What is the value of 11^x-11^(x+2) where x is the largest : GMAT Problem Solving (PS)
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# What is the value of 11^x-11^(x+2) where x is the largest

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

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25 Aug 2011, 12:34
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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 12 Jul 2012, 00:51, edited 2 times in total.
EDITED THE QUESTION.
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25 Aug 2011, 12:46
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siddharthvaid wrote:
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

By 11(x^+2) do you mean 11* x*x or 11(x*x + 2) ?
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25 Aug 2011, 16:10
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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25 Aug 2011, 21:06
i saw this questions on the kaplan problem set and am confused as well. am beginning to think that kaplan's questions are diminishing in quality.

so first step, I tried to solve for x. x=largest integer so that 11x is a factor of 30,030.

See if 30,030 is divisible by 11. IT IS! 11x2730=30,030.

Therefore, largest integer of x = 2730. since, 30,030 is a factor of itself.

11x-11x^2=11(2730)-11(2730^2) = some INCREDIBLY HUGE NUMBER... uhh. something is wrong here kaplan.
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25 Aug 2011, 21:10
Might just be an odd one
Gr8 . one less question to worry about
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25 Aug 2011, 22:53
siddharthvaid wrote:
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

siddharthvaid:
 ! Please post PS questions in the PS sub-forum: gmat-problem-solving-ps-140/Please post DS questions in the DS sub-forum: gmat-data-sufficiency-ds-141/No posting of PS/DS questions is allowed in the main Math forum.

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31 Aug 2011, 21:51
siddharthvaid wrote:
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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11 Jul 2012, 19:53
Correct expression is 11^x - 11^(x+2).

x = 1 => answer is –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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12 Jul 2012, 00:55
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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

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 [#permalink]

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13 Jul 2012, 08:32
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 [#permalink]

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13 Jul 2012, 23:53
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 [#permalink]

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14 Jul 2012, 02:32
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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 [#permalink]

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14 Jul 2012, 04:24
Should Be A, I didnt read the questions fully
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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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14 Jul 2012, 04:26
asax wrote:
Should Be A, I didnt read the questions fully

OA for this question is B, not A. Check this: what-is-the-value-of-11-x-11-x-2-where-x-is-the-largest-119607.html#p1103719
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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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01 Oct 2012, 05:21
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 [#permalink]

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05 Nov 2012, 03:53
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, 05:56
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.

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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, 06:21
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 [#permalink]

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10 Dec 2012, 07:09
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 [#permalink]

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27 Feb 2014, 19:31
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   [#permalink] 27 Feb 2014, 19:31

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