if S is the sum of all the numbers of the form 1/n

Question

if S is the sum of all the numbers of the form 1/n, where n is an integer from 33 to 64, inclusive, then S lies in which of the following intervals.

A) 0 < S < 1/64

B) 1/64 < S < 1/32

C) 1/32 < S < 1/2

D) 1/2 < S < 1

E) 1 < S < 2

can someone please explain the solution?

avigoesforMBA · Answer

Hey!

S = 1/33 + 1/34 + 1/35.....1/64

No. of terms = 64 - 33 + 1 (since 33 is inclusive) = 32

Now, in the entire series, 1/33 > 1/34 > 1/35 and so on...

Let's assume every value in the series to be = to the largest term of the series = 1/33

So series will become and S will be = to 1/33 + 1/33 + 1/33 .... (32 terms)

S = 32/33 < 1
----------------------------- (1)

Now, lets assume every value in the series = smallest terms of series = 1/64

So series will become 1/64 + 1/64 .... (32 terms)

S = 1/64 * 32 = 32/64 = 1/2

------------------------------- (2)

Now, look at 1 and 2

If I make every thing smaller my least sum will still be 1/2 and if I make everything bigger, my max sum will be 1

But since this series lies in btw, for example 1/34 is bigger than 1/64 and smaller than 1/33. So is every other term right.

Hence ... 1/2 < Sum < 1

Hope you understand!

SubhraDhara

if S is the sum of all the numbers of the form 1/n, where n is an integer from 33 to 64, inclusive, then S lies in which of the following intervals.

A) 0 < S < 1/64

B) 1/64 < S < 1/32

C) 1/32 < S < 1/2

D) 1/2 < S < 1

E) 1 < S < 2

can someone please explain the solution?

Kinshook · Answer

If S is the sum of all the numbers of the form 1/n, where n is an integer from 33 to 64, inclusive, then S lies in which of the following intervals.

S = 1/33 + 1/34 + ..... + 1/64 
Number of terms = 64-33+1 = 32

S > 1/64 * 32 = 1/2
S < 1/32 * 32 = 1

1/2 < S < 1

IMO D

Omnoui · Answer

Every time you read Sum , think first to the following formula : SUM = Number of Terms * Average of Terms

Here, Number of Terms = 64-33+1= 32 and Average of Terms (reciprocal of this -->)=(64+33)/2=48.5 let's considere 49

Then, S=Number of Terms * AVerage = 32*(1/49)=32/49 . You can clearly see that this number is more than 1/2 and less than 1.

Correct answer : D

Bunuel · Answer

This question is discussed here: https://gmatclub.com/forum/if-s-is-the- ... 14550.html This topic is locked and archived.

if S is the sum of all the numbers of the form 1/n

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