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# What is the value of 11^x-11^(x+2), where x is the largest integer

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

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25 Aug 2011, 13:34
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What is the value of $$11^x-11^{(x+2)}$$, where x is the largest integer such that $$11^x$$ is a factor of 30,030?

A. -1331
B. -1320
C. -121
D. -120
E. -1
[Reveal] Spoiler: OA

Last edited by Bunuel on 04 Oct 2017, 04:29, edited 3 times in total.
EDITED THE QUESTION.

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

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12 Jul 2012, 01:55
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The question should read:

What is the value of $$11^x-11^{(x+2)}$$, where x is the largest integer such that $$11^x$$ is a factor of 30,030?

A. -1331
B. -1320
C. -121
D. -120
E. -1

Given that $$11^x$$ is a factor of $$30,030=2*3*5*7*11*13$$. Since $$x$$ is an integer then $$x=1$$.

$$11^x-11^{x+2}=11-11^3=11(1-11^2)=-11*120=-1320$$.

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

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13 Jul 2012, 09:32
11^x - 11^(x+2 ) = 11^x(1-121)

=> 11^x (-120)

given 11^x is a factor of 30030.

the only option which satisfies is -1320 (11 * -120 =-1320)

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

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14 Jul 2012, 00:53
how did we infer that x=1?

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

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14 Jul 2012, 03:32
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pavanpuneet wrote:
how did we infer that x=1?

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 integer [#permalink]

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01 Oct 2012, 06:21
We have 11 ^ x - 11 ^x+2

Simplifying : 11 ^ x - 11^x * 11^2

Taking 11^x as common we get : 11^x (1 - 11^2)

--> 11^x * -120

The question asks us to find the max. value for x so that 11^x is a factor of 30030

Prime Factors of 30030 are 5 x 3 x 2 x 11 x 7 x 13..

Because 11 appears only once , therefore the maximum value that x can have is 1 ....

Using the value of x as 1 and adding it the equation we simplified we get

11 x -120 = - 1320 (B)
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Re: What is the value of 11^x-11^(x+2), where x is the largest integer [#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 integer [#permalink]

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10 Dec 2012, 06:56
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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.

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

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10 Dec 2012, 07:21
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.

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.

Hope it's clear.
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Re: What is the value of 11^x-11^(x+2), where x is the largest integer [#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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Re: What is the value of 11^x-11^(x+2), where x is the largest integer [#permalink]

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27 Feb 2014, 20:31
30,030 has 11 as a factor
So largest value of x possible = 1

Just place x = 1 in the equation

11 - 1331 = -1320 = Answer = B
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Re: What is the value of 11^x-11^(x+2), where x is the largest integer [#permalink]

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09 Aug 2016, 19:12
Bunuel wrote:
mcdude123 wrote:
What is the value of 11^x – 11^(x+2), where x is the largest integer such that 11^x is a factor of 30,030?

A. –1,331
B. –1,320
C. –121
D. –120
E. –1

What is your fastest methodology to solve this problem

[Reveal] Spoiler:
B

Merging topics. Please refer to the discussion on previous pages.

In 30030 there's only one 11, so x = 1.

11^x - 11^(x+2) = 11^x(1-11^2) = -120. 11^x

With x = 1 --> -120.11^1 = -1320 --> B

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

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11 Aug 2016, 00:06
What is the value of 11^x-11^(x+2), where x is the largest integer such that 11^x is a factor of 30,030?

A. -1331
B. -1320
C. -121
D. -120
E. -1

Looks to be simple enough

11^x(1 - 11^2) = 11^x(1 - 121) = -120*11^x

now 11^x is a factor of 30,030 -------> is it divisible by 11
if not divisible by 11 then largest 11^0 = 1 will always be a factor of 30,030

Anywaz 30,030 is divisble by 11 (30030/11 = 2730)

Now the product of -120*11^x will be -ve and will end with a 0. Only answer choices B and D fit

D) If 11 was not divisible by 30030 then this could be it but since it is divisible by 11, it must be something higher (in this a lower value since its -ve)

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

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Re: What is the value of 11^x-11^(x+2), where x is the largest integer   [#permalink] 26 Aug 2017, 02:24
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