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# GRE Weekly Challenge #1

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Senior Manager
Joined: 25 Jul 2011
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23 Aug 2011, 10:42
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GMAT Club invites you to test your GRE knowledge for a chance to win! Each week, we will post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week’s drawing for a free Manhattan GRE Strategy guide. Tell your friends to get out their scrap paper and start solving! Click here to view contest & prize details

This week's question:

Sequence S is such that $$S_n = S_{n-1} + \frac{3}{2}$$, and $$S_1 = 2$$

Sequence A is such that $$A_n = A_{n-1} - 1.5$$, and $$A_1 = 18.5$$

 A B The sum of the terms in S from $$S_1 to S_{13}$$, inclusive The sum of the terms in A from $$A_1 to A_{13}$$, inclusive

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Edit: Thank you for participating. The correct answer, and the winner will be announced shortly.

Solution

Many students find sequence notation intimidating, but it doesn’t have to be. Let’s rephrase each sequence in normal language.

Sn = Sn – 1 + is just saying that every term in S is equal to the term before it, plus 3/2.

An = An – 1 – 1.5 is just saying that every term in A is equal to the term before it, minus 1.5.

Of course, 3/2 and 1.5 are the same, which is a good clue that there’s probably some simple way to solve this problem without actually summing up a sequence.

Since S1 = 2 and every term in S is just 3/2 greater than the term before it, Sequence S begins like this: 2, 3.5, 5, 6.5, 8, 9.5, 11....

Since A1 =18.5 and every term in A is just 1.5 less than the term before it, Sequence A begins like this: 18.5, 17, 15.5, 14, 12.5, 11, 9.5....

At this point, it looks as though the two sequences in Column A and Column B are going to have a lot of terms in common! Remember, any common elements appearing in both A and B can just be canceled out.

You could just write out all 13 terms for each column, or you could “skip up” to S13 by noting that S13 is just going to be S1 plus 1.5, twelve times (since it takes twelve “jumps” to get from 1 to 13). 2 plus 18 is 20, so S13 = 20.

You can also “skip up” to the final term in A. To get to A13, take A1 and subtract 1.5 twelve times (since it takes twelve “jumps” to get from 1 to 13). 18.5 minus 18 is 0.5.
So,

 Column A looks like this: And Column B looks like this: 2, 3.5, 5, ... 18.5, 20 18.5, 17, 15.5.... 2, 0.5

That is, all the terms from 2 to 18.5 are held in common by both sets, so we can safely subtract them out. Here’s what’s left:

 Column A Column B 20 0.5

The winner of this Week's Challenge is... (drum roll).... linkiswickeddank. Congratulations! Please send me a pm with your shipping address, and choice of Manhattan GRE Guide

Stay tuned for an update on next week's competition
_________________
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Joined: 23 Aug 2011
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Kudos [?]: 0 [0], given: 0

Re: GRE Weekly Challenge #1 [#permalink]

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23 Aug 2011, 22:34
This reply is hidden until the winner is announced.
Manager
Joined: 08 Jun 2010
Posts: 172
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Kudos [?]: 26 [0], given: 15

Re: GRE Weekly Challenge #1 [#permalink]

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24 Aug 2011, 05:27
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VP
Joined: 24 Jul 2011
Posts: 1028
GMAT 1: 780 Q51 V48
GRE 1: 1540 Q800 V740
Followers: 109

Kudos [?]: 483 [0], given: 18

Re: GRE Weekly Challenge #1 [#permalink]

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24 Aug 2011, 06:56
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Re: GRE Weekly Challenge #1 [#permalink]

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24 Aug 2011, 21:27
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Current Student
Joined: 19 Nov 2010
Posts: 20
Location: United States
Concentration: Operations, General Management
GMAT 1: 760 Q50 V42
GPA: 2.5
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Kudos [?]: 8 [0], given: 4

Re: GRE Weekly Challenge #1 [#permalink]

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25 Aug 2011, 13:43
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Intern
Joined: 13 Jul 2011
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Location: Turkey
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Re: GRE Weekly Challenge #1 [#permalink]

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25 Aug 2011, 13:52
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Schools: HKUST '15
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Re: GRE Weekly Challenge #1 [#permalink]

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25 Aug 2011, 15:35
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Senior Manager
Joined: 20 Dec 2010
Posts: 258
Schools: UNC Duke Kellogg
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Kudos [?]: 36 [0], given: 4

Re: GRE Weekly Challenge #1 [#permalink]

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25 Aug 2011, 21:17
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Re: GRE Weekly Challenge #1 [#permalink]

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25 Aug 2011, 23:23
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Kudos [?]: 24 [0], given: 183

Re: GRE Weekly Challenge #1 [#permalink]

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26 Aug 2011, 00:55
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Re: GRE Weekly Challenge #1 [#permalink]

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26 Aug 2011, 01:54
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Re: GRE Weekly Challenge #1 [#permalink]

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26 Aug 2011, 02:04
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26 Aug 2011, 03:39
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Re: GRE Weekly Challenge #1 [#permalink]

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26 Aug 2011, 05:13
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Re: GRE Weekly Challenge #1   [#permalink] 26 Aug 2011, 05:13
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