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

It is currently 18 Aug 2018, 07:53

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

Arc XYZ lies on a circle centered at O. Is a < 55?

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

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47983
Arc XYZ lies on a circle centered at O. Is a < 55?  [#permalink]

Show Tags

New post 27 Jan 2015, 07:40
2
5
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

67% (01:30) correct 33% (01:24) wrong based on 209 sessions

HideShow timer Statistics

Image
Arc XYZ lies on a circle centered at O. Is a < 55?

(1) Angle ZOY = 35
(2) Angle XOY = 75

Kudos for a correct solution.

Attachment:
Q14_1.png
Q14_1.png [ 21.9 KiB | Viewed 2994 times ]

_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 6549
Re: Arc XYZ lies on a circle centered at O. Is a < 55?  [#permalink]

Show Tags

New post 27 Jan 2015, 09:35
ans C...
both statements are required to get angle zox which is equal to 2a..
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47983
Arc XYZ lies on a circle centered at O. Is a < 55?  [#permalink]

Show Tags

New post 02 Feb 2015, 02:39
Bunuel wrote:
Image
Arc XYZ lies on a circle centered at O. Is a < 55?

(1) Angle ZOY = 35
(2) Angle XOY = 75

Kudos for a correct solution.

Attachment:
The attachment Q14_1.png is no longer available


VERITAS PREP OFFICIAL SOLUTION:

The correct response is (C).

If we draw a radius from O to Y, we can fill in the two given values: ZOY = 35, and XOY = 75. OX and OZ are both radii of the same circle, so their opposite angles must be equal. We can use this information to solve for angle XYZ, and in term find the value for a.

To do the math, here’s how it would look:

Attachment:
Q14_2.png
Q14_2.png [ 24.07 KiB | Viewed 2568 times ]


180 = 35 + OYZ + OZY
145/2 = 72.5 = OYZ = OZY

180 = 75 + OXY + OYX
105/2 = 52.5 = OXY + OYX

Angle XYZ = 72.5 + 52.5 = 125

Angle a = 180 – 125
Angle a = 55

The answer to the question would always be “no.”

If you chose (A), this would allow us to solve for XYO, but we’d also need angle OYZ to find a.

If you chose (B), this would allow us to find OYZ, but we’d also need to know angle XOY to find angle XYO.

If you chose (D), both pieces of information are important, but neither is independently sufficient.

If you chose (E), you may have missed that XO = OY = OZ, since all radii in a circle must be equal, as well as the fact that angles opposite equal sides are also equal.
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
Joined: 18 Apr 2011
Posts: 43
Location: United States
WE: Information Technology (Computer Software)
GMAT ToolKit User
Arc XYZ lies on a circle centered at O. Is a < 55?  [#permalink]

Show Tags

New post 02 Sep 2015, 09:03
Bunuel wrote:
Bunuel wrote:
Image
Arc XYZ lies on a circle centered at O. Is a < 55?

(1) Angle ZOY = 35
(2) Angle XOY = 75

Kudos for a correct solution.

Attachment:
The attachment Q14_1.png is no longer available


The correct response is (C).

If we draw a radius from O to Y, we can fill in the two given values: ZOY = 35, and XOY = 75. OX and OZ are both radii of the same circle, so their opposite angles must be equal. We can use this information to solve for angle XYZ, and in term find the value for a.

To do the math, here’s how it would look:

Attachment:
The attachment Q14_2.png is no longer available


180 = 35 + OYZ + OZY
145/2 = 72.5 = OYZ = OZY

180 = 75 + OXY + OYX
105/2 = 52.5 = OXY + OYX

Angle XYZ = 72.5 + 52.5 = 125

Angle a = 180 – 125
Angle a = 55

The answer to the question would always be “no.”

If you chose (A), this would allow us to solve for XYO, but we’d also need angle OYZ to find a.

If you chose (B), this would allow us to find OYZ, but we’d also need to know angle XOY to find angle XYO.

If you chose (D), both pieces of information are important, but neither is independently sufficient.

If you chose (E), you may have missed that XO = OY = OZ, since all radii in a circle must be equal, as well as the fact that angles opposite equal sides are also equal.


Bunuel,

can the solution be like this ?

an inscribed angle is exactly half the corresponding central angle, so all inscribed angle that subtends to the same arc, are equal.
so - 75+35 = 110/2 = 55 ?
Attachments

File comment: example image
Capture.PNG
Capture.PNG [ 79.32 KiB | Viewed 2150 times ]

Intern
Intern
avatar
Joined: 28 Oct 2015
Posts: 21
Re: Arc XYZ lies on a circle centered at O. Is a < 55?  [#permalink]

Show Tags

New post 28 Oct 2015, 07:53
Hi there,

How do you guys know zox is 2a?

Thanks!
Director
Director
User avatar
P
Joined: 05 Mar 2015
Posts: 985
Re: Arc XYZ lies on a circle centered at O. Is a < 55?  [#permalink]

Show Tags

New post 02 Aug 2016, 11:50
Bunuel wrote:
Image
Arc XYZ lies on a circle centered at O. Is a < 55?

(1) Angle ZOY = 35
(2) Angle XOY = 75

Kudos for a correct solution.

Attachment:
The attachment Q14_1.png is no longer available

here is alternate solution
please follow attached fig.
(1)ZOY=35 means YXZ=17.5 (central angle theorem)
not suff....
(2) similarly XOY=75 means XZY = 37.5
not suff...

combining both as angle a = sum of 2opp.internal angles of the triangle XYZ
so a=37.5+17.5----------->55
suff...

Ans C
Attachments

Q14_1.png
Q14_1.png [ 24.4 KiB | Viewed 1470 times ]

Director
Director
User avatar
P
Joined: 05 Mar 2015
Posts: 985
Re: Arc XYZ lies on a circle centered at O. Is a < 55?  [#permalink]

Show Tags

New post 02 Aug 2016, 12:40
Bunuel wrote:
Image
Arc XYZ lies on a circle centered at O. Is a < 55?

(1) Angle ZOY = 35
(2) Angle XOY = 75

Kudos for a correct solution.

Attachment:
The attachment Q14_1.png is no longer available


Ans is C as both internal angles of triangle XYZ is known and is nothing but sum of those angles =a=55

Ans C
Attachments

Q14_1.png
Q14_1.png [ 24.4 KiB | Viewed 1460 times ]

Intern
Intern
avatar
B
Joined: 26 Dec 2016
Posts: 29
Re: Arc XYZ lies on a circle centered at O. Is a < 55?  [#permalink]

Show Tags

New post 18 Oct 2017, 10:58
why are 145 and 105 divided by 2? Is it because they're inscribed angles?
Intern
Intern
avatar
B
Joined: 24 Oct 2016
Posts: 25
GMAT ToolKit User
Re: Arc XYZ lies on a circle centered at O. Is a < 55?  [#permalink]

Show Tags

New post 23 Oct 2017, 08:31
Another way to solve this question would be to use the concept of central angle and inscribed angle i.e. inscribed angle is half of the central angle.
Re: Arc XYZ lies on a circle centered at O. Is a < 55? &nbs [#permalink] 23 Oct 2017, 08:31
Display posts from previous: Sort by

Arc XYZ lies on a circle centered at O. Is a < 55?

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

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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®.