It is currently 17 Oct 2017, 23:20

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Is the area of the triangular region above less than 20?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
3 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41872

Kudos [?]: 128641 [3], given: 12181

Is the area of the triangular region above less than 20? [#permalink]

Show Tags

New post 26 Jun 2017, 02:15
3
This post received
KUDOS
Expert's post
7
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

65% (01:17) correct 35% (01:08) wrong based on 349 sessions

HideShow timer Statistics

Image
Is the area of the triangular region above less than 20?

(1) x^2 + y^2≠ z^2
(2) x + y < 13


[Reveal] Spoiler:
Attachment:
2017-06-26_1314.png
2017-06-26_1314.png [ 9.06 KiB | Viewed 2564 times ]
[Reveal] 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

Kudos [?]: 128641 [3], given: 12181

BSchool Forum Moderator
User avatar
P
Joined: 26 Feb 2016
Posts: 1449

Kudos [?]: 593 [0], given: 16

Location: India
Concentration: General Management, Leadership
WE: Sales (Retail)
Premium Member CAT Tests
Is the area of the triangular region above less than 20? [#permalink]

Show Tags

New post 26 Jun 2017, 02:27
Is the area of the triangular region above less than 20?

1) \(x^2 + y^2≠ z^2\)
\(x^2 + y^2\) , not being equal to \(z^2\)
could mean any of the following :
\(x^2 + y^2 < z^2\)
\(x^2 + y^2 > z^2\)
We cannot clearly ascertain what the values of x and y are.
Therefore, we cannot tell anything about the area of the triangular region. Insufficient.

2) x + y < 13
If x+y < 13 the sum could be as less as 3 and as big as 12.
x = 1,y=2 will give us an area lesser than 20
x = 5,y=7 will give us an area greater than 20. Insufficient

Combining the statements, we can't clearly tell anything about the area of the triangle.
Insufficient(Option E)
_________________

Stay hungry, Stay foolish

2017-2018 MBA Deadlines

Class of 2020: Rotman Thread | Schulich Thread
Class of 2019: Sauder Thread

Kudos [?]: 593 [0], given: 16

Expert Post
Top Contributor
SVP
SVP
User avatar
G
Joined: 12 Sep 2015
Posts: 1794

Kudos [?]: 2446 [0], given: 356

Location: Canada
Re: Is the area of the triangular region above less than 20? [#permalink]

Show Tags

New post 26 Jun 2017, 08:00
Expert's post
Top Contributor
3
This post was
BOOKMARKED
Bunuel wrote:
Image
Is the area of the triangular region above less than 20?

(1) x^2 + y^2≠ z^2
(2) x + y < 13


[Reveal] Spoiler:
Attachment:
2017-06-26_1314.png


Target question: Is the area of the triangular region above less than 20?

I'm going to head straight to....

Statements 1 and 2 combined
Consider the following two scenarios, each of which satisfies BOTH statements.

case a: The triangles is an equilateral triangles and each side has length 0.001. As you can imagine, we need not find the area of this triangle since it's clear that the area is LESS THAN 20

case b: Even though statement 1 tells us that x and y cannot be the legs of a right triangle, let's see what would happen if those sides WERE the legs of a right triangle. Also, let's say that x and y are both equal to 6.5. In this case, the base has length 6.5 and the height has length 6.5. So, the area = (base)/(height)/2 = (6.5)(6.5)/2 = 21.125
Granted this scenario breaks both of the given conditions (x and y ARE the legs of a right triangle AND x+y is NOT less than 13, HOWEVER, we need only recognize that if were were to reduce the angle between x and y from 90 degrees to 89.9999999 degrees, then the area of the triangle would be a teeeeny bit less than 21.125. This would mean that x and y are NOT the legs of a right triangle, so statement 1 is satisfied.
Likewise, if we were to reduce the length of x from 6.5 to 6.49999999, then the area of the triangle would be a teeeeny bit less than 21.125. This would mean that x+y < 13, so statement 2 is satisfied.
As we can see, we can make it so that case b satisfies both conditions, and have it so that the area of the triangle is GREATER THAN 20
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer:
[Reveal] Spoiler:
E


RELATED VIDEO

_________________

Brent Hanneson – Founder of gmatprepnow.com

Image

Kudos [?]: 2446 [0], given: 356

Manager
Manager
User avatar
B
Joined: 17 Feb 2016
Posts: 106

Kudos [?]: 21 [0], given: 59

Location: India
Concentration: General Management, Entrepreneurship
GMAT 1: 660 Q47 V36
GPA: 3.12
WE: Education (Internet and New Media)
Reviews Badge
Is the area of the triangular region above less than 20? [#permalink]

