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Manhattan GMAT 700+ challenge problem - July 24, 2006

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Manhattan GMAT 700+ challenge problem - July 24, 2006

by Kevin » Wed Jul 26, 2006 12:13 pm
Most of our students Manhattan GMAT are trying to break the 700+ barrier. As a result, we've developed our own math problems written at the 700+ level; these are the types of questions you'll WANT to see, when you are working at that level. Try to solve this 700+ level Problem Solving problem (I'll post the solution next Monday).


Question
Sequentially Speaking

Sequence S is defined as Image, for all n > 1.
If S1= 201, then which of the following must be true of Q, the sum of the first 50 terms of S?

(A) 13,000 < Q < 14,000
(B) 12,000 < Q < 13,000
(C) 11,000 < Q < 12,000
(D) 10,000 < Q < 11,000
(E) 9,000 < Q < 10,000

[/img]
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The Answer

by achal.kumble » Wed Jul 26, 2006 9:45 pm
We knpw that S1=201.
Now by looking at the formula,we can choose to ignore the fraction part as it will tend to zero.
So the question basically translates to S1+1+S2+1+....
Now, S2=S1+1 (The fraction part is ignored as mentioned earlier)
Therefore, S2=202.
Similarly S3=203;S4=204 and so on.
Therefore S50=250
Hence S1+S2+S3+...+S50 will be 201+202+203+...+250 which is 11275.
Hence the answer is (c)
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Challenge problem

by Prashant » Wed Jul 26, 2006 10:03 pm
(C) 11,000 < Q < 12,000 i think

SUm of Sn = sum of AP + sum HP ....
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by Kevin » Mon Jul 31, 2006 12:04 pm
Answer

To find each successive term in S, we add 1 to the previous term and add this to the reciprocal of the previous term plus 1.

S1= 201

Image

Image

The question asks to estimate (Q), the sum of the first 50 terms of S. If we look at the endpoints of the intervals in the answer choices, we see have quite a bit of leeway as far as our estimation is concerned. In fact, we can simply ignore the fractional portion of each term. Let’s use S2 &#8776; 202, S3 &#8776; 203. In this way, the sum of the first 50 terms of S will be approximately equal to the sum of the fifty consecutive integers 201, 202 … 250.

To find the sum of the 50 consecutive integers, we can multiply the mean of the integers by the number of integers since average = sum / (number of terms).

The mean of these 50 integers = (201 + 250) / 2 = 225.5

Therefore, the sum of these 50 integers = 50 x 225.5 = 11,275, which falls between 11,000 and 12,000. The correct answer is C.
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by STEVEN SPIELBERG » Mon Mar 15, 2010 11:23 am
IMOC
I want to win an OSCAR on the GMAT !!!
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