Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 21 Apr 2010
Posts: 3

The area bounded by the curves x + y = 1 andx  y = 1 is
[#permalink]
Show Tags
21 Apr 2010, 21:09
Question Stats:
59% (01:27) correct 41% (01:14) wrong based on 1117 sessions
HideShow timer Statistics
The area bounded by the curves x + y = 1 and x  y = 1 is A. 3 B. 4 C. 2 D. 1 E. None
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 47983

Re: area bounded by the curves
[#permalink]
Show Tags
25 Feb 2012, 01:24
fortsill wrote: fivezero7 wrote: anni wrote: thank you for the reply, is it required to plot these lines and then calculate? can we get directly i mean is there any formula to solve this problem? thanks hi anni, there is no need to plot it, once you have mastered the art of visualization. the way i did it is as under. take x+y=1 it intersects the axes at (1,0) and (0,1) and makes a right angled triangle with the axes with each side (other than the hypotenuse) as 1 hence the area of this triangle is 0.5*1*1 = 0.5 sq. units. all other lines are symmetrical and form 3 more congruent triangles with the axes at different points. so the total area will be 0.5+0.5+0.5+0.5 = 2 sq units. hope i am clear Very clear, and amazed to see how much was packed under that question. But, am curious if there's any other way to solve the problem? The area bounded by the curves x + y = 1, x  y = 1 is A. 3 B. 4 C. 2 D. 1 E. None x+y=1 represents two lines: x+y=1 and x+y=1 > y=1x and y=1x. Find the x and y intercept of these lines to plot; xy=1 represents two lines: xy=1 and xy=1 > y=x1 and y=x+1. Find the x and y intercept of these lines to plot; Notice that these lines are mirror images of each other. Here is a square you get when you plot them: Attachment:
Area.gif [ 4.93 KiB  Viewed 38382 times ]
Notice that the diagonal of this square is equal to 2 (the difference between x intercepts). Area of a square is diagonal^2/2=2^2/2=2. Answer: C. Check similar questions to practice: m065absolutevalue108191.htmlgraphsmodulushelp86549.htmlm06q572817.htmlifequationenclosesacertainregion110053.htmlareaofregion126117.htmlHope it helps.
_________________
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? Extrahard Quant Tests with Brilliant Analytics




Intern
Joined: 08 Apr 2010
Posts: 27

Re: area bounded by the curves
[#permalink]
Show Tags
21 Apr 2010, 22:05
anni wrote: The area bounded by the curves \(x + y = 1,\) \(x  y = 1\) is
A.3 B.4 C.2 D.1 E. None
please, help how to solve ? hi, these equations represent four different equations x+y=1 x+y=1 xy=1 xy=1 once you plot these on the graph, you will easily find the area under these equations. just for the record, the answer shall be 2.
_________________
CHEERS fivezero7




Intern
Joined: 21 Apr 2010
Posts: 3

Re: area bounded by the curves
[#permalink]
Show Tags
21 Apr 2010, 22:12
fivezero7 wrote: anni wrote: The area bounded by the curves \(x + y = 1,\) \(x  y = 1\) is
A.3 B.4 C.2 D.1 E. None
please, help how to solve ? hi, these equations represent four different equations x+y=1 x+y=1 xy=1 xy=1 once you plot these on the graph, you will easily find the area under these equations. just for the record, the answer shall be 2. thank you for the reply, is it required to plot these lines and then calculate? can we get directly i mean is there any formula to solve this problem? thanks



Intern
Joined: 08 Apr 2010
Posts: 27

Re: area bounded by the curves
[#permalink]
Show Tags
21 Apr 2010, 22:20
anni wrote: thank you for the reply, is it required to plot these lines and then calculate? can we get directly i mean is there any formula to solve this problem? thanks hi anni, there is no need to plot it, once you have mastered the art of visualization. the way i did it is as under. take x+y=1 it intersects the axes at (1,0) and (0,1) and makes a right angled triangle with the axes with each side (other than the hypotenuse) as 1 hence the area of this triangle is 0.5*1*1 = 0.5 sq. units. all other lines are symmetrical and form 3 more congruent triangles with the axes at different points. so the total area will be 0.5+0.5+0.5+0.5 = 2 sq units. hope i am clear
_________________
CHEERS fivezero7



Intern
Joined: 24 Feb 2012
Posts: 31

Re: area bounded by the curves
[#permalink]
Show Tags
25 Feb 2012, 00:06
fivezero7 wrote: anni wrote: thank you for the reply, is it required to plot these lines and then calculate? can we get directly i mean is there any formula to solve this problem? thanks hi anni, there is no need to plot it, once you have mastered the art of visualization. the way i did it is as under. take x+y=1 it intersects the axes at (1,0) and (0,1) and makes a right angled triangle with the axes with each side (other than the hypotenuse) as 1 hence the area of this triangle is 0.5*1*1 = 0.5 sq. units. all other lines are symmetrical and form 3 more congruent triangles with the axes at different points. so the total area will be 0.5+0.5+0.5+0.5 = 2 sq units. hope i am clear Very clear, and amazed to see how much was packed under that question. But, am curious if there's any other way to solve the problem?



