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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

If arc PQR above is a semicircle, what is the length of diameter PR?

You should know the following properties to solve this question: • A right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. The reverse is also true: if the diameter of the circle is also the triangle’s hypotenuse, then that triangle is a right triangle.

So, as given that PR is a diameter then angle PQR is a right angle.

• Perpendicular to the hypotenuse will always divide the triangle into two triangles with the same properties as the original triangle.

Thus, the perpendicular QT divides right triangle PQR into two similar triangles PQT and QRT (which are also similar to big triangle PQR). Now, in these three triangles the ratio of the corresponding sides will be equal (corresponding sides are the sides opposite the same angles). For example: QR/PR=QT/PQ=TR/QR. This property (sometimes along with Pythagoras) will give us the following: if we know ANY 2 values from PR, PQ, QR, PT, QT, TR then we'll be able to find other 4. We are given that QT=2 thus to find PR we need to know the length of any other line segment.

Re: If arc PQR above is a semicircle, what is the length of [#permalink]

Show Tags

22 Dec 2012, 05:04

Walkabout wrote:

Attachment:

The attachment Semicircle2.png is no longer available

If arc PQR above is a semicircle, what is the length of diameter PR ?

(1) a = 4 (2) b= 1

Another approach that could be implemented in thsi question is: Since there is a perpendicular drawn to the hypotenuese, therefore the two triangles that are formed must be similar to each other and to the larger one.

So if one side of a triangle reduces by a certain ratio, the other side must also reduce. In the diagram attached, if one considers any of the statement then he will be able to find out the other side. Consider statement 1) a=4

Look into the diagram. In the middle triangle, "a" or PI=4. We are given with the fact that IQ=2. Now in the smallest triangle, the corresponding side of PI=IQ. IQ=2. Therefore the factor with which PI has reduced is 2. Therefore other side must also reduce by the same factor. Hence IR=1. Sufficient

Statement 2) b=1. "b" is the corresponding side of IQ. So IQ , in the middle traingle, has reduced by a factor of 2. In the smallest triangle IQ=2. Therefore PI must be 4. Sufficient.

Attachments

geometry solution.png [ 13.23 KiB | Viewed 17382 times ]

Re: If arc PQR above is a semicircle, what is the length of [#permalink]

Show Tags

22 Dec 2012, 05:05

Bunnel can you explain the below part little elaboarately

For example: QR/PR=QT/PQ=TR/QR. This property (sometimes along with Pythagoras) will give us the following: if we know ANY 2 values from PR, PQ, QR, PT, QT, TR then we'll be able to find other 4. We are given that QT=2 thus to find PR we need to know the length of any other line segment.

I really dont understand the concept
_________________

"Giving kudos" is a decent way to say "Thanks" and motivate contributors. Please use them, it won't cost you anything

Re: If arc PQR above is a semicircle, what is the length of [#permalink]

Show Tags

14 Jan 2013, 10:38

1

This post received KUDOS

Marcab wrote:

Walkabout wrote:

Attachment:

Semicircle2.png

If arc PQR above is a semicircle, what is the length of diameter PR ?

(1) a = 4 (2) b= 1

Another approach that could be implemented in thsi question is: Since there is a perpendicular drawn to the hypotenuese, therefore the two triangles that are formed must be similar to each other and to the larger one.

So if one side of a triangle reduces by a certain ratio, the other side must also reduce. In the diagram attached, if one considers any of the statement then he will be able to find out the other side. Consider statement 1) a=4

Look into the diagram. In the middle triangle, "a" or PI=4. We are given with the fact that IQ=2. Now in the smallest triangle, the corresponding side of PI=IQ. IQ=2. Therefore the factor with which PI has reduced is 2. Therefore other side must also reduce by the same factor. Hence IR=1. Sufficient

Statement 2) b=1. "b" is the corresponding side of IQ. So IQ , in the middle traingle, has reduced by a factor of 2. In the smallest triangle IQ=2. Therefore PI must be 4. Sufficient.

Little complex for me... don u think bunuel's method is easier?
_________________

I've failed over and over and over again in my life and that is why I succeed--Michael Jordan Kudos drives a person to better himself every single time. So Pls give it generously Wont give up till i hit a 700+

Re: If arc PQR above is a semicircle, what is the length of [#permalink]

Show Tags

06 Mar 2014, 09:16

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.
_________________

Re: If arc PQR above is a semicircle, what is the length of [#permalink]

Show Tags

29 Mar 2014, 02:55

Can anybody explain why the area of the triangle PQR : Which is a right angle triangle in the figure above at Q, is not 1/2*QR*PQ ? Assuming this triangle was drawn without the semi-circle and if I slightly redraw the triangle keeping the base at QR, and PQ becomes the height and PR is the hypotenuse, then isnt the area of the triangle 1/2*QR*PQ?

