Question 131 Problem Solving 2018 GMAT Official Guide

Question 131 Problem Solving 2018 GMAT Official Guide

Video explanation: M is the sum of the reciprocals of the consecutive integers from…

Comments

Katsays

Hi,

I am confused to how you got the sum to be 100/300 =1/3? At video 1:05.

I understood that 300 – 201 + 1 = 100 terms but how does the sum to come to be 1/3? there are 100 of 1/300 and how does (1/300 + 1/300 + 1/300 +…+ 1/300) hundred of these become 1/3?…

Adding 100 terms where each one is equal to 1/300 is equivalent to multiplying 1/300 by 100, which is equal to 1/3. I hope this clarifies your question, if not I will elaborate further.

For the largest limit: why did we do- 1/201+1/201… 100 terms, ie we know that 1/201 is the largest term, so why are we multiplying it by 100 for 100 terms. My thought is we already know that M = 1/201+ 1/202+… 1/300 , where 1/201 is the largest term, so if we multiply 1/201 *100 terms, will not the sum give us even a greater range than 1/201.

Not sure, if I could put my question into words, please let me know if you would like additional inputs. Thanks

What we are trying to do is to establish an upper limit for the summation. By replacing each term by 1/201, which is clearly greater than all of the terms, we know that the actual value of M in the question would be less than this resulting sum of 100 times 1/201. And yes, by replacing each term by 1/201, the resulting sum would be greater than the actual expression M. We are essentially trying to find an upper and lower limit to the summation. Does this make sense?

Kat says

Hi,

I am confused to how you got the sum to be 100/300 =1/3? At video 1:05.

I understood that 300 – 201 + 1 = 100 terms but how does the sum to come to be 1/3? there are 100 of 1/300 and how does (1/300 + 1/300 + 1/300 +…+ 1/300) hundred of these become 1/3?…

Not really understanding the missing steps.

Thanks

Kat

GMAT Quantum says

Hi Kat,

Adding 100 terms where each one is equal to 1/300 is equivalent to multiplying 1/300 by 100, which is equal to 1/3. I hope this clarifies your question, if not I will elaborate further.

Dabral

Jayita Ghosh says

Hi,

For the largest limit: why did we do- 1/201+1/201… 100 terms, ie we know that 1/201 is the largest term, so why are we multiplying it by 100 for 100 terms. My thought is we already know that M = 1/201+ 1/202+… 1/300 , where 1/201 is the largest term, so if we multiply 1/201 *100 terms, will not the sum give us even a greater range than 1/201.

Not sure, if I could put my question into words, please let me know if you would like additional inputs. Thanks

GMAT Quantum says

Hi Jayita,

What we are trying to do is to establish an upper limit for the summation. By replacing each term by 1/201, which is clearly greater than all of the terms, we know that the actual value of M in the question would be less than this resulting sum of 100 times 1/201. And yes, by replacing each term by 1/201, the resulting sum would be greater than the actual expression M. We are essentially trying to find an upper and lower limit to the summation. Does this make sense?

Dabral