Is triangle ABC a right triangle? (1) The ratio of the largest to the : Data Sufficiency (DS)

My Profile Logout

Test's Subscription Expires:

My Follow Feed Kudos My Error Log

Messages and Replies

Settings Mark All Read

See All

Applicant Notifications

Settings Mark All Read

See All

Global notifications

Settings Mark All Read

See All

Is triangle ABC a right triangle? (1) The ratio of the largest to the

Sort by Date

Sort by Kudos

Author

Message

TAGS:

Hide Tags

Math Expert

Joined: 02 Sep 2009

Posts: 50708

Is triangle ABC a right triangle? (1) The ratio of the largest to the [#permalink]

Show Tags

09 Sep 2018, 07:50

00:00

Difficulty:

35% (medium)

Question Stats:

60% (00:40) correct

40% (00:43) wrong

based on 33 sessions

HideShow timer Statistics

Is triangle ABC a right triangle?

(1) The ratio of the largest to the smallest side of the triangle is 5 : 3.
(2) The ratio of the smallest side to the next larger side is 3 : 4.

Spoiler: OA

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.

What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Senior Manager

Joined: 17 Jan 2017

Posts: 300

Location: India

GPA: 4

WE: Information Technology (Computer Software)

Is triangle ABC a right triangle? (1) The ratio of the largest to the [#permalink]

Show Tags

Updated on: 09 Sep 2018, 18:51

Bunuel wrote:

Is triangle ABC a right triangle?

(1) The ratio of the largest to the smallest side of the triangle is 5 : 3.
(2) The ratio of the smallest side to the next larger side is 3 : 4.

We can use the property Sum of 2 sides of a triangle should be larger than the third side

Statement 1:
This tells us that the two sides are 5 (largest) and 3(Smallest). For the third side we can take values from 3 to 6, but as the statement mentions 5 is largest and 3 is smallest. Hence, we can take values from 3 to 5 such as 3.5 or 4.5. Hence, insuff to determine if its a Right triangle.

Statement 2:
This tells us that the two sides are 3(Smallest) and 4(Second largest). For the third side we can take values from 3 to any value. Hence, insuff to determine if its a Right triangle.

Combining both we get 3:4:5 which forms a right angled triangle.

+1 for C
_________________

Only those who risk going too far, can possibly find out how far one can go

Originally posted by Akash720 on 09 Sep 2018, 08:00.
Last edited by Akash720 on 09 Sep 2018, 18:51, edited 1 time in total.

Director

Status: Learning stage

Joined: 01 Oct 2017

Posts: 930

WE: Supply Chain Management (Energy and Utilities)

Re: Is triangle ABC a right triangle? (1) The ratio of the largest to the [#permalink]

Show Tags

09 Sep 2018, 18:47

Bunuel wrote:

Is triangle ABC a right triangle?

(1) The ratio of the largest to the smallest side of the triangle is 5 : 3.
(2) The ratio of the smallest side to the next larger side is 3 : 4.

Question stem:- Is ABC a right triangle?

St1:- The ratio of the largest to the smallest side of the triangle is 5 : 3.
Note:- Ratio relationship with the third side is not given.
Length of third side lies between 3x to 5x (both 3x and 5x are exclusive)

a)Say x=1,then measure of third side=4 , so it's a right angled triangle(3,4,5)
b)Say x=1,when measure of third side=Any value between 3 to 5 (not necessarily integers, say 3.5,4.1 etc), then it's not a right angled triangle Insufficient.

St2:- The ratio of the smallest side to the next larger side is 3 : 4
As per triangle inequality theorem, the measure of third side can be any number less than 7x(=3x+4x) and greater than x(=4x-3x).

say x=1, then the sides of the triangle would be 3,4, and 1<3rd side<7.
Insufficient.

Combined,
Sides of the triangle are in the ration 3k:4k:5k.

So, the triangle ABC is a right angled triangle.

Ans. (C)
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine