Oct 20 07:00 AM PDT  09:00 AM PDT Get personalized insights on how to achieve your Target Quant Score. Oct 22 08:00 PM PDT  09:00 PM PDT On Demand for $79. For a score of 4951 (from current actual score of 40+) AllInOne Standard & 700+ Level Questions (150 questions) Oct 23 08:00 AM PDT  09:00 AM PDT Join an exclusive interview with the people behind the test. If you're taking the GMAT, this is a webinar you cannot afford to miss! Oct 26 07:00 AM PDT  09:00 AM PDT Want to score 90 percentile or higher on GMAT CR? Attend this free webinar to learn how to prethink assumptions and solve the most challenging questions in less than 2 minutes.
Author 
Message 
TAGS:

Hide Tags

Intern
Status: Fortune favours the brave
Joined: 17 Jul 2019
Posts: 9
Location: Russian Federation
GPA: 3.98

If x^2+y^2=1 and x0.34+0.66=y, how many values can x take?
[#permalink]
Show Tags
27 Aug 2019, 04:05
Question Stats:
21% (02:07) correct 79% (02:22) wrong based on 76 sessions
HideShow timer Statistics
If \(x^2+y^2=1\) and \(x0.34+0.66=y\), than how many values can \(x\) take? A. 0 B. 1 C. 2 D. 3 E. 4 ______ Smth similar I met in my GMAT exam, thus make sure you are familiar with such questions Kudos are always appreciated
Official Answer and Stats are available only to registered users. Register/ Login.



Director
Joined: 19 Oct 2018
Posts: 981
Location: India

Re: If x^2+y^2=1 and x0.34+0.66=y, how many values can x take?
[#permalink]
Show Tags
27 Aug 2019, 06:49
1 Kudos for an excellent question. IMO graphical approach can save lot of time in this question. We just need to figure out whether point of minima of x0.34+0.66=y lies within the circle or not, and whether local maxima at x=0 lies within circle or not. \(x^2+y^2=1\) is a curve of a circle of radius 1. At x=0, x0.34+0.66= 1, which lies on the circle. Minima of \(x0.34+0.66=y\) occurs when x0.34=0 or x=+0.34 and 0.34, and y=0.66, lie inside the circle. Now we are good to draw the curve. There are 3 points where both curves meet. D Philipp98 wrote: If \(x^2+y^2=1\) and \(x0.34+0.66=y\), than how many values can \(x\) take? A. 0 B. 1 C. 2 D. 3 E. 4 ______ Smth similar I met in my GMAT exam, thus make sure you are familiar with such questions Kudos are always appreciated
Attachments
1111.PNG [ 18.44 KiB  Viewed 1081 times ]



Intern
Status: Fortune favours the brave
Joined: 17 Jul 2019
Posts: 9
Location: Russian Federation
GPA: 3.98

If x^2+y^2=1 and x0.34+0.66=y, how many values can x take?
[#permalink]
Show Tags
27 Aug 2019, 06:52
Such tasks are easy to solve graphically: solutions to the system of equation are points of intersection of graphs of each equation. Remember: When a module sign is "layed" on F(x), graphical part of F(x), which lays below the Xaxis, is reflected over the Xaxis. This operation gives you the graph of F(x). Thus, the given task is solved with consequent graphics: As already discussed, to obtain x0.34 graph, we reflect "negative" part of x0.34 over Xaxis. Then shift x0.34 by 0.66 upwards to obtain x0.34+0.66. Than we draw the plot of x^2+y^2=1 Finally, one can see 3 points of intersection > 3 solutions to the system > x can take 3 values > answer is D



Intern
Joined: 22 Aug 2019
Posts: 1

Re: If x^2+y^2=1 and x0.34+0.66=y, how many values can x take?
[#permalink]
Show Tags
27 Aug 2019, 07:38
This question is a tough one