Intern
Joined: 12 Mar 2012
Posts: 16

Re: The area bounded by the curves x + y = 1, x  y = 1 is
[#permalink]
Show Tags
12 Apr 2012, 08:17
anni wrote: The area bounded by the curves x + y = 1, x  y = 1 is
A. 3 B. 4 C. 2 D. 1 E. None
please, help how to solve ? One more method: solve following equns: X+Y=1 Xy=1 Xy=1 X+y=1 Out put X= +_ 1 Y=+_1 Plot the values of X and Y on graph, you will see the square Now use pythagoras thm to find diagonal,which will be the side of that square. = Sqaure root 2 square it and ans will be 2



Manager
Joined: 27 Dec 2011
Posts: 61

Re: The area bounded by the curves x + y = 1, x  y = 1 is
[#permalink]
Show Tags
22 Sep 2012, 18:11
the question threw me away when it said "curves" and I started thinking about parabola, It should have said "lines" instead.
@Bunuel, Does gmat confuses us with this kind of language?
thanks!



Senior Manager
Joined: 13 Aug 2012
Posts: 441
Concentration: Marketing, Finance
GPA: 3.23

Re: The area bounded by the curves x + y = 1, x  y = 1 is
[#permalink]
Show Tags
05 Dec 2012, 21:27
(1) Derive all equations x + y = 1 eq1: x + y = 1 eq2: x + y = 1 x  y = 1 eq3: x  y = 1 eq4: y  x = 1 (2) Plot your graph using x=0 and y=0. eq1: 0,1 and 1,0 eq2: 0,1 and 1,0 eq3: 01 and 1,0 eq4: 0,1 and 1,0 (3) You will recognize a region that is a square with a diagonal of 2 (4) Calculate the area. diagonal = side * \(\sqrt{2}\) side = \(\frac{2}{\sqrt{2}}\) side = \(\sqrt{2}\) Area = \(side^2\) = \(\sqrt{2}^2\) = \(2\) For detailed solutions for other similar problems. http://burnoutorbreathe.blogspot.com/2012/12/absolutevaluessolvingforareaof.html
_________________
Impossible is nothing to God.



Math Expert
Joined: 02 Sep 2009
Posts: 47983

Re: The area bounded by the curves x + y = 1 andx  y = 1 is
[#permalink]
Show Tags
04 Jul 2013, 01:44



Manager
Joined: 22 Feb 2009
Posts: 189

Re: The area bounded by the curves x + y = 1 andx  y = 1 is
[#permalink]
Show Tags
04 Aug 2014, 00:06
anni wrote: The area bounded by the curves x + y = 1 and x  y = 1 is
A. 3 B. 4 C. 2 D. 1 E. None The question seems confusing at first since it said the curves. But if you know how to deal with absolute values, you can come up with the solution pretty quickly. C
_________________
......................................................................... +1 Kudos please, if you like my post



Intern
Joined: 03 Jul 2015
Posts: 31

Re: The area bounded by the curves x + y = 1 andx  y = 1 is
[#permalink]
Show Tags
04 Sep 2015, 05:11
Bunuel wrote: Bumping for review and further discussion*. Get a kudos point for an alternative solution! *New project from GMAT Club!!! Check HEREwhy only (0,1) (1,0) should only pick? for x+y=1, if i chose (10,9) then it still become 1, can you please explain me what exactly the method of chosing number while finding area for this type of math



Retired Moderator
Joined: 23 Sep 2015
Posts: 386
Location: France
GMAT 1: 690 Q47 V38 GMAT 2: 700 Q48 V38
WE: Real Estate (Mutual Funds and Brokerage)

The area bounded by the curves x + y = 1 andx  y = 1 is
[#permalink]
Show Tags
29 Dec 2015, 06:47
Hi Bunuel, just a question, I am getting confused with this. Can't we just find all the solutions for x and y by using just one equation? If we take the first equation: x + y = 1 and say that y = 0 then x = 1 or 1 and if x = 0 then y =1 and 1 Would that be incorrect? And if that's the case, what is the difference between this equation x + y = 1 and this one x+y=1 Thanks a lot
_________________
New Application Tracker : update your school profiles instantly!



