Series

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anishprabhu: Senior | Next Rank: 100 Posts; Posts: 46; Joined: Sun Feb 15, 2009 3:09 pm; Thanked: 1 times; GMAT Score:720

by anishprabhu » Thu Mar 12, 2009 3:46 pm

If the terms of a series are either "2" or "24" and the sum of all the terms of the series is 124, then which of the following could be the number of "2s" in the series?

A. 48

B. 35

C. 38

D. 28

E. 26

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Source: Beat The GMAT — Problem Solving | Thu Mar 12, 2009 3:46 pm

Feep: Senior | Next Rank: 100 Posts; Posts: 69; Joined: Wed Mar 04, 2009 4:15 pm; Thanked: 17 times; GMAT Score:780

by Feep » Thu Mar 12, 2009 4:08 pm

We may note that there are only six possibilities for the sequence: 5 "24"s, 4 "24"s, 3 "24"s, 2 "24"s, 1 "24", or no "24"s at all. The fewest number of twos will obviously result from having 5 "24"s and 2 "2"s, resulting in two "2"s.

For each "24" term we replace with "2"s, we gain 12 additional "2"s. Therefore, possibilities are 2, 14, 26, 38, 50, and 62. Of these, only 38 is an answer. C.

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anishprabhu: Senior | Next Rank: 100 Posts; Posts: 46; Joined: Sun Feb 15, 2009 3:09 pm; Thanked: 1 times; GMAT Score:720

by anishprabhu » Thu Mar 12, 2009 4:12 pm

What about E. 26??

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krisraam: Master | Next Rank: 500 Posts; Posts: 221; Joined: Wed Jan 21, 2009 10:33 amFollowed by: 1 member; Thanked: 12 times

by krisraam » Thu Mar 12, 2009 4:51 pm

Both E and C.

Thanks
raama

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franciskyle: Senior | Next Rank: 100 Posts; Posts: 32; Joined: Wed Mar 11, 2009 9:56 pm; Location: Whitler, BC, Canada

by franciskyle » Thu Mar 12, 2009 9:06 pm

2x + 24y = 124

Rearrange: 24y = (124 - 2x)

Now quickly go through the solutions (y must equal an integer).

A: 24y = 26, therefore no good
B: 24y = 54, therefore no good
C: 24y = 48, therefore this is a solution, since y = 2
D: 24y = 68, therefore no good
E: 24y = 72, therefore this is ALSO a solution, since y = 3

Am I missing something in the question? Both answers work accordingly.

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cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Thu Mar 12, 2009 9:11 pm

The question is missing a "maximum" or "mininum"....

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franciskyle: Senior | Next Rank: 100 Posts; Posts: 32; Joined: Wed Mar 11, 2009 9:56 pm; Location: Whitler, BC, Canada

by franciskyle » Thu Mar 12, 2009 9:14 pm

That's kind of what I thought.

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somlop: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Sat Dec 27, 2008 2:49 am

by somlop » Fri Mar 13, 2009 1:59 am

Another series questions I need some help on. Don not see how this is solved:

"For a finite sequence of nonzero numbers, the number of variations in sings is defined as the number of pairs of consecutive terms of the sequence for which the product of the two consecutive terms is negative. What is the number of variations in sings of the sequence 1,-3,2,5,-4,-6?"

- 1
- 2
- 3
- 4
- 5

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sureshbala: Master | Next Rank: 500 Posts; Posts: 319; Joined: Wed Feb 04, 2009 10:32 amFollowed by: 9 members; Location: Delhi; Thanked: 84 times

Re: Series

by sureshbala » Fri Mar 13, 2009 9:57 am

anishprabhu wrote:If the terms of a series are either "2" or "24" and the sum of all the terms of the series is 124, then which of the following could be the number of "2s" in the series?

A. 48

B. 35

C. 38

D. 28

E. 26

Let us find the minimum number of 2's. For this we should have maximum number of 24's. Since the sum is 124, we can have a
maximum of 5 24's and hence we should have a minimum of two 2's.

Now, from here every 24 can be replaced with 12 2's. So the number of 2's will always be 2 more than a multiple of 12.

From the given choices, it could be 28 or 38.

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

Re: Series

by Ian Stewart » Fri Mar 13, 2009 10:06 am

sureshbala wrote: From the given choices, it could be 28 or 38.

I'm sure you mean '26', not '28'.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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sureshbala: Master | Next Rank: 500 Posts; Posts: 319; Joined: Wed Feb 04, 2009 10:32 amFollowed by: 9 members; Location: Delhi; Thanked: 84 times

Re: Series

by sureshbala » Fri Mar 13, 2009 10:13 am

Ian Stewart wrote:
sureshbala wrote: From the given choices, it could be 28 or 38.
I'm sure you mean '26', not '28'.

Hey Stewart, Thank you for the correction

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