Author 
Message 
TAGS:

Hide Tags

Director
Joined: 05 Jan 2008
Posts: 661

In ΔPQS above, if PQ =3 and PS = 4, then PR =?
[#permalink]
Show Tags
26 Jun 2008, 21:39
Question Stats:
73% (01:33) correct 27% (02:07) wrong based on 336 sessions
HideShow timer Statistics
In ΔPQS above, if PQ =3 and PS = 4, then PR =? A. 9/4 B. 12/5 C. 16/5 D. 15/4 E. 20/3 Attachment:
Untitled.png [ 6.03 KiB  Viewed 776 times ]
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Persistence+Patience+Persistence+Patience=G...O...A...L




Math Expert
Joined: 02 Sep 2009
Posts: 49303

Re: In ΔPQS above, if PQ =3 and PS = 4, then PR =?
[#permalink]
Show Tags
05 Mar 2012, 11:52




Manager
Joined: 10 Mar 2008
Posts: 66

Re: In ΔPQS above, if PQ =3 and PS = 4, then PR =?
[#permalink]
Show Tags
26 Jun 2008, 21:58
prasannar wrote: In ΔPQS attached, if PQ =3 and PS = 4, then PR=?
(A) 9/4 (B) 12/5 (C) 16/5 (D) 15/4 (E) 20/3 its just equating the ares 1/2(pq*ps)=1/2(qs*pr) 1/2(3*4)=1/2 (5*pr) pr=12/5




Manager
Joined: 24 Apr 2008
Posts: 157

Re: In ΔPQS above, if PQ =3 and PS = 4, then PR =?
[#permalink]
Show Tags
26 Jun 2008, 21:51
Let QR=x and PR=h
x^2 +h^2 = 9
5x)^2 + h^2 = 16
Solving for x = 9/5 and h=12/5



Director
Joined: 23 Sep 2007
Posts: 758

Re: In ΔPQS above, if PQ =3 and PS = 4, then PR =?
[#permalink]
Show Tags
26 Jun 2008, 21:53
B
345 triangle
let qr = x then rs = 5x
let pr = h
2 equations:
3^2 = h^2 + x^2 and 4^2 = h^2 + (5x)^2
expand and substract them to get x = 9/5
substitute 9/5 into the first equation (or second, your choice) to get 9 = h^2 + 81/25
solve the equation to get h = 12/5



GMAT Tutor
Joined: 24 Jun 2008
Posts: 1344

Re: In ΔPQS above, if PQ =3 and PS = 4, then PR =?
[#permalink]
Show Tags
27 Jun 2008, 07:39
This is quite a wellknown diagram in mathematics: it can be used to prove the Pythagorean Theorem (using a and b for the two legs, and not 3 and 4). There are (at least) three entirely different ways to solve this problem, two of which were described above. Call the length we're looking for 'd': The area of the triangle must be the same no matter which base you choose. Thus 3*4/2 = 5*d/2 > d = 12/5. Let QR = c; then QS = 5c. We have two right angled triangles, and can use Pythagoras to set up two equations, two unknowns (c and d; this is the most timeconsuming approach). The approach not mentioned above: notice that the two smaller triangles in the diagram are each similar to the 345 triangle. Because PQR is similar to QSP, we have d/3 = 4/5 > d = 12/5. It's the similarity of the triangles that can let you prove Pythagoras, incidentally.
_________________
GMAT Tutor in Toronto
If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com



Manager
Joined: 30 Sep 2010
Posts: 55

Re: In ΔPQS above, if PQ =3 and PS = 4, then PR =?
[#permalink]
Show Tags
09 Nov 2010, 16:36
PQ =3 and PS = 4, So QS = 5
area of the triangle = 1/2 * PQ * PS = 1/2*QS*PR
OR, 1/2 * 3 * 4 = 1/2 * QS * PR OR PR = 12/5



Board of Directors
Joined: 01 Sep 2010
Posts: 3416

Re: In ΔPQS above, if PQ =3 and PS = 4, then PR =?
[#permalink]
Show Tags
05 Mar 2012, 11:45



