Veritas Practice Test - IR #7

Question

Can someone please help with this IR problem I got from the Veritas Free Practice Test?

For triangle JKL, angle JKL measures 90 degrees, and side JL has a length of 260 centimeters. If side JK > side KL, which of the following could be a combination of the lengths of sides JK and KL?

50/100/120/200/240

How can I find two sides of the triangle if I only have one?

erahn1 · Answer

I think the key to this one, and to a lot of IR questions, is to look at the answers afforded to you. If JL is 260, and none of the answers are greater than 260, then JL is surely the hypotenuse.

At this point, and at every point when you are given a right triangle, you should be looking for the three common right triangles, and multiples of those angles,

3 - 4 - 5
5 - 12- 13
8 - 15 - 17

In the problem, 260 is a multiple of 13; 13*20 = 260. So just grab the 5-12-13 triangle, and just multiple each of the other sides by 20; in this case, 20*5 = 100 and 20*12 = 240.

This same approach wouldn't work if you weren't sure that 260 was the hypotenuse, but since it clearly is, I believe the triangle is necessarily a 5-12-13 triangle.

tpz · Answer

Thank you so much! Are the ratios that you mentioned just for the sides of the right triangles or for the angles as well?

RG800 · Answer

JL should be the hypotenuse here, since the triangle is right-angled at K (JKL is the right angle, not KLJ or LJK - the ordering matters I believe).

jainshally33 · Answer

are these the only possible combinations for right triangle?
3 - 4 - 5
5 - 12- 13
8 - 15 - 17

EMPOWERgmatRichC · Answer

Hi jainshally33,

MOST right triangles do not actually have 3 integer sides. That having been said, when a right triangle shows up on the GMAT, it's likely that the triangle is one of the commonly-tested "special" right triangles (30/60/90, 45/45/90, 3/4/5, 5/12/13). There are other right triangles with integers sides: 'multiples' of the 3/4/5 and 5/12/13 - for example, the 6/8/10 and 9/12/15 are 3/4/5s that have been "doubled" and 'tripled' respectively. There's also a relatively rare right triangle that has shown up on the Official GMAT: the 7/24/25.

GMAT assassins aren't born, they're made,
Rich

BhaveshGMAT · Answer

Official Answer:-

JK = 240 and KL = 100.

If you notice that these answer choices form a 5 : 12 : 13 ratio (100 : 240 : 260 -- divide by 20 and you get 5 : 12 : 13), then you can fit the shorter sides to the hypotenuse without having to use the Pythagorean Theorem with such large numbers.

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Veritas Practice Test - IR #7

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