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

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Math Revolution GMAT Instructor
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Which of the following is the closest to 11*1020–9*1010? [#permalink]

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23 Aug 2017, 01:24
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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. $$10^{21}$$
[Reveal] Spoiler: OA

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

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23 Aug 2017, 02:34
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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 $$= 10^{10}$$

$$(10^{11})(10^{10})$$

$$10^{(11+10)}$$ $$= 10^{21}$$

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

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23 Aug 2017, 05:39
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)
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Which of the following is the closest to 11*1020–9*1010? [#permalink]

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23 Aug 2017, 19:26
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.
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Re: Which of the following is the closest to 11*1020–9*1010? [#permalink]

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25 Aug 2017, 01:13
=> $$9*10^{10}$$ 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
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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, 09:01
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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

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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, 09:04
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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, 17:21
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, 17:21
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