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

 It is currently 16 Oct 2018, 12:21

### 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

# For the cube shown above, what is the degree measure of PQR

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

### Hide Tags

Director
Joined: 19 Nov 2004
Posts: 529
Location: SF Bay Area, USA
For the cube shown above, what is the degree measure of PQR  [#permalink]

### Show Tags

Updated on: 30 Jun 2012, 07:40
13
64
00:00

Difficulty:

45% (medium)

Question Stats:

52% (00:56) correct 48% (00:59) wrong based on 1715 sessions

### HideShow timer Statistics

Attachment:

cube.gif [ 2.13 KiB | Viewed 40634 times ]
For the cube shown above, what is the degree measure of PQR?

A. 30
B. 45
C. 60
D. 75
E. 90

Originally posted by nocilis on 02 Feb 2005, 22:35.
Last edited by Bunuel on 30 Jun 2012, 07:40, edited 1 time in total.
Edited the question and added the OA.
Math Expert
Joined: 02 Sep 2009
Posts: 49915
For the cube shown above, what is the degree measure of PQR  [#permalink]

### Show Tags

30 Jun 2012, 07:43
18
12
For the cube shown above, what is the degree measure of PQR?

A. 30
B. 45
C. 60
D. 75
E. 90

Note that triangle PQR is equilateral: it's made by the diagonals of the adjacent faces of the given cube (and as faces of a cube are squares its diagonals are equal). Thus angle BEG=60 degrees.

Attachment:

cube.gif [ 2.28 KiB | Viewed 42700 times ]

_________________
Director
Joined: 25 Jan 2004
Posts: 695
Location: Milwaukee

### Show Tags

02 Feb 2005, 23:03
17
3
60 as well

because the figure in question is a cube sides pq,qr,pr are equal. Hence pqr is an equilateral triangle. So you get 60 for each included angle.
Had this been a cuboid, then it is a different story.
_________________

Praveen

##### General Discussion
Intern
Joined: 19 Jan 2008
Posts: 16
Re: For the cube shown above, what is the degree measure of PQR  [#permalink]

### Show Tags

23 May 2014, 11:38
1
Hi Bunuel, since the face of a cube forms the square and the diagonal of the square bisects the angles.The 2 diagonals shown in the pictures and each makes an angle of 45.Thus,why not the answer is 45+45=90?Can you please help me to understand this.
Intern
Joined: 13 May 2014
Posts: 33
Concentration: General Management, Strategy
Re: For the cube shown above, what is the degree measure of PQR  [#permalink]

### Show Tags

23 May 2014, 12:22
12
3
ankushbassi wrote:
Hi Bunuel, since the face of a cube forms the square and the diagonal of the square bisects the angles.The 2 diagonals shown in the pictures and each makes an angle of 45.Thus,why not the answer is 45+45=90?Can you please help me to understand this.

Hi Ankush,
The angle in question is as shown.Please refer the diagram below:
Attachment:

g2.png [ 17.85 KiB | Viewed 35608 times ]

It would be an equilateral triangle made up by 3 face diagonals.

What you are referring are the two angles in two different planes.
which are angle POA and angle AOR each 45 degrees

They are on adjacent faces of the cube,which you cannot combine.
Attachment:

G5.png [ 11.18 KiB | Viewed 35596 times ]

Hope this helps.
Press kudos if it was of help.

Kindly check the following post with the poll and revert with your replies
10-straight-lines-no-two-of-which-are-parallel-and-no-three-171525.html
Math Expert
Joined: 02 Sep 2009
Posts: 49915
For the cube shown above, what is the degree measure of PQR  [#permalink]

### Show Tags

23 May 2014, 12:24
7
ankushbassi wrote:
Hi Bunuel, since the face of a cube forms the square and the diagonal of the square bisects the angles.The 2 diagonals shown in the pictures and each makes an angle of 45.Thus,why not the answer is 45+45=90?Can you please help me to understand this.

Because these two squares are not in the same plane. If the square were in the same plane (as shown below), then you would be correct:

Does this make sense?

Attachment:

squares.png [ 1.8 KiB | Viewed 36083 times ]

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 49915
For the cube shown above, what is the degree measure of PQR  [#permalink]

### Show Tags

14 Sep 2014, 17:57
1
1
Director
Joined: 04 Jun 2016
Posts: 569
GMAT 1: 750 Q49 V43
For the cube shown above, what is the degree measure of PQR  [#permalink]

### Show Tags

17 Jul 2016, 01:13
Attachment:
cube.gif

For the cube shown above, what is the degree measure of PQR?

