20-7-5)/2 = 8/2=4
so N = 4+3+3=10

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