Why is it that in these type of triangles which are drawn in such manner, that the hypotenuse is the base, the height is drawn from one vertex to another and then area is calculated?

This question is just to douse this silly doubt lingering in my head.

Can anybody explain why the area of the triangle PQR : Which is a right angle triangle in the figure above at Q, is not 1/2*QR*PQ ? Assuming this triangle was drawn without the semi-circle and if I slightly redraw the triangle keeping the base at QR, and PQ becomes the height and PR is the hypotenuse, then isnt the area of the triangle 1/2*QR*PQ?

Why is it that in these type of triangles which are drawn in such manner, that the hypotenuse is the base, the height is drawn from one vertex to another and then area is calculated?

This question is just to douse this silly doubt lingering in my head.

The area of triangle PQR IS 1/2*PQ*QR but it's ALSO 1/2*PR*QT.
_________________

If arc PQR above is a semicircle, what is the length of [#permalink]

Show Tags

16 Jul 2014, 22:12

Bunuel wrote:

If arc PQR above is a semicircle, what is the length of diameter PR?

Also in such kind of triangles might be useful to equate the areas to find the length of some line segment, for example area of PQR=1/2*QT*PR=1/2*QP*QR

(1) a = 4. Sufficient.

(2) b = 1. Sufficient.

Answer: D.

1/2*QT*PR=1/2*QP*QR => PR = (QP*QR)/2

With this equation, how statement 1 or 2 is being judged. Will you please fill up the gap?
_________________

______________ KUDOS please, if you like the post or if it helps "Giving kudos" is a decent way to say "Thanks"

If arc PQR above is a semicircle, what is the length of diameter PR?

Also in such kind of triangles might be useful to equate the areas to find the length of some line segment, for example area of PQR=1/2*QT*PR=1/2*QP*QR

(1) a = 4. Sufficient.

(2) b = 1. Sufficient.

Answer: D.

1/2*QT*PR=1/2*QP*QR => PR = (QP*QR)/2

With this equation, how statement 1 or 2 is being judged. Will you please fill up the gap?

It's better to use ratios for this question.

For (1) use the following ratio: PT/QT = QT/RT --> 4/2 = 2/RT --> RT = 1 --> PR = PT + RT = 4 + 1 = 5.

For (2) use the the same ratio: PT/QT = QT/RT --> PT/2 = 2/1--> PT = 4 --> PR = PT + RT = 4 + 1 = 5.

Re: If arc PQR above is a semicircle, what is the length of [#permalink]

Show Tags

05 Aug 2014, 20:38

1

This post received KUDOS

Bunuel wrote:

Attachment:

Semicircle2.PNG

If arc PQR above is a semicircle, what is the length of diameter PR?

You should know the following properties to solve this question: • A right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. The reverse is also true: if the diameter of the circle is also the triangle’s hypotenuse, then that triangle is a right triangle.

So, as given that PR is a diameter then angle PQR is a right angle.

• Perpendicular to the hypotenuse will always divide the triangle into two triangles with the same properties as the original triangle.

Thus, the perpendicular QT divides right triangle PQR into two similar triangles PQT and QRT (which are also similar to big triangle PQR). Now, in these three triangles the ratio of the corresponding sides will be equal (corresponding sides are the sides opposite the same angles). For example: QR/PR=QT/PQ=TR/QR. This property (sometimes along with Pythagoras) will give us the following: if we know ANY 2 values from PR, PQ, QR, PT, QT, TR then we'll be able to find other 4. We are given that QT=2 thus to find PR we need to know the length of any other line segment.

Re: If arc PQR above is a semicircle, what is the length of [#permalink]

Show Tags

02 Jun 2015, 00:02

Bunuel wrote:

Attachment:

Semicircle2.PNG

If arc PQR above is a semicircle, what is the length of diameter PR?

You should know the following properties to solve this question: • A right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. The reverse is also true: if the diameter of the circle is also the triangle’s hypotenuse, then that triangle is a right triangle.

So, as given that PR is a diameter then angle PQR is a right angle.

• Perpendicular to the hypotenuse will always divide the triangle into two triangles with the same properties as the original triangle.

