(1/33)+(1/34)+ . . . +(1/63)+(1/64) is including in which of the following ranges?
A. (1/6)~(1/5)
B. (1/5)~(1/4)
C. (1/4)~(1/3)
D. (1/3)~(1/2)
E. (1/2)~1
The OA is E.
How could I determine the correct range? Experts, I don't know how to solve it.
(1/33)+(1/34)+ . . . +(1/63)+(1/64)
This topic has expert replies
GMAT/MBA Expert
- ceilidh.erickson
- GMAT Instructor
- Posts: 2095
- Joined: Tue Dec 04, 2012 3:22 pm
- Thanked: 1443 times
- Followed by:247 members
The key is that this question is asking you for the RANGE that the answer falls in - it's not actually asking you to calculate. You definitely should not try to actually calculate! That would take far too much time.
Instead, find a good way to approximate. If we go from 33 to 64, that's 32 terms (64 - 33 + 1).
First, image that we were adding 1/32 + 1/32 + 1/32.... 32 times. That would add up to 1. Since all of our terms are smaller than 1/32, we know that the sum is less than 1.
Now, imagine that all 32 terms were 1/64. (32)(1/64) would give us 1/2. Since all but the last term is actually greater than 1/64, we know that the overall sum must be greater than 1/2.
Using that reasoning, the only answer that makes sense is E.
Instead, find a good way to approximate. If we go from 33 to 64, that's 32 terms (64 - 33 + 1).
First, image that we were adding 1/32 + 1/32 + 1/32.... 32 times. That would add up to 1. Since all of our terms are smaller than 1/32, we know that the sum is less than 1.
Now, imagine that all 32 terms were 1/64. (32)(1/64) would give us 1/2. Since all but the last term is actually greater than 1/64, we know that the overall sum must be greater than 1/2.
Using that reasoning, the only answer that makes sense is E.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
GMAT/MBA Expert
- ceilidh.erickson
- GMAT Instructor
- Posts: 2095
- Joined: Tue Dec 04, 2012 3:22 pm
- Thanked: 1443 times
- Followed by:247 members
By the way, this question is very similar in structure to this OG question: https://www.beatthegmat.com/m-is-the-sum ... tml#793900
See if you can try it without calculating!
Please POST THE SOURCE of your question - it's a copyright violation not to do so!
See if you can try it without calculating!
Please POST THE SOURCE of your question - it's a copyright violation not to do so!
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
GMAT/MBA Expert
- ceilidh.erickson
- GMAT Instructor
- Posts: 2095
- Joined: Tue Dec 04, 2012 3:22 pm
- Thanked: 1443 times
- Followed by:247 members
M7MBA, following up.
What was the source of this question?
What was the source of this question?
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education