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 Author: Gennadiy [ Mon Jan 24, 2011 5:12 pm ] Post subject: Re: math (test 1, question 28): algebra. ax² = ax² = 1x = 1 or x = -1If x = 1, then ax² + bx³ = a × 1² + b × 1³ = a + b = 5If x = -1, then ax² + bx³ = a × (-1)² + b × (-1)³ = a – b = 5But we don't know what a + b equals to in this case (if x = 1).Therefore statement (1) by itself is NOT sufficient.

Author:  questioner [ Mon Feb 28, 2011 2:35 pm ]
Post subject:  Re: math (test 1, question 28): algebra.

By default, all the numbers in GMAT are real. Therefore, both x = 1 and x = are valid solutions for (2). While 1 yields the right answer, does not. In conclusion, we have to use Statement 1 to make sure, that x = 1, not .

 Author: Gennadiy [ Mon Feb 28, 2011 2:44 pm ] Post subject: Re: math (test 1, question 28): algebra. The values and 1 are equal.The second statement yields x³ = 1. This equation has only one solution: x = ³√1 = 1.

 Author: questioner [ Thu Sep 01, 2011 12:55 pm ] Post subject: Re: math (test 1, question 28): algebra. In case of 1, if x is -1, then we get a – b = 5 and when x is 1, we get a + b =5. Since we get only 1 value of a + b from (1), I feel the answer to this should be D.

 Author: Gennadiy [ Thu Sep 01, 2011 1:21 pm ] Post subject: Re: math (test 1, question 28): algebra. Quote:Since we get only 1 value of a + b from (1)The situation when x is -1 does NOT give us any specific value of a + b. It gives only the value of a – b. This is NOT sufficient.For example, at least two of the possible variants are:If a = 4, b = 5, then a – b = -1, a + b = 9.If a = 5, b = 6, then a – b = -1, BUT a + b = 11.Therefore statement (1) does NOT give us a definite value of a + b.

 Author: questioner [ Tue Sep 20, 2011 5:23 pm ] Post subject: Re: math (test 1, question 28): algebra. a, b and x could be rational numbers, it is not mentioned that they are integers. Hence, the inference that x could only be 1 or -1 is wrong; e.g. x = 1/2, a = 4 and b = 32.

 Author: Gennadiy [ Tue Sep 20, 2011 5:32 pm ] Post subject: Re: math (test 1, question 28): algebra. questioner wrote:a, b and x could be rational numbers, it is not mentioned that they are integers. Hence, the inference that x could only be 1 or -1 is wrong; e.g. x = 1/2, a = 4 and b = 32.The proposed values do NOT fit in any statement:Statement (1) will transform into 4 × (1/2)² = 4. This is NOT correct.Statement (2) will transform into 32 × (1/2)³ = 32. This is NOT correct.The basic question statement does NOT specify that x is an integer, but each additional statement gives us some specific possible values of x. Statement (1) yields x = -1 and x = 1. Statement (2) yields x = 1 only.

 Author: cjuarezh [ Tue Aug 07, 2012 2:36 am ] Post subject: Re: GMAT Algebra (Data Sufficiency) I desagree with the given answer, we have:If ax² + bx³ = 5, where a and b are non-zero numbers, what is the value of a + b?(1) ax² = a(2) bx³ = bI agree that with (1) we cannot answer the question, but (2) isn't enough either.number 2 says that x³ = 1 (with b non-zero), which has 3 solutions, not 1:x³ - 1 = 0(x – 1) × (x² + x + 1)=0Either (x – 1) = 0 or (x² + x + 1) = 0. Only x – 1 = 0 gives x = 1.But the 3 solutions are:1, -1/2 + (√3 / 2) × i, -1/2 – (√3 / 2) × iThe second and third solution, when squared, don't equal 1, so we need the first statement to know that x can't take these values. Therefore, the answer is C and not B.

 Author: Gennadiy [ Wed Aug 08, 2012 1:20 pm ] Post subject: Re: GMAT Algebra (Data Sufficiency) Quote:But the 3 solutions are:1, -1/2 + (√3 / 2) × i, -1/2 – (√3 / 2) × iYour solution would be true, if x were a complex variable. But x is a real variable, not a complex one.NEVER assume in GMAT that we deal with complex numbers (variables).ALWAYS assume that a number (variable) is a real number, if nothing else is stated.

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