Show Tags

New post 26 Jun 2017, 10:22
Area of triangle= \(\frac{1}{2}*Base * height\)
(1) x^2 + y^2≠ z^2
This option states that the triangle is not right angled
No data on base and height
NS
(2) x + y < 13
Two variable one equation and an inequality
Clearly NS

St 1+2 states no info on base and height

Option E
_________________

Never stop fighting until you arrive at your destined place - that is, the unique you. Have an aim in life, continuously acquire knowledge, work hard, and have the perseverance to realise the great life. A. P. J. Abdul Kalam

Kudos [?]: 21 [0], given: 59

Expert Post
Top Contributor
1 KUDOS received
SVP
SVP
User avatar
G
Joined: 12 Sep 2015
Posts: 1794

Kudos [?]: 2446 [1], given: 356

Location: Canada
Re: Is the area of the triangular region above less than 20? [#permalink]

Show Tags

New post 26 Jun 2017, 12:01
1
This post received
KUDOS
Expert's post
Top Contributor
1
This post was
BOOKMARKED
RaguramanS wrote:
Area of triangle= \(\frac{1}{2}*Base * height\)
(1) x^2 + y^2≠ z^2
This option states that the triangle is not right angled
No data on base and height
NS
(2) x + y < 13
Two variable one equation and an inequality
Clearly NS

St 1+2 states no info on base and height

Option E


I thought I'd point out that your rationale to conclude that the combined statement are not sufficient (i.e., "1+2 states no info on base and height") is not quite correct.
If the target question had asked "Is the area less than 22?" (instead of asking "Is the area less than 20?", then statement 2 would be sufficient.

Cheers,
Brent
_________________

Brent Hanneson – Founder of gmatprepnow.com

Image

Kudos [?]: 2446 [1], given: 356

Manager
Manager
User avatar
B
Joined: 17 Feb 2016
Posts: 106

Kudos [?]: 21 [0], given: 59

Location: India
Concentration: General Management, Entrepreneurship
GMAT 1: 660 Q47 V36
GPA: 3.12
WE: Education (Internet and New Media)
Reviews Badge
Is the area of the triangular region above less than 20? [#permalink]

Show Tags

New post 26 Jun 2017, 14:34
GMATPrepNow wrote:

If the target question had asked "Is the area less than 22?" (instead of asking "Is the area less than 20?", then statement 2 would be sufficient.

Cheers,
Brent


@Brent, thankyou for your observation on my approach. But I need clarification on the proposed approach.

So if the question had been
\(Area<22\)

B.\(x+y<13\)

Approach 1:
There are two cases


Case 1: Right angle triangle
Case 2: Other triangles (Scalene, equilateral)

Case 1: Assume any values for x,y such that the sum is less than 13,
And the area can be found and it is less than 22.

Case 2: How can I find the area of other triangles.

Should I assume a Value for x and y and get the range of values for z by formula
\(x-y<z<x+y\)
and then I can find height and consider z as base

Approach 2:
Orelse it's safer to find the case for equilateral triangle area, as it has the greatest area of all the triangles
_________________

Never stop fighting until you arrive at your destined place - that is, the unique you. Have an aim in life, continuously acquire knowledge, work hard, and have the perseverance to realise the great life. A. P. J. Abdul Kalam

Kudos [?]: 21 [0], given: 59

Expert Post
Top Contributor
SVP
SVP
User avatar
G
Joined: 12 Sep 2015
Posts: 1794

Kudos [?]: 2446 [0], given: 356

Location: Canada
Re: Is the area of the triangular region above less than 20? [#permalink]

Show Tags

New post 26 Jun 2017, 20:26
Expert's post
Top Contributor
RaguramanS wrote:
@Brent, thankyou for your observation on my approach. But I need clarification on the proposed approach.

So if the question had been
\(Area<22\)

B.\(x+y<13\)

Approach 1:
There are two cases


Case 1: Right angle triangle
Case 2: Other triangles (Scalene, equilateral)

Case 1: Assume any values for x,y such that the sum is less than 13,
And the area can be found and it is less than 22.

Case 2: How can I find the area of other triangles.