Manager
Joined: 17 Jul 2017
Posts: 194

Re: If x^2+y^2=1 and x0.34+0.66=y, how many values can x take?
[#permalink]
Show Tags
27 Aug 2019, 08:42
Philipp98 wrote: If \(x^2+y^2=1\) and \(x0.34+0.66=y\), than how many values can \(x\) take? A. 0 B. 1 C. 2 D. 3 E. 4 ______ Smth similar I met in my GMAT exam, thus make sure you are familiar with such questions Kudos are always appreciated nick1816BunuelWhat is wrong with the given solution in the image: here x=0 or 1 0r 1 but i consider case last one in pic (from d) here i get x=.84 and y =.52 then also x^2+y^2=1 then y are we nopt considering such cases
Attachments
IMG20190827210630.jpg [ 3.48 MiB  Viewed 1011 times ]
IMG20190827210624.jpg [ 3.52 MiB  Viewed 1014 times ]



Director
Joined: 19 Oct 2018
Posts: 981
Location: India

Re: If x^2+y^2=1 and x0.34+0.66=y, how many values can x take?
[#permalink]
Show Tags
27 Aug 2019, 09:23
There are couple of problems with this approach for this particular question. 1. This approach can take a lot of time. Whenever you see second order equations, go for the graphical approach. 2. You didn't find the domain for x, for each equation. For example x0.34+0.66=y y=x0.34+0.66, when x≥0.34y=0.34x+0.66, when \(0.34 ≥x ≥0\)y=0.34+x+0.66, when 0≥x≥0.34y=0.34x+0.66, when x≤0.34Now you can solve each case, and look whether the solution lies in the domain or not. vanam52923 wrote: Philipp98 wrote: If \(x^2+y^2=1\) and \(x0.34+0.66=y\), than how many values can \(x\) take? A. 0 B. 1 C. 2 D. 3 E. 4 ______ Smth similar I met in my GMAT exam, thus make sure you are familiar with such questions Kudos are always appreciated nick1816BunuelWhat is wrong with the given solution in the image: here x=0 or 1 0r 1 but i consider case last one in pic (from d) here i get x=.84 and y =.52 then also x^2+y^2=1 then y are we nopt considering such cases



Manager
Joined: 17 Jul 2017
Posts: 194

Re: If x^2+y^2=1 and x0.34+0.66=y, how many values can x take?
[#permalink]
Show Tags
27 Aug 2019, 10:08
nick1816 wrote: There are couple of problems with this approach for this particular question. 1. This approach can take a lot of time. Whenever you see second order equations, go for the graphical approach. 2. You didn't find the domain for x, for each equation. For example x0.34+0.66=y y=x0.34+0.66, when x≥0.34y=0.34x+0.66, when \(0.34 ≥x ≥0\)y=0.34+x+0.66, when 0≥x≥0.34y=0.34x+0.66, when x≤0.34Now you can solve each case, and look whether the solution lies in the domain or not. vanam52923 wrote: Philipp98 wrote: If \(x^2+y^2=1\) and \(x0.34+0.66=y\), than how many values can \(x\) take? A. 0 B. 1 C. 2 D. 3 E. 4 ______ Smth similar I met in my GMAT exam, thus make sure you are familiar with such questions Kudos are always appreciated nick1816BunuelWhat is wrong with the given solution in the image: here x=0 or 1 0r 1 but i consider case last one in pic (from d) here i get x=.84 and y =.52 then also x^2+y^2=1 then y are we nopt considering such cases My bad ,thanks a lot But are such questions asked on GMAT?



