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

 It is currently 25 Mar 2019, 19:22

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

In a recent street fair students were challenged to hit one of the sha

Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 53831
In a recent street fair students were challenged to hit one of the sha  [#permalink]

Show Tags

07 Sep 2016, 04:27
2
2
00:00

Difficulty:

15% (low)

Question Stats:

81% (01:45) correct 19% (01:47) wrong based on 132 sessions

HideShow timer Statistics

In a recent street fair students were challenged to hit one of the shaded triangular regions on the large equilateral triangular board below with a ping pong ball. Each of the triangular regions is an equilateral triangle whose side is a third of the length of the large triangle board. If the ping pong ball hits the large triangular region, what is the probability of hitting a shaded triangle?

A. 1/5
B. 1/4
C. 1/3
D. 1/2
E. 2/3

Attachment:

T7080.png [ 6.37 KiB | Viewed 1851 times ]

_________________
Board of Directors
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3621
Re: In a recent street fair students were challenged to hit one of the sha  [#permalink]

Show Tags

07 Sep 2016, 05:49
2
Bunuel wrote:

In a recent street fair students were challenged to hit one of the shaded triangular regions on the large equilateral triangular board below with a ping pong ball. Each of the triangular regions is an equilateral triangle whose side is a third of the length of the large triangle board. If the ping pong ball hits the large triangular region, what is the probability of hitting a shaded triangle?

A. 1/5
B. 1/4
C. 1/3
D. 1/2
E. 2/3

Attachment:
T7080.png

Since, the side of each smaller equilateral = 1/3 side of larger equilateral, we can say ratio of areas = 1/9 ( as the area of equilateral triangle is sqrt(3)/4 *a^2)

Ratio of areas of 3 such smaller to the overall = 3 *1/9 = 1/3.

Hence, C
_________________
My GMAT Story: From V21 to V40
My MBA Journey: My 10 years long MBA Dream
My Secret Hacks: Best way to use GMATClub | Importance of an Error Log!
Verbal Resources: All SC Resources at one place | All CR Resources at one place

GMAT Club Inbuilt Error Log Functionality - View More.
New Visa Forum - Ask all your Visa Related Questions - here.
New! Best Reply Functionality on GMAT Club!
Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for free
Check our new About Us Page here.
GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 911
Re: In a recent street fair students were challenged to hit one of the sha  [#permalink]

Show Tags

07 Nov 2018, 17:23
1
Bunuel wrote:

In a recent street fair students were challenged to hit one of the shaded triangular regions on the large equilateral triangular board below with a ping pong ball. Each of the triangular regions is an equilateral triangle whose side is a third of the length of the large triangle board. If the ping pong ball hits the large triangular region in a random point, what is the probability of hitting a shaded triangle?

A. 1/5
B. 1/4
C. 1/3
D. 1/2
E. 2/3

$$? = P\left( {{\text{hit}}\,\,{\text{shaded}}\,\,{\text{region}}} \right)$$

$$\frac{{{S_{{\text{each}}\,\Delta {\text{shaded}}}}}}{{{S_{\Delta {\text{large}}}}}} = {\left( {\frac{1}{3}} \right)^2} = \frac{1}{9}\,\,\,\,\,\,\,\left[ {\,{\text{each}}\,\,\Delta {\text{shaded}}\,\,{\text{is}}\,\,{\text{similar}}\,\,{\text{to}}\,\,{\text{the}}\,\,\Delta {\text{large}}\,} \right]$$

$$? = 3 \cdot \frac{1}{9} = \frac{1}{3}\,\,\,\,\,\,\left( {{\text{geometric}}\,\,{\text{probability}}} \right)$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 5435
Location: United States (CA)
Re: In a recent street fair students were challenged to hit one of the sha  [#permalink]

Show Tags

09 Nov 2018, 13:25
1
Bunuel wrote:

In a recent street fair students were challenged to hit one of the shaded triangular regions on the large equilateral triangular board below with a ping pong ball. Each of the triangular regions is an equilateral triangle whose side is a third of the length of the large triangle board. If the ping pong ball hits the large triangular region, what is the probability of hitting a shaded triangle?

A. 1/5
B. 1/4
C. 1/3
D. 1/2
E. 2/3

Attachment:
T7080.png

We see that each of the smaller shaded equilateral triangle has the same area. Furthermore, the unshaded region is a regular hexagon that can divide into 6 equilateral triangles each equalling to the area of a shaded triangle. Thus there are 3 + 6 = 9 equilateral triangles of the same area and the probability hitting a shaded triangle is 3/9 = 1/3.

Alternate Solution:

Let’s assume that each side of the large triangle is 6 units. The area of the large triangle is thus (1/2)(6)(6√3) = 18√3.

A side of any of the shaded triangles is 2. The area of one shaded triangle is (1/2)(2)(2√3) = 2√3. There are 3 shaded triangles, so their total area is 6√3.

The probability of hitting any shaded triangle is the total area of the shaded triangles divided by the total area of the entire large triangle: 6√3 / 18√3 = 1/3.

_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
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

Intern
Joined: 18 Oct 2017
Posts: 5
Re: In a recent street fair students were challenged to hit one of the sha  [#permalink]

Show Tags

08 Mar 2019, 02:58
No need of huge calculations. Since there exists only three shaded region and at a time ping pong ball can hit only one shaded region . So the probability is 1/3 ie 3 been the total of conditions elaborating as 3 shaded region. One shaded region to be hit so 1. Conclusion : 1/3
Re: In a recent street fair students were challenged to hit one of the sha   [#permalink] 08 Mar 2019, 02:58
Display posts from previous: Sort by