EMNA Q.6

0. An Egyptian fraction has a numerator equal to 1, and its denominator is a positive integer. What is the maximum number of different Egyptian fraction such that their sum is equal to 1, and their denominators are equal to 10 or less?

Answer
Comment
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Option : A
Explanation :
We ignore 1/7 and 1/9 because no sum of other denominator.numbers is going to give 7ths or 9ths in the denominator
Also, 1/5 and 1/10 are not enough to add up to anything (1/10, 2/10 and 3/10 are going to leave tenths left over no matter what else you add)
What's left is 1/2, 1/3, 1/4, 1/6, 1/8.
Sum total of these is 11/8. So we need all of them except 3/8, which means 1/2+1/3+1/6.
Which is the only way to do this with egyptian fractions whose denominators are 10 or less.
Hence maximum number of Egyptian fractions needed is 3

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