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

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

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

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