GMAT Club Forumhttps://gmatclub.com:443/forum/ If 4<=x<=6 and 2<=y<=3, then the minimum possible value ofhttps://gmatclub.com/forum/if-4-x-6-and-2-y-3-then-the-minimum-possible-value-of-288737.html Page 1 of 1

 Author: fskilnik [ 14 Feb 2019, 12:11 ] Post subject: If 4<=x<=6 and 2<=y<=3, then the minimum possible value of GMATH practice exercise (Quant Class 11)If $$\,4 \le x \le 6\,$$ and $$\,2 \le y \le 3$$ , the minimum possible value of $$\,\left| {\left( {y - x} \right)\left( {y + x} \right)} \right|\,$$ is:(A) 4(B) 5(C) 6(D) 7(E) 8

 Author: fskilnik [ 14 Feb 2019, 18:21 ] Post subject: Re: If 4<=x<=6 and 2<=y<=3, then the minimum possible value of fskilnik wrote:GMATH practice exercise (Quant Class 11)If $$\,4 \le x \le 6\,$$ and $$\,2 \le y \le 3$$ , the minimum possible value of $$\,\left| {\left( {y - x} \right)\left( {y + x} \right)} \right|\,$$ is:(A) 4(B) 5(C) 6(D) 7(E) 8$$?\,\, = \,\,\min \,\left| {\left( {y - x} \right)\left( {y + x} \right)} \right|\,\, = \,\,\min \,\left| {{y^2} - {x^2}} \right|$$$$2 \le y \le 3\,\,\,\,\, \Rightarrow \,\,\,\,\,4 \le {y^2} \le 9$$$$4 \le x \le 6\,\,\,\,\, \Rightarrow \,\,\,\,\,16 \le {x^2} \le 36\,\,\,\,\, \Rightarrow \,\,\,\,\, - 36 \le - {x^2} \le - 16$$$$\left. \matrix{\\ 4 \le {y^2} \le 9 \hfill \cr \\ - 36 \le - {x^2} \le - 16\,\,\, \hfill \cr} \right\}\,\,\,\mathop \Rightarrow \limits^{\left( + \right)} \,\,\, - 32 \le {y^2} - {x^2} \le - 7\,\,\,\,\, \Rightarrow \,\,\,\,\,7 \le \left| {{y^2} - {x^2}} \right| \le 32\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = 7$$The correct answer is (D).We follow the notations and rationale taught in the GMATH method. Regards, Fabio.

 Author: KSBGC [ 17 Feb 2019, 01:56 ] Post subject: If 4<=x<=6 and 2<=y<=3, then the minimum possible value of fskilnik wrote:GMATH practice exercise (Quant Class 11)If $$\,4 \le x \le 6\,$$ and $$\,2 \le y \le 3$$ , the minimum possible value of $$\,\left| {\left( {y - x} \right)\left( {y + x} \right)} \right|\,$$ is:(A) 4(B) 5(C) 6(D) 7(E) 8$$4\leq x \leq6$$$$2\leq y \leq3$$Given, $$|y^2 - x^2|$$but we are asked to find out the minimum value of |y^2 - x^2| . we must work with corner values / extremes values of x and y. $$2^2 - 4^2$$ = 4 - 16 = - 12 = | -12 | = 12$$2^2 - 6^2$$= 4 - 36 = -32 = | -32| = 32$$3^2 - 4^2$$= 9 - 16 = -7 = | - 7| = 7.$$3^2 - 6^2$$= 9 - 36 = -27 = | -27| = 27.D is the correct answer.

 Author: GMATinsight [ 17 Feb 2019, 07:23 ] Post subject: If 4<=x<=6 and 2<=y<=3, then the minimum possible value of fskilnik wrote:GMATH practice exercise (Quant Class 11)If $$\,4 \le x \le 6\,$$ and $$\,2 \le y \le 3$$ , the minimum possible value of $$\,\left| {\left( {y - x} \right)\left( {y + x} \right)} \right|\,$$ is:(A) 4(B) 5(C) 6(D) 7(E) 8For minimum Possible value of ∣(y−x)(y+x)∣ the absolute values of (y-x) and (y+x) must be MINIMUMMinimum ABSOLUTE Value of y-x = l3-4l = l-1l = 1Minimum ABSOLUTE Value of y+x = l3+4l = l7l = 7i.e. Minimum value of l(y-x)(y+x)l = l1*7l = 7Answer: Option D

 Author: KanishkM [ 17 Feb 2019, 08:20 ] Post subject: Re: If 4<=x<=6 and 2<=y<=3, then the minimum possible value of fskilnik wrote:GMATH practice exercise (Quant Class 11)If $$\,4 \le x \le 6\,$$ and $$\,2 \le y \le 3$$ , the minimum possible value of $$\,\left| {\left( {y - x} \right)\left( {y + x} \right)} \right|\,$$ is:(A) 4(B) 5(C) 6(D) 7(E) 8So the given expression can be written as $$|y^2 - x^2|$$Only case possible is when we maximize y = 4 and minimize x = 3 |9-16|7

