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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
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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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Question Stats: 71% (01:53) correct 29% (02:05) wrong based on 194 sessions

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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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Director  V
Joined: 04 Dec 2015
Posts: 730
Location: India
Concentration: Technology, Strategy
WE: Information Technology (Consulting)
Re: If x/100+x/1,000+x/10,000+x/100,000=111, what is the approximation of  [#permalink]

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3
2
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)...
##### General Discussion
Manager  S
Joined: 30 Mar 2017
Posts: 67
Re: If x/100+x/1,000+x/10,000+x/100,000=111, what is the approximation of  [#permalink]

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Only A fits the bills. Others are too big.

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Senior Manager  G
Joined: 28 May 2017
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Concentration: Finance, General Management
If x/100+x/1,000+x/10,000+x/100,000=111, what is the approximation of  [#permalink]

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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

$$\frac{x}{100}+\frac{x}{1,000}+\frac{x}{10,000}+\frac{x}{100,000}=111$$
$$x\frac{(1000+100+10+10)}{100000} = 111$$
$$x\frac{(1111)}{100000} = 111$$
$$x\frac{(10.009)}{100000} = 1$$
$$x\frac{(1)}{10000} = 1$$
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4221
Re: If x/100+x/1,000+x/10,000+x/100,000=111, what is the approximation of  [#permalink]

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Top Contributor
1
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

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Math Revolution GMAT Instructor V
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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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==> Since it is approximation, you get _. Then, only x/100=111 is left, and thus you get x=11,100.

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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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2
$$\frac{x}{100}+\frac{x}{1,000}+\frac{x}{10,000}+\frac{x}{100,000}=111$$

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

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

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

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

$$x = 111 * 100$$

$$x = 111,100$$

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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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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 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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