SVP
Joined: 03 Jun 2019
Posts: 1724
Location: India

Re: If x^2+y^2=1 and x0.34+0.66=y, how many values can x take?
[#permalink]
Show Tags
27 Aug 2019, 10:20
nick1816 VeritasKarishma Bunuel chondro48 Is there an algebra way to solve this question? nick1816 wrote: 1 Kudos for an excellent question. IMO graphical approach can save lot of time in this question. We just need to figure out whether point of minima of x0.34+0.66=y lies within the circle or not, and whether local maxima at x=0 lies within circle or not. \(x^2+y^2=1\) is a curve of a circle of radius 1. At x=0, x0.34+0.66= 1, which lies on the circle. Minima of \(x0.34+0.66=y\) occurs when x0.34=0 or x=+0.34 and 0.34, and y=0.66, lie inside the circle. Now we are good to draw the curve. There are 3 points where both curves meet. D Philipp98 wrote: If \(x^2+y^2=1\) and \(x0.34+0.66=y\), than how many values can \(x\) take? A. 0 B. 1 C. 2 D. 3 E. 4 ______ Smth similar I met in my GMAT exam, thus make sure you are familiar with such questions Kudos are always appreciated
_________________
"Success is not final; failure is not fatal: It is the courage to continue that counts." Please provide kudos if you like my post. Kudos encourage active discussions. My GMAT Resources:  Efficient LearningAll you need to know about GMAT quantTele: +911140396815 Mobile : +919910661622 Email : kinshook.chaturvedi@gmail.com



Senior Manager
Joined: 30 Sep 2017
Posts: 380
Concentration: Technology, Entrepreneurship
GPA: 3.8
WE: Engineering (Real Estate)

If x^2+y^2=1 and x0.34+0.66=y, how many values can x take?
[#permalink]
Show Tags
Updated on: 28 Aug 2019, 00:39
Kinshook wrote: nick1816 VeritasKarishma Bunuel chondro48 Is there an algebra way to solve this question? nick1816 wrote: 1 Kudos for an excellent question. IMO graphical approach can save lot of time in this question. We just need to figure out whether point of minima of x0.34+0.66=y lies within the circle or not, and whether local maxima at x=0 lies within circle or not. \(x^2+y^2=1\) is a curve of a circle of radius 1. At x=0, x0.34+0.66= 1, which lies on the circle. Minima of \(x0.34+0.66=y\) occurs when x0.34=0 or x=+0.34 and 0.34, and y=0.66, lie inside the circle. Now we are good to draw the curve. There are 3 points where both curves meet. D Philipp98 wrote: If \(x^2+y^2=1\) and \(x0.34+0.66=y\), than how many values can \(x\) take? A. 0 B. 1 C. 2 D. 3 E. 4 Kudos are always appreciated Hi Kinshook nick1816 VeritasKarishma and Bunuel, Yes, there is. Below is a framework to do so. Correct me, experts, if I make mistake. Note that using algebra, the solution is laborious and time consuming. Transform \(x^2=1y^2\) to x=√(1y^2). Substituting x with √(1y^2) into the second equation, we get: √(1y^2)0.34=y0.66. If √(1y^2) > 0.34, then √(1y^2)0.34 = y0.66 > √(1y^2)= y0.34. After squaring both sides and performing tedious calculation, we will find that there are two solution points available when √(1y^2) > 0.34. If √(1y^2) <= 0.34, then 0.34√(1y^2) = y0.66 > √(1y^2)=1y. It is obvious that y=1 satisfies the equation and correspondingly x=√(1y^2)=0. Thus, there is one solution point (0,1) when √(1y^2) <= 0.34. Finally, there are 3 values that x can take. Final answer is (D)
Originally posted by chondro48 on 27 Aug 2019, 17:04.
Last edited by chondro48 on 28 Aug 2019, 00:39, edited 1 time in total.



