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What values of X will be closer to the point A = -5 than the

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What values of X will be closer to the point A = -5 than the  [#permalink]

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New post 17 May 2014, 00:13
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What values of X will be closer to the point A = -5 than the point B = 7 on the number line?

I) 0 < x < 2
II) 1 < x < 1.5
III) x < -10

A) Only I
B) Only II
C) Only III
D) Both I and III
E) Both II and III

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Re: What values of X will be closer to the point A = -5 than the  [#permalink]

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New post 17 May 2014, 05:04
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Narenn wrote:
What values of X will be closer to the point A = -5 than the point B = 7 on the number line?

I) 0 < x < 2
II) 1 < x < 1.5
III) x < -10

A) Only I
B) Only II
C) Only III
D) Both I and III
E) Both II and III


x is closer to -5 than to 7 means \(|x-(-5)|<|x-7|\) --> \(|x+5|<|x-7|\).

Both sides are non-negative, thus we can safely square: \(x^2+10x+25<x^2-14x+49\) --> \(x<1\). So, we have that for x to be closer to -5 than it is to 7, x must be less than 1. Only the third option gives the values of x all of which are less than 1.

Answer: C (III only).
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Re: What values of X will be closer to the point A = -5 than the  [#permalink]

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New post 08 Jan 2016, 06:28
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From a logic perspective, you see the question is asking about distances from -5 and 7. The distance between -5 and 7 is (7- (-5)) = 12. One half of 12 is 6, so 6 + (-5) is +1 and 7 - 6 = +1 as well, which is the mid-point between -5 and 7. Therefore, we are trying to find if the points in the given answers are < +1. The only answer that fulfills this requirement for all possible numbers is choice III.
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Re: What values of X will be closer to the point A = -5 than the  [#permalink]

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New post 17 May 2014, 01:25
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I solved this by drawing a number a line and then getting the minimum and maximum distance from both points A and B for each option of X.

I) 0 < x < 2 - (Min,Max) distances from A: (5,7) and B:(5,7)
II) 1 < x < 1.5 -(Min,Max) distances from A: (6,6.5) and B:(6,5.5)
III) x < -10 -(Min,Max) distances from A: (5,undefined) and B:(17,undefined)

So we see that only option 3 satisfies X being closer to A than B.Hence, the answer is C.
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Re: What values of X will be closer to the point A = -5 than the  [#permalink]

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New post 17 May 2014, 01:26
1
Narenn wrote:
What values of X will be closer to the point A = -5 than the point B = 7 on the number line?

I) 0 < x < 2
II) 1 < x < 1.5
III) x < -10

A) Only I
B) Only II
C) Only III
D) Both I and III
E) Both II and III


Sol: Consider Range in option I

If x =0.9 then x is close to pt A but if x= 1.9 then pt x is close to pt B so option A and D can be ruled out
Consider range in option II. All the points in this range is close to Pt B. So option B and E is ruled out

Ans is III only or Option C only

Alternatively the question can be done by drawing a no. line. We can clearly see that that values to the left of Pt A will be closer to it than Pt B. Points to the right may or may not be close to Pt A in the given ranges in option I and II. Ans is C
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Re: What values of X will be closer to the point A = -5 than the  [#permalink]

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New post 16 Feb 2019, 20:14
Narenn wrote:
What values of X will be closer to the point A = -5 than the point B = 7 on the number line?

I) 0 < x < 2
II) 1 < x < 1.5
III) x < -10

A) Only I
B) Only II
C) Only III
D) Both I and III
E) Both II and III


So when we plot the given lines on the umber line, we can actually see that 1 and 2 will be giving values that will be far from A.

Only 3, will give you a value which will be nearer to point A

C
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Re: What values of X will be closer to the point A = -5 than the   [#permalink] 16 Feb 2019, 20:14
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