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

It is currently 20 Nov 2019, 20:47

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

In the figure above, what is the length of AB?

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59182
In the figure above, what is the length of AB?  [#permalink]

Show Tags

New post 23 Oct 2019, 22:15
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

67% (00:48) correct 33% (00:47) wrong based on 60 sessions

HideShow timer Statistics

SVP
SVP
User avatar
P
Joined: 03 Jun 2019
Posts: 1853
Location: India
Premium Member Reviews Badge CAT Tests
Re: In the figure above, what is the length of AB?  [#permalink]

Show Tags

New post 23 Oct 2019, 22:53
Bunuel wrote:
Image
In the figure above, what is the length of AB?

(A) 5
(B) 7
(C) 2√7
(D) 4√2
(E) 10

Attachment:
2017-08-08_2111_001.png


\(AB = 2\sqrt{4^2 - 3^2} = 2\sqrt{7}\)

IMO C
_________________
"Success is not final; failure is not fatal: It is the courage to continue that counts."

Please provide kudos if you like my post. Kudos encourage active discussions.

My GMAT Resources: -

Efficient Learning
All you need to know about GMAT quant

Tele: +91-11-40396815
Mobile : +91-9910661622
E-mail : kinshook.chaturvedi@gmail.com
e-GMAT Representative
User avatar
V
Joined: 04 Jan 2015
Posts: 3142
Re: In the figure above, what is the length of AB?  [#permalink]

Show Tags

New post 31 Oct 2019, 04:55

Solution


Given:
A triangle ABC,
    AC = BC = 4 units
    And the length of perpendicular dropped from C on AB = 3 units

To find:
    The length of AB

Approach and Working Out:
    Let us assume that that the foot of the perpendicular as D

In triangle ACD,
    \(AC^2 = AD^2 + CD^2\)
    \(4^2 = AD^2 + 3^2\)
    Implies, \(AD^2 = 16 – 9 = 7\)
    Thus AD = √7

Similarly, we can find DB = √7

Therefore, AB = AD + DB = 2√7

Hence, the correct answer is Option C.

Answer: C
_________________
Intern
Intern
avatar
B
Joined: 27 Oct 2019
Posts: 3
Re: In the figure above, what is the length of AB?  [#permalink]

Show Tags

New post 13 Nov 2019, 05:40
Why are those not two 3-4-5 triangles?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59182
Re: In the figure above, what is the length of AB?  [#permalink]

Show Tags

New post 13 Nov 2019, 05:47
1
Intern
Intern
avatar
B
Joined: 22 Oct 2018
Posts: 7
GMAT ToolKit User
Re: In the figure above, what is the length of AB?  [#permalink]

Show Tags

New post 18 Nov 2019, 19:35
Hello Bunuel,

Why can't the answer be 4 sqrt(2) here? The way i reached the solution was consider the entire triangle as an isosceles triangle and AB as the hypotenuse and angle ACB = 90 deg.

Thank you :)
Intern
Intern
avatar
B
Joined: 22 Oct 2018
Posts: 7
GMAT ToolKit User
Re: In the figure above, what is the length of AB?  [#permalink]

Show Tags

New post 18 Nov 2019, 19:51
SiddharthR wrote:
Hello Bunuel,

Why can't the answer be 4 sqrt(2) here? The way i reached the solution was consider the entire triangle as an isosceles triangle and AB as the hypotenuse and angle ACB = 90 deg.

Thank you :)



Sorry my bad. Just realized that just because the sides are equal it doesn't mean the angles would be 45 - 45. Pretty big blunder on my part.
CrackVerbal Quant Expert
User avatar
G
Joined: 12 Apr 2019
Posts: 280
Re: In the figure above, what is the length of AB?  [#permalink]

Show Tags

New post 18 Nov 2019, 22:47
This is a fairly easy question on the properties of isosceles and right angled triangles.

Triangle ABC is an isosceles triangle with AC = CB. Therefore, AB is the unequal side and angle ACB is the unequal angle. Let D be the point where the perpendicular from C meets AB. Then, triangles ACD and triangles BCD are right angled triangles with the right angle at D.

In an isosceles triangle, the perpendicular drawn from the vertex containing the unequal angle bisects the unequal side. Additionally, it also bisects the unequal angle. In short, this line acts as the perpendicular bisector of the unequal side and as the angle bisector of the unequal angle.

Therefore, in the isosceles triangle ABC, AD = DB. In right angled triangle ACD, the hypotenuse AC = 4 and the perpendicular CD = 3. Using Pythagoras theorem, \({AC}^2 = {AD}^2 + {CD}^2\). Substituting the values of AC and CD in the equation above, we can calculate AD to be √7.

Since triangle BCD is exactly the same as triangle ACD (which is to say that triangle ACD is congruent with congruent BCD), it’s not hard to figure out that DB will also be √7.
AB = AD + DB. Therefore, AD = √7+ √7 = 2√7.
The correct answer option is C.

The fact that AD and DB are equal also ties in with angle bisector theorem. The angle bisector theorem states “The angle bisector of an interior angle of a triangle divides the opposite side in the ratio of the arms of the angle bisected by it”.

In this question, CD is the angle bisector of inteior angle ACB (as per the property of an isosceles triangle). The arms of this angle ACB are AC and CB which are equal and hence in the ratio of 1:1. You can now observe that the angle bisector is bisecting the opposite side AB in the ratio of 1:1 i.e. AD = DB, which is what we proved.

Hope that helps!
_________________
Target Test Prep Representative
User avatar
V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8453
Location: United States (CA)
Re: In the figure above, what is the length of AB?  [#permalink]

Show Tags

New post 20 Nov 2019, 19:22
Bunuel wrote:
Image
In the figure above, what is the length of AB?

(A) 5
(B) 7
(C) 2√7
(D) 4√2
(E) 10

Attachment:
2017-08-08_2111_001.png


Both triangles have the same angles, height, and hypotenuse, so they must also have the same base. We can solve for one base and multiply it by 2. So, we have:

3^2 + b^2 = 4^2

b^2 = 7

b = √7

Thus, AB = 2√7.

Answer: C
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

GMAT Club Bot
Re: In the figure above, what is the length of AB?   [#permalink] 20 Nov 2019, 19:22
Display posts from previous: Sort by

In the figure above, what is the length of AB?

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





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne