It is currently 28 May 2020, 03:46

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# In the figure, ABC and ADC are right triangles. Which of the

Author Message
TAGS:
Founder
Joined: 18 Apr 2015
Posts: 11158
Followers: 237

Kudos [?]: 2785 [0], given: 10592

In the figure, ABC and ADC are right triangles. Which of the [#permalink]  17 Mar 2019, 03:02
Expert's post
00:00

Question Stats:

52% (02:10) correct 47% (03:06) wrong based on 17 sessions
Attachment:

#GREpracticequestion In the figure, ABC and ADC are right triangle..jpg [ 16.2 KiB | Viewed 2857 times ]

In the figure, ABC and ADC are right triangles. Which of the following could be the lengths of AD and DC, respectively?

(I) $$\sqrt{3}$$ and $$\sqrt{4}$$
(II) 4 and 6
(III) 1 and $$\sqrt{24}$$
(IV) 1 and $$\sqrt{26}$$

(A) I and II only
(B) II and III only
(C) III and IV only
(D) IV and I only
(E) I, II and III only
[Reveal] Spoiler: OA

_________________

Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos
GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests.

Manager
Joined: 04 Feb 2019
Posts: 204
Followers: 4

Kudos [?]: 203 [0], given: 0

Re: In the figure, ABC and ADC are right triangles. Which of the [#permalink]  20 Mar 2019, 10:54
Expert's post
We can use the Pythagorean theorem to find the length of AC:

$$3^{2} + 4^{2} = (AC)^{2}$$

$$9 + 16 = (AC)^{2}$$

$$25 = (AC)^{2}$$

$$5 = AC$$

We should also recognize this as a 3-4-5 triangle, one of the Pythagorean triplets.

In any case, we know that ADC is a right triangle, but we don't know which angle is the right angle. So, any of these three possibilities could be correct, depending on which side is the hypotenuse:

$$AD^{2} + DC^{2} = AC^{2}$$

$$AD^{2} + AC^{2} = DC^{2}$$

$$AC^{2} + DC^{2} = AD^{2}$$

Plug in AC = 5, and we get these possible equations:

$$AD^{2} + DC^{2} = 25$$

$$AD^{2} + 25 = DC^{2}$$

$$25 + DC^{2} = AD^{2}$$

I want to isolate the known value, 25:

$$25 = AD^{2} + DC^{2}$$

$$25 = DC^{2} - AD^{2}$$

$$25 = AD^{2} - DC^{2}$$

Now we can just plug in the answer choices. Clearly the first statement won't work, as 3 and 4 are much too small to add up to 25. Already that eliminates choices A, D, and E.

The second statement is pretty easy to eliminate as well, since 4² and 6² = 16 and 36, respectively. But no combination of adding or subtract 16 and 36 will give us an answer of 25. So Statement II must be false, and the answer must be C.
Intern
Joined: 12 Nov 2018
Posts: 25
Followers: 0

Kudos [?]: 10 [0], given: 17

Re: In the figure, ABC and ADC are right triangles. Which of the [#permalink]  10 May 2019, 08:01
Can someone please explain C (especially IV option) is correct ? Thank you
Founder
Joined: 18 Apr 2015
Posts: 11158
Followers: 237

Kudos [?]: 2785 [0], given: 10592

Re: In the figure, ABC and ADC are right triangles. Which of the [#permalink]  10 May 2019, 10:33
Expert's post
In the case AC is the hypotenuse of the triangle, we have by The Pythagorean Theorem, $$AC^2 = AD^2 + DC^2$$

$$5^2 = AD^2 + DC^2$$

This equation is satisfied by III since $$5^2 = 1^2 + (\sqrt{24})^2$$ .

Therefore, III is possible.

Hope is more clear now to you Sir.

regards
_________________

Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos
GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests.

GRE Instructor
Joined: 10 Apr 2015
Posts: 3253
Followers: 124

Kudos [?]: 3642 [1] , given: 61

Re: In the figure, ABC and ADC are right triangles. Which of the [#permalink]  11 May 2019, 06:32
1
KUDOS
Expert's post
JelalHossain wrote:
Can someone please explain C (especially IV option) is correct ? Thank you

The trick here is to recognize that the right angle in triangle ACD could be in 3 different places.
∠CDA could be 90°
∠DCA could be 90°

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com

Re: In the figure, ABC and ADC are right triangles. Which of the   [#permalink] 11 May 2019, 06:32
Display posts from previous: Sort by