Board of Directors
Joined: 17 Jul 2014
Posts: 2717
Location: United States (IL)
Concentration: Finance, Economics
GPA: 3.92
WE: General Management (Transportation)

Re: The area bounded by the curves x + y = 1 andx  y = 1 is
[#permalink]
Show Tags
23 Mar 2016, 19:00
anni wrote: The area bounded by the curves x + y = 1 and x  y = 1 is
A. 3 B. 4 C. 2 D. 1 E. None x+y=1 > y=x+1 > slope 1. x+y=1 > y=x1 > slope 1. we have 2 parallel lines. xy=1 > y=x1 => slope 1. xy=1 > y=x+1 > slope 1. > we have another 2 parallel lines. i simply drew the lines, and for the sake of getting the image, try x=1 then y=1 for all the equations. i got a square like shape, with the points of intersection at (1; 0); (0; 1); (1; 0); (0; 1) since the diagonal of the square is the x axis, and it has a length of 2, we can apply the 454590 triangle rule, and see that 2=x*sqrt(2), where x is the side of the square. the side of the square is sqrt(2). now, we need to find the area > sqrt(2) squared is equal to 2.



Board of Directors
Joined: 17 Jul 2014
Posts: 2717
Location: United States (IL)
Concentration: Finance, Economics
GPA: 3.92
WE: General Management (Transportation)

Re: The area bounded by the curves x + y = 1 andx  y = 1 is
[#permalink]
Show Tags
23 Mar 2016, 19:03
anik19890 wrote: Bunuel wrote: Bumping for review and further discussion*. Get a kudos point for an alternative solution! *New project from GMAT Club!!! Check HEREwhy only (0,1) (1,0) should only pick? for x+y=1, if i chose (10,9) then it still become 1, can you please explain me what exactly the method of chosing number while finding area for this type of math you would find more points on THE LINE, but we are asked for the area of the figure when the 4 lines intersect. the 4 points of intersection are as shown in the figure in bunuel's post.



Manager
Joined: 14 Jun 2016
Posts: 70
Location: India
WE: Engineering (Manufacturing)

Re: The area bounded by the curves x + y = 1 andx  y = 1 is
[#permalink]
Show Tags
06 Aug 2017, 08:56
Excellent question... Tested understanding of Inequalities, Geometry and visualization... Is it a Q 51 level question?
_________________
If you appreciate my post then please click +1Kudos



Senior Manager
Joined: 15 Jan 2017
Posts: 367

Re: The area bounded by the curves x + y = 1 andx  y = 1 is
[#permalink]
Show Tags
19 Aug 2017, 07:56
I have a query with the wording of the question it says : The area bounded by the curves x + y = 1, x  y = 1 is A. 3 B. 4 C. 2 D. 1 E. None
Based on answers here it appears we consider them as four straight lines (not curves). Curves usually are written by x^2 + y^2 format; but since it said curves I thought it would be circular> so in case its a non  square in the equation;I assume it to be lines not curves?? Will keep in mind in case I come across such language/ format later



Senior Manager
Joined: 29 Jun 2017
Posts: 493
GPA: 4
WE: Engineering (Transportation)

Re: The area bounded by the curves x + y = 1 andx  y = 1 is
[#permalink]
Show Tags
30 Aug 2017, 08:49
Answer is C:An easy question instead <700 probably x+y=1 , gives 2 equations x+y = + 1 and x+y =1 xy =1 gives xy=1 and xy = 1 we know they will form an enclosed figure on x and y axis. so directly find the points = put x=0 and y=0 we get (0,1) (0,1) (1,0) (1,0) when u actually plot the distance between opposite points are = 2 on each diogonal which cut at 90 degrees at O , origin there fore A = 0.5 D1D2 = 0.5x2x2 = 2 which is C
_________________
Give Kudos for correct answer and/or if you like the solution.



Senior Manager
Joined: 31 Jul 2017
Posts: 404
Location: Malaysia
WE: Consulting (Energy and Utilities)

Re: The area bounded by the curves x + y = 1 andx  y = 1 is
[#permalink]
Show Tags
05 Feb 2018, 21:59
anni wrote: The area bounded by the curves x + y = 1 and x  y = 1 is
A. 3 B. 4 C. 2 D. 1 E. None The total Area = \(4*\frac{1}{2}*1*1\)
_________________
If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!




Re: The area bounded by the curves x + y = 1 andx  y = 1 is &nbs
[#permalink]
05 Feb 2018, 21:59






