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If x/100+x/1,000+x/10,000+x/100,000=111, what is the approximation of

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New post 19 Jun 2017, 02:14
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If \(\frac{x}{100}+\frac{x}{1,000}+\frac{x}{10,000}+\frac{x}{100,000}=111\), what is the approximation of x?

A. 11,100
B. 111,000
C. 1,111,000
D. 11,111,000
E. 111,111,000

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Re: If x/100+x/1,000+x/10,000+x/100,000=111, what is the approximation of  [#permalink]

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New post 19 Jun 2017, 03:10
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MathRevolution wrote:
If \(\frac{x}{100}+\frac{x}{1,000}+\frac{x}{10,000}+\frac{x}{100,000}=111\), what is the approximation of x?

A. 11,100
B. 111,000
C. 1,111,000
D. 11,111,000
E. 111,111,000


Method 1: \(\frac{x}{100}+\frac{x}{1,000}+\frac{x}{10,000}+\frac{x}{100,000}=111\)

\(\frac{x}{100}(1+\frac{1}{10}+\frac{1}{100}+\frac{1}{1000})=111\)

\(\frac{x}{100} (1 + 0.1 + 0.01 + 0.001) = 111\)

\(\frac{x}{100} * 1.111 = Approximately = \frac{x}{100} * 1\)

\(\frac{x}{100} * 1 = 111\)

\(x = 111 * 100 = 11,100.\) Answer (A)...

Method 2: \(\frac{x}{1000}\), \(\frac{x}{10,000}\) and \(\frac{x}{100,000}\) are very small values compared to \(\frac{x}{100}\).

Hence we can ignore those fractions and equate only \(\frac{x}{100} = 111 ==> x = 11,100\). Answer (A)...
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Re: If x/100+x/1,000+x/10,000+x/100,000=111, what is the approximation of  [#permalink]

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New post 19 Jun 2017, 02:21
Only A fits the bills. Others are too big.

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If x/100+x/1,000+x/10,000+x/100,000=111, what is the approximation of  [#permalink]

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New post 19 Jun 2017, 02:58
MathRevolution wrote:
If \(\frac{x}{100}+\frac{x}{1,000}+\frac{x}{10,000}+\frac{x}{100,000}=111\), what is the approximation of x?

A. 11,100
B. 111,000
C. 1,111,000
D. 11,111,000
E. 111,111,000


\(\frac{x}{100}+\frac{x}{1,000}+\frac{x}{10,000}+\frac{x}{100,000}=111\)
\(x\frac{(1000+100+10+10)}{100000} = 111\)
\(x\frac{(1111)}{100000} = 111\)
\(x\frac{(10.009)}{100000} = 1\)
\(x\frac{(1)}{10000} = 1\)
Hence Answer A
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Re: If x/100+x/1,000+x/10,000+x/100,000=111, what is the approximation of  [#permalink]

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New post 19 Jun 2017, 05:51
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MathRevolution wrote:
If \(\frac{x}{100}+\frac{x}{1,000}+\frac{x}{10,000}+\frac{x}{100,000}=111\), what is the approximation of x?

A. 11,100
B. 111,000
C. 1,111,000
D. 11,111,000
E. 111,111,000


Another approach is to test the answer choices

A) 11,100
We get: 11,100/100 + 11,100/1000 + 11,100/10000 + 11,100/100000 = 111 + 11.1 +....STOP
Our sum is ALREADY greater than 111, and since the subsequent values in the sum are all positive, the sum will just get bigger and bigger
So, 11,100 is already a little too big

Since the other 4 answer choices are even bigger than 11,100, we can see that A is the best answer

Answer:

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Re: If x/100+x/1,000+x/10,000+x/100,000=111, what is the approximation of  [#permalink]

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New post 21 Jun 2017, 01:04
==> Since it is approximation, you get _. Then, only x/100=111 is left, and thus you get x=11,100.

The answer is A.
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Re: If x/100+x/1,000+x/10,000+x/100,000=111, what is the approximation of  [#permalink]

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New post 24 Jun 2017, 14:38
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\(\frac{x}{100}+\frac{x}{1,000}+\frac{x}{10,000}+\frac{x}{100,000}=111\)

\((\frac{x}{100}) ( 1+ \frac{1}{10} + \frac{1}{100} + \frac{1}{1000}) = 111\)

\((\frac{x}{100}) ( 1 + 0.1 + 0.01 + 0.001) = 111\)

\((\frac{x}{100}) (1.11) = 111\) OR

\((\frac{x}{100}) (1) = 111\)

\(x = 111 * 100\)

\(x = 111,100\)

Hence, Answer is A
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If x/100+x/1,000+x/10,000+x/100,000=111, what is the approximation of  [#permalink]

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New post 07 Dec 2019, 16:53
MathRevolution wrote:
If \(\frac{x}{100}+\frac{x}{1,000}+\frac{x}{10,000}+\frac{x}{100,000}=111\), what is the approximation of x?

A. 11,100
B. 111,000
C. 1,111,000
D. 11,111,000
E. 111,111,000


10^3 x + 10^2 x + 10 x + x/10^5 = 111
or, x (1000 + 100 + 10 + 1) / 10^5 = 111
or, 1111 x = 111 * 10^5
or, x ~ 1/10 * 100,000
so, x ~ 10,000

A is the answer.
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If x/100+x/1,000+x/10,000+x/100,000=111, what is the approximation of   [#permalink] 07 Dec 2019, 16:53
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