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A set of n numbers has a sum S
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06 Dec 2021, 10:40
06 Dec 2021, 10:40
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A set of n numbers has a sum S. If 3 is added to each element of the set followed by each element multiplied by 5 and then divided by 7, choose the condition for which the sum of the new set is greater than that of the original set.
A. S > 100
B. 2S < 15n
C. 2S > 15n
D. S = \(\frac{5}{7}\)n
E. None of the above.
A. S > 100
B. 2S < 15n
C. 2S > 15n
D. S = \(\frac{5}{7}\)n
E. None of the above.
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Re: A set of n numbers has a sum S
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07 Dec 2021, 10:12
07 Dec 2021, 10:12
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This one took me a moment 
. Start with this idea: if the process works for any number of numbers in the set, then we might as well work it out for ONLY ONE NUMBER. In other words, n = 1.
If we have one number with the sum S, then we adjust as follows:
S + 3
then
(S + 3) * 5
then
5(S+3) / 7
This gives us:
(5S + 15) / 7
or
5S/7 + 15/7, and we are told that these must be greater than the sum of the original set, or S.
That is, 5S/7 + 15/7 > S
Put all the S-terms together:
15/7 > 2S/7
Multiply this by 7:
15 > 2S, or 2S < 15. Remember that n = 1, so we can say 2S < 15n.
Answer B.
. Start with this idea: if the process works for any number of numbers in the set, then we might as well work it out for ONLY ONE NUMBER. In other words, n = 1.If we have one number with the sum S, then we adjust as follows:
S + 3
then
(S + 3) * 5
then
5(S+3) / 7
This gives us:
(5S + 15) / 7
or
5S/7 + 15/7, and we are told that these must be greater than the sum of the original set, or S.
That is, 5S/7 + 15/7 > S
Put all the S-terms together:
15/7 > 2S/7
Multiply this by 7:
15 > 2S, or 2S < 15. Remember that n = 1, so we can say 2S < 15n.
Answer B.
gmatclubot
Re: A set of n numbers has a sum S [#permalink]
07 Dec 2021, 10:12
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