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If x equals all prime numbers that satisfy the inequality

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GMAT Club Legend
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Joined: 07 Jun 2014
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If x equals all prime numbers that satisfy the inequality [#permalink] New post 09 Dec 2017, 18:29
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Question Stats:

80% (01:43) correct 20% (01:43) wrong based on 10 sessions
If x equals all prime numbers that satisfy the inequality
\(|\frac{1}{10-x}|\leq \frac{5}{x^2}\)

what is the average value of x ?

Drill 3
Question: 6
Page: 529


[Reveal] Spoiler: OA
\(\frac{10}{3}\)

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GMAT Club Legend
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Joined: 07 Jun 2014
Posts: 4750
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 93

Kudos [?]: 1662 [0], given: 396

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Re: If x equals all prime numbers that satisfy the inequality [#permalink] New post 29 Dec 2017, 14:27
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Explanation

The most efficient way to approach this tough problem is to plug in prime numbers to determine the set of values that satisfies the inequality. Plugging 2 in for x yields \(\frac{1}{8} \leq \frac{5}{4}\) which is true.

Plugging in 3 yields \(\frac{1}{7} \leq \frac{5}{9}\) which is also true.

Plugging in 5 yields \(\frac{1}{5} \leq \frac{5}{25}\) so the two sides are equal, so that’s probably the maximum value of x.

To be sure, check the next prime number, 7: \(\frac{1}{7} \leq \frac{5}{49}\) which is false.

You should also check a large prime number to confirm {2, 3, 5} is the solution set. If you do, you’ll find the inequality is false and {2, 3, 5} is the full set of values. To find the average of the numbers, use the Average Pie: \(\frac{2+3+5}{3}=10/3\).
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Re: If x equals all prime numbers that satisfy the inequality [#permalink] New post 26 Sep 2018, 11:19
is there another way to do this ? faster maybe..
Re: If x equals all prime numbers that satisfy the inequality   [#permalink] 26 Sep 2018, 11:19
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If x equals all prime numbers that satisfy the inequality

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