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# If R, S, and T are points on a line, and if R is 5 meters from T and 2

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If R, S, and T are points on a line, and if R is 5 meters from T and 2  [#permalink]

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26 Apr 2019, 02:24
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If R, S, and T are points on a line, and if R is 5 meters from T and 2 meters from S, how far is S from T ?

(1) R is between S and T.
(2) S is to the left of R, and T is to the right of R.

DS04602.0
OG2020 NEW QUESTION

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Re: If R, S, and T are points on a line, and if R is 5 meters from T and 2  [#permalink]

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26 Apr 2019, 04:20
Each statement is individually Sufficient.

Refer to the attached figure.

Attachments

PS1.png [ 2.41 KiB | Viewed 508 times ]

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Re: If R, S, and T are points on a line, and if R is 5 meters from T and 2  [#permalink]

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27 Apr 2019, 06:11
Bunuel wrote:
If R, S, and T are points on a line, and if R is 5 meters from T and 2 meters from S, how far is S from T ?

(1) R is between S and T.
(2) S is to the left of R, and T is to the right of R.

DS04602.0
OG2020 NEW QUESTION

We know that $$RT=5$$ and $$RS=2$$. The original question: $$ST=?$$

1) We know that $$R$$ is between $$S$$ and $$T$$. It doesn't matter whether $$S$$ is to the left of $$T$$ or $$S$$ is to the right of $$T$$ since $$ST=RT+RS=5+2=7$$ in both cases. Thus, the answer to the original question is a unique value. $$\implies$$ Sufficient

2) We can infer that $$R$$ is between $$S$$ and $$T$$, so $$ST=7$$ again. Thus, the answer to the original question is a unique value. $$\implies$$ Sufficient

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Re: If R, S, and T are points on a line, and if R is 5 meters from T and 2  [#permalink]

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29 Apr 2019, 10:07
Top Contributor
Bunuel wrote:
If R, S, and T are points on a line, and if R is 5 meters from T and 2 meters from S, how far is S from T ?

(1) R is between S and T.
(2) S is to the left of R, and T is to the right of R.

Given: R, S, and T are points on a line, and if R is 5 meters from T and 2 meters from S
There are 4 possible scenarios that meet the above conditions:

Target question: How far is S from T?

Statement 1: R is between S and T.
When we check the 4 possible scenarios, we see that scenarios #2 and #3 meet the conditions of statement 1
For both scenarios, the answer to the target question is the distance from S to T is 7
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: S is to the left of R, and T is to the right of R.
When we check the 4 possible scenarios, we see that only scenario #2 meets the conditions of statement 2
For scenario #2, the answer to the target question is the distance from S to T is 7
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

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Brent
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Re: If R, S, and T are points on a line, and if R is 5 meters from T and 2  [#permalink]

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06 May 2019, 20:14
Bunuel wrote:
If R, S, and T are points on a line, and if R is 5 meters from T and 2 meters from S, how far is S from T ?

(1) R is between S and T.
(2) S is to the left of R, and T is to the right of R.

DS04602.0
OG2020 NEW QUESTION

We are given the distance from R to T and from R to S; and we need to determine the distance from S to T. To be able to determine the distance from S to T, we need to know in what order R, S and T are positioned on the line.

Statement One Alone:

R is between S and T.
Since R is between S and T, the distance between S and T is equal to the sum of the distances from R to T and from R to S. Since we are given both of those distances, we have enough information to calculate the distance from S to T. Statement one alone is sufficient.

Eliminate answer choices B, C and E.

Statement Two Alone:

S is to the left of R, and T is to the right of R.

Notice that this could only happen if R is between S and T. If R is not between S and T, either both S and T are to the left of R or both S and T are to the right of R. Since we know R is between S and T, we can proceed as in the previous statement to calculate the distance between S and T. Statement two alone is sufficient.

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Re: If R, S, and T are points on a line, and if R is 5 meters from T and 2  [#permalink]

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21 May 2019, 16:10
Hi All,

We're told that R, S, and T are points on a line, R is 5 meters from T and R is 2 meters from S. We're asked for the distance between S and T. This question can be solved with a bit of logic and Arithmetic (and you might find it helpful to draw some actual number lines).

(1) R is between S and T.

With the information in Fact1, we know that R is somewhere between S and T. Regardless of where you place those 3 values on a number line, since R is 5 meters from S and 2 meters from T, then the line ST will be exactly 5+2 = 7 meters in length.
Fact 1 is SUFFICIENT

(2) S is to the left of R, and T is to the right of R.

The information in Fact 2 takes the information that's in Fact1 and 'restricts' it a bit more (placing S to the 'left' and T to the 'right' - relative to R's position - on the number line. The deduction that we made in Fact1 also applies to Fact2. ST will be exactly 5+2 = 7 meters in length.
Fact 2 is SUFFICIENT

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Re: If R, S, and T are points on a line, and if R is 5 meters from T and 2   [#permalink] 21 May 2019, 16:10
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