Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 20 Jul 2019, 00:33

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# In the rectangular coordinate system above, if OP < PQ, is

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 16 Nov 2016
Posts: 274
Re: In the rectangular coordinate system above, if OP < PQ, is  [#permalink]

### Show Tags

07 Aug 2018, 06:45
Bunuel wrote:

In the rectangular coordinate system above, if OP < PQ, is the area of region OPQ greater than 48 ?

(1) The coordinates of point P are (6,8). Now, if OP were equal to PQ then the triangle OPQ would be isosceles and OS would be equal to SQ and the area would be: 1/2*base*height=1/2(OS+SQ)*PS=1/2*(6+6)*8=48. Since OP<PQ then OS<SQ and the base OQ is more than 12, which makes the area more than 48. Sufficient.

(2) The coordinates of point Q are (13,0) --> we know the length of the base (OQ=13) but know nothing about the height (PS), which may be 1 or 100, so the area may or may not be more than 48. Not sufficient.

Hope it's clear.

Attachment:
Triangle.png

Hi Bunuel,

how do we know that OS<SQ? I mean how do we deduce that from OP<OQ
_________________
If you find my post useful, please give me a kudos.

Thank you.
Regards,
ENEM

If you wish to spend wisely on your gmat prep material, check my post titled: How to Spend Money On GMAT Material Wisely, link: https://gmatclub.com/forum/how-to-buy-gmat-material-wisely-tag-free-gmat-resources-236174.html

Simple and handy template for CR: https://gmatclub.com/forum/simple-and-handy-template-for-cr-242255.html

simple template for more vs greater and fewer vs less: https://gmatclub.com/forum/simple-template-for-more-vs-greater-and-fewer-vs-less-242216.html
GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 937
Re: In the rectangular coordinate system above, if OP < PQ, is  [#permalink]

### Show Tags

30 Aug 2018, 12:41
eybrj2 wrote:

In the rectangular coordinate system above, if OP < PQ, is the area of region OPQ greater than 48 ?

(1) The coordinates of point P are (6,8)

(2) The coordinates of point Q are (13,0)

Attachment:
The attachment Triangle.png is no longer available

$$?\,\,\,:\,\,\,{S_\Delta }\,\,\mathop > \limits^? \,\,48$$

$$\left( 1 \right)\,\,{S_\Delta }\,\,\mathop > \limits^{{\text{see}}\,\,{\text{our}}\,\,{\text{figure !}}} \,\,{S_{\Delta OPQ\,dash}} = \frac{{\left( {6 + 6} \right) \cdot 8}}{2} = 48\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle$$

$$\left( 2 \right)\,\,{\text{Geometric}}\,\,{\text{Bifurcation}}$$

> The first figure (on the right) is "the same" as the one we used in our first statement (see our figure), in which we answered <YES>
> The second figure (on the right-below) shows that the area-focus may be as small as we which (but still positive, of course) , hence <NO>

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

30Ago18_7q.gif [ 18.03 KiB | Viewed 279 times ]

_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
Manager
Joined: 05 Oct 2017
Posts: 66
Location: India
Schools: GWU '21, Isenberg'21
Re: In the rectangular coordinate system above, if OP < PQ, is  [#permalink]

### Show Tags

09 Dec 2018, 04:44
Its such a good trap question !!!

How one can be aware of such trap questions ?
Is practice and seeing the pattern is the solution ?
_________________
Manager
Joined: 05 Oct 2017
Posts: 66
Location: India
Schools: GWU '21, Isenberg'21
Re: In the rectangular coordinate system above, if OP < PQ, is  [#permalink]

### Show Tags

09 Dec 2018, 04:55
ENEM wrote:
Bunuel wrote:

In the rectangular coordinate system above, if OP < PQ, is the area of region OPQ greater than 48 ?

(1) The coordinates of point P are (6,8). Now, if OP were equal to PQ then the triangle OPQ would be isosceles and OS would be equal to SQ and the area would be: 1/2*base*height=1/2(OS+SQ)*PS=1/2*(6+6)*8=48. Since OP<PQ then OS<SQ and the base OQ is more than 12, which makes the area more than 48. Sufficient.

(2) The coordinates of point Q are (13,0) --> we know the length of the base (OQ=13) but know nothing about the height (PS), which may be 1 or 100, so the area may or may not be more than 48. Not sufficient.

Hope it's clear.

Attachment:
Triangle.png

Hi Bunuel,

how do we know that OS<SQ? I mean how do we deduce that from OP<OQ

From the question we have OP < OQ .....(a)
also from Pythagoras theorem we have $$OP^2$$ = $$PS^2$$ +$$OS^2$$ and $$OQ^2$$ = $$PS^2$$ +$$SQ^2$$
Putting these value in equation a we have
$$PS^2$$ +$$OS^2$$ < $$PS^2$$ +$$SQ^2$$
=> OS<SQ

Hope its clear now
_________________
Re: In the rectangular coordinate system above, if OP < PQ, is   [#permalink] 09 Dec 2018, 04:55

Go to page   Previous    1   2   [ 24 posts ]

Display posts from previous: Sort by