GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 20 Nov 2019, 07:23

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

What is the area of triangle ABC above, with side lengths x,y, and z?

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59180
What is the area of triangle ABC above, with side lengths x,y, and z?  [#permalink]

Show Tags

New post 02 Jul 2019, 08:00
3
3
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

80% (01:16) correct 20% (01:22) wrong based on 345 sessions

HideShow timer Statistics

Most Helpful Community Reply
Director
Director
User avatar
V
Status: Manager
Joined: 27 Oct 2018
Posts: 726
Location: Egypt
Concentration: Strategy, International Business
GPA: 3.67
WE: Pharmaceuticals (Health Care)
GMAT ToolKit User
Re: What is the area of triangle ABC above, with side lengths x,y, and z?  [#permalink]

Show Tags

New post 02 Jul 2019, 08:20
2
the question is asking about the value of \(\frac{x*y}{2}\)

from statement (1), 4xy = 80, xy = 20, \(\frac{x*y}{2}\) = 10 --> sufficient

from statement (2), x is taller than y by 1 unit, but no constrains about the values of each --> insufficient
A
_________________
Thanks for Kudos
General Discussion
Manager
Manager
avatar
B
Joined: 31 Dec 2018
Posts: 114
Location: India
GMAT ToolKit User Premium Member
Re: What is the area of triangle ABC above, with side lengths x,y, and z?  [#permalink]

Show Tags

New post 02 Jul 2019, 08:09
2
1) (x+y)²−(x−y)²=80
gives,
x²+y²+2xy-x²-y²+2xy=80
4xy=80
xy=20

Possible values of x,y can be 4,5 or 5,4

Voila!!
A is sufficient.

2. (x-y)=1
could be any value.
Naah... Insufficient.

So,
IMO A.

Posted from my mobile device
Intern
Intern
avatar
B
Joined: 15 Feb 2019
Posts: 3
What is the area of triangle ABC above, with side lengths x,y, and z?  [#permalink]

Show Tags

New post 02 Jul 2019, 08:13
1
(X+y)^2 -(x-y)^2 equals 4xy
4XY =80
XY=20
1/2 XY =10...Answer A

Statement B is good for nothing
So,the answer is A
Hit Like and give a kudos if u like the solution

Posted from my mobile device
Manager
Manager
User avatar
G
Joined: 11 Feb 2013
Posts: 216
Location: United States (TX)
GMAT 1: 490 Q44 V15
GMAT 2: 690 Q47 V38
GPA: 3.05
WE: Analyst (Commercial Banking)
GMAT ToolKit User Premium Member Reviews Badge
What is the area of triangle ABC above, with side lengths x,y, and z?  [#permalink]

Show Tags

New post Updated on: 02 Jul 2019, 08:53
1
Question: (1/2) xy=?
Here, (1/2) is fixed numerical term.
So, if we find the value of xy, we can can easily find the value of (1/2) xy i.e. AREA of the triangle.
SO, WE SIMPLY NEED the value of xy.
Thus, question becomes xy=?

Statement 1:
(x+y)^2- (x-y)^2=80
=> x^2+2xy+y^2-x^2+2xy-y^2=80
=> 4xy=80
=> xy=20
SUFFICIENT

Statement 2: x-y= 1
Case 1: if x=2 & y=1, then xy=2,
Case 2: if x=5 & y=4, then xy=20,

Not SUFFICIENT.
Answer:A

Originally posted by BelalHossain046 on 02 Jul 2019, 08:18.
Last edited by BelalHossain046 on 02 Jul 2019, 08:53, edited 1 time in total.
VP
VP
User avatar
D
Joined: 19 Oct 2018
Posts: 1080
Location: India
Premium Member CAT Tests
Re: What is the area of triangle ABC above, with side lengths x,y, and z?  [#permalink]

Show Tags

New post 02 Jul 2019, 08:18
1
Area of triangle = 1/2*x*y

Statement 1=(x+y)^2−(x−y)^2= (x^2+y^2+2xy)- (x^2+y^2-2xy)=4xy=80

4xy=80
1/2*x*y=10
Sufficient

Statment 2 x-y=1
We can't find x*y with the given information
Insufficient

A
Intern
Intern
avatar
B
Joined: 10 Jan 2018
Posts: 15
Re: What is the area of triangle ABC above, with side lengths x,y, and z?  [#permalink]

Show Tags

New post 02 Jul 2019, 08:21
1
Area is dependent on XY , clearly we get XY from 1 using a2-b2 equals (a+b)(a-b), so we get ans from A , while 2 will give a equation with infinite possible ans

Posted from my mobile device
Senior Manager
Senior Manager
avatar
P
Joined: 09 Jun 2014
Posts: 351
Location: India
Concentration: General Management, Operations
Reviews Badge
Re: What is the area of triangle ABC above, with side lengths x,y, and z?  [#permalink]

Show Tags

New post 02 Jul 2019, 08:22
1
I guess A is the answer for above problem.

