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(11+1/11)^2-(11-1/11)^2=?

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Math Revolution GMAT Instructor
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23 Jun 2017, 01:12
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$$(11+\frac{1}{11})^2-(11-\frac{1}{11})^2=?$$

A. 2
B. 3
C. 4
D. 5
E. 9

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"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Director Joined: 04 Dec 2015 Posts: 701 Location: India Concentration: Technology, Strategy Schools: ISB '19, IIMA , IIMB, XLRI WE: Information Technology (Consulting) Re: (11+1/11)^2-(11-1/11)^2=? [#permalink] Show Tags 23 Jun 2017, 01:35 1 MathRevolution wrote: $$(11+\frac{1}{11})^2-(11-\frac{1}{11})^2=?$$ A. 2 B. 3 C. 4 D. 5 E. 9 Let $$(11+\frac{1}{11}) = x$$ and $$(11-\frac{1}{11}) = y$$ $$(11+\frac{1}{11})^2-(11-\frac{1}{11})^2 = x^2 - y^2 = (x+y)(x-y)$$ $$(x+y)(x-y) = (11+\frac{1}{11} + 11-\frac{1}{11})(11+\frac{1}{11} - (11-\frac{1}{11}))$$ $$(11+11) (11 - 11+\frac{1}{11}+\frac{1}{11}) = (22) (\frac{1+1}{11})$$ $$(22)(\frac{2}{11})$$ $$= 2*2 = 4$$ . Answer (C)... Manager Joined: 17 Feb 2016 Posts: 101 Location: India Concentration: General Management, Entrepreneurship GMAT 1: 660 Q47 V36 GPA: 3.12 WE: Education (Internet and New Media) (11+1/11)^2-(11-1/11)^2=? [#permalink] Show Tags 23 Jun 2017, 02:02 $$a^2-b^2=(a+b)(a-b)$$ $$a=11+\frac{1}{11}$$ $$b=11-\frac{1}{11}$$ Solving , $$22\frac{2}{11}$$ 4 _________________ 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 BSchool Forum Moderator Joined: 26 Feb 2016 Posts: 3131 Location: India GPA: 3.12 Re: (11+1/11)^2-(11-1/11)^2=? [#permalink] Show Tags 23 Jun 2017, 02:24 We need to find out the value of the expression $$(11+\frac{1}{11})^2-(11-\frac{1}{11})^2$$ Let 11 = a, $$\frac{1}{11}$$ = b So the expression becomes $$(a+b)^2 - (a-b)^2$$ = $$a^2 + 2ab + b^2 - (a^2 - 2ab + b^2)$$ =4ab Since $$(a+b)^2 = a^2 + 2ab + b^2 and (a-b)^2 = a^2 - 2ab + b^2$$ Substituting the values of a and b, we get the value of expression to be 4(Option C) _________________ You've got what it takes, but it will take everything you've got Board of Directors Status: QA & VA Forum Moderator Joined: 11 Jun 2011 Posts: 4031 Location: India GPA: 3.5 WE: Business Development (Commercial Banking) Re: (11+1/11)^2-(11-1/11)^2=? [#permalink] Show Tags 23 Jun 2017, 08:36 MathRevolution wrote: $$(11+\frac{1}{11})^2-(11-\frac{1}{11})^2=?$$ A. 2 B. 3 C. 4 D. 5 E. 9 $$(11+\frac{1}{11})^2$$ = $$11^2 + 1/11^2 + 2*11*\frac{1}{11}$$ = $$121 + \frac{1}{121} + 2$$ = $$123 + \frac{1}{121}$$ $$(11-\frac{1}{11})^2$$ = $$11^2 + 1/11^2 - 2*11*\frac{1}{11}$$ = $$121 + \frac{1}{121} - 2$$ = $$119 + \frac{1}{121}$$ So, $$(11+\frac{1}{11})^2-(11-\frac{1}{11})^2=?$$ = $$123 + 1/121$$ - $$119 + 1/121$$ = $$123 - 119 + \frac{1}{121} - \frac{1}{121}$$ = $$4$$ Hence, answer will be (C) _________________ Thanks and Regards Abhishek.... PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only ) Intern Joined: 07 Jun 2017 Posts: 10 Re: (11+1/11)^2-(11-1/11)^2=? [#permalink] Show Tags 23 Jun 2017, 11:08 (11+1/11)^2-(11-1/11)^2 is in the form of a^2 - b^2 = (a+b)(a-b), =(11+1/11+11-1/11)(11+1/11-11+1/11), =(22)(2/11), =4 Ans = C Retired Moderator Joined: 19 Mar 2014 Posts: 962 Location: India Concentration: Finance, Entrepreneurship GPA: 3.5 Re: (11+1/11)^2-(11-1/11)^2=? [#permalink] Show Tags 23 Jun 2017, 11:29 $$(11+\frac{1}{11})^2-(11-\frac{1}{11})^2=?$$ Simplifying in the form of (a+b)^2 - (a-b)^2 After substituting the values we get: 11^2 + 2 + (1/11)^2 - 11^2 + 2 - (1/11)^2 Cancelling the terms we are left with 2+2 = 4 Hence, the answer is C = 4 _________________ "Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent." Best AWA Template: https://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html#p470475 Senior Manager Joined: 23 May 2017 Posts: 251 Concentration: Finance, Accounting WE: Programming (Energy and Utilities) Re: (11+1/11)^2-(11-1/11)^2=? [#permalink] Show Tags 23 Jun 2017, 11:52 This can be written as = $$(a + b)^{2}$$ - $$( a - b)^{2}$$ = $$a^{2}$$ + $$b^{2}$$ + 2ab - $$a^{2}$$- $$b^{2}$$ + 2ab = 4ab where a = 11 & b = $$\frac{1}{11}$$ = 4 * 11 * $$\frac{1}{11}$$ = 4 = C _________________ If you like the post, please award me Kudos!! It motivates me Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6219 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: (11+1/11)^2-(11-1/11)^2=? [#permalink] Show Tags 25 Jun 2017, 18:17 ==> You get $$(11+\frac{1}{11})^2-(11-\frac{1}{11})^2=[(11+\frac{1}{11})-(11-\frac{1}{11})][(11+\frac{1}{11})+(11-\frac{1}{11})]= \frac{2}{11}(22)=4.$$ The answer is C. Answer: C _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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25 Jun 2017, 23:41
imo C
We can solve this problem by using identity
(a+b)^2=a^2+b^2+2ab
(a-b)^2=a^2+b^2-2ab
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26 Jun 2017, 17:56
MathRevolution wrote:
$$(11+\frac{1}{11})^2-(11-\frac{1}{11})^2=?$$

A. 2
B. 3
C. 4
D. 5
E. 9

We can use the difference of squares concept, for which we let x = 11 + 1/11 and y =11 - 1/11, so we have:

x^2 - y^2

(x - y)(x + y)

[(11 + 1/11) - (11 - 1/11)][(11 + 1/11) + (11 - 1/11)]

(2/11)(22) = 4

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27 Jun 2018, 07:46
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