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What is the value of 10^8 - 6^7?

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What is the value of 10^8 - 6^7?  [#permalink]

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New post 27 Feb 2012, 08:11
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What is the value of 10^8 - 6^7?

A. 99,720,064
B. 99,720,069
C. 99,721,022
D. 99,722,055
E. 99,723,097
Intern
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Re: What is the value of 10^8 - 6^7?"  [#permalink]

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New post 27 Feb 2012, 08:18
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Answer A

As 10^n will always have last digit as 0 AND 6^n will always as last digit 6.. hence difference of such sum should always be ending with "4" and there is only on option ..
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Re: What is the value of 10^8 - 6^7?  [#permalink]

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New post 27 Feb 2012, 08:34
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Re: What is the value of 10^8 - 6^7?  [#permalink]

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New post 12 Aug 2014, 17:39
domu904 wrote:
What is the value of 10^8 - 6^7?

A. 99,720,064
B. 99,720,069
C. 99,721,022
D. 99,722,055
E. 99,723,097


\(10^8\) ends with 0; \(6^7\) ends with 6

Difference will provide 4 at the units place

Answer = A
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Re: What is the value of 10^8 - 6^7?  [#permalink]

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New post 19 Jun 2017, 09:50
domu904 wrote:
What is the value of 10^8 - 6^7?

A. 99,720,064
B. 99,720,069
C. 99,721,022
D. 99,722,055
E. 99,723,097


We can attack this question a bit differently using some properties

Rule 1

10^n power = 1 with n amount of zeros... 10^2 is 100 (2 zero) 10^5 100,000 (five zero)

so

100000000 -6^7

Rule 2

What is unit digits of 6? 6 is a special number 6^n will always have a units digit of 6 so the units digits of the answer must be 4

Thus
"A"
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Re: What is the value of 10^8 - 6^7?  [#permalink]

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New post 19 Jun 2017, 09:58
domu904 wrote:
What is the value of 10^8 - 6^7?

A. 99,720,064
B. 99,720,069
C. 99,721,022
D. 99,722,055
E. 99,723,097


\(10^8\) Will have units digit as 0
\(6^7\) Will have units digit as 6

Now, \(10^8 - 6^7\) will have units digit as \(0 - 6 = 4\)

Among the given options only (A) satisfies, so that is the answer...
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Re: What is the value of 10^8 - 6^7?  [#permalink]

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New post 06 Jul 2017, 16:40
domu904 wrote:
What is the value of 10^8 - 6^7?

A. 99,720,064
B. 99,720,069
C. 99,721,022
D. 99,722,055
E. 99,723,097


Since we know that the GMAT would not expect us to carry out the computation of the exact value of 10^8 - 6^7, we can focus on the units digits of the resulting difference.

When we raise 10 to any power, the units digit of the answer is always 0. For example, 10^2 = 100 and 10^4 = 10,000. Similarly, the units digit of 6 raised to any power is 6. For example, 6^2 = 36, 6^3 = 216, etc.
In this problem, the units digit of 10^8 will be 0 and the units digit of 6^7 will be 6. Thus, subtracting 6 from 10 (after 0 “borrows” a 1 from the tens digit) will result in a units digit of 4. Therefore, 10^8 - 6^7 must be equal to 99,720,064 since that is the only answer choice with a units digit of 4.

Answer: A
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Re: What is the value of 10^8 - 6^7?  [#permalink]

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New post 22 Aug 2018, 09:20
domu904 wrote:
What is the value of 10^8 - 6^7?

A. 99,720,064
B. 99,720,069
C. 99,721,022
D. 99,722,055
E. 99,723,097


OA:A

Unit digit of \(10^8\) is \(0\) and unit digit of \(6^7\) is \(6\), Unit digit of expression \(10^8 - 6^7\) will be \(10-6 = 4\), as \(10^8>6^7\).
Only Option A has 4 at unit's digit.
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Re: What is the value of 10^8 - 6^7? &nbs [#permalink] 22 Aug 2018, 09:20
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