by: krrishabh96
10 mins
|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
61% (01:31) correct
39%
(01:42)
wrong
based on 87
sessions
History
Date
Time
Result
Not Attempted Yet
Is the area of the rectangle more than the area of the square?
(1) The side of the square is half the sum of the length and the breadth of the rectangle.
(2) The length and breadth of the rectangle are 15 cm and 10 cm respectively.
(1) The side of the square is half the sum of the length and the breadth of the rectangle.
(2) The length and breadth of the rectangle are 15 cm and 10 cm respectively.
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
shashanksagar
Joined: 03 Apr 2016
Last visit: 14 Oct 2019
Posts: 62
Location: India
Concentration: Technology, General Management
GMAT 1: 720 Q50 V37
WE:Analyst (Computer Software)
Updated on: 02 Jul 2016, 04:39
Originally posted by shashanksagar on 02 Jul 2016, 04:01.
Last edited by shashanksagar on 02 Jul 2016, 04:39, edited 1 time in total.
Last edited by shashanksagar on 02 Jul 2016, 04:39, edited 1 time in total.
IMO A..
a = (l+b)/2
Squaring both sides..
a^2 = ( l^2 + b^2 )/2 + lb
So area of square = some positive number + area of rectangle
So area of square > area of rectangle
P.s. : there was a mistake in my solution. . The denominator would be 4 not 2.
Sent from my SM-N910H using Tapatalk
a = (l+b)/2
Squaring both sides..
a^2 = ( l^2 + b^2 )/2 + lb
So area of square = some positive number + area of rectangle
So area of square > area of rectangle
P.s. : there was a mistake in my solution. . The denominator would be 4 not 2.
Sent from my SM-N910H using Tapatalk
Is the area of the rectangle more than the area of the square?
Say the length of a side of the square is x and the lengths of the length and breadth of the rectangle are a and b. So, the question is whether ab > x^2.
(1) The side of the square is half the sum of the length and the breadth of the rectangle --> x = (a+b)/2. The question becomes whether ab > ((a+b)/2)^2 --> is 4ab > a^2 + 2ab + b^2 --> is 0 > (a - b)^2. Since the square of a number cannot be negative, then the answer to this question is NO. Sufficient.
(2) The length and breadth of the rectangle are 15 cm and 10 cm respectively. We don't know x. Not sufficient.
Answer: A.
Hope it's clear.
_________________
Say the length of a side of the square is x and the lengths of the length and breadth of the rectangle are a and b. So, the question is whether ab > x^2.
(1) The side of the square is half the sum of the length and the breadth of the rectangle --> x = (a+b)/2. The question becomes whether ab > ((a+b)/2)^2 --> is 4ab > a^2 + 2ab + b^2 --> is 0 > (a - b)^2. Since the square of a number cannot be negative, then the answer to this question is NO. Sufficient.
(2) The length and breadth of the rectangle are 15 cm and 10 cm respectively. We don't know x. Not sufficient.
Answer: A.
Hope it's clear.
_________________
New to the GMAT Club?
- • Questions: Question Bank | Bunuel's Signature Collection
• Tests: GMAT Club Tests | Forum Quiz
• Guides: Quantitative | Critical Reasoning | Reading Comprehension | Ultimate Quant Guide | All You Need for Quant
• Rules: Quantitative | Verbal
shashanksagar
Hi Shashank!
Thanks for the answer. But I have a question.
Why do you say - a^2 = ( l^2 + b^2 )/2 + lb?
Isn't this how it should be - a^2 = ( l^2 + b^2 )/4 + (lb/2)? If this is the case then we cannot say - "Area of square = Some positive number + Area of Rectangle". It would rather be - "Area of square = Some positive number + Area of Rectangle/2". Which is not sufficient.
Bunuel
Perfect Bunuel!!
Though I got a bit lost at - is 0 > (a - b)^2. I understand it now. You just took all the terms to RHS and made the LHS = 0. This is something worth taking note of!
Thank you.
shashanksagar
Joined: 03 Apr 2016
Last visit: 14 Oct 2019
Posts: 62
Location: India
Concentration: Technology, General Management
GMAT 1: 720 Q50 V37
WE:Analyst (Computer Software)
susheelh
Hi Susheelh,
You are absolutely correct. . Sorry I did the calculations in my head and missed the /4 .. thanks for correcting me. [emoji3]
Sent from my SM-N910H using Tapatalk
susheelh
(1) consider two cases
(a)Rectangle L=0.5; B=0.1
Then Side of sq.= 0.3
(b)Rectangle L=100; B=50
Then Side of sq.= 75
Both the cases area sq.> area rectangle.
suff...
(2) no info on side of square
Insuff..
Ans A
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.
_________________
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.
_________________
Solving this question helps.
Taking a timed set of similar questions in
GMAT Club Forum Quiz →
is even better.
Moderator:
Announcements
How to Tell If Your GMAT Prep Resources Are Actually Helping You
Subscribe to GMAT Club for New Podcast Episodes, Debriefs, & Insightful Sessions on GMAT Preparation
Subscribe to GMAT Club for New Podcast Episodes, Debriefs, & Insightful Sessions on GMAT Preparation
Tuck at Dartmouth
AI at Dartmouth Tuck: How the School Is Preparing Leaders for the Age of Artificial Intelligence
Inside the courses, research, and hands-on learning defining wise, decisive leadership in an AI-driven world.
Read More
Inside the courses, research, and hands-on learning defining wise, decisive leadership in an AI-driven world.
Read More
Top 5 GMAT Debrief Videos
Success stories and strategies from high-scoring candidates.