On the number line, point R has coordinate r and point T has

This topic has expert replies
Moderator
Posts: 7187
Joined: Thu Sep 07, 2017 4:43 pm
Followed by:23 members

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

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

OA C

Source: Official Guide

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3008
Joined: Mon Aug 22, 2016 6:19 am
Location: Grand Central / New York
Thanked: 470 times
Followed by:34 members

by Jay@ManhattanReview » Fri Sep 14, 2018 3:28 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

BTGmoderatorDC 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

OA C

Source: Official Guide
Given: On the number line, point R has coordinate r and point T has coordinate t.

Question: Is t < 0?

Let's take each statement one by one.

(1) -1 < r < 0

We do not have any information about point T. Insufficient.

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

Certainly insufficient. T can be on either side of the number line. Insufficient.

(1) and (2) together

We know that the coordinate of point R is -1 < r < 0 and the distance between R and T is equal to r^2.

Note that if -1 < r < 0, r^2 < |r|

Thus, the coordinate of point T must also be negative. Sufficient.

The correct answer: C

Hope this helps!

-Jay
_________________
Manhattan Review GRE Prep

Locations: GRE Classes Seattle | GMAT Prep Course Hong Kong | GRE Prep San Francisco | SAT Prep Classes NYC | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

User avatar
GMAT Instructor
Posts: 1449
Joined: Sat Oct 09, 2010 2:16 pm
Thanked: 59 times
Followed by:33 members

by fskilnik@GMATH » Fri Sep 14, 2018 1:25 pm

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

BTGmoderatorDC 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

Source: Official Guide
\[t\,\,\mathop < \limits^? \,\,0\]
\[\left( 1 \right)\,\,\, - 1 < r < 0\,\,\,\left\{ \begin{gathered}
\,{\text{Take}}\,\,\left( {r,t} \right) = \left( { - 0.5,0} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{NO}}} \right\rangle \hfill \\
\,{\text{Take}}\,\,\left( {r,t} \right) = \left( { - 0.5, - 1} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \hfill \\
\end{gathered} \right.\]
\[\left( 2 \right)\,\,\,\left| {r - t} \right| = {r^2}\,\,\,\left\{ \begin{gathered}
\,{\text{Take}}\,\,\left( {r,t} \right) = \left( {0,0} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{NO}}} \right\rangle \hfill \\
\,{\text{Take}}\,\,\left( {r,t} \right) = \left( { - 1, - 2} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \hfill \\
\end{gathered} \right.\]
\[\left( {1 + 2} \right)\,\,\,\,\,\left| {r - t} \right| = {r^2}\,\,\,\,\mathop \Rightarrow \limits^{{\text{squaring}}} \,\,\,\,\,{\left( {r - t} \right)^2} = {r^4}\,\,\,\,\, \Rightarrow \,\,\,\,{r^2} - 2rt + {t^2} = {r^4}\,\,\,\,\,\left( * \right)\]
\[ - 1 < r < 0\,\,\,\,\,\, \Rightarrow \,\,\,\,{r^4} < {r^2}\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\, - 2rt + {t^2} = {r^4} - {r^2} < 0\]
\[\left. \begin{gathered}
- 2rt + {t^2} < 0 \hfill \\
{t^2} \geqslant 0 \hfill \\
\end{gathered} \right\}\,\,\,\,\,\, \Rightarrow \,\,\,\, - 2rt < 0\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{r\, < \,\,0} \,\,\,t < 0\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{SUFF}}.\,\]


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

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

BTGmoderatorDC wrote:
Thu Sep 13, 2018 8:52 pm
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

OA C

Source: Official Guide
Target question: Is t NEGATIVE?

Statement 1: -1 < r < 0
No information about t
So, statement 1 is NOT SUFFICIENT

Statement 2: The distance between R and T is equal to r²
There are several values of r and t that satisfy statement 2. Here are two:
Case a: r = -1 and t = -2. The distance between r and t is 1 (aka r²). So, these values of r and t satisfy statement 2. In this case, t IS negative
Case b: r = -1 and t = 0. The distance between r and t is 1 (aka r²). So, these values of r and t satisfy statement 2. In this case, t is NOT negative
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that -1 < r < 0
ASIDE: If j and k are on the number line, then |j - k| = the distance between j and k
So, from statement 2, we can write: |t - r| = r²

-----------------ASIDE-------------------------------------
There are 3 steps to solving equations involving ABSOLUTE VALUE:
1. Apply the rule that says: If |x| = k, then x = k and/or x = -k
2. Solve the resulting equations
3. Plug solutions into original equation to check for extraneous roots
--------BACK TO THE QUESTION---------------------------

Since |t - r| = r², we'll examine two possible cases:
t - r = r² and t - r = -(r²)

case a: t - r = r²
Rearrange to get: t = r + r²
Factor: t = r(1 + r)
Since -1 < r < 0, we can conclude that (1 + r) is POSITIVE
So, t = r(1 + r) = (NEGATIVE)(POSITIVE) = NEGATIVE
So, t is negative

case b: t - r = -(r²)
Rearrange to get: t = r - r²
Factor: t = r(1 - r)
Since -1 < r < 0, we can conclude that (1 - r) is POSITIVE
So, t = r(1 - r) = (NEGATIVE)(POSITIVE) = NEGATIVE
So, t is negative

In both of the two possible cases, t is negative
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image