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

 It is currently 15 Jun 2019, 21:55 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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  In ΔABC above, which of the following must be true?

Author Message
TAGS:

Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 55609
In ΔABC above, which of the following must be true?  [#permalink]

Show Tags 00:00

Difficulty:   35% (medium)

Question Stats: 69% (01:27) correct 31% (01:35) wrong based on 132 sessions

HideShow timer Statistics In ΔABC above, which of the following must be true?

I. x > 50
II. AC < 10
III. AB > 10

A. I only
B. III only
C. I and II only
D. I and III only
E. I, II, and III

Attachment: 2015-12-27_2143.png [ 12.19 KiB | Viewed 2891 times ]

_________________
Senior Manager  B
Joined: 28 Feb 2014
Posts: 294
Location: United States
Concentration: Strategy, General Management
Re: In ΔABC above, which of the following must be true?  [#permalink]

Show Tags

1
Bunuel wrote: In ΔABC above, which of the following must be true?

I. x > 50
II. AC < 10
III. AB > 10

Attachment:
2015-12-27_2143.png

I. x > 50
3x-15=180
x=65
True

II. AC < 10
The side opposite of angle x is 10, so the side opposite of angle x-15 must be less than 10
True

III. AB > 10
The side opposite of angle x is 10, so the side opposite of angle x-15 must be less than 10
False

C. I and II only
EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 14338
Location: United States (CA)
GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: In ΔABC above, which of the following must be true?  [#permalink]

Show Tags

Hi All,

In Roman Numeral questions, it helps to pay attention to how the answer choices are designed - there will almost always be some type of built-in 'logic shortcut' that will allow you to avoid some of the work involved. This question is built around a subtle rule regarding triangle side lengths and the angles that are across from them:

The BIGGER the angle, the BIGGER the side that's across from it (and similarly, the SMALLER the angle, the SMALLER the side that's across from it).

From the diagram, we know that we're dealing with an ISOSCELES triangle (angles A and C are the same), so we know that the sides that are across from those two angles are the SAME (they're both 10). The third angle (angle B) is SMALLER than the other two angles, so the side across from angle B is SMALLER than the other two sides (it's LESS than 10).

With this knowledge, we know that Roman Numeral 2 is TRUE and Roman Numeral 3 is NOT TRUE. There's only one answer that matches (and we don't even have to deal with Roman Numeral 1).

GMAT assassins aren't born, they're made,
Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Rich Cohen

Co-Founder & GMAT Assassin Follow
Special Offer: Save \$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/
Director  V
Joined: 27 May 2012
Posts: 800
Re: In ΔABC above, which of the following must be true?  [#permalink]

Show Tags

Bunuel wrote: In ΔABC above, which of the following must be true?

I. x > 50
II. AC < 10
III. AB > 10

A. I only
B. III only
C. I and II only
D. I and III only
E. I, II, and III

Attachment:
2015-12-27_2143.png

My silly question ,
we know the Triangle equality theorem which states that the third side will be greater than the difference of the other two sides and less than the sum of the other two sides. Based on this rule a triangle having two sides as 10 and 10 should allow a third side between 1 and 19. So third side being 15 or 16 etc is a possibility according to this rule.

So why in this question this rule is literally not followed? Or do we need to additionally check the angles to make sure , that both the triangle inequality rule and angle rule is maintained?
_________________
- Stne
Math Expert V
Joined: 02 Sep 2009
Posts: 55609
Re: In ΔABC above, which of the following must be true?  [#permalink]

Show Tags

1
stne wrote:
Bunuel wrote: In ΔABC above, which of the following must be true?

I. x > 50
II. AC < 10
III. AB > 10

A. I only
B. III only
C. I and II only
D. I and III only
E. I, II, and III

Attachment:
2015-12-27_2143.png

My silly question ,
we know the Triangle equality theorem which states that the third side will be greater than the difference of the other two sides and less than the sum of the other two sides. Based on this rule a triangle having two sides as 10 and 10 should allow a third side between 1 and 19. So third side being 15 or 16 etc is a possibility according to this rule.

So why in this question this rule is literally not followed? Or do we need to additionally check the angles to make sure , that both the triangle inequality rule and angle rule is maintained?

If we knew only that there is an isosceles triangle with two equal sides of 10, then the third side could be 0 < (third side) < 20. Notice that it's NOT 1 < (third side) < 19, as you've written.

But in the question at hand we know more. Usually every bit of additional information allows us to narrow the answer. So, here knowing that the third side is opposite the smallest angle in the triangle allows us to conclude that the third side must be the shortest among the three, thus (third side) < 10.
_________________
Director  V
Joined: 27 May 2012
Posts: 800
Re: In ΔABC above, which of the following must be true?  [#permalink]

Show Tags

Bunuel wrote:
stne wrote:
Bunuel wrote: In ΔABC above, which of the following must be true?

I. x > 50
II. AC < 10
III. AB > 10

A. I only
B. III only
C. I and II only
D. I and III only
E. I, II, and III

Attachment:
2015-12-27_2143.png

My silly question ,
we know the Triangle equality theorem which states that the third side will be greater than the difference of the other two sides and less than the sum of the other two sides. Based on this rule a triangle having two sides as 10 and 10 should allow a third side between 1 and 19. So third side being 15 or 16 etc is a possibility according to this rule.

So why in this question this rule is literally not followed? Or do we need to additionally check the angles to make sure , that both the triangle inequality rule and angle rule is maintained?

If we knew only that there is an isosceles triangle with two equal sides of 10, then the third side could be 0 < (third side) < 20. Notice that it's NOT 1 < (third side) < 19, as you've written.

But in the question at hand we know more. Usually every bit of additional information allows us to narrow the answer. So, here knowing that the third side is opposite the smallest angle in the triangle allows us to conclude that the third side must be the shortest among the three, thus (third side) < 10.

Thank you, initially convinced myself that perhaps this rule was not applicable for isosceles triangle , though couldn't find anything anywhere about such an exception.Your reply really helped to clear this up.
_________________
- Stne Re: In ΔABC above, which of the following must be true?   [#permalink] 27 Jan 2019, 04:01
Display posts from previous: Sort by

In ΔABC above, which of the following must be true?   