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9706
Location: Pune, India

Re: If x^2+y^2=1 and x0.34+0.66=y, how many values can x take?
[#permalink]
Show Tags
28 Aug 2019, 00:36
Kinshook wrote: nick1816 VeritasKarishma Bunuel chondro48 Is there an algebra way to solve this question? nick1816 wrote: 1 Kudos for an excellent question. IMO graphical approach can save lot of time in this question. We just need to figure out whether point of minima of x0.34+0.66=y lies within the circle or not, and whether local maxima at x=0 lies within circle or not. \(x^2+y^2=1\) is a curve of a circle of radius 1. At x=0, x0.34+0.66= 1, which lies on the circle. Minima of \(x0.34+0.66=y\) occurs when x0.34=0 or x=+0.34 and 0.34, and y=0.66, lie inside the circle. Now we are good to draw the curve. There are 3 points where both curves meet. D Philipp98 wrote: If \(x^2+y^2=1\) and \(x0.34+0.66=y\), than how many values can \(x\) take? A. 0 B. 1 C. 2 D. 3 E. 4 ______ Smth similar I met in my GMAT exam, thus make sure you are familiar with such questions Kudos are always appreciated You can solve it using the usual method of definition of absolute values (as done by others here) but if you are unable to solve it graphically, it is probably a good idea to skip the question. With algebra, it will be far too time consuming and error prone.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Intern
Joined: 26 Oct 2010
Posts: 14

Re: If x^2+y^2=1 and x0.34+0.66=y, how many values can x take?
[#permalink]
Show Tags
29 Aug 2019, 11:01
nick1816 The explanation given by you to find out the value of y at the equation's minima is crystal clear. We have arrived at y = 0.66 at minima i.e x = +/ 0.34. Now, how do we figure if y = 0.66 falls inside the circle? Ofcourse we can substitute x = 0.34 in the circle equation to find out the value of y. And if the value of y > 0.66, we can deduce that 0.66 is inside the circle. However, this is a time consuming process that requires squaring and squareroots Is there are short cut to find if 0.66 falls inside the circle? VeritasKarishma Bunuel Philipp98  Please help me with this.



Director
Joined: 19 Oct 2018
Posts: 981
Location: India

Re: If x^2+y^2=1 and x0.34+0.66=y, how many values can x take?
[#permalink]
Show Tags
29 Aug 2019, 11:12
0.34≃1/3 0.66≃2/3 \((\frac{1}{3})^2+(\frac{2}{3})^2\)= \(\frac{1}{9}+\frac{4}{9}\)= \(\frac{5}{9}\)<1GMATaspirant641 wrote: nick1816 The explanation given by you to find out the value of y at the equation's minima is crystal clear. We have arrived at y = 0.66 at minima i.e x = +/ 0.34. Now, how do we figure if y = 0.66 falls inside the circle? Ofcourse we can substitute x = 0.34 in the circle equation to find out the value of y. And if the value of y > 0.66, we can deduce that 0.66 is inside the circle. However, this is a time consuming process that requires squaring and squareroots Is there are short cut to find if 0.66 falls inside the circle? VeritasKarishma Bunuel Philipp98  Please help me with this.



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9706
Location: Pune, India

If x^2+y^2=1 and x0.34+0.66=y, how many values can x take?
[#permalink]
Show Tags
29 Aug 2019, 23:13
GMATaspirant641 wrote: nick1816 The explanation given by you to find out the value of y at the equation's minima is crystal clear. We have arrived at y = 0.66 at minima i.e x = +/ 0.34. Now, how do we figure if y = 0.66 falls inside the circle? Ofcourse we can substitute x = 0.34 in the circle equation to find out the value of y. And if the value of y > 0.66, we can deduce that 0.66 is inside the circle. However, this is a time consuming process that requires squaring and squareroots Is there are short cut to find if 0.66 falls inside the circle? VeritasKarishma Bunuel Philipp98  Please help me with this. Check the solution given by Philipp98 above. Notice how the graph of x  0.34 + 0.66 = y is drawn. Also note that each green line has slope 1 or 1. Since the graph intersects the circle at (0, 1), the line of slope 1 will be inside the circle (45 degrees line). Hence you know that it will intersect the circle in 3 points. Check out these two posts on how to draw absolute value graphs: https://www.veritasprep.com/blog/2011/0 ... htomods/https://www.veritasprep.com/blog/2014/1 ... solutions/
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >




If x^2+y^2=1 and x0.34+0.66=y, how many values can x take?
[#permalink]
29 Aug 2019, 23:13






