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M18-35

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M18-35  [#permalink]

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New post 16 Sep 2014, 01:04
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If set \(M\) consists of the root(s) of equation \(2-x^2 = (x-2)^2\), what is the range of set \(M\)?

A. 0
B. \(\frac{1}{\sqrt{2}}\)
C. 1
D. \(\sqrt{2}\)
E. 2

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Re M18-35  [#permalink]

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New post 16 Sep 2014, 01:05
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Official Solution:

If set \(M\) consists of the root(s) of equation \(2-x^2 = (x-2)^2\), what is the range of set \(M\)?

A. 0
B. \(\frac{1}{\sqrt{2}}\)
C. 1
D. \(\sqrt{2}\)
E. 2


\(2-x^2 = (x-2)^2\);

\(2-x^2=x^2-4x+4\);

\(x^2-2x+1=0\);

\((x-1)^2=0\);

\(x=1\). So, set \(M\) consists of only one element.

The range of a single element set is 0.


Answer: A
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Re: M18-35  [#permalink]

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New post 25 May 2015, 14:43
Is there anyway that someone can show me how they got the answer of 0? I can get this far:

2-x^2 = (X-2)^2

2-X^2 = (X-2) (X-2)

2-X^ 2 = X^2-4X+4

What to do after this. I don't understand the break down on the free GMAT text. It's not clicking at this moment.
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Re: M18-35  [#permalink]

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New post 26 May 2015, 06:32
whitdiva23 wrote:
Is there anyway that someone can show me how they got the answer of 0? I can get this far:

2-x^2 = (X-2)^2

2-X^2 = (X-2) (X-2)

2-X^ 2 = X^2-4X+4

What to do after this. I don't understand the break down on the free GMAT text. It's not clicking at this moment.


\(2 - x^ 2 = x^2 - 4x + 4\);

Re-arrange: \(2x^2 - 4x +2 = 0\);

Reduce by 2: \(x^2 -2x + 1 = 0\), which is the same as \((x−1)^2=0\), so \(x=1\).
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Re: M18-35  [#permalink]

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New post 10 Feb 2017, 09:47
Hi Bunuel

I think

\((x−1)^2\)=0 will give 2 equal values for X(1,1) not single value . So range will be 0.

Is this correct ?

Thanks
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Re: M18-35  [#permalink]

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New post 16 Nov 2017, 08:56
Bunuel wrote:
whitdiva23 wrote:
Is there anyway that someone can show me how they got the answer of 0? I can get this far:

2-x^2 = (X-2)^2

2-X^2 = (X-2) (X-2)

2-X^ 2 = X^2-4X+4

What to do after this. I don't understand the break down on the free GMAT text. It's not clicking at this moment.


\(2 - x^ 2 = x^2 - 4x + 4\);

Re-arrange: \(2x^2 - 4x +2 = 0\);

Reduce by 2: \(x^2 -2x + 1 = 0\), which is the same as \((x−1)^2=0\), so \(x=1\).


How would one know when to reduce the equation as opposed to trying to solve a quadratic equation ax^2 +bx + c when a>1. For example factoring out the 2x^2?
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Re: M18-35  [#permalink]

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New post 23 May 2018, 11:39
What about x=0 as another root.
I agree that x=1 is one solution to the squared quadratic but then there are two roots to the solution right, x=0 and x=1. Hence, i thought the range should be 1.

Please help.
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Re: M18-35  [#permalink]

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New post 23 May 2018, 21:25
nshivapu wrote:
What about x=0 as another root.
I agree that x=1 is one solution to the squared quadratic but then there are two roots to the solution right, x=0 and x=1. Hence, i thought the range should be 1.

Please help.


x = 0 does NOT satisfy \(2-x^2 = (x-2)^2\).

LHS = 2 - 0 = 2, while RHS = (0 - 2)^2 = 4.
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Re: M18-35  [#permalink]

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New post 11 Jul 2018, 10:02
\(x=1\). So, set \(M\) consists of only one element.

The range of a single element set is 0.


Answer: A[/quote]

I didn't understand from here on. What's the logic? I know that range is the output, but how do we determine it?
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Re: M18-35  [#permalink]

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New post 11 Jul 2018, 11:14
Tanisha_shasha wrote:
\(x=1\). So, set \(M\) consists of only one element.

The range of a single element set is 0.


Answer: A


I didn't understand from here on. What's the logic? I know that range is the output, but how do we determine it?[/quote]

The range is the difference between the largest and smallest elements of a set. The range of a single element set is therefore 0 because in a single element set the largest and smallest elements are the same.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: M18-35 &nbs [#permalink] 11 Jul 2018, 11:14
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