 Author: jamalabdullah100 [ 11 Sep 2019, 12:55 ] Post subject: Re: If 4<=x<=6 and 2<=y<=3, then the minimum possible value of GMATinsight wrote:fskilnik wrote:GMATH practice exercise (Quant Class 11)If $$\,4 \le x \le 6\,$$ and $$\,2 \le y \le 3$$ , the minimum possible value of $$\,\left| {\left( {y - x} \right)\left( {y + x} \right)} \right|\,$$ is:(A) 4(B) 5(C) 6(D) 7(E) 8For minimum Possible value of ∣(y−x)(y+x)∣ the absolute values of (y-x) and (y+x) must be MINIMUMMinimum ABSOLUTE Value of y-x = l3-4l = l-1l = 1Minimum ABSOLUTE Value of y+x = l3+4l = l7l = 7i.e. Minimum value of l(y-x)(y+x)l = l1*7l = 7Answer: Option DWhy can't the Minimum ABSOLUTE Value of y+x = 2+4 = 6? Both y=2 and x=4 are included in the boundaries..

 Author: vishakha23 [ 17 Sep 2019, 07:04 ] Post subject: Re: If 4<=x<=6 and 2<=y<=3, then the minimum possible value of Why can't the Minimum ABSOLUTE Value of y+x = 2+4 = 6? Both y=2 and x=4 are included in the boundaries.

 Author: Abhishek009 [ 17 Sep 2019, 07:19 ] Post subject: Re: If 4<=x<=6 and 2<=y<=3, then the minimum possible value of fskilnik wrote:GMATH practice exercise (Quant Class 11)If $$\,4 \le x \le 6\,$$ and $$\,2 \le y \le 3$$ , the minimum possible value of $$\,\left| {\left( {y - x} \right)\left( {y + x} \right)} \right|\,$$ is:(A) 4(B) 5(C) 6(D) 7(E) 8Values of x can be 4 , 5 & 6 ; Values of y can be 2 , 3SO, the Possible min value of $$\,\left| {\left( {y - x} \right)\left( {y + x} \right)} \right|\,$$Will be $$\,\left| {\left( {3 - 4} \right)\left( {4 + 3} \right)} \right|\,$$ = 1*7 = 7 , Answer must be (D)

 Author: jamalabdullah100 [ 23 Sep 2019, 05:06 ] Post subject: Re: If 4<=x<=6 and 2<=y<=3, then the minimum possible value of jamalabdullah100 wrote:GMATinsight wrote:fskilnik wrote:GMATH practice exercise (Quant Class 11)If $$\,4 \le x \le 6\,$$ and $$\,2 \le y \le 3$$ , the minimum possible value of $$\,\left| {\left( {y - x} \right)\left( {y + x} \right)} \right|\,$$ is:(A) 4(B) 5(C) 6(D) 7(E) 8For minimum Possible value of ∣(y−x)(y+x)∣ the absolute values of (y-x) and (y+x) must be MINIMUMMinimum ABSOLUTE Value of y-x = l3-4l = l-1l = 1Minimum ABSOLUTE Value of y+x = l3+4l = l7l = 7i.e. Minimum value of l(y-x)(y+x)l = l1*7l = 7Answer: Option DWhy can't the Minimum ABSOLUTE Value of y+x = 2+4 = 6? Both y=2 and x=4 are included in the boundaries..Can someone help with the above please? It doesn't make sense to me..

 Author: rishab0507 [ 07 Jul 2020, 14:12 ] Post subject: Re: If 4<=x<=6 and 2<=y<=3, then the minimum possible value of GMATinsight wrote:fskilnik wrote:GMATH practice exercise (Quant Class 11)If $$\,4 \le x \le 6\,$$ and $$\,2 \le y \le 3$$ , the minimum possible value of $$\,\left| {\left( {y - x} \right)\left( {y + x} \right)} \right|\,$$ is:(A) 4(B) 5(C) 6(D) 7(E) 8For minimum Possible value of ∣(y−x)(y+x)∣ the absolute values of (y-x) and (y+x) must be MINIMUMMinimum ABSOLUTE Value of y-x = l3-4l = l-1l = 1Minimum ABSOLUTE Value of y+x = l3+4l = l7l = 7i.e. Minimum value of l(y-x)(y+x)l = l1*7l = 7Answer: Option Dwhy is Minimum value 4+3 , and why not 4+2 =6, and answer can be 6*1 = 6, and not 7 Bunuel, Kinshook , can you help

 Author: himtheGMATE [ 07 Jul 2020, 19:38 ] Post subject: Re: If 4<=x<=6 and 2<=y<=3, then the minimum possible value of The answer to why min is 4+3 and not 4+2 is.When we take y=2 and x=4Min abs |y-x|is = 2 & |y+x|is=6 which gives total value of expression is = 12 hence it is not min. Hope this clarifies.Posted from my mobile device

 Author: Subhrajyoti [ 12 Dec 2021, 07:34 ] Post subject: Re: If 4<=x<=6 and 2<=y<=3, then the minimum possible value of Minimum absolute value of |y-x| is 1, and the min abs value of |y+x| is 6 so |(y-x)(y+x)| why the answer is 7 and not 6. Not sure i understand

 Author: bumpbot [ 20 Dec 2022, 17:16 ] Post subject: Re: If 4<=x<=6 and 2<=y<=3, then the minimum possible value of Hello from the GMAT Club BumpBot!Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

 Page 1 of 1 All times are UTC - 8 hours [ DST ] Powered by phpBB © phpBB Grouphttp://www.phpbb.com/