Area= 1/2 *x*y

So we need xy.

Now simplifying equation 1
we know a^2 - b^2 = (a+b)(a-b)

So (x+y)^2−(x−y)^2=80

(x+y+ x−y)(x+y-x+y) = 80

2x*2y= 80
xy = 20

So statement 1 is sufficient to find the area.

STAT2:
(x−y)=1

we dont' know what is xy.No other information is provided.

Clearly ,STAT2 is insufficient.

So A is answer.
Manager
Manager
avatar
G
Joined: 08 Jan 2018
Posts: 145
Location: India
Concentration: Operations, General Management
WE: Project Management (Manufacturing)
Re: What is the area of triangle ABC above, with side lengths x,y, and z?  [#permalink]

Show Tags

New post 02 Jul 2019, 08:22
1
St 1- (x+y)^2- (x-y)^2=80
=> (x+y+x-y)(x+y-x+y)=80
=> 2x*2y=80
=.xy=20
Area= 1/2xy------ ------sufficient

St2- (x−y)=1
x=y+1
x can take any value depending o value of y.-----------not sufficient

Ans.A
Senior Manager
Senior Manager
User avatar
P
Joined: 31 May 2018
Posts: 451
Location: United States
Concentration: Finance, Marketing
Re: What is the area of triangle ABC above, with side lengths x,y, and z?  [#permalink]

Show Tags

New post 02 Jul 2019, 08:24
1
since triangle, ABC is a right-angled triangle right angle at B

area of triangle ABC = \(\frac{1}{2}\)xy

so we need to find the value of xy

statement (1) \((x+y)^2 - (x-y)^2\) = 80
\(x^2+y^2\)+2xy - \(x^2-y^2\)+2xy = 80
4xy =80
xy = \(\frac{80}{4}\)
so from here we can find the area of the triangle so SUFFICIENT

statement (2) (x−y) = 1
from this statement, we cannot get the definite values of x and y
hence we cannot get the difinite value of xy so this statement is INSUFFICIENT

correct answer is A
Intern
Intern
avatar
B
Joined: 29 May 2019
Posts: 32
GMAT ToolKit User CAT Tests
Re: What is the area of triangle ABC above, with side lengths x,y, and z?  [#permalink]

Show Tags

New post 02 Jul 2019, 08:24
1
A is sufficient to answer considering the expansion we get xy = 20 and area is 1/2*xy and triplets in B option not sufficient to answer the question

Posted from my mobile device
Manager
Manager
User avatar
S
Joined: 27 Mar 2018
Posts: 79
Location: India
GMAT ToolKit User
Re: What is the area of triangle ABC above, with side lengths x,y, and z?  [#permalink]

Show Tags

New post 02 Jul 2019, 08:24
1
Area of triangle ABC = \(\frac{xy}{2}\)

1) Considering (x+y) = a and (x-y)=b, we have
a^2-b^2=80 => (a-b) (a+b)=80
=> xy = 20
Area of ABC = 10. Sufficient

2) Given, (x-y)=1
For x=5 and y=4, area of ABC=10
For x=6 and y=5, area of ABC=15

Not sufficient.

Hence, answer A. IMO
_________________
Thank you for the kudos. You are awesome! :)
Director
Director
avatar
G
Joined: 22 Nov 2018
Posts: 562
Location: India
GMAT 1: 640 Q45 V35
GMAT 2: 660 Q48 V33
GMAT ToolKit User Premium Member
Re: What is the area of triangle ABC above, with side lengths x,y, and z?  [#permalink]

Show Tags

New post 02 Jul 2019, 08:26
1
i) Sufficient as when the equation is expanded gives 4xy=80; xy=20 and area of triangle is 1/2*leg1*leg2=1/2xy=10
ii)Insufficient as neither xy or individual values of x and y can be found from x-y=1

IMO A
_________________
Give +1 kudos if this answer helps..!!
Manager
Manager
avatar
S
Joined: 24 Jan 2019
Posts: 107
Location: India
Concentration: Strategy, Finance
GMAT 1: 730 Q51 V38
GPA: 4
Re: What is the area of triangle ABC above, with side lengths x,y, and z?  [#permalink]

Show Tags

New post 02 Jul 2019, 08:27
1
We have to find the area of the given triangle. So, indirectly we have to see whether we can find the value of XY from the given information.

(1) Solving the given equation will give us the value of XY. So one can easily find an area of the given triangle.

So, 1 can independently answer the question.

(2) Values of X, Y & Z can be fractions or integers. (We don't have enough information about them in the question)

Therefore (X, Y, Z) pair can be anything like (3, 4, 5) / (4, 5, 6.4) and so on.

So, 2 can not answer the question independently.