Board of Directors
Joined: 01 Sep 2010
Posts: 3416

Re: In ΔPQS above, if PQ =3 and PS = 4, then PR =?
[#permalink]
Show Tags
05 Mar 2012, 12:18
Be patient. I have not fully understood Why 5/2 * PQ...should be QS ?? Secondly why my reasoning do not lead me to the answer and is flawed, completely wrong ??? We have a right triangle PQS where angle P is 90. Also two sides PS=3 and PQ= 4 so from this we have a 306090 triangle. So, if we look at angle R is 90, from this we can see that angle P is shared between PQS and PRS so P for PRS should be 60 (likewise angle P for triangle PRQ should be 30, so angle P is 60+30=90). So, we have: for triangle PRS angle R is 90 (PS is the hypotenuse), angle P is 60 (RS long leg) and angle S is 30 (short leg PR). If PS is 3 (hypotenuse opposite 90 angle) PR should be 1.5 (short leg opposite angle S that is 30). This based on ratio 30:60:90. I know that it does not hold anywater, but is useful to understand Thanks
_________________
COLLECTION OF QUESTIONS AND RESOURCES Quant: 1. ALL GMATPrep questions Quant/Verbal 2. Bunuel Signature Collection  The Next Generation 3. Bunuel Signature Collection ALLINONE WITH SOLUTIONS 4. Veritas Prep Blog PDF Version 5. MGMAT Study Hall Thursdays with Ron Quant Videos Verbal:1. Verbal question bank and directories by Carcass 2. MGMAT Study Hall Thursdays with Ron Verbal Videos 3. Critical Reasoning_Oldy but goldy question banks 4. Sentence Correction_Oldy but goldy question banks 5. Readingcomprehension_Oldy but goldy question banks



Math Expert
Joined: 02 Sep 2009
Posts: 49303

Re: In ΔPQS above, if PQ =3 and PS = 4, then PR =?
[#permalink]
Show Tags
05 Mar 2012, 12:33
carcass wrote: Be patient. I have not fully understood Why 5/2 * PQ...should be QS ?? Secondly why my reasoning do not lead me to the answer and is flawed, completely wrong ??? We have a right triangle PQS where angle P is 90. Also two sides PS=3 and PQ= 4 so from this we have a 306090 triangle. So, if we look at angle R is 90, from this we can see that angle P is shared between PQS and PRS so P for PRS should be 60 (likewise angle P for triangle PRQ should be 30, so angle P is 60+30=90). So, we have: for triangle PRS angle R is 90 (PS is the hypotenuse), angle P is 60 (RS long leg) and angle S is 30 (short leg PR). If PS is 3 (hypotenuse opposite 90 angle) PR should be 1.5 (short leg opposite angle S that is 30). This based on ratio 30:60:90. I know that it does not hold anywater, but is useful to understand Thanks First of all 5/2 * PQ does not equal to QS. We equate the areas, which can be found in two ways: 1. 1/2*Leg1*Leg2 > \(area=\frac{1}{2}*PQ*PS=6\); 2. 1/2*Perpendicular to hypotenuse*Hypotenuse > \(area=\frac{1}{2}*PR*QS=\frac{5}{2}*PR\) (since hypotenuse QS=5); Now, equate the areas: \(6=\frac{5}{2}*PR\) > \(PR=\frac{12}{5}\). Next, in a right triangle where the angles are 30°, 60°, and 90° the sides are always in the ratio \(1 : \sqrt{3}: 2\). In PQS sides PQ and PS are NOT in the ratio \(1 : \sqrt{3}\), so PQS is not a 30°, 60°, and 90° right triangle. I think you are mixing 345 Pythagorean Triples triangle with 30°60°90° triangle. Hope it's clear.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Board of Directors
Joined: 01 Sep 2010
Posts: 3416

Re: In ΔPQS above, if PQ =3 and PS = 4, then PR =?
[#permalink]
Show Tags
05 Mar 2012, 14:19



Senior Manager
Joined: 24 Aug 2009
Posts: 476
Schools: Harvard, Columbia, Stern, Booth, LSB,

