GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 18 Nov 2019, 20:21

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

What is the area of the trapezoid if PQ is parallel to RS, RS > PQ, th

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59125
What is the area of the trapezoid if PQ is parallel to RS, RS > PQ, th  [#permalink]

Show Tags

New post 17 Sep 2019, 22:05
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

72% (01:24) correct 28% (01:22) wrong based on 53 sessions

HideShow timer Statistics

Competition Mode Question



Image
What is the area of the trapezoid if PQ is parallel to RS, RS > PQ, the distance between the two parallel lines is 15, and the distance from R to the perpendicular drawn from P to RS is 10?

(1) \(PR =\sqrt{325}\)
(2) \(QS =\sqrt{325}\)


Attachment:
pic.jpg
pic.jpg [ 7.44 KiB | Viewed 563 times ]

_________________
Senior Manager
Senior Manager
User avatar
P
Joined: 31 May 2018
Posts: 451
Location: United States
Concentration: Finance, Marketing
Re: What is the area of the trapezoid if PQ is parallel to RS, RS > PQ, th  [#permalink]

Show Tags

New post 17 Sep 2019, 22:43
1
What is the area of the trapezoid if PQ is parallel to RS, RS > PQ, the distance between the two parallel lines is 15, and the distance from R to the perpendicular drawn from P to RS is 10?

STATEMENT (1)--PR=\(\sqrt{325}\)

this statement gives no new information about the trapezoid
we can derive it from the question prompt
still, we don't know anything about QS (trapezoid can be scalene , isosceles we don't know)
so we cant find RS

area of trapezoid = \(\frac{(PQ+RS)*15}{2}\)

we don't know anything about RS so, we can't find the area of a trapezoid
INSUFFICIENT

STATEMENT (2)--QS=\(\sqrt{325}\)

we know that PR = \(\sqrt{325}\)
from this statement we know QS = \(\sqrt{325}\)
this proves that trapezoid is isoceles

so we can find the value of RS that is = 10+30+10 = 50

area of trapezoid = \(\frac{(PQ+RS)*15}{2}\) = \(\frac{(30+50)*15}{2}\) = 600

SUFFICIENT

B is the correct answer
Senior Manager
Senior Manager
User avatar
P
Status: Whatever it takes!
Joined: 10 Oct 2018
Posts: 383
GPA: 4
Re: What is the area of the trapezoid if PQ is parallel to RS, RS > PQ, th  [#permalink]

Show Tags

New post 17 Sep 2019, 22:49
2
IMO ANSWER IS OPTION B. Here's how I did:

Posted from my mobile device
Attachments

IMG_20190918_111234.jpg
IMG_20190918_111234.jpg [ 3.35 MiB | Viewed 474 times ]


_________________
Kudos OK Please!!

ALL ABOUT GMAT- \(https://exampal.com/gmat/blog/gmat-score-explained\)
Senior Manager
Senior Manager
avatar
P
Joined: 18 May 2019
Posts: 457
GMAT ToolKit User Premium Member CAT Tests
Re: What is the area of the trapezoid if PQ is parallel to RS, RS > PQ, th  [#permalink]

Show Tags

New post 17 Sep 2019, 23:10
1
From the information given in connection with the trapezoid, I need information on QS in order to compute the area of trapezoid.

1. Statement 1 gives the distance of PR=325^0.5, an information that can already be deduced from the question stem. In addition it gives no information whatsoever about QS, which is needed in order to determine the length of RS. Statement 1 is therefore insufficient.

2. Statement gives information about the QS=325^0.5, and that is sufficient to compute the area of the trapezoid. Statement 2 alone is therefore sufficient in this case.