Final answer : A
Manager
Manager
avatar
P
Joined: 27 Feb 2017
Posts: 123
Location: United States (WA)
GMAT 1: 760 Q50 V42
GRE 1: Q169 V168
Re: What is the area of triangle ABC above, with side lengths x,y, and z?  [#permalink]

Show Tags

New post 02 Jul 2019, 08:27
1
My answer is (A). This is a relatively simple question.

In order to know the area of the right triangle, we just need to know the product of x and y.

From (a), we can tell 4xy = 80. That is sufficient.
From (b), x = y + 1. There are indefinite number of possibilities. Not sufficient.

So, we should choose (A).
Manager
Manager
avatar
G
Joined: 27 May 2010
Posts: 199
CAT Tests
What is the area of triangle ABC above, with side lengths x,y, and z?  [#permalink]

Show Tags

New post Updated on: 02 Jul 2019, 22:23
1
Think answer is A.

Area = xy/2, so if we can find xy, we can determine the area.

Statement 1:
(X+y)^2 - (x-y)^2 = 80
x^2 + y^2 +2xy -x^2 - y^2 +2xy = 80
4xy = 80 => xy = 20
Therefore we can get value of xy and hence area.

So statement 1 is sufficient.

Statement 2: x-y=1.
We cannot determine xy using this.
So statement 2 is not sufficient.

So answer would be A.

Posted from my mobile device
_________________
Please give Kudos if you like the post

Originally posted by prashanths on 02 Jul 2019, 08:28.
Last edited by prashanths on 02 Jul 2019, 22:23, edited 2 times in total.
Manager
Manager
User avatar
S
Joined: 18 Sep 2018
Posts: 100
CAT Tests
Re: What is the area of triangle ABC above, with side lengths x,y, and z?  [#permalink]

Show Tags

New post 02 Jul 2019, 08:28
1
IMO A

By the image and sign of the angle, we can find it's a right triangle.
So the area is 1/2*base*height = 1/2*y*x

St1: (x+y)^2−(x−y)^2=80 => 4xy = 80 [by simplifying (a+b)^2 and (a-b)^2 formula)
xy = 20, 1/2*x*y = 10
Sufficient

St2: (x−y)=1 => x=1+y => Area = 1/2*y*(1+y) => Not sufficient
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 18 Aug 2017
Posts: 5304
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member CAT Tests
What is the area of triangle ABC above, with side lengths x,y, and z?  [#permalink]

Show Tags

New post Updated on: 03 Jul 2019, 08:06
#1
(X+y)^2 - (x-y)^2 = 80
x^2 + y^2 +2xy -x^2 - y^2 +2xy = 80
4xy = 80 => xy = 20
sufficient
#2
(x-y)=1
again x & y can be any integer value
insufficient

IMO A
What is the area of triangle ABC above, with side lengths x, y, and z?


(1) (x+y)2−(x−y)2=80(x+y)2−(x−y)2=80

(2) (x−y)=1

Originally posted by Archit3110 on 02 Jul 2019, 08:30.
Last edited by Archit3110 on 03 Jul 2019, 08:06, edited 1 time in total.
Senior Manager
Senior Manager
User avatar
P
Joined: 12 Dec 2015
Posts: 439
Re: What is the area of triangle ABC above, with side lengths x,y, and z?  [#permalink]

Show Tags

New post 02 Jul 2019, 08:30
1
What is the area of triangle ABC above, with side lengths x, y, and z?
means (1/2)xy =?


(1) (x+y)^2−(x−y)^2=80 ==> correct : 4xy = 80 => (1/2)xy =10

(2) (x−y)=1 ==> can't say (1/2)xy =?
so the answer is A
VP
VP
avatar
D
Joined: 20 Jul 2017
Posts: 1088
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: What is the area of triangle ABC above, with side lengths x,y, and z?  [#permalink]

Show Tags

New post 02 Jul 2019, 08:32
Area of triangle = 1/2*base*height = 1/2*y*x

(1) (x+y)^2−(x−y)^2=80
--> x^2 + y^2 + 2xy - (x^2 + y^2 - 2xy) = 80
--> x^2 + y^2 + 2xy - x^2 - y^2 + 2xy = 80
--> 4xy = 80
--> xy = 20

Area = 1/2*xy = 1/2*20 = 10

Sufficient

(2) (x−y)=1
--> x = y + 1

Area = 1/2*(y + 1)*y
--> Many values are possible

Insufficient

IMO Option A

Pls Hit Kudos if you like the solution
GMAT Club Bot
Re: What is the area of triangle ABC above, with side lengths x,y, and z?   [#permalink] 02 Jul 2019, 08:32

Go to page    1   2   3   4   5    Next  [ 93 posts ] 

Display posts from previous: Sort by

What is the area of triangle ABC above, with side lengths x,y, and z?

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





cron

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