Should I assume a Value for x and y and get the range of values for z by formula
\(x-y<z<x+y\)
and then I can find height and consider z as base

Approach 2:
Orelse it's safer to find the case for equilateral triangle area, as it has the greatest area of all the triangles


If the question were "Is the area < 22?" , we don't need to do as much work.

(2) x+y<13
Let's just consider a triangle where two of the sides have lengths 6.5 and 6.5
What's the greatest area possible?
Let's make the base have length 6.5
Since area = (base)(height)/2, we will MAXIMIZE the area if we can MAXIMIZE the height.
If the other side has length 6.5, we can maximize the height by making that side PERPENDICULAR to the base, in which case the area = (6.5)(6.5)/2 = 21.125
If x+y = 13, then the MAXIMUM area = 21.25
If x+y < 13, then the MAXIMUM area is less than 21.25
If the maximum area is less than 21.25, then the answer to the target question is "No! The area is definitely less than 22"
So, statement 2 is sufficient.

Cheers,
Brent
_________________

Brent Hanneson – Founder of gmatprepnow.com

Image

Kudos [?]: 2446 [0], given: 356

4 KUDOS received
Senior Manager
Senior Manager
avatar
S
Joined: 22 Aug 2013
Posts: 432

Kudos [?]: 130 [4], given: 260

Location: India
Re: Is the area of the triangular region above less than 20? [#permalink]

Show Tags

New post 03 Jul 2017, 00:48
4
This post received
KUDOS
1
This post was
BOOKMARKED
As in the attached picture. Even after combining, area could still be > 20 or < 20. Insufficient.

E answer
Attachments

IMG_20170703_131437-2.jpg
IMG_20170703_131437-2.jpg [ 55.87 KiB | Viewed 1930 times ]

Kudos [?]: 130 [4], given: 260

Director
Director
avatar
G
Joined: 02 Sep 2016
Posts: 778

Kudos [?]: 41 [0], given: 267

Premium Member CAT Tests
Re: Is the area of the triangular region above less than 20? [#permalink]

Show Tags

New post 07 Jul 2017, 06:59
1) This statement just tells us that it is not a right angled triangle i.e. x is not the height.

No way we could find the area.

BCE

2) x+y<13

This is fine but how do we know what is the height of this triangle?

Not sufficient

Both

Not a right angled triangle and we can't find the height.


E
_________________

Help me make my explanation better by providing a logical feedback.

If you liked the post, HIT KUDOS !!

Don't quit.............Do it.

Kudos [?]: 41 [0], given: 267

Director
Director
avatar
G
Joined: 02 Sep 2016
Posts: 778

Kudos [?]: 41 [0], given: 267

Premium Member CAT Tests
Re: Is the area of the triangular region above less than 20? [#permalink]

Show Tags

New post 07 Jul 2017, 07:03
GMATPrepNow wrote:
RaguramanS wrote:
Area of triangle= \(\frac{1}{2}*Base * height\)
(1) x^2 + y^2≠ z^2
This option states that the triangle is not right angled
No data on base and height
NS
(2) x + y < 13
Two variable one equation and an inequality
Clearly NS

St 1+2 states no info on base and height

Option E


I thought I'd point out that your rationale to conclude that the combined statement are not sufficient (i.e., "1+2 states no info on base and height") is not quite correct.
If the target question had asked "Is the area less than 22?" (instead of asking "Is the area less than 20?", then statement 2 would be sufficient.

Cheers,
Brent



Hello Brent

Just by looking at the figure how can we determine which one is the height?



Thanks

Kudos [?]: 41 [0], given: 267

Intern
Intern
User avatar
B
Joined: 16 Feb 2016
Posts: 25

Kudos [?]: 3 [0], given: 21

GMAT ToolKit User
Re: Is the area of the triangular region above less than 20? [#permalink]

Show Tags

New post 10 Jul 2017, 13:57
GMATPrepNow wrote:
RaguramanS wrote:
@Brent, thankyou for your observation on my approach. But I need clarification on the proposed approach.

So if the question had been
\(Area<22\)

B.\(x+y<13\)

Approach 1:
There are two cases


Case 1: Right angle triangle
Case 2: Other triangles (Scalene, equilateral)

Case 1: Assume any values for x,y such that the sum is less than 13,
And the area can be found and it is less than 22.

Case 2: How can I find the area of other triangles.

Should I assume a Value for x and y and get the range of values for z by formula
\(x-y<z<x+y\)
and then I can find height and consider z as base

Approach 2:
Orelse it's safer to find the case for equilateral triangle area, as it has the greatest area of all the triangles


If the question were "Is the area < 22?" , we don't need to do as much work.

