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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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Math Revolution GMAT Instructor
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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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19 Jun 2017, 01:14
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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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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" ##### Most Helpful Community Reply Director Joined: 04 Dec 2015 Posts: 722 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] ### Show Tags 19 Jun 2017, 02:10 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 GMAT Club Legend Joined: 11 Sep 2015 Posts: 4345 Location: Canada Re: If x/100+x/1,000+x/10,000+x/100,000=111, what is the approximation of [#permalink] ### Show Tags 19 Jun 2017, 04:51 2 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 Answer: RELATED VIDEO _________________ Test confidently with gmatprepnow.com Retired Moderator Joined: 19 Mar 2014 Posts: 912 Location: India Concentration: Finance, Entrepreneurship GPA: 3.5 Re: If x/100+x/1,000+x/10,000+x/100,000=111, what is the approximation of [#permalink] ### Show Tags 24 Jun 2017, 13:38 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 $$(\frac{x}{100}) (1) = 111$$ $$x = 111 * 100$$ $$x = 111,100$$ Hence, Answer is A _________________ "Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent." Best AWA Template: https://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html#p470475 Manager 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] ### Show Tags 19 Jun 2017, 01:21 Only A fits the bills. Others are too big. Sent from my Moto G (5) Plus using GMAT Club Forum mobile app Senior Manager Joined: 28 May 2017 Posts: 276 Concentration: Finance, General Management If x/100+x/1,000+x/10,000+x/100,000=111, what is the approximation of [#permalink] ### Show Tags 19 Jun 2017, 01:58 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 Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8590 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If x/100+x/1,000+x/10,000+x/100,000=111, what is the approximation of [#permalink] ### Show Tags 21 Jun 2017, 00:04 ==> Since it is approximation, you get _. Then, only x/100=111 is left, and thus you get x=11,100. The answer is A. _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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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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07 Dec 2019, 15:53
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

If x/100+x/1,000+x/10,000+x/100,000=111, what is the approximation of   [#permalink] 07 Dec 2019, 15:53
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