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If x is a positive integer, is x<16?

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If x is a positive integer, is x<16? [#permalink]

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New post 12 Jan 2016, 09:34
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If x is a positive integer, is x<16?

1) x is less than the average (arithmetic mean) of the first ten positive integers
2) x is the square of an integer.

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Re: If x is a positive integer, is x<16? [#permalink]

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New post 12 Jan 2016, 09:48
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St1: Average of first 10 positive integers = Sum/10 = ((10/2)(1 + 10))/10 = 55/10 = 5.5
x < 5.5 --> Sufficient

St2: x = Integer^2 = 1, 4, 9, 16, 25
x can be less than 16 or greater than 16 --> not sufficient

Answer: A
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Re: If x is a positive integer, is x<16? [#permalink]

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New post 22 Mar 2017, 04:12
Vyshak wrote:
St1: Average of first 10 positive integers = Sum/10 = ((10/2)(1 + 10))/10 = 55/10 = 5.5
x < 5.5 --> Sufficient

St2: x = Integer^2 = 1, 4, 9, 16, 25
x can be less than 16 or greater than 16 --> not sufficient

Answer: A


Could you please explain from where did you get the first formula: (10/2(1+10)/10)
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Re: If x is a positive integer, is x<16? [#permalink]

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New post 01 May 2017, 03:11
Bouka2311 wrote:
Vyshak wrote:
St1: Average of first 10 positive integers = Sum/10 = ((10/2)(1 + 10))/10 = 55/10 = 5.5
x < 5.5 --> Sufficient

St2: x = Integer^2 = 1, 4, 9, 16, 25
x can be less than 16 or greater than 16 --> not sufficient

Answer: A


Could you please explain from where did you get the first formula: (10/2(1+10)/10)


instead of this , u can use an easier formula for average of first 10 integers= first term+ last term/2 = 1+10/2 = 11/2 = 5.5
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Re: If x is a positive integer, is x<16? [#permalink]

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New post 01 May 2017, 19:48
1. Obviously sufficient, as the average of the integers between 1 and 10 is somewhere between 1 and 10 (we don't even need to know exactly where, just that it's less than 16)
2. Obviously insufficient. x could equal 1, 4, 9, 16, 25.. etc.
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Re: If x is a positive integer, is x<16? [#permalink]

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New post 23 May 2017, 08:03
sealberg wrote:
1. Obviously sufficient, as the average of the integers between 1 and 10 is somewhere between 1 and 10 (we don't even need to know exactly where, just that it's less than 16)
2. Obviously insufficient. x could equal 1, 4, 9, 16, 25.. etc.


The average of the first positive ten integers - but the first positive ten integers of what? Why can't the first ten integers be part of a set that, for instance, goes from 100 to 109?

I was aware that (A) would be sufficient if the GMAT refers to 1-10 but I refused this option as the questions doesn't exactly determine the set.

What do u think?
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Re: If x is a positive integer, is x<16? [#permalink]

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New post 23 May 2017, 11:25
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Bouka2311 wrote:
Vyshak wrote:
St1: Average of first 10 positive integers = Sum/10 = ((10/2)(1 + 10))/10 = 55/10 = 5.5
x < 5.5 --> Sufficient

St2: x = Integer^2 = 1, 4, 9, 16, 25
x can be less than 16 or greater than 16 --> not sufficient

Answer: A


Could you please explain from where did you get the first formula: (10/2(1+10)/10)


If we are given 'n' numbers in Arithmetic Progression (evenly spaced), there is a formula for their sum which is:

Sum = n/2 (First term + Last term)
Here we are looking at first 10 positive integers: 1, 2, 3, ....10 (these are obviously evenly spaced)

So n=10, first term = 1, last term = 10
Hence sum = (10/2) (1 + 10) = 55

But average = Sum/n = 55/10 = 5.5
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Re: If x is a positive integer, is x<16? [#permalink]

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New post 23 May 2017, 11:29
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guenthermat wrote:
sealberg wrote:
1. Obviously sufficient, as the average of the integers between 1 and 10 is somewhere between 1 and 10 (we don't even need to know exactly where, just that it's less than 16)
2. Obviously insufficient. x could equal 1, 4, 9, 16, 25.. etc.


The average of the first positive ten integers - but the first positive ten integers of what? Why can't the first ten integers be part of a set that, for instance, goes from 100 to 109?

I was aware that (A) would be sufficient if the GMAT refers to 1-10 but I refused this option as the questions doesn't exactly determine the set.

What do u think?


Hi

Good query I think. I believe that when a question states 'first 10 positive integers' without giving any other set,
then it means 'universal first 10 positive integers'.. which means starting from 1 and going upto 10

So first n positive integers = 1,2, 3, 4, ....n
First n non-negative integers = 0, 1, 2, 3, ...

First 4 positive even numbers = 2, 4, 6, 8,
First two positive multiples of 5 = 5, 10

and so on..
Re: If x is a positive integer, is x<16?   [#permalink] 23 May 2017, 11:29
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