If the lengths of perpendicular sides of a park that is in the shape

Question

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

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

LeoN88 · Accepted Answer

Let area (1/2)a*b = 630; so a*b= Integer = 1260

Let's check if 6 can be the LCM of a,b ? To check if X,Y can be co-primes whose product is an integer! 
6x * 6y = 1260
xy = 35 = 7*5 possible.

For 10,

xy= 12.6 Not possible

For 21
xy= 20/7 Not Possible

QuantMadeEasy · Answer

Area of right angled triangle is 630, that means product of two perpendicular lengths is 630x2.
Prime factors of product of two lengths is 2^2 x 3^2 x 5 x 7.
From above factorisation 6 can be a factor of both the perpendicular lengths

A is correct.

Kritisood · Answer

BH = 2^2 * 3^2 * 5* 7

The power of 5 and 7 is just one in the product, this means only one of the dimensions (either B or H) would contain that power

Since the power of 2 and 3 is 2 in the product, it can be a part of B and H both individually and hence 6 would be able to divide B and H both.

ScottTargetTestPrep · Answer

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

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

If the lengths of perpendicular sides of a park that is in the shape

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

If the lengths of perpendicular sides of a park that is in the shape

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards