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GRE Prep Club Legend  Joined: 07 Jun 2014
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GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
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If x equals all prime numbers that satisfy the inequality [#permalink]
Expert's post 00:00

Question Stats: 81% (01:59) correct 18% (01:43) wrong based on 11 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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Sandy
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GRE Prep Club Legend  Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 105

Kudos [?]: 1776 , given: 397

Re: If x equals all prime numbers that satisfy the inequality [#permalink]
Expert's post
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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Intern Joined: 24 Sep 2018
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Re: If x equals all prime numbers that satisfy the inequality [#permalink]
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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