Thus, the perpendicular QT divides right triangle PQR into two similar triangles PQT and QRT (which are also similar to big triangle PQR). Now, in these three triangles the ratio of the corresponding sides will be equal (corresponding sides are the sides opposite the same angles). For example: QR/PR=QT/PQ=TR/QR. This property (sometimes along with Pythagoras) will give us the following: if we know ANY 2 values from PR, PQ, QR, PT, QT, TR then we'll be able to find other 4. We are given that QT=2 thus to find PR we need to know the length of any other line segment.

we do not need to know this property. just make an equation in which b is a unknown number . we can solve

we can not remember this property in the test room.

the og explanation of this problem is good enough.

there are 5 or 6 person who following me whenever I go out of my house. I feel not safe. those persons prevent me from looking for the British I met in Halong bay. before I worked for a janapese company

If arc PQR above is a semicircle, what is the length of diameter PR? [#permalink]

Show Tags

22 Jul 2015, 17:48

This is a new question (DS 131) from the 2016 edition of the Official Guide.

Note that there are three right triangles total (small, medium, large). A right angle is marked at the bottom of the medium triangle, but there is another in the large as well (esoteric geometry rule: all triangles inscribed in semicircles are 90 degrees--knowing this is vital or you cannot solve the question), and of course in the small triangle (straight line = 180 degrees).

Pythagorean theorem time!

1) Given a, we can solve for PQ in terms of a. 2) Given b, we can solve for QR in terms of b.

This means we have two variables, a and b. a + b = PR, so given either a or b we can solve for PR.

1) a = 4. sufficient

2) b = 1. sufficient

The answer is D.
_________________

Harvard grad and 770 GMAT scorer, offering high-quality private GMAT tutoring, both in-person and via Skype, since 2002.

This is a new question (DS 131) from the 2016 edition of the Official Guide.

Note that there are three right triangles total (small, medium, large). A right angle is marked at the bottom of the medium triangle, but there is another in the large as well (esoteric geometry rule: all triangles inscribed in semicircles are 90 degrees--knowing this is vital or you cannot solve the question), and of course in the small triangle (straight line = 180 degrees).

Pythagorean theorem time!

1) Given a, we can solve for PQ in terms of a. 2) Given b, we can solve for QR in terms of b.

This means we have two variables, a and b. a + b = PR, so given either a or b we can solve for PR.

1) a = 4. sufficient

2) b = 1. sufficient

The answer is D.

Welcome to GC Quant Forums. Please search for a topic before posting as this will prevent duplication of topics and discussion threads that are already active.

If arc PQR above is a semicircle, what is the length of [#permalink]

Show Tags

10 May 2016, 05:04

1

This post received KUDOS

Do you seriously think that question will ask what is a+b = ? So that , from stat (1) + (2) you can say a + b = 5 ; GMAT will never ask addition of two numbers , so cut out the option C and try to get the soln from A and from B alone.

Re: If arc PQR above is a semicircle, what is the length of [#permalink]

Show Tags

31 Jul 2016, 00:01

1

This post received KUDOS

Walkabout wrote:

Attachment:

Semicircle.png

If arc PQR above is a semicircle, what is the length of diameter PR ?

(1) a = 4 (2) b = 1

I did this in a different way and still got the same answer, So if you look at the property of a semicircle, then if the triangle is formed using the diameter of the semicircle the the angle subtended by the angle formed at the arc is 90

Now given that Pythagorus theorem for the bog triangle PQR, \(PQ^2=QR^2+PR^2\); \(PR^2= (a+b)^2\) Now let PQ be x and QR be y then \(x^2+y^2= (a+b)^2\)---eq1

Smaller triangles PQa \(x^2=a^2+4\); QRb \(y^2= b^2+4\)--- eq2,3 now eq 2+3 \(x^2+y^2=a^2+b^2+8\) equate the same with eq 1 and get rid of x and y

\((a+b)^2=a^2+b^2+8\) \(a^2+b^2+2ab=a^2+b^2+8\)

2ab=8 ab=4

Now the question is actually asking if ab=4 what is a+b

knowing either the value of a or b we will know the other variable because of the multiplication constraint and get a+b

It’s quickly approaching two years since I last wrote anything on this blog. A lot has happened since then. When I last posted, I had just gotten back from...

Since my last post, I’ve got the interview decisions for the other two business schools I applied to: Denied by Wharton and Invited to Interview with Stanford. It all...

Marketing is one of those functions, that if done successfully, requires a little bit of everything. In other words, it is highly cross-functional and requires a lot of different...