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If the average (arithmetic mean) of n consecutive odd [#permalink]
 09 Dec 2010, 15:43
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If the average (arithmetic mean) of n consecutive odd integers is 10, what is the least of the integers? (1) The range of the n integers is 14 (2) The greatest of the n integers is 17"
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Re: Quant Rev v.2, DS # 66: Consecutive Integer Problem [#permalink]
09 Dec 2010, 15:59
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tonebeeze wrote: Hello All,
I got this problem correct. I just would like to see a technical explanation of how to arrive at both occasions of sufficiency.
Thanks!
"If the average (arithmetic mean) of n consecutive odd integers is 10, what is the least of the integers?
(1) The range of the n integers is 14
(2) The greatest of the n integers is 17" Odd consecutive integers is an evenly spaced set. For any evenly spaced set the mean equals to the average of the first and the last terms, so in our case mean=10=\frac{x_1+x_{n}}{2} --> x_1+x_{n}=20. Question: x_1=?(1) The range of the n integers is 14 --> the range of a set is the difference between the largest and smallest elements of a set, so x_{n}-x_1=14 --> solving for x_1 --> x_1=3. Sufficient. (2) The greatest of the n integers is 17 --> x_n=17 --> x_1+17=20 --> x_1=3. Sufficient. Answer: D.
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Re: Quant Rev v.2, DS # 66: Consecutive Integer Problem [#permalink]
10 Dec 2010, 07:20
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Re: Quant Rev v.2, DS # 66: Consecutive Integer Problem [#permalink]
12 Dec 2010, 05:24
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tonebeeze wrote: Hello All,
I got this problem correct. I just would like to see a technical explanation of how to arrive at both occasions of sufficiency.
Thanks!
"If the average (arithmetic mean) of n consecutive odd integers is 10, what is the least of the integers?
(1) The range of the n integers is 14
(2) The greatest of the n integers is 17" If mean of consecutive odd integers is 10, the sequence of numbers will be something like this: 9, 11 or 7, 9, 11, 13 or 5, 7, 9, 11, 13, 15 or 3, 5, 7, 9, 11, 13, 15, 17 or 1, 3, 5, 7, 9, 11, 13, 15, 17, 19 etc Every time you add a number to the left, you need to add one to the right to keep the mean 10. The smallest sequence will have 2 numbers 9 and 11, the largest will have infinite numbers. Stmnt 1: Only one possible sequence: 3, 5, 7, 9, 11, 13, 15, 17 will have range 14. Least of the integers is 3. Sufficient. Stmnt 2: Only one possible sequence:3, 5, 7, 9, 11, 13, 15, 17 Least of the integers is 3. Sufficient. Answer (D). Note: You don't actually have to do all this. All such sequences will have distinct number of elements, greatest number, smallest number and range. So each statement alone will be sufficient.
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Re: Quant Rev v.2, DS # 66: Consecutive Integer Problem [#permalink]
06 Apr 2011, 08:28
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(1) so (a + a + 14)/2 = 10 => 2a = 20 - 14 = 6 => a =3 (2) (a+17)/2 = 10 => a = 3 Answer - D (a+17)
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Re: If the average (arithmetic mean) of n consecutive odd [#permalink]
14 Apr 2012, 11:11
Awesome explanation Bunuel!
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If the average (Arithmetic mean) of n consecutive odd intege [#permalink]
24 Apr 2012, 09:18
If the average (Arithmetic mean) of n consecutive odd integers is 10, what is the least of the integers?
1. The range of the n integers is 14.
2. The greatest of the n integers is 17.
Please do explain your answer choice.
Thanks
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Re: If the average (arithmetic mean) of n consecutive odd [#permalink]
29 Sep 2012, 23:27
I think solution D is wrong, what is numbers are : -5, -3, -1, 1, 3,5,7, 9 then range is 14 thus least value in set is : -5
However, if we consider numbers from 3 to 11 then least value is 3.
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Re: If the average (arithmetic mean) of n consecutive odd [#permalink]
29 Sep 2012, 23:41
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bandgmat wrote: I think solution D is wrong, what is numbers are : -5, -3, -1, 1, 3,5,7, 9 then range is 14 thus least value in set is : -5
However, if we consider numbers from 3 to 11 then least value is 3. Yeah, but is the average of these numbers 10?
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If the average of n consecutive odd integers... [#permalink]
27 Oct 2012, 13:47
If the average of n consecutive odd integers is 10, what is the least of the integers?
1) The range of the n integers is 14
2) The greatest of the n integers is 17
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Re: If the average of n consecutive odd integers... [#permalink]
27 Oct 2012, 15:23
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Re: Quant Rev v.2, DS # 66: Consecutive Integer Problem [#permalink]
28 Oct 2012, 11:36
Bunuel wrote: tonebeeze wrote: Hello All,
I got this problem correct. I just would like to see a technical explanation of how to arrive at both occasions of sufficiency.
Thanks!
"If the average (arithmetic mean) of n consecutive odd integers is 10, what is the least of the integers?
(1) The range of the n integers is 14
(2)The greatest of the n integers is 17" Odd consecutive integers is an evenly spaced set. For any evenly spaced set the mean equals to the average of the first and the last terms, so in our case mean=10=\frac{x_1+x_{n}}{2} --> x_1+x_{n}=20. Question: x_1=?(1) The range of the n integers is 14 --> the range of a set is the difference between the largest and smallest elements of a set, so x_{n}-x_1=14 --> solving for x_1 --> x_1=3. Sufficient. (2) The greatest of the n integers is 17 --> x_n=17 --> x_1+17=20 --> x_1=3. Sufficient. Answer: D. Doesn't the highlighted statement actually mean that the highest number in the series is 17??
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Re: Quant Rev v.2, DS # 66: Consecutive Integer Problem [#permalink]
29 Oct 2012, 02:26
avaneeshvyas wrote: Bunuel wrote: tonebeeze wrote: Hello All,
I got this problem correct. I just would like to see a technical explanation of how to arrive at both occasions of sufficiency.
Thanks!
"If the average (arithmetic mean) of n consecutive odd integers is 10, what is the least of the integers?
(1) The range of the n integers is 14
(2)The greatest of the n integers is 17" Odd consecutive integers is an evenly spaced set. For any evenly spaced set the mean equals to the average of the first and the last terms, so in our case mean=10=\frac{x_1+x_{n}}{2} --> x_1+x_{n}=20. Question: x_1=?(1) The range of the n integers is 14 --> the range of a set is the difference between the largest and smallest elements of a set, so x_{n}-x_1=14 --> solving for x_1 --> x_1=3. Sufficient. (2) The greatest of the n integers is 17 --> x_n=17 --> x_1+17=20 --> x_1=3. Sufficient. Answer: D. Doesn't the highlighted statement actually mean that the highest number in the series is 17?? Yes. We generally use the terms greatest/largest.
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Re: Quant Rev v.2, DS # 66: Consecutive Integer Problem
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