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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] New post 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) \(2x^2 - 7x + 5 = 0\)
[Reveal] Spoiler: OA
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Re: If 2 < x < 4, what is the median of the numbers 0, 5, x, 1, [#permalink] New post 30 Nov 2013, 11:05
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(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
[Reveal] Spoiler:
D

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Re: If 2 < x < 4, what is the median of the numbers 0, 5, x, 1, [#permalink] New post 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] New post 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.

Factoring Quadratics: http://www.purplemath.com/modules/factquad.htm

Solving Quadratic Equations: http://www.purplemath.com/modules/solvquad.htm

Hope this helps.
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Re: If 2 < x < 4, what is the median of the numbers 0, 5, x, 1, [#permalink] New post 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.

The answer is D
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Re: If 2 < x < 4, what is the median of the numbers 0, 5, x, 1, [#permalink] New post 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] New post 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] New post 09 Nov 2015, 07:46
the second eqn gives two values x =1 and 5/2 and when you insert you get two different median 1 and 5/2. SO that is why I choose a beause it gives only one value.
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Re: If 2 < x < 4, what is the median of the numbers 0, 5, x, 1, [#permalink] New post 09 Nov 2015, 08:58
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Question stem: 2<x<5; median of (0, 5, x, 1, 7, 3)

1: 2x-5 = 0 i.e. x = 2.5
This complies with question stem condition 2<x<5. Also, median can be easily determined.
Sufficient

2. 2x^2 - 7x + 5 = 0

i.e. 2x^2 - 5x - 2x + 5 = 0
(2x-5) (x-1) = 0
x = 5/2 or x = 1
As per the question stem, x cannot be 1. Therefore, x = 5/2.
Sufficient

Answer: D (Either statement are sufficient).
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Re: If 2 < x < 4, what is the median of the numbers 0, 5, x, 1, [#permalink] New post 09 Nov 2015, 12:03
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Hi alice7,

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] New post 09 Nov 2015, 12:47
Thanks for clarification, I completely forgot initial x value provided.
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Re: If 2 < x < 4, what is the median of the numbers 0, 5, x, 1, [#permalink] New post 10 Nov 2015, 10:56
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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

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

There is one variable (X) and 2 equations from the 2 conditions, so (D) is our likely answer.
For condition 1, x=5/2. This is sufficient.
For condition 2, (2x-5)(x-1)=0, x=5/2, 1, but 1 is not possible, so x=5/2. This is sufficient as well, making the answer (D).

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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Re: If 2 < x < 4, what is the median of the numbers 0, 5, x, 1,   [#permalink] 10 Nov 2015, 10:56
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