A. 30
B. 45
C. 60
D. 75
E. 90

Don't be in a hurry and say it is 90 degrees.
If you look closely , you will notice PQ and QR are two diagonals to the cube; therefore they will be equal in dimension. Now see If you join QR you will get another diagonal with.
NOW we get a triangle in which PQ=PR=RQ ; An equilateral triangle.

ALL angles of an equilateral triangle are 60 degrees.

_________________

Posting an answer without an explanation is "GOD COMPLEX". The world doesn't need any more gods. Please explain you answers properly.
FINAL GOODBYE :- 17th SEPTEMBER 2016. .. 16 March 2017 - I am back but for all purposes please consider me semi-retired.

Current Student
Joined: 28 Nov 2014
Posts: 867
Concentration: Strategy
Schools: Fisher '19 (M)
GPA: 3.71
Re: For the cube shown above, what is the degree measure of PQR  [#permalink]

### Show Tags

25 Jul 2016, 01:50
Bunuel - What will be the value of each diagonal in the equilateral triangle that is formed here ? (triangle PQR)
Math Expert
Joined: 02 Sep 2009
Posts: 49915
Re: For the cube shown above, what is the degree measure of PQR  [#permalink]

### Show Tags

25 Jul 2016, 01:56
Keats wrote:
Bunuel - What will be the value of each diagonal in the equilateral triangle that is formed here ? (triangle PQR)

Do you mean angles instead of diagonals? Triangle does not have diagonals. If you mean angles, then each angle in equilateral triangle is 60 degrees.
_________________
Current Student
Joined: 28 Nov 2014
Posts: 867
Concentration: Strategy
Schools: Fisher '19 (M)
GPA: 3.71
Re: For the cube shown above, what is the degree measure of PQR  [#permalink]

### Show Tags

25 Jul 2016, 02:34
Bunuel wrote:
Keats wrote:
Bunuel - What will be the value of each diagonal in the equilateral triangle that is formed here ? (triangle PQR)

Do you mean angles instead of diagonals? Triangle does not have diagonals. If you mean angles, then each angle in equilateral triangle is 60 degrees.

Sorry that I didn't put it up correctly. I wanted to ask that what will be the value of each side of the equilateral triangle (which happens to be the diagonal of the cube), Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 49915
Re: For the cube shown above, what is the degree measure of PQR  [#permalink]

### Show Tags

25 Jul 2016, 02:37
Keats wrote:
Bunuel wrote:
Keats wrote:
Bunuel - What will be the value of each diagonal in the equilateral triangle that is formed here ? (triangle PQR)

Do you mean angles instead of diagonals? Triangle does not have diagonals. If you mean angles, then each angle in equilateral triangle is 60 degrees.

Sorry that I didn't put it up correctly. I wanted to ask that what will be the value of each side of the equilateral triangle (which happens to be the diagonal of the cube), Bunuel

If we assume that the length of a side of the cube is x, then the length of each diagonal = $$\sqrt{x^2 + x^2} = \sqrt{2}x$$
_________________
CEO
Joined: 08 Jul 2010
Posts: 2537
Location: India
GMAT: INSIGHT
WE: Education (Education)
Re: For the cube shown above, what is the degree measure of PQR  [#permalink]

### Show Tags

01 Aug 2016, 10:36
2
nocilis wrote:
Attachment:
The attachment cube.gif is no longer available
For the cube shown above, what is the degree measure of PQR?

A. 30
B. 45
C. 60
D. 75
E. 90

Draw a construction (Pink Line) and

Attachments

File comment: www.GMATinsight.com

Answer 3.jpg [ 58.96 KiB | Viewed 6714 times ]

_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Manager
Joined: 18 Mar 2015
Posts: 103
Location: India
Schools: ISB '19
GMAT 1: 600 Q47 V26
GPA: 3.59
Re: For the cube shown above, what is the degree measure of PQR  [#permalink]

### Show Tags

21 Aug 2017, 10:28
interesting! I have get an actual wooden box to understand this concept
Intern
Joined: 20 Dec 2014
Posts: 37
Re: For the cube shown above, what is the degree measure of PQR  [#permalink]

### Show Tags

09 Apr 2018, 09:27
ferrarih wrote:
Hi, I understood the answer and I agree, but I can't find out why my logic isn't right.

Since it's a cube, all angles are 90 degrees, and since PO and RO are the bisectrix of the angle 90, than PQR would have to be 90, which is not the answer. What am thinking wrong?

Thanks.

You are looking at it 2D imagine in 3D...
Also like everyone said all sides are equal hence angle in 60
Note its a triangle
_________________

Kindly press "+1 Kudos" to appreciate

Re: For the cube shown above, what is the degree measure of PQR &nbs [#permalink] 09 Apr 2018, 09:27
Display posts from previous: Sort by

# For the cube shown above, what is the degree measure of PQR

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

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.