BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Triangles in a heptagon

Expert replies
by rahulvsd » Mon Mar 05, 2012 6:46 am
How many triangles can be inscribed in the heptagon pictured, where the three vertices of the triangle are also vertices of the heptagon?

Image

A.9 B. 21 C. 35 D. 140 E. 210.

[spoiler]Ans: C. Grockit solves this by using combinations method and I agree with this solution. If the question mentions non-overlapping triangle, will the answer be 5. By using formula (n-2) *180, so here it will be 5 * 180 so 5 triangles, is this approach correct? And if the question was rephrased as number of triangles (does not mention non - overlapping) in a hexagon by the combination method answer will be 6 factorial / 3 factorial * 3 factorial. So 20 triangles, is this correct too? please confirm... [/spoiler]
Join the discussion
Source: — Problem Solving |

by pemdas » Mon Mar 05, 2012 10:58 am
i selected this option --> one vertice needs two more vertices to form triangle and in total three vertices will be required out of seven, 7C3=35

c
Success doesn't come overnight!
Join the discussion

by Jim@StratusPrep » Mon Mar 05, 2012 11:14 am
35 is the answer: 7*6*5/3!
GMAT Answers provides a world class adaptive learning platform.
-- Push button course navigation to simplify planning
-- Daily assignments to fit your exam timeline
-- Organized review that is tailored based on your abiility
-- 1,000s of unique GMAT questions
-- 100s of handwritten 'digital flip books' for OG questions
-- 100% Free Trial and less than $20 per month after.
-- Free GMAT Quantitative Review

Image
Join the discussion

by Scott@TargetTestPrep » Thu Jan 17, 2019 5:47 pm
rahulvsd wrote:How many triangles can be inscribed in the heptagon pictured, where the three vertices of the triangle are also vertices of the heptagon?

Image

A.9 B. 21 C. 35 D. 140 E. 210.
Since there are 7 vertices on the heptagon and any of its 3 vertices will form a triangle, then the number of possible triangles is 7C3 = 7!/(3! x 4!) = (7 x 6 x 5)/3! = (7 x 6 x 5)/(3 x 2) = 35.

Answer: C

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Join the discussion