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If s and t are two different numbers on the number line, is

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by BTGmoderatorDC » Mon Dec 03, 2018 8:51 pm

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If s and t are two different numbers on the number line, is s + t = 0 ?

(1) Distance between s and 0 is the same as distance between t and 0
(2) 0 is between s and t

OA A

Source: GMAT Prep
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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Mon Dec 03, 2018 9:05 pm
BTGmoderatorDC wrote:If s and t are two different numbers on the number line, is s + t = 0 ?

(1) Distance between s and 0 is the same as distance between t and 0
(2) 0 is between s and t

OA A

Source: GMAT Prep
Given: s and t are two different numbers on the number line.

=> s ≠ t

Question: Is s + t = 0 ?

Let's take each statement one by one.

(1) Distance between s and 0 is the same as distance between t and 0.

There can be two possibilities:

1. s = t; however, this is not possible since we know that s ≠ t.
2. s = -t => s + t = 0. Sufficient.

(2) 0 is between s and t.

Case 1: Say 0 is at midway between s and t; thus, s = -t => s + t = 0. The answer is Yes.
Case 2: Say 0 is at not midway between s and t; thus, s ≠ -t => s + t ≠ 0. The answer is No.

No unique answer. Insufficient.

The correct answer: A

Hope this helps!

-Jay
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by [email protected] » Tue Dec 04, 2018 1:04 pm
Hi All,

We're told that S and T are two DIFFERENT numbers on the number line. We're asked if S + T = 0. This is a YES/NO question and can be solved by TESTing VALUES and a bit of Number Property logic.

1) The distance between S and 0 is the SAME as the distance between T and 0

Since S and T are DIFFERENT numbers, the only way for their respective distances from 0 to be the SAME is if S and T are 'opposites.'

IF....
S = +1, T = -1; the distances from 0 are the same and S+T = (1) + (-1) = 0, so the answer to the question is YES
S = -2, T = +2; the distances from 0 are the same and S+T = (-2) + (+2) = 0, so the answer to the question is YES.
Etc.
The answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT

2) 0 is between S and T

With the information in Fact 2, we know that 0 is some point between S and T, but that does NOT necessarily mean the "exact midpoint."

IF...
S = +1, T = -1; then S+T = (1) + (-1) = 0, so the answer to the question is YES
S = +1, T = -2; then S+T = (1) + (-2) = -1, so the answer to the question is NO
Fact 2 is INSUFFICIENT

Final Answer: A

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Rich
Contact Rich at [email protected]
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by fskilnik@GMATH » Tue Dec 04, 2018 5:57 pm
BTGmoderatorDC wrote:If s and t are two different numbers on the number line, is s + t = 0 ?

(1) Distance between s and 0 is the same as distance between t and 0
(2) 0 is between s and t
Source: GMAT Prep
$$s \ne t\,\,\,\,\left( * \right)$$
$$s + t\,\,\mathop = \limits^? \,\,0$$

$$\left( 1 \right)\,\,\,\left| s \right| = \left| t \right|\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,s = - t\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle $$

$$\left( 2 \right)\,\,\,st < 0\,\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {s,t} \right) = \left( { - 1,1} \right)\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \hfill \cr
\,{\rm{Take}}\,\,\left( {s,t} \right) = \left( { - 1,0.5} \right)\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \hfill \cr} \right.$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
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