(2) x+y<13
Let's just consider a triangle where two of the sides have lengths 6.5 and 6.5
What's the greatest area possible?
Let's make the base have length 6.5
Since area = (base)(height)/2, we will MAXIMIZE the area if we can MAXIMIZE the height.
If the other side has length 6.5, we can maximize the height by making that side PERPENDICULAR to the base, in which case the area = (6.5)(6.5)/2 = 21.125
If x+y = 13, then the MAXIMUM area = 21.25 (21.125)
If x+y < 13, then the MAXIMUM area is less than 21.25
If the maximum area is less than 21.25, then the answer to the target question is "No! The area is definitely less than 22"
So, statement 2 is sufficient.

Cheers,
Brent


Hey Brent,

I think the maximum area, if 2 perpendicular sides totalled 13, would be 21.125

Kudos [?]: 3 [0], given: 21

Manager
Manager
avatar
G
Joined: 28 Jul 2016
Posts: 125

Kudos [?]: 11 [0], given: 39

Premium Member CAT Tests
Re: Is the area of the triangular region above less than 20? [#permalink]

Show Tags

New post 02 Aug 2017, 05:31
pushpitkc wrote:
Is the area of the triangular region above less than 20?

1) \(x^2 + y^2≠ z^2\)
\(x^2 + y^2\) , not being equal to \(z^2\)
could mean any of the following :
\(x^2 + y^2 < z^2\)
\(x^2 + y^2 > z^2\)
We cannot clearly ascertain what the values of x and y are.
Therefore, we cannot tell anything about the area of the triangular region. Insufficient.

2) x + y < 13
If x+y < 13 the sum could be as less as 3 and as big as 12.
x = 1,y=2 will give us an area lesser than 20
x = 5,y=7 will give us an area greater than 20. Insufficient

Combining the statements, we can't clearly tell anything about the area of the triangle.
Insufficient(Option E)


This is not the best explanation:
"x = 5,y=7 will give us an area greater than 20. Insufficient"

For X=5;Y=7, Area will be less than 20 (to be precise - less than or equal to 17.5).

Only for X >= 5.72 and Y = 7, area will be equal to or more than 20

Area of triangular region is the greatest for right triangle:
Formula is: 1/2* X * Y = 1/2*5*7 = 17.5 (less than 20)
For all triangles other than right triangle, area will be even smaller for given X and Y.

Tested using following calculator for all possible angles (1-189):
https://www.google.com.ua/search?q=tria ... F-8&skip=s

Please correct me if I'm wrong.

Kudos [?]: 11 [0], given: 39

Intern
Intern
avatar
Joined: 29 Dec 2016
Posts: 3

Kudos [?]: [0], given: 7

Re: Is the area of the triangular region above less than 20? [#permalink]

Show Tags

New post 28 Sep 2017, 05:15
GMATPrepNow wrote:
RaguramanS wrote:
@Brent, thankyou for your observation on my approach. But I need clarification on the proposed approach.

So if the question had been
\(Area<22\)

B.\(x+y<13\)

Approach 1:
There are two cases


Case 1: Right angle triangle
Case 2: Other triangles (Scalene, equilateral)

Case 1: Assume any values for x,y such that the sum is less than 13,
And the area can be found and it is less than 22.

Case 2: How can I find the area of other triangles.

Should I assume a Value for x and y and get the range of values for z by formula
\(x-y<z<x+y\)
and then I can find height and consider z as base

Approach 2:
Orelse it's safer to find the case for equilateral triangle area, as it has the greatest area of all the triangles


If the question were "Is the area < 22?" , we don't need to do as much work.

(2) x+y<13
Let's just consider a triangle where two of the sides have lengths 6.5 and 6.5
What's the greatest area possible?
Let's make the base have length 6.5
Since area = (base)(height)/2, we will MAXIMIZE the area if we can MAXIMIZE the height.
If the other side has length 6.5, we can maximize the height by making that side PERPENDICULAR to the base, in which case the area = (6.5)(6.5)/2 = 21.125
If x+y = 13, then the MAXIMUM area = 21.25
If x+y < 13, then the MAXIMUM area is less than 21.25
If the maximum area is less than 21.25, then the answer to the target question is "No! The area is definitely less than 22"
So, statement 2 is sufficient.

