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# Which of the following is the closest to 11*1020–9*1010?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 9018
GMAT 1: 760 Q51 V42
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Which of the following is the closest to 11*1020–9*1010?  [#permalink]

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23 Aug 2017, 00:24
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35% (medium)

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63% (01:24) correct 37% (01:29) wrong based on 151 sessions

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Which of the following is the closest to $$11*10^{20}–9*10^{10}$$?

A. $$10^2$$
B. $$10^7$$
C. $$10^{10}$$
D. $$10^{20}$$
E. $$10^{21}$$

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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" Director Joined: 04 Dec 2015 Posts: 725 Location: India Concentration: Technology, Strategy WE: Information Technology (Consulting) Which of the following is the closest to 11*1020–9*1010? [#permalink] ### Show Tags 23 Aug 2017, 01:34 1 MathRevolution wrote: Which of the following is the closest to $$11*10^{20}–9*10^{10}$$? A. $$10^2$$ B. $$10^7$$ C. $$10^{10}$$ D. $$10^{20}$$ E. $$10^{21}$$ $$11*10^{20}–9*10^{10}$$ We can use approximate value. Hence we can use $$10$$ in place of $$11$$ and $$10$$ in place of $$9$$. $$(10*10^{20}) – (10*10^{10})$$ $$10^{(20+1)}–10^{(10+1)}$$ $$10^{21}–10^{11}$$ $$10^{11}(10^{10}–1)$$ $$1$$ is very small value compared to $$10^{10}$$. Hence $$1$$ can be ignored. Therefore $$(10^{10}–1) =$$ approximately $$= 10^{10}$$ $$(10^{11})(10^{10})$$ $$10^{(11+10)}$$ $$= 10^{21}$$ Answer (E)... _________________ Please Press "+1 Kudos" to appreciate. Senior PS Moderator Joined: 26 Feb 2016 Posts: 3253 Location: India GPA: 3.12 Which of the following is the closest to 11*1020–9*1010? [#permalink] ### Show Tags 23 Aug 2017, 04:39 We have been asked to find the value of the expression $$11*10^{20}–9*10^{10}$$ $$11*10^{20}–9*10^{10}$$ = $$11*10^{10}*10^{10} – 9*10^{10}$$ = $$10^{10}(11*10^{10} – 9)$$ Since we need an approximate value and the overall expression has extremely large numbers, we can assume both 11 and 9 to be equal to 10 The expression now becomes $$10^{10}(10*10^{10} – 10) = 10^{10}*10^1(10^{10} – 1) = 10^{10+1}(10^{10} – 1)$$ = $$10^{11}(10^{10})$$ Since a difference of 1 does not influence the value of the expression to that extent, the value must be $$10^{21}$$ approximately (Option E) _________________ You've got what it takes, but it will take everything you've got Manager Joined: 27 Dec 2016 Posts: 218 Concentration: Marketing, Social Entrepreneurship GPA: 3.65 WE: Marketing (Education) Which of the following is the closest to 11*1020–9*1010? [#permalink] ### Show Tags 23 Aug 2017, 18:26 MathRevolution wrote: Which of the following is the closest to $$11*10^{20}–9*10^{10}$$? A. $$10^2$$ B. $$10^7$$ C. $$10^{10}$$ D. $$10^{20}$$ E. $$10^{21}$$ 1. Factoring $$10^{10}$$ out = $$10^{10} (11*10^{10} - 9)$$ 2. Since we are asked about approximation, so we can use our estimation. 3. 11 and 10 is closest to 10, so I can change them to 10 --> $$10^{10} (10^1*10^{10} - 10^1)$$ --> $$10^{10} (10^{11} - 10^1)$$ 4. Difference between $$10^{11}$$ and $$10^{10}$$ is so HUGE, so can we can IGNORED this subtraction by $$10^1$$. 5. Therefore, $$10^{10} * 10^{11} = 10^{21}$$. E. _________________ There's an app for that - Steve Jobs. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 9018 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Which of the following is the closest to 11*1020–9*1010? [#permalink] ### Show Tags 25 Aug 2017, 00:13 => $$9*10^{10}$$ is a relatively small number compared with $$11*10^{20}$$. $$11*10^{20}–9*10^{10}$$ is approximate to $$11*10^{20}$$, which is similar to $$10^{21}$$. Ans: E _________________ 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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Manager
Joined: 30 Dec 2016
Posts: 224
GMAT 1: 650 Q42 V37
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Re: Which of the following is the closest to 11*1020–9*1010?  [#permalink]

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28 Aug 2017, 08:01
1
i did it this way.

Factor out 10^20 .

10^20 ( 11 - 9 * 10^-10 )
Now,
10^20 ( 11 - 0.000000009) we know from here that ( 11 - 0.000000009 ) will be 10.something .

So,
10^20 * 10.something = 10^21 .

Regards

SandySilva
Manager
Joined: 02 Nov 2015
Posts: 160
GMAT 1: 640 Q49 V29
Re: Which of the following is the closest to 11*1020–9*1010?  [#permalink]

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28 Aug 2017, 08:04
1
sandysilva wrote:
i did it this way.

Factor out 10^20 .

10^20 ( 11 - 9 * 10^-10 )
Now,
10^20 ( 11 - 0.000000009) we know from here that ( 11 - 0.000000009 ) will be 10.something .

So,
10^20 * 10.something = 10^21 .

Regards

SandySilva

Great one !!!!

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Re: Which of the following is the closest to 11*1020–9*1010?  [#permalink]

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29 Aug 2017, 16:21
MathRevolution wrote:
Which of the following is the closest to $$11*10^{20}–9*10^{10}$$?

A. $$10^2$$
B. $$10^7$$
C. $$10^{10}$$
D. $$10^{20}$$
E. $$10^{21}$$

Since 9 x 10^10 is much smaller than 11 x 10^20, magnitude-wise, subtracting it from 11 x 10^20 would still be about 11 x 10^20. Since 11 is close to 10, 11 x 10^20 is approximately 10 x 10^20, magnitude-wise, and we have:

10 x 10^20 = 10^21

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Re: Which of the following is the closest to 11*1020–9*1010?   [#permalink] 29 Aug 2017, 16:21