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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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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, 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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"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" 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, 02:21 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: 287 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, 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 _________________ If you like the post, show appreciation by pressing Kudos button Director Joined: 04 Dec 2015 Posts: 701 Location: India Concentration: Technology, Strategy Schools: ISB '19, IIMA , IIMB, XLRI 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, 03:10 1 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)... CEO Joined: 12 Sep 2015 Posts: 3031 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, 05:51 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 _________________ Brent Hanneson – GMATPrepNow.com Sign up for our free Question of the Day emails Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6406 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, 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. _________________ 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$99 for 3 month Online Course"
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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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24 Jun 2017, 14:38
1
$$\frac{x}{100}+\frac{x}{1,000}+\frac{x}{10,000}+\frac{x}{100,000}=111$$

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

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

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

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

$$x = 111 * 100$$

$$x = 111,100$$

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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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26 Jul 2018, 11:47
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