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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 ## Confusing problem tagged by: Brent@GMATPrepNow ##### This topic has 2 expert replies and 4 member replies If x>0, what is the least possible value of (x)+(4/x)? (A)0 (B)1 (C)2 (D)3 (E)4 OA is E ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 13038 messages Followed by: 1251 members Upvotes: 5254 GMAT Score: 770 knight247 wrote: If x>0, what is the least possible value of (x)+(4/x)? (A)0 (B)1 (C)2 (D)3 (E)4 OA is E If this were something other than the GMAT, I'd use calculus to solve the question (i.e., find the derivative of x + 4/x and locate the value of x such that the slope = 0) But given that it's a GMAT question, we'll use some number sense. First, if x>0, we know that 4/x>0 This means that x + (4/x) > 0 So, we can already rule out A Now let's try a few values of x. If x=1 then (x)+(4/x)= 5 If x=2 then (x)+(4/x)= 4 If x=3 then (x)+(4/x)= 4 1/3 If x=4 then (x)+(4/x)= 5 We don't need to check any values of x greater than x=4 since these values will make the value of (x)+(4/x) even bigger. At this point, the question becomes, "Are there any values of x such that (x)+(4/x) is less than 4 (if x>0)?" For example, perhaps there's a value of x between 1 and 2 that yields an even smaller value of (x)+(4/x). The answer to the question is no, but it's hard to prove unless we use some calculus or we know how the graph of y = (x)+(4/x) looks. Both of these, however, are beyond the scope of the GMAT. At this point, I'd look at my previous results and hope that the answer is E But to be more precise, we could check each answer choice. D) is there a value of x such that (x)+(4/x) = 3? To solve this, we'll multiply both sides by x to get x^2 + 4 = 3x If we rewrite this as x^2 - 3x + 4 = 0 we can see that this equation has no solution. To prove that this equation has no solution, we'll need to use the quadratic formula Aside: I have never seen an official GMAT question that required the quadratic formula, so this next part may be out of scope. The quadratic formula says that, if ax^2 + bx + c = 0, then x = [-b + sqrt(b^2 - 4ac)] / 2a For this question, we need only focus on this part: sqrt(b^2 - 4ac) In the equation x^2 - 3x + 4 = 0, a=1, b=-3 and c=4 So, we get: sqrt(b^2 - 4ac) = sqrt((-3)^2 - 4(1)(4)) = sqrt(-7) Since we cannot evaluate sqrt(-7), we can conclude that x^2 - 3x + 4 = 0 has no solution. This means we can eliminate answer choice D. We can use similar logic to eliminate B and C as well, but I think it's safe to say that this question might be out of scope. Nonetheless, the answer is E Cheers, Brent _________________ Brent Hanneson – Creator of GMATPrepNow.com Use my video course along with Sign up for free Question of the Day emails And check out all of these free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months! ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15386 messages Followed by: 1872 members Upvotes: 13060 GMAT Score: 790 knight247 wrote: If x>0, what is the least possible value of (x)+(4/x)? (A)0 (B)1 (C)2 (D)3 (E)4 OA is E I received a PM asking me to comment. Another approach: Let y = the least possible value. x + 4/x = y. x² + 4 = yx x² - yx + 4 = 0. The discriminant of a quadratic with equation ax²+bx+c=0 is b²-4ac. For a quadratic to have one or more real solutions, b²-4ac ≥ 0. In the quadratic above, a=1, b=(-y), and c=4. Thus: (-y)² - 4(1)(4) ≳ 0. y² ≳ 16. Of the answer choices, only E offers a viable value for y: 4² ≳ 16 16 ≳ 16. The correct answer is E. _________________ Mitch Hunt Private Tutor for the GMAT and GRE GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Student Review #1 Student Review #2 Student Review #3 Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. Legendary Member Joined 15 Apr 2011 Posted: 1085 messages Followed by: 21 members Upvotes: 158 knight247 wrote: If x>0, what is the least possible value of (x)+(4/x)? (A)0 (B)1 (C)2 (D)3 (E)4 OA is E (x^2+4)/x >=1 by supplying choice B) as 0 isn't possible here (all values are +ve) since x>0, x^2+4>=x and x^2-x+4>=0 x(1,2)=[1+-Sqrt(1-16)]/2 -> Reject as Discriminant is negative. Supply choice E) to have non-negative Discriminant Correct answer e _________________ Success doesn't come overnight! Master | Next Rank: 500 Posts Joined 25 Jan 2010 Posted: 406 messages Followed by: 4 members Upvotes: 23 Test Date: March 14, 2014 GMAT Score: 740 Calculus rocks! I know that we're not expected to know how to find a derivative, but it can really help! Brent@GMATPrepNow wrote: knight247 wrote: If x>0, what is the least possible value of (x)+(4/x)? (A)0 (B)1 (C)2 (D)3 (E)4 OA is E If this were something other than the GMAT, I'd use calculus to solve the question (i.e., find the derivative of x + 4/x and locate the value of x such that the slope = 0) But given that it's a GMAT question, we'll use some number sense. First, if x>0, we know that 4/x>0 This means that x + (4/x) > 0 So, we can already rule out A Now let's try a few values of x. If x=1 then (x)+(4/x)= 5 If x=2 then (x)+(4/x)= 4 If x=3 then (x)+(4/x)= 4 1/3 If x=4 then (x)+(4/x)= 5 We don't need to check any values of x greater than x=4 since these values will make the value of (x)+(4/x) even bigger. At this point, the question becomes, "Are there any values of x such that (x)+(4/x) is less than 4 (if x>0)?" For example, perhaps there's a value of x between 1 and 2 that yields an even smaller value of (x)+(4/x). The answer to the question is no, but it's hard to prove unless we use some calculus or we know how the graph of y = (x)+(4/x) looks. Both of these, however, are beyond the scope of the GMAT. At this point, I'd look at my previous results and hope that the answer is E But to be more precise, we could check each answer choice. D) is there a value of x such that (x)+(4/x) = 3? To solve this, we'll multiply both sides by x to get x^2 + 4 = 3x If we rewrite this as x^2 - 3x + 4 = 0 we can see that this equation has no solution. To prove that this equation has no solution, we'll need to use the quadratic formula Aside: I have never seen an official GMAT question that required the quadratic formula, so this next part may be out of scope. The quadratic formula says that, if ax^2 + bx + c = 0, then x = [-b + sqrt(b^2 - 4ac)] / 2a For this question, we need only focus on this part: sqrt(b^2 - 4ac) In the equation x^2 - 3x + 4 = 0, a=1, b=-3 and c=4 So, we get: sqrt(b^2 - 4ac) = sqrt((-3)^2 - 4(1)(4)) = sqrt(-7) Since we cannot evaluate sqrt(-7), we can conclude that x^2 - 3x + 4 = 0 has no solution. This means we can eliminate answer choice D. We can use similar logic to eliminate B and C as well, but I think it's safe to say that this question might be out of scope. Nonetheless, the answer is E Cheers, Brent _________________ I'm really old, but I'll never be too old to become more educated. Master | Next Rank: 500 Posts Joined 11 Jun 2011 Posted: 370 messages Followed by: 2 members Upvotes: 27 Test Date: Late November Target GMAT Score: 700+ I have a very basic way to solve this. 0 is straight away out as explained by Brent above. now to find least possible value of x + 4/x lets equate it to each answer choice. So, x + 4/x = 1 ; x^2 + 4 = x ; x^2 - x + 4 =0 _____ (1) similarly, equation with 2, 3 and 4 you get, x^2 -2x + 4 = 0_____(2) , x^2 -3x + 4 = 0_____(3) , x^2 -4x + 4 = 0_____(4) . As x^2 & 4 is common in all the 4 equations above the deciding factor is the value of the middle term . As x>0 its common sense that equation 4 will yield the least value. Hence, E. Legendary Member Joined 09 Nov 2010 Posted: 934 messages Followed by: 14 members Upvotes: 63 Test Date: N.A Target GMAT Score: 750 Thank you all the guyzzz for a wonderful explanation... _________________ IT IS TIME TO BEAT THE GMAT LEARNING, APPLICATION AND TIMING IS THE FACT OF GMAT AND LIFE AS WELL... KEEP PLAYING!!! Whenever you feel that my post really helped you to learn something new, please press on the 'THANK' button. • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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