Re: In ΔPQS above, if PQ =3 and PS = 4, then PR =?
[#permalink]
Show Tags
07 Sep 2012, 01:39
As mentioned by Bunuel, there are other methods as well to solve this problem One of the method is SimilarityTriangle QPS is similar to PRS (because one common side & angle is 3 & 90 degree) So, QS/QP = PS/PR 5/4 = 3/x x = 12/5 Hope it helps.
_________________
If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS. Kudos always maximizes GMATCLUB worth Game Theory
If you have any question regarding my post, kindly pm me or else I won't be able to reply



Senior Manager
Joined: 15 Oct 2015
Posts: 336
Concentration: Finance, Strategy
GPA: 3.93
WE: Account Management (Education)

Re: In ΔPQS above, if PQ =3 and PS = 4, then PR =?
[#permalink]
Show Tags
24 Feb 2016, 04:26
prasannar wrote: Attachment: Diag1.JPG In ΔPQS above, if PQ =3 and PS = 4, then PR =? A. 9/4 B. 12/5 C. 16/5 D. 15/4 E. 20/3 Two approaches. the area is 6. so area of pqr + area of prs = 6. solution will result in 12/5. B second: testing answer choices. if assume that line(pr) is an answer choice and try to rearrange to get line(rs), then you discover line rs is squareroot of some negative numbers in all the options except B



Moderator
Joined: 22 Jun 2014
Posts: 1042
Location: India
Concentration: General Management, Technology
GPA: 2.49
WE: Information Technology (Computer Software)

Re: In ΔPQS above, if PQ =3 and PS = 4, then PR =?
[#permalink]
Show Tags
09 Apr 2016, 10:19
prasannar wrote: Attachment: Diag1.JPG In ΔPQS above, if PQ =3 and PS = 4, then PR =? A. 9/4 B. 12/5 C. 16/5 D. 15/4 E. 20/3 QS will be 5 being the hypotenuse of 90 degree triangle. As we can calculate the area by two ways here: 1/2 * PS * PQ = 1/2 * PR * QS 4 * 3 = PR * 5 PR = 12/5
_________________
 Target  720740 http://gmatclub.com/forum/informationonnewgmatesrreportbeta221111.html http://gmatclub.com/forum/listofoneyearfulltimembaprograms222103.html



Senior Manager
Status: Active
Affiliations: NA
Joined: 24 Oct 2012
Posts: 291
GMAT 1: 590 Q50 V21 GMAT 2: 600 Q48 V25 GMAT 3: 730 Q51 V37
GPA: 3.5

Re: In ΔPQS above, if PQ =3 and PS = 4, then PR =?
[#permalink]
Show Tags
05 Oct 2016, 11:22
Very simple hypotenuse will be 5 as right angle triangle (3,4,5) . A perpendicular drawn to hypotenuse will bisect it , that means 5/2 or 2.5 ; 12/5 nearest option.
_________________
#If you like my post , please encourage me by giving Kudos



Intern
Joined: 09 Dec 2014
Posts: 37

Re: In ΔPQS above, if PQ =3 and PS = 4, then PR =?
[#permalink]
Show Tags
04 Aug 2017, 01:32
Let QR=x and RS=y. Area of QPS= 1/2*4*3 = 6 We know, Area of QPS = Area of QRP + Area of PRQ > (1) Let PR=a. From Pythagoras Theorem, QS=5. ==> x+y=5 In (1), 6 = 1/2*y*a +1/2*x*a ==> 1/2(ay + ax) ==> a(x+y) =12 As x+y=5, a*5=12 ==> a=12/5 = PR Answer: B
_________________
Thanks, Ramya



NonHuman User
Joined: 09 Sep 2013
Posts: 8150

Re: In ΔPQS above, if PQ =3 and PS = 4, then PR =?
[#permalink]
Show Tags
06 Sep 2018, 07:19
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: In ΔPQS above, if PQ =3 and PS = 4, then PR =? &nbs
[#permalink]
06 Sep 2018, 07:19