The answer is therefore B.
Senior Manager
Senior Manager
avatar
G
Joined: 01 Mar 2019
Posts: 278
Location: India
Concentration: Strategy, Social Entrepreneurship
Schools: Ross '22, ISB '20, NUS '20
GPA: 4
Reviews Badge
Re: What is the area of the trapezoid if PQ is parallel to RS, RS > PQ, th  [#permalink]

Show Tags

New post 17 Sep 2019, 23:29
As we know Area of trapezoid = (a+b)h
HERE a=30,h=15, to find b we need RS length= 10+15+X(CAN BE FIND USING QS)
So OA:B
Senior Manager
Senior Manager
User avatar
G
Joined: 10 Sep 2013
Posts: 315
Location: India
GMAT 1: 720 Q50 V38
GPA: 4
Re: What is the area of the trapezoid if PQ is parallel to RS, RS > PQ, th  [#permalink]

Show Tags

New post 17 Sep 2019, 23:40
B.


We need B to locate point S. A is already Stated in the argument

Posted from my mobile device
Senior Manager
Senior Manager
avatar
P
Joined: 07 Mar 2019
Posts: 384
Location: India
GMAT 1: 580 Q43 V27
WE: Sales (Energy and Utilities)
CAT Tests
Re: What is the area of the trapezoid if PQ is parallel to RS, RS > PQ, th  [#permalink]

Show Tags

New post 18 Sep 2019, 00:25
Given here PQ = 30, Let T be the point at RS such that PT ⊥ RS. Given PT = 15 and RT = 10. Since RS > PQ
RS > 30

Area of Trapezoid PQSR \(=\frac{1}{2} (PQ + RS) * PT\)

Only unknown in the formula is RS. So RS = ?

(1) PR = √325
It only reiterates what is mentioned in the question. No new information given about RS neither can be deduced. Since QS can have following possibilities:

a. QS < PR
b. QS = PR
c. QS > PR

RS would vary accordingly.

INSUFFICIENT.

(2) QS = √325
Since RT = 10 and PT = 15, PR = √325. Hence PR = QS
 RS = 10 + 30 + 10 = 50

Thus, only one value of RS is possible.

SUFFICIENT.

Answer(B).
_________________
Ephemeral Epiphany..!

GMATPREP1 590(Q48,V23) March 6, 2019
GMATPREP2 610(Q44,V29) June 10, 2019
GMATPREPSoft1 680(Q48,V35) June 26, 2019
Director
Director
avatar
P
Joined: 24 Nov 2016
Posts: 783
Location: United States
Re: What is the area of the trapezoid if PQ is parallel to RS, RS > PQ, th  [#permalink]

Show Tags

New post 18 Sep 2019, 03:20
Quote:
What is the area of the trapezoid if PQ is parallel to RS, RS > PQ, the distance between the two parallel lines is 15, and the distance from R to the perpendicular drawn from P to RS is 10?

(1) PR=√325
(2) QS=√325


area trapezoid: \(\frac{base_1+base_2}{2}•height=\frac{31+(10+30+X)}{2}•15\)
X is the distance from S to the perpendicular drawn from Q to RS;

(1) PR=√325: no info about perpendicular, insufic.
(2) QS=√325: if we draw a right triangle from this perpendicular we can find X with this info, sufic.

Answer (B)
Intern
Intern
avatar
B
Joined: 21 Mar 2019
Posts: 22
CAT Tests
Re: What is the area of the trapezoid if PQ is parallel to RS, RS > PQ, th  [#permalink]

Show Tags

New post 18 Sep 2019, 10:37
B
Area = (B1+B2) * h /2
= 30*x*15/2
st1 useless
st2 we can calculate the length of the base of the second " triangle " which is 10
like the one of the first triangle.
Therefore the middle part is also equal to 30 so x = 10+30+10 = 50 --> Sufficient

B
GMAT Club Bot
Re: What is the area of the trapezoid if PQ is parallel to RS, RS > PQ, th   [#permalink] 18 Sep 2019, 10:37
Display posts from previous: Sort by

What is the area of the trapezoid if PQ is parallel to RS, RS > PQ, th

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





cron

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne