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I think there is some problem with either the values in the ques stem or the ans choices. something is wrong. What is the source of this ques?
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Q. What is the value of 11x-11(x^+2) where x is the largest integer such that 11x is a factor of 30030?

a) -1331 b) -1320 c) -121 d) -120 e) -1

The given expression is \(11x - 11x^2\) = \(11x (1 - x)\)

11x needs to be factor of 30030 and x needs to be the largest integer possible. This means 11x needs to be the largest factor possible. The largest factor of a number is the number itself. The largest factor of 30030 is 30030 = (11 * 2730) x must be 2730

The value of 11x(1-x) = 30030*(-2729) There is definitely something wrong in the expression, either in the book or in this particular reproduction.
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We have that \(30,030=2*3*5*7*11*13\) is divisible by \(11^x\) (where \(x\) is an integer). Now, ask yourself what can be the largest integer value of \(x\). Could it be 2 or more?
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Re: What is the value of 11^x-11^(x+2) where x is the largest [#permalink]

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05 Nov 2012, 04:53

Here 30030/11 gives 2730. This cannot be divided further and hence 11 can have the power of only 1. substituting in the given equation gives the ans -1320.
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Re: What is the value of 11^x-11^(x+2) where x is the largest [#permalink]

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10 Dec 2012, 06:56

Given x is the largest integer 30030

Find the Value of 11^x - 11^(x + 2)

Simplify 11^x - 11^(x + 2) we get (11^x)(1-11^2) -> (11^x)(1-11)(1+11) -> (11^x)(-10)(12)

Elimination (11^x)(-10)(12) 1.From this we know that the value has to be -ve 2.The units digit must be a 0.

Hence eliminate options A,C,E. Now we are left with B and D

Look at the equation again (11^x)(-10)(12) -> (11^x)(-120) Now in option D we have -120 this can possible only if x is the above equation is 0. However we are told that 11^X is a factor of 30030. So x has to be greater than 0. Which eliminates the option D.

Simplify 11^x - 11^(x + 2) we get (11^x)(1-11^2) -> (11^x)(1-11)(1+11) -> (11^x)(-10)(12)

Elimination (11^x)(-10)(12) 1.From this we know that the value has to be -ve 2.The units digit must be a 0.

Hence eliminate options A,C,E. Now we are left with B and D

Look at the equation again (11^x)(-10)(12) -> (11^x)(-120) Now in option D we have -120 this can possible only if x is the above equation is 0. However we are told that 11^X is a factor of 30030. So x has to be greater than 0. Which eliminates the option D.

Answer is B

11^x would be a factor of 30,030 even if x=0, since 11^0=1 and 1 is a factor of every integer. The point is that we are looking for the largest possible value of integer x such that 11^x is a factor of 30,030, which is for x=1.

Re: What is the value of 11^x-11^(x+2) where x is the largest [#permalink]

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10 Dec 2012, 08:09

Agree. So just to make sure we can see if 30030 is divisible by 11. If it is then we really dont care by how much because we know that x is not 0 now. So the only option we are left with is now B.

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