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Series

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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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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by anishprabhu » Thu Mar 12, 2009 4:12 pm
What about E. 26??
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by krisraam » Thu Mar 12, 2009 4:51 pm
Both E and C.

Thanks
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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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by cramya » Thu Mar 12, 2009 9:11 pm
The question is missing a "maximum" or "mininum"....
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by franciskyle » Thu Mar 12, 2009 9:14 pm
That's kind of what I thought.
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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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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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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'.
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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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