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If ax^2 + bx^3 = 5, where a and b are non-zero numbers, what

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If ax^2 + bx^3 = 5, where a and b are non-zero numbers, what  [#permalink]

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If ax^2 + bx^3 = 5, where a and b are non-zero numbers, what is the value of a + b?

(1) ax^2 = a
(2) bx^3 = b

As per the 800score, it is .

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Originally posted by atalpanditgmat on 14 Jun 2013, 23:57.
Last edited by Bunuel on 19 Jun 2013, 13:39, edited 3 times in total.
Edited the OA.
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Re: If ax² + bx³ = 5, where a and b are non-zero numbers, what i  [#permalink]

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New post 15 Jun 2013, 00:19
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The correct answer is neither C nor D. Please check OA.

If ax^2 + bx^3 = 5, where a and b are non-zero numbers, what is the value of a + b?

(1) ax^2 = a --> since \(a\) is non-zero reduce by it: \(x^2 = 1\) --> \(x = 1\) or \(x = -1\). If \(x = 1\), then \(a + b= 5\) but if \(x = -1\), then \(a - b = 5\), from which we cannot get the value of \(a+b\). Not sufficient.

(2) bx^3 = b --> since \(b\) is non-zero reduce by it: \(x^3 = 1\) --> \(x = 1\) --> \(ax^2 + bx^3 = 5\) becomes \(a + b= 5\). Sufficient.

Answer: B.
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Re: If ax^2 + bx^3 = 5, where a and b are non-zero numbers, what  [#permalink]

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New post 19 Jun 2013, 12:04
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I arrived at B as well, atalpanditgmat can you please correct the OA
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Re: If ax^2 + bx^3 = 5, where a and b are non-zero numbers, what  [#permalink]

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New post 20 Jun 2013, 00:40
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Re: If ax^2 + bx^3 = 5, where a and b are non-zero numbers, what  [#permalink]

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New post 05 Sep 2015, 05:48
Bunuel wrote:
bugzor wrote:
I arrived at B as well, atalpanditgmat can you please correct the OA


OA edited. Thank you.


Hi,

From Statement 1 , a + b = 5 is obtained right. Why is it insufficient then? Pls help.
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If ax^2 + bx^3 = 5, where a and b are non-zero numbers, what  [#permalink]

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New post 05 Sep 2015, 21:56
Forget conventional ways of solving math questions. In DS, Variable approach is

the easiest and quickest way to find the answer without actually solving the

problem. Remember equal number of variables and equations ensures a solution.


If ax^2 + bx^3 = 5, where a and b are non-zero numbers, what is the value of a + b?

(1) ax^2 = a
(2) bx^3 = b

Transforming the original condition and the question we have 3 variables (a,b,x) and 1 equation (ax^2 + bx^3 = 5). Since we need to match the number of variables and equations,we need 2 more, therefore C is likely the answer. Using both 1) & 2) together, ax^2 + bx^3 = 5--> a+b=5 thus the answer is C. However, this is a 'trivial' case and thus is not our answer. Therefore using common mistake type 4(A),
1) ax^2=a--> x=-1,1. Substituting x=-1 to ax^2+bx^3=5 we have a-b=5 thus a=6, b=1 or a=7, b=2. Our answer is a+b=7,9..etc which is not unique and therefore not sufficient.
2) bx^3=b --> b=1, thus substituting it inside ax^2 + bx^3 = 5 gives us a+b=5. the answer is unique, therefore the answer is B.
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Re: If ax^2 + bx^3 = 5, where a and b are non-zero numbers, what  [#permalink]

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New post 06 Sep 2015, 03:17
deepthij wrote:
Bunuel wrote:
bugzor wrote:
I arrived at B as well, atalpanditgmat can you please correct the OA


OA edited. Thank you.


Hi,

From Statement 1 , a + b = 5 is obtained right. Why is it insufficient then? Pls help.


From (1) we have that IF x = 1, then a + b = 5, but IF x = -1, then a - b = 5. Now, if x = -1, then from a - b = 5 we cannot say whether a + b = 5.
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Re: If ax^2 + bx^3 = 5, where a and b are non-zero numbers, what  [#permalink]

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