Hello,
I tried searching a solution for above question as the explanation given in the OG is too complicated.
can you help answer the question in any different way?
Q:
M is the sum of the reciprocals of the consecutive integers from 201 to 300, inclusive. Which of the following is true?
A. 1/3 < M < 1/2
B. 1/5 < M < 1/3
C. 1/7 < M < 1/5
D. 1/9 < M < 1/7
E. 1/12 < M < 1/9
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OG 2015, PS Q#80 ( M is the sum of the reciprocals..........
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If all of the 100 values were 1/300, the result would be the following sum:M is the sum of reciprocals of the consecutive integers from 201 to 300 inclusive. which of the following is true?
A. 1/3 < M < 1/2
B. 1/5 < M < 1/3
C. 1/7 < M < 1/5
D. 1/9 < M < 1/7
E. 1/12 < M < 1/9
100(1/300) = 1/3.
Since all but one of the values are actually GREATER THAN 1/300, the value of M must be GREATER THAN 1/3.
If all of the 100 values were 1/200, the result would be the following sum:
100(1/200) = 1/2.
Since all of the values are actually LESS THAN 1/200, the value of M must be LESS THAN 1/2.
Thus:
1/3 < M < 1/2.
The correct answer is A.
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Hi baalok88,
In this prompt, the answer choices are "ranges"; this usually means that there's a way to avoid doing lots of math and instead use patterns and logic to save you time.
Mitch's already pointed out the easiest way to figure out the minimum and maximum values of the sum of the reciprocals. You can actually stop working once you figure out the minimum though:
Since 1/300 < 1/201 and the sum of those 100 terms would be 1/3 AT THE MINIMUM, the only answer that's possible would be A. The extra work that Mitch did just confirms the maximum value of the sum, but it's unnecessary.
As you continue to study, be mindful of how the answer choices are written - they can sometimes provide a huge hint into the fastest way to answer the question.
GMAT assassins aren't born, they're made,
Rich
In this prompt, the answer choices are "ranges"; this usually means that there's a way to avoid doing lots of math and instead use patterns and logic to save you time.
Mitch's already pointed out the easiest way to figure out the minimum and maximum values of the sum of the reciprocals. You can actually stop working once you figure out the minimum though:
Since 1/300 < 1/201 and the sum of those 100 terms would be 1/3 AT THE MINIMUM, the only answer that's possible would be A. The extra work that Mitch did just confirms the maximum value of the sum, but it's unnecessary.
As you continue to study, be mindful of how the answer choices are written - they can sometimes provide a huge hint into the fastest way to answer the question.
GMAT assassins aren't born, they're made,
Rich
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Jeff@TargetTestPrep
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Let's first analyze the question. We are trying to find a potential range for M, and M is equal to the sum of the reciprocals from 201 to 300, inclusive. Thus, M is:baalok88 wrote:
M is the sum of the reciprocals of the consecutive integers from 201 to 300, inclusive. Which of the following is true?
A. 1/3 < M < 1/2
B. 1/5 < M < 1/3
C. 1/7 < M < 1/5
D. 1/9 < M < 1/7
E. 1/12 < M < 1/9
1/201 + 1/202 + 1/203 + ...+ 1/300
Since the GMAT does not expect us to do the math above, that is why the answer choices give a range of values for M. Thus, we do not need to know the EXACT value of M. The easiest way to determine the RANGE of M is to use easy numbers that can quickly be manipulated.
Note that 1/200 is greater than each of the addends and that 1/300 is less than or equal each of the addends. Therefore, instead of trying to add together 1/201 + 1/202 + 1/203 + ...+ 1/300, we are instead going to add 1/200 one hundred times and 1/300 one hundred times. These two sums will give us a high estimate of M and a low estimate of M. Again, we are adding 1/200, one hundred times, and 1/300, one hundred times, because there are 100 numbers from 1/201 to 1/300.
Instead of actually adding each one of these values one hundred times, we will simply multiply each value by 100. We have:
1/300 x 100 = 1/3
1/200 x 100 = 1/2
We see that M is between 1/3 and 1/2.
Answer A
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