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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 ## The sum of two numbers is 1 and their product is -1. What is tagged by: Max@Math Revolution ##### This topic has 3 expert replies and 1 member reply ### GMAT/MBA Expert ## The sum of two numbers is 1 and their product is -1. What is ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult [GMAT math practice question] The sum of two numbers is 1 and their product is -1. What is the sum of their cubes? A. 1 B. 2 C. 3 D. 4 E. 5 _________________ Math Revolution Finish GMAT Quant Section with 10 minutes to spare. The one-and-only Worldâ€™s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. Only$149 for 3 month Online Course
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Call the numbers X and Y.

So X+Y=1 and XY=-1 given the problem statement.

Let's square X+Y = X^2+2XY+Y^2 = 1.

Since XY=-1, we can substitute: X^2+Y^2-2 = 1. So,

X^2+Y^2 = 3.

Multiplying X^2+Y^2 by X+Y = (X+Y)(X^2+Y^2) = X^3 + Y^3 +XY^2 + YX^2 = (3)(1)

Factor an XY from the last two terms: X^3+Y^3 + XY(Y+X) = 3

Substitute XY=-1 and X+Y=1 into the above yields

X^3+Y^3 -(1)(1) = 3

therefore X^3+Y^3 = 4,D

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Max@Math Revolution wrote:
[GMAT math practice question]

The sum of two numbers is 1 and their product is -1. What is the sum of their cubes?

A. 1
B. 2
C. 3
D. 4
E. 5
xÂ³ + yÂ³ = (x+y)(xÂ²+yÂ²-xy)

Since x+y=1, we get:
(x+y)Â² = 1Â²
xÂ² + yÂ² + 2xy = 1

Substituting xy=-1 into xÂ² + yÂ² + 2xy = 1, we get:
xÂ² + yÂ² + 2(-1) = 1
xÂ² + yÂ² = 3

Substituting x+y=1, xÂ²+yÂ²=3 and xy=-1 into xÂ³ + yÂ³ = (x+y)(xÂ²+yÂ²-xy), we get:
xÂ³ + yÂ³ = (1)(3-(-1)) = (1)(4) = 4

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### GMAT/MBA Expert

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Let the numbers be x and y. Then x + y = 1 and xy = -1.
Since (x+y)^2 = x^2 + 2xy + y^2 = x^2 + y^2 - 2, we have x^2 + y^2 = 3,
and x^3 + y^3 = (x+y)(x^2-xy+y^2) = 1*(x^2+ 1 + y^2) = x^2+y^2+1 = 4.

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Only $149 for 3 month Online Course Free Resources-30 day online access & Diagnostic Test Unlimited Access to over 120 free video lessons-try it yourself Email to : info@mathrevolution.com ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2950 messages Followed by: 19 members Upvotes: 43 Max@Math Revolution wrote: [GMAT math practice question] The sum of two numbers is 1 and their product is -1. What is the sum of their cubes? A. 1 B. 2 C. 3 D. 4 E. 5 We can let a and b be the two numbers. So we have a + b = 1 and ab = -1 and we need to determine the value of a^3 + b^3. Notice that (a + b)^3 = a^3 + 3a^2*b + 3a*b^2 + b^3. So we have: 1^3 = a^3 + b^3 + 3a^2*b + 3a*b^2 1 = a^3 + b^3 + 3ab(a + b) 1 = a^3 + b^3 + 3(-1)(1) 1 = a^3 + b^3 - 3 4 = a^3 + b^3 Alternate Solution: Letting a and b denote the numbers, we can use the identity a^3 + b^3 = (a + b)(a^2 - ab + b^2). We already know a + b = 1 and ab = -1, we need to find a^2 + b^2. Notice that (a + b)^2 = a^2 + 2ab + b^2. Since a + b = 1 and ab = -1, we have 1^2 = a^2 + 2(-1) + b^2 a^2 + b^2 = 1 + 2 = 3. Now, a^3 + b^3 = (a + b)(a^2 - ab + b^2) = (1)(a^2 + b^2 - ab) = 3 -(-1) = 3 + 1 = 4. Answer: D _________________ Scott Woodbury-Stewart Founder and CEO scott@targettestprep.com See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews • Award-winning private GMAT tutoring Register now and save up to$200

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