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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 9022
GMAT 1: 760 Q51 V42
GPA: 3.82
The figure shows that l is parallel to m and points A, B, C, D, E are  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 71% (01:43) correct 29% (01:51) wrong based on 51 sessions

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[GMAT math practice question]

The figure shows that $$l$$ is parallel to $$m$$ and points $$A, B, C, D, E$$ are on line $$l$$, and points $$F, G, H, I$$ are on the line $$m$$. How many quadrilaterals are possible with $$4$$ points out of the above $$8$$ points?

Attachment: 10.30ps.png [ 15.36 KiB | Viewed 706 times ]

$$A. 48$$

$$B. 56$$

$$C. 60$$

$$D. 72$$

$$E. 108$$

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Manager  S
Joined: 19 Jan 2019
Posts: 109
Re: The figure shows that l is parallel to m and points A, B, C, D, E are  [#permalink]

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A quadrilateral has 4 vertices and we have 9 points.. (5+4)
Select two from 5(line l) = 5c2 = 10
Select two from 4(line m) = 4c2 = 6
10*6 = 60

C

P.s = there are 9 points, not 8*...

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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 9022
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: The figure shows that l is parallel to m and points A, B, C, D, E are  [#permalink]

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=>

To create a quadrilateral, we should choose $$2$$ points out of $$5$$ points on line $$l,$$ and $$2$$ points out of $$4$$ points on the line m and connect them.

Then we have 5C2*4C2 = $$[\frac{(5*4)}{(1*2)}][\frac{(4*3)}{(1*2)}] = 10*6 = 60.$$

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CEO  V
Joined: 03 Jun 2019
Posts: 2935
Location: India
GMAT 1: 690 Q50 V34 WE: Engineering (Transportation)
Re: The figure shows that l is parallel to m and points A, B, C, D, E are  [#permalink]

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MathRevolution wrote:
[GMAT math practice question]

The figure shows that $$l$$ is parallel to $$m$$ and points $$A, B, C, D, E$$ are on line $$l$$, and points $$F, G, H, I$$ are on the line $$m$$. How many quadrilaterals are possible with $$4$$ points out of the above $$8$$ points?

Attachment:
10.30ps.png

$$A. 48$$

$$B. 56$$

$$C. 60$$

$$D. 72$$

$$E. 108$$

Quadrilaterals can be formed by choosing 2 points on line l and 2 points on line m

Number of ways = 5C2 * 4C2 = 10 * 6 = 60

IMO C
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Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com Re: The figure shows that l is parallel to m and points A, B, C, D, E are   [#permalink] 31 Mar 2020, 09:19

# The figure shows that l is parallel to m and points A, B, C, D, E are  