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If x is a positive integer, is x<16? [#permalink]
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12 Jan 2016, 08:34
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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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12 Jan 2016, 08:48
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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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22 Mar 2017, 03:12
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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01 May 2017, 02:11
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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01 May 2017, 18:48
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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23 May 2017, 07:03
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 110 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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23 May 2017, 10:25
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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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23 May 2017, 10:29
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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 110 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 nonnegative 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?
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