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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 What is the value of a^4 - b^4? tagged by: VJesus12 This topic has 1 expert reply and 1 member reply Top Member Timer 00:00 Your Answer A B C D E Global Stats Difficult What is the value of $$a^4 - b^4?$$ (1) $$a^2 - b^2 = 16$$ (2) $$a + b = 8$$ OA=C Source: GMAT Prep Legendary Member Joined 07 Sep 2017 Posted: 831 messages Followed by: 3 members Upvotes: 6 VJesus12 wrote: What is the value of $$a^4 - b^4?$$ (1) $$a^2 - b^2 = 16$$ (2) $$a + b = 8$$ OA=C Source: GMAT Prep Hi Vjesus12. Let's take a look at your question. Statement 1: Quote: (1) $$a^2 - b^2 = 16$$ Using this fact we can get that $$a^4-b^4=\left(a^2-b^2\right)\left(a^2+b^2\right)=16\cdot\left(a^2+b^2\right).$$ Since we don't know the value of the second factor, this statement is NOT SUFFICIENT. Statement 2: Quote: (2) $$a + b = 8$$ Similar to the case above, we get $$a^4-b^4=\left(a^2-b^2\right)\left(a^2+b^2\right)=\left(a+b\right)\left(a-b\right)\left(a^2+b^2\right)=8\left(a-b\right)\left(a^2+b^2\right)$$ but we can't find the value of the two remaining factors. So, this statement is NOT SUFFICIENT. Statement 1 + Statement 2: We have that $$a^2-b^2=16\ \Rightarrow\ \left(a+b\right)\left(a-b\right)=16\ \Rightarrow\ 8\left(a-b\right)=16\ \Rightarrow\ a-b=2.$$ Hence, we get the system of equations $$a+b=8$$ $$a-b=2$$ Adding them we get $$2a=10$$ which implies that $$a=5$$. Hence, $$5+b=8$$ implies that $$b=3$$. Therefore, $$a^4-b^4=5^4-3^2=544.$$ So, using both statements together is SUFFICIENT. In conclusion, the correct answer is the option _C_. I hope it is clear. GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12987 messages Followed by: 1249 members Upvotes: 5254 GMAT Score: 770 VJesus12 wrote: What is the value of $$a^4 - b^4?$$ (1) $$a^2 - b^2 = 16$$ (2) $$a + b = 8$$ OA=C Source: GMAT Prep Target question: What is the value of a⁴ - b⁴? NOTE: a⁴ - b⁴ is a difference of square, which we can factor. a⁴ - b⁴ = (a² - b²)(a² + b²) So, we can REPHRASE the target question as... REPHRASED target question: What is the value of (a² - b²)(a² + b²)? Statement 1: a² - b² = 16 Okay, so we know the value of HALF of the target expression to get (16)(a² + b²), but we still don't know the value of a² + b², so statement 1 is NOT SUFFICIENT We can also demonstrate that statement 1 is NOT SUFFICIENT by finding values of a and b that satisfy this condition. Here are two: Case a: a = 4 and b = 0, in which case (a² - b²)(a² + b²) = (16)(16) = 256 Case b: a = √17 and b = 1, in which case (a² - b²)(a² + b²) = (16)(18) = something other than 256 Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT Statement 2: a + b = 8 There are several values of a and b that satisfy this condition. Here are two: Case a: a = 8 and b = 0, in which case (a² - b²)(a² + b²) = (64)(64) = 64² Case b: a = 4 and b = 4, in which case (a² - b²)(a² + b²) = (0)(32) = 0 Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT Statements 1 and 2 combined Statement 1 says that a² - b² = 16 Since we can factor a² - b² to get (a + b)(a - b), statement 1 is actually telling us that (a + b)(a - b) = 16 Statement 2 says that a + b = 8 So, let's take (a + b)(a - b) = 16 and replace (a+b) with 8 to get: (8)(a - b) = 16 This means that (a - b) = 2 At this point, we're done. We now know that a - b = 2 AND we know that a + b = 8 Here we have 2 linear equations, which we COULD solve for a and b. Once we know the exact values of a and b, we can definitely determine the value of (a² - b²)(a² + b²) Since we can answer the REPHRASED target question with certainty, the combined statements are SUFFICIENT Answer: C Aside: If we solve the system, a - b = 2 and a + b = 8, we get a = 5 and b = 3. This means that (5² - 3²)(5² + 3²) = (16)(34) 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! • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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