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

Redeem

If the lengths of perpendicular sides of a park that is in the shape of a right-angled triangle park are integers and

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 1622
Joined: Thu Mar 01, 2018 7:22 am
Followed by:2 members

If the lengths of perpendicular sides of a park that is in the shape of a right-angled triangle park are integers and

by Gmat_mission » Thu May 21, 2020 1:17 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

If the lengths of perpendicular sides of a park that is in the shape of a right-angled triangle park are integers and the area of the triangular park is 630 square units, which of the following can be the greatest number that divides the lengths of both the perpendicular sides?

I. 6
II. 10
III. 21


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

[spoiler]OA=A[/spoiler]

Source: e-GMAT
Top
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8086
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members

Re: If the lengths of perpendicular sides of a park that is in the shape of a right-angled triangle park are integers an

by Scott@TargetTestPrep » Sun May 31, 2020 9:52 am
Gmat_mission wrote: ↑
Thu May 21, 2020 1:17 am
 If the lengths of perpendicular sides of a park that is in the shape of a right-angled triangle park are integers and the area of the triangular park is 630 square units, which of the following can be the greatest number that divides the lengths of both the perpendicular sides?

I. 6
II. 10
III. 21


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

[spoiler]OA=A[/spoiler]

Solution:

If the two perpendicular sides of the right triangle are a and b, we have:

½ x a x b = 630

a x b = 1260

Now let’s prime factorize 1260:

1260 = 126 x 10 = 6 x 21 x 2 x 5 = 2 x 3 x 3 x 7 x 2 x 5 = 2^2 x 3^2 x 5 x 7.

We see that 6 can be the greatest number that divides the lengths of both sides if, for example, a = 2 x 3 x 5 and b = 2 x 3 x 7. This is possible because 1260 has two factors of 2 and two factors of 3. Therefore, we see that neither 10 nor 21 can be the greatest number that divides the lengths of both the perpendicular sides since there is only one factor of 5 and one factor of 7 in 1260.

Answer: A

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
Top
Post new topic Post Reply
• Page 1 of 1