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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Must see for Maximum/Minimum value problems ##### This topic has 10 member replies ## Must see for Maximum/Minimum value problems Hi, There are few problems for Maximum/Minimum value deduction that are tricky and time consuming. Pl. see below few examples of those with Take Away approach Q.What is the Maximum value of =(7-x)^5 (7+x)^4? A.7^9 B.14^4 C.0 D.7^9.2^17.5^5/3^18 E.7^9.2^7.5^7/3^18 ------------------------------------------------ Take Away... If a,b, c are variables and a+b+c is constant, & Let X=a^p.b^q.c^r then for x to be maximum... a/p=b/q=c/r In above problem, say x=(7-x)^5 (7+x)^4, where a=(7-x); b=(7+x); p=5; q=4. As a+b=(7-x)+(7+x)=14 (Constant), hence to get max of X... => Do (7-x)/5=(7+x)/4 =>which yields...x=-7/9 => by putting the value of x=-7/9 in (7-x)^5 (7+x)^4, we get 7^9.2^17.5^5/3^18. Answer is D. _________________ Shalabh Jain, e-GMAT Instructor Master | Next Rank: 500 Posts Joined 06 Apr 2012 Posted: 134 messages Followed by: 5 members Upvotes: 35 Q.What is the minimum value of x+1/x ? If x>0. A.2 B.1 C.1/2 D.sqrt 2 E.3/2 -------------------------------------------- Take Away.. If A*B=constant; where A & B are variables, then A+B=Minimum , when A=B. Since in given problem x+1/x, x*1/x= 1 (Constant), hence x+1/x will be minimum when x= 1/x => so, x= 1/x => x^2=1 => x= 1, -1. => Take x=1 only as x>0. Hence Minimum value of x+1//x=2. _________________ Shalabh Jain, e-GMAT Instructor Master | Next Rank: 500 Posts Joined 06 Apr 2012 Posted: 134 messages Followed by: 5 members Upvotes: 35 Q.What is the maximum value of xy ? If 3x+4Y=24. A.24 B.12 C.120 D.0 E.infinity -------------------------------------------- Take Away.. If A+B=constant; where A & B are variables, then A*B=maximum, when A=B. We can write xy as 3x.4y/12. As 3x+4Y=24, so for 3x.4y to be max 3x=4y=24/2=12. This gives x=4, y=3 The maximum value of xy would be 4.3=12. _________________ Shalabh Jain, e-GMAT Instructor Master | Next Rank: 500 Posts Joined 06 Apr 2012 Posted: 134 messages Followed by: 5 members Upvotes: 35 Q.What is the minimum value of 1/x+1/y+1/z ? If x+y+z=1. A.1 B.3 C.6 D.8 E.9 -------------------------------------------- Take Away.. If A+B+C=constant; where A, B & C are variables, then A*B*C=maximum, when A=B=C. => 1/x+1/y+1/z = (xy+yz+xz)/xyz; => for (xy+yz+xz)/xyz to be minimum; denominator xyz should be maximum. => since x+y+z=1, hence at x=y=z, xyz will be max. => this gives x=y=z=1/3, or, 1/x+1/y+1/z= 9. _________________ Shalabh Jain, e-GMAT Instructor Master | Next Rank: 500 Posts Joined 06 Apr 2012 Posted: 134 messages Followed by: 5 members Upvotes: 35 Q. What is the minimum possible value of f(x)=max {(3-x), (2+x), (5-x)} ? Where X is an integer. A.5 B.6 C.0 D.3 E.4 --------------------------------------- We need to get Minimum of [f(x)= max {(3-x), (2+x), (5-x)}] Check for 0, +ive and -ive values of x and see the behaviour of fn. By Putting x=0, f(0)= max {(3-0), (2+0), (5-0)}= max {3, 2, 5} = 5. Similarly... => x=0, f(x)=5, => x=-1, f(x)=6, => x=1, f(x)=4, => x=2, f(x)=4, => x=3, f(x)=5, As we take higher +ive values, f(x) increase so is the case with -ive values. Hence f(x) will have minimum value as 4. _________________ Shalabh Jain, e-GMAT Instructor Newbie | Next Rank: 10 Posts Joined 10 Apr 2012 Posted: 6 messages Shalabh's Quants wrote: Q.What is the maximum value of xy ? If 3x+4Y=24. A.24 B.12 C.120 D.0 E.infinity -------------------------------------------- Take Away.. If A+B=constant; where A & B are variables, then A*B=maximum, when A=B. We can write xy as 3x.4y/12. As 3x+4Y=24, so for 3x.4y to be max 3x=4y=24/2=12. This gives x=4, y=3 The maximum value of xy would be 4.3=12. Can anyone explain...Why to maximise 3x.4y? We want to maximise xy. Senior | Next Rank: 100 Posts Joined 07 Nov 2011 Posted: 58 messages Upvotes: 1 Test Date: Soon! Target GMAT Score: 700 hi Shalabh Good tips. Can you tell us where did you get these questions from? Are these from OG? Thanks Master | Next Rank: 500 Posts Joined 06 Apr 2012 Posted: 134 messages Followed by: 5 members Upvotes: 35 iwillsurvive101 wrote: hi Shalabh Good tips. Can you tell us where did you get these questions from? Are these from OG? Thanks Thanks! These are compilations from various GMAT TestPrep cos..Not from OG though. _________________ Shalabh Jain, e-GMAT Instructor Master | Next Rank: 500 Posts Joined 06 Apr 2012 Posted: 134 messages Followed by: 5 members Upvotes: 35 sureshs wrote: Shalabh's Quants wrote: Q.What is the maximum value of xy ? If 3x+4Y=24. A.24 B.12 C.120 D.0 E.infinity -------------------------------------------- Take Away.. If A+B=constant; where A & B are variables, then A*B=maximum, when A=B. We can write xy as 3x.4y/12. As 3x+4Y=24, so for 3x.4y to be max 3x=4y=24/2=12. This gives x=4, y=3 The maximum value of xy would be 4.3=12. Can anyone explain...Why to maximise 3x.4y? We want to maximise xy. Since given is 3x+4Y=24 = constant. We can maximise the product of elements present in 3x+4Y=24 only i.e. 3x and 4y. By way of maximising 3x.4y = 12xy, we can also deduce maximim value of xy. _________________ Shalabh Jain, e-GMAT Instructor Newbie | Next Rank: 10 Posts Joined 10 Apr 2012 Posted: 6 messages Shalabh's Quants wrote: sureshs wrote: Shalabh's Quants wrote: Q.What is the maximum value of xy ? If 3x+4Y=24. A.24 B.12 C.120 D.0 E.infinity -------------------------------------------- Take Away.. If A+B=constant; where A & B are variables, then A*B=maximum, when A=B. We can write xy as 3x.4y/12. As 3x+4Y=24, so for 3x.4y to be max 3x=4y=24/2=12. This gives x=4, y=3 The maximum value of xy would be 4.3=12. Can anyone explain...Why to maximise 3x.4y? We want to maximise xy. Since given is 3x+4Y=24 = constant. We can maximise the product of elements present in 3x+4Y=24 only i.e. 3x and 4y. By way of maximising 3x.4y = 12xy, we can also deduce maximim value of xy. Ok Ok. I got it sir. thank you v. much. Junior | Next Rank: 30 Posts Joined 13 Aug 2011 Posted: 14 messages Hi Shalabh Can You also explain where all we can use this concept in detail regards Vegi • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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