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# If 2 < x < 4, what is the median of the numbers 0, 5, x, 1,

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If 2 < x < 4, what is the median of the numbers 0, 5, x, 1, [#permalink]  30 Nov 2013, 10:54
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If 2 < x < 4, what is the median of the numbers 0, 5, x, 1, 7, and 3?

(1) $$2x - 5 = 0$$

(2) $$2x^2 - 7x + 5 = 0$$
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Re: If 2 < x < 4, what is the median of the numbers 0, 5, x, 1, [#permalink]  30 Nov 2013, 11:05
Expert's post
(1) gives you a single solution: 5/2.
(2) gives you two solutions: 1 and 5/2.

Each equation only gives you a single solution in the given range (2 < x < 4). Thus, you know the answer is
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Re: If 2 < x < 4, what is the median of the numbers 0, 5, x, 1, [#permalink]  01 Jan 2014, 17:18
How do you get 1 and 5/2 for the 2nd statement? I am getting x=2 & x=5. Thanks.
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Re: If 2 < x < 4, what is the median of the numbers 0, 5, x, 1, [#permalink]  02 Jan 2014, 04:25
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jeremyl3763 wrote:
How do you get 1 and 5/2 for the 2nd statement? I am getting x=2 & x=5. Thanks.

Substitute 2 and 5 into 2x^2 - 7x + 5 = 0 to see that neither is the root of the equation, while 1 and 5/2 are.

Hope this helps.
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Re: If 2 < x < 4, what is the median of the numbers 0, 5, x, 1, [#permalink]  05 Jan 2014, 19:53
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What's important to remember when faced with a Data Sufficiency Question is that you don't not need to solve. You need to figure out if you have enough information to solve.

First look at the prompt to figure out exactly what you need for sufficiency. If we know the value of x we can find the median. So when you evaluate the statements, ask yourself - "Can I find the value of x?"

Statement1: We have a linear equation with one variable, x. We can solve for x - Sufficient

Statement 2: Here we have a quadratic equation which typically has two solutions. Remember though that we have a range for x in the prompt, so it is possible only one of the solutions will fit in the range and lead us to sufficiency. 2x^2 -7x + 5 = 0 factors into (2x -5)(x-1) = 0 Leading us to the solutions x = 2.5 and x =1. Only x= 2.5 fits in the range 2<x<4, so we have one value for x and sufficiency.

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Re: If 2 < x < 4, what is the median of the numbers 0, 5, x, 1, [#permalink]  11 Apr 2015, 06:01
Bunuel wrote:
Substitute 2 and 5 into 2x^2 - 7x + 5 = 0 to see that neither is the root of the equation, while 1 and 5/2 are.

Here the 2(1, 2.5) values lead to 2 different medians so how is this sufficient?

I understand the fact that both values lie within the range specified, but it leads to 2 different answers- which is grounds for insufficiency. Can you pls explain how this explanation is wrong?
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Re: If 2 < x < 4, what is the median of the numbers 0, 5, x, 1, [#permalink]  11 Apr 2015, 15:26
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Hi TuringMachine,

You have to pay attention to ALL of the information that you've been given.

Notice at the beginning of the prompt, we were told that 2 < X < 4. That 'restriction' still applies.

With Fact 2, we have two potential values for X: 1 and 5/2, but ONLY 5/2 fits that initial range that we were given. Thus, 5/2 is the only possible value for X and we now have enough information answer to the question. Fact 2 is SUFFICIENT.

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Re: If 2 < x < 4, what is the median of the numbers 0, 5, x, 1,   [#permalink] 11 Apr 2015, 15:26
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