Cheers,
Brent




Hi Brent,

I couldn't understand this part of your explanation "If the other side has length 6.5, we can maximize the height by making that side PERPENDICULAR to the base, in which case the area = (6.5)(6.5)/2 = 21.125". Is area of a triangle highest when the triangle is a right angle triangle? Also, i presume that when two sides are equal and the given triangle is a right triangle, then both 6.5 ought to be legs as third side will be hypotenuse and hence greater than two other sides. Hence, you took 6.5 as a height.

Kudos [?]: [0], given: 7

Expert Post
Top Contributor
SVP
SVP
User avatar
G
Joined: 12 Sep 2015
Posts: 1794

Kudos [?]: 2446 [0], given: 356

Location: Canada
Re: Is the area of the triangular region above less than 20? [#permalink]

Show Tags

New post 28 Sep 2017, 07:44
Expert's post
Top Contributor
adid1512 wrote:
GMATPrepNow wrote:
RaguramanS wrote:
@Brent, thankyou for your observation on my approach. But I need clarification on the proposed approach.

So if the question had been
\(Area<22\)

B.\(x+y<13\)

Approach 1:
There are two cases


Case 1: Right angle triangle
Case 2: Other triangles (Scalene, equilateral)

Case 1: Assume any values for x,y such that the sum is less than 13,
And the area can be found and it is less than 22.

Case 2: How can I find the area of other triangles.

Should I assume a Value for x and y and get the range of values for z by formula
\(x-y<z<x+y\)
and then I can find height and consider z as base

Approach 2:
Orelse it's safer to find the case for equilateral triangle area, as it has the greatest area of all the triangles


If the question were "Is the area < 22?" , we don't need to do as much work.

(2) x+y<13
Let's just consider a triangle where two of the sides have lengths 6.5 and 6.5
What's the greatest area possible?
Let's make the base have length 6.5
Since area = (base)(height)/2, we will MAXIMIZE the area if we can MAXIMIZE the height.
If the other side has length 6.5, we can maximize the height by making that side PERPENDICULAR to the base, in which case the area = (6.5)(6.5)/2 = 21.125
If x+y = 13, then the MAXIMUM area = 21.25
If x+y < 13, then the MAXIMUM area is less than 21.25
If the maximum area is less than 21.25, then the answer to the target question is "No! The area is definitely less than 22"
So, statement 2 is sufficient.

Cheers,
Brent




Hi Brent,

I couldn't understand this part of your explanation "If the other side has length 6.5, we can maximize the height by making that side PERPENDICULAR to the base, in which case the area = (6.5)(6.5)/2 = 21.125". Is area of a triangle highest when the triangle is a right angle triangle? Also, i presume that when two sides are equal and the given triangle is a right triangle, then both 6.5 ought to be legs as third side will be hypotenuse and hence greater than two other sides. Hence, you took 6.5 as a height.


If the lengths of two sides of a triangle are x and y, then we will maximize the area of that triangle if we make those sides PERPENDICULAR to each other.
Why is this?
Since any side of a triangle can be considered the base, let's let the side with length x be the base.
Area of triangle = (base)(height)/2 = (x)(height)/2
To maximize the area, we must now maximize the height. If we make the sides with length x and y PERPENDICULAR to each other, then the height of the triangle will EQUAL y
If the sides with length x and y are NOT perpendicular, then the height of the triangle will be LESS THAN y

Does that help?

Cheers,
Brent
_________________

Brent Hanneson – Founder of gmatprepnow.com

Image

Kudos [?]: 2446 [0], given: 356

Manager
Manager
avatar
B
Joined: 29 Jun 2017
Posts: 130

Kudos [?]: 8 [0], given: 314

Re: Is the area of the triangular region above less than 20? [#permalink]

Show Tags

New post 04 Oct 2017, 08:59
Bunuel wrote:
Image
Is the area of the triangular region above less than 20?

(1) x^2 + y^2≠ z^2
(2) x + y < 13


[Reveal] Spoiler:
Attachment:
2017-06-26_1314.png


when x and y are two sides of a square angle, the are is biggest.

if x side turn to right or to left, the area is smaller because the side y is the same and h of the triangle is smaller.

if x+y<13 this mean x, y < 6 and 7
6x7=42= tw time the area
so, combine two statement, xy<21
we can not know whether xy<20

E

Kudos [?]: 8 [0], given: 314

Re: Is the area of the triangular region above less than 20?   [#permalink] 04 Oct 2017, 08:59
Display posts from previous: Sort by

Is the area of the triangular region above less than 20?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.