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Re: On the number line, point R has coordinate r and point T has coordinat [#permalink]

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16 Jun 2016, 06:09

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On the number line, point R has coordinate r and point T has coordinate t. Is t < 0?

(1) -1 < r < 0: Tells us r is a (negative) proper fraction Does not tell us anything about the coordinates of t. Hence INSUFFICIENT

(2) The distance between R and T is equal to r^2:

If r is +ve and >1 t can be positive or negative If r is +ve and <1 t will be positive since square of a proper fraction is less than the fraction itself If r is -ve and <-1 t can be positive or negative If r is -ve and >-1 t will be negative since square of a proper fraction is less than the fraction itself

Multiple cases hence INSUFFICIENT

Combining, it conforms to case 4.

Hence Ans = C
_________________

Appreciate any KUDOS given !

Last edited by rishi02 on 17 Jun 2016, 21:57, edited 2 times in total.

Re: On the number line, point R has coordinate r and point T has coordinat [#permalink]

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16 Jun 2016, 06:10

4

This post received KUDOS

On the number line, point R has coordinate r and point T has coordinate t. Is t < 0?

(1) -1 < r < 0 (2) The distance between R and T is equal to r^2

r can take values from -0.99 to -.01 approx if r = -0.99 then distance between r an t is r^2 = .98 the absolute value is the distance which can be both right side and left side. But in whichever case it will less than 0. Hence C is the answer.
_________________

On the number line, point R has coordinate r and point T has coordinate t. Is t < 0?

(1) -1 < r < 0 (2) The distance between R and T is equal to r^2

We are given that on the number line, point R has coordinate r and point T has coordinate t, and we need to determine whether t < 0.

Statement One Alone:

-1 < r < 0

Statement one tells us that r is a negative proper fraction. However, without knowing anything about t, statement one is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

The distance between R and T is equal to r^2.

The distance between two values on the number line is the absolute value of the difference between the two values. Thus statement two gives us the equation |r - t| = r^2. However, without knowing anything about r and t, we can’t determine whether t is less than zero. For instance, r could be 2 and t could be -2; or r could be -2 and t could be 2. In each of the cases, |r - t| = 4 = r^2; but in one case t > 0 and in the other t < 0. Statement two is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

Using statements one and two, we know that r is a negative proper fraction and |r - t| = r^2. Thus, r - t = r^2 OR r - t = -r^2. Solving each of these for t, we get: t = r - r^2 OR t = r + r^2.

Since r is a negative proper fraction, no matter what the value of r is, t will always be a negative number. For instance, if r = -1/2, then r^2 = 1/4 and t will either be -1/2 - 1/4 = -3/4 or -1/2 + 1/4 = -1/4.

The reason why t cannot be positive is that when we square r (a negative proper fraction), the value of r^2 (though positive) will be less than the absolute value of r. Recall that t = r - r^2 or t = r + r^2. When a positive proper fraction with a smaller absolute value is added to (or subtracted from) a negative proper fraction with a larger absolute value, the sum (or difference) will always be less than zero.

Answer: C
_________________

Scott Woodbury-Stewart Founder and CEO

GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

Re: On the number line, point R has coordinate r and point T has coordinat [#permalink]

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14 Mar 2017, 18:12

Thanks. can you please explain this in context of the problem?

ScottTargetTestPrep wrote:

Bunuel wrote:

On the number line, point R has coordinate r and point T has coordinate t. Is t < 0?

When a positive proper fraction with a smaller absolute value is added to (or subtracted from) a negative proper fraction with a larger absolute value, the sum (or difference) will always be less than zero.

Re: On the number line, point R has coordinate r and point T has coordinat [#permalink]

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15 Mar 2017, 17:07

[quote="Bunuel"]On the number line, point R has coordinate r and point T has coordinate t. Is t < 0?

Can someone help? I keep on seeing this explained in questions, but I am not getting it ("Point R has coordinate r"). Can someone give me a break down of what this is saying. EX: on an xy plane point Q could be at (1,0). It's x coordinate is 1, and it's Y coordinate is 0....

what is ("Point R has coordinate r") saying? can you give me an example if it were in number format?

On the number line, point R has coordinate r and point T has coordinate t. Is t < 0?

Can someone help? I keep on seeing this explained in questions, but I am not getting it ("Point R has coordinate r"). Can someone give me a break down of what this is saying. EX: on an xy plane point Q could be at (1,0). It's x coordinate is 1, and it's Y coordinate is 0....

what is ("Point R has coordinate r") saying? can you give me an example if it were in number format?

It means that point R is at r on the number line. For example if r = -3, then we'd have the below case:

Attachments

MSP771229ab39762b67b1000004e1c46g1e825775i.gif [ 661 Bytes | Viewed 3836 times ]

Re: On the number line, point R has coordinate r and point T has coordinat [#permalink]

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09 Apr 2017, 11:26

FightToSurvive wrote:

On the number line, point R has coordinate r and point T has coordinate t. Is t < 0?

(1) -1 < r < 0 (2) The distance between R and T is equal to r^2

r can take values from -0.99 to -.01 approx if r = -0.99 then distance between r an t is r^2 = .98 the absolute value is the distance which can be both right side and left side. But in whichever case it will less than 0. Hence C is the answer.

so the key is that squaring a fraction always results in a smaller number... right ?
_________________

On the number line, point R has coordinate r and point T has coordinat [#permalink]

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12 Aug 2017, 09:58

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Can you please tell me what is the difficulty level of this problem? I find it hard to answer these kinds of questions and not really able to gauge myself where I stand in my preparation if I am not able to answer these type of questions. I have my exam scheduled this september end.

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