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# m16#36

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05 Feb 2009, 05:42
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What is the sum of digits in decimal notation of number $$10^{20} - 16$$ ?

(A) 158
(B) 162
(C) 165
(D) 174
(E) 183

Source: GMAT Club Tests - hardest GMAT questions

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06 Oct 2009, 22:11
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Right answer (taken from the test) is:

$$10^{20} - 16 = 10...(20 \text{ zeros})...0 - 16 = 9...(18 \text{ nines})...984$$ . The sum of digits $$= 18*9 + 8 + 4 = 174$$ .
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27 Apr 2010, 08:35
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10-6 always gives 4 in the units place ..the only answer choice that has 4 in the units place is D.

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27 Apr 2010, 12:58
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I did it the dinosaur way which still didn't take too long.

100000000000000000000
- 16
99999999999999999984

(9 * 18) + 8 + 4 = 174

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12 May 2010, 17:55
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Well, $$10^2-16=84$$ and $$10^3-16 = 984$$. So, we see the exponent tells us the number of digits involved in our answer (2 in the former case, 3 in the latter).

$$10^2^0-16=999...984$$; two numbers are the 8 and the 4, whereas the other eighteen are 9s!

$$(18*9)+8+4=174$$
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05 Feb 2009, 05:49
10^20 will have one 1 and twenty 0's.

10^20 - 16 will have one 4, one 8 and seventeen 9's

Hence, sum of digits = 4 + 8 + 17*9
= 12 + 153 = 165

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27 Apr 2010, 06:43
Yes D is correct answer. If you subtract 1 from 10^20 it will be 999(20 times) if you subtract 15 more from that, you will get last digit 4 second last 8 and all others 9. So answer is D.

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29 Apr 2010, 12:24
amitjash wrote:
Yes D is correct answer. If you subtract 1 from 10^20 it will be 999(20 times) if you subtract 15 more from that, you will get last digit 4 second last 8 and all others 9. So answer is D.

I did it the same way. Subtracting 1 first seemed to help me visualize it.

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29 Apr 2011, 05:21
$$10^2^0$$ would be a 21 digit number ... subtract 16 and you are left with a 20 digit number with 2 digits as 4 and 8 and the rest 9s. The total is $$8+4+18*9 = 174$$ therefore (D)
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29 Apr 2011, 05:39
Last two digits = 84 and there are 18 9s

8 + 4 + 9 * 18

= 12 + 162

= 174

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03 May 2012, 18:36
zz0vlb wrote:
10-6 always gives 4 in the units place ..the only answer choice that has 4 in the units place is D.

If it was 10^2-16=100-16=84, the sum of the digits would be 8+4=12. So I don't think we can use the shortcut suggested.

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05 May 2012, 10:37
zz0vlb wrote:
10-6 always gives 4 in the units place ..the only answer choice that has 4 in the units place is D.

i liked the way u have answered mate....no need of calculation, but just keen observation.. +1 to u
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06 May 2013, 06:26
topmbaseeker wrote:
What is the sum of digits in decimal notation of number $$10^{20} - 16$$ ?

(A) 158
(B) 162
(C) 165
(D) 174
(E) 183

Source: GMAT Club Tests - hardest GMAT questions

What is the sum of the digits in decimal notation of number $$10^{20}-16$$?

A. 158
B. 162
C. 165
D. 174
E. 183

$$10^{20}$$ has 21 digits: 1 followed by 20 zeros;
$$10^{20}-16$$ has 20 digits: 18 9's and 84 in the end;

So, the sum of the digits of $$10^{20}-16$$ equals to 18*9+8+4=174.

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06 May 2013, 22:59
I don't see the need of subtracting the entire number and finding out the number of 9's .

1000 - 16 = 984
10000 -16 = 9984
So, the number of 9's would be the power of 10 minus 2.
So, answer = (20-2)*9 + (8+4) = 174

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07 May 2013, 01:36
18*9+8+4=174
I will go with 'D'

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07 May 2013, 13:19
zz0vlb wrote:
10-6 always gives 4 in the units place ..the only answer choice that has 4 in the units place is D.

You got one +1 from me in the first place but actually the way you "solved" problem is wrong.

It would only be right, if the sum of the previous numbers is 0.
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21 Apr 2014, 05:11
Bunuel wrote:
topmbaseeker wrote:
What is the sum of digits in decimal notation of number $$10^{20} - 16$$ ?

(A) 158
(B) 162
(C) 165
(D) 174
(E) 183

Source: GMAT Club Tests - hardest GMAT questions

What is the sum of the digits in decimal notation of number $$10^{20}-16$$?

A. 158
B. 162
C. 165
D. 174
E. 183

$$10^{20}$$ has 21 digits: 1 followed by 20 zeros;
$$10^{20}-16$$ has 20 digits: 18 9's and 84 in the end;

So, the sum of the digits of $$10^{20}-16$$ equals to 18*9+8+4=174.

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the-sum-of-the-digits-of-64-279-what-is-the-141460.html
what-is-the-sum-of-all-digits-for-the-number-147057.html
10-25-560-is-divisible-by-all-of-the-following-except-126300.html
if-x-is-a-positive-integer-and-10-x-74-in-decimal-notation-61013.html

Hope it helps.
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04 May 2014, 14:12
Bunuel wrote:
topmbaseeker wrote:
What is the sum of digits in decimal notation of number $$10^{20} - 16$$ ?

(A) 158
(B) 162
(C) 165
(D) 174
(E) 183

Source: GMAT Club Tests - hardest GMAT questions

What is the sum of the digits in decimal notation of number $$10^{20}-16$$?

A. 158
B. 162
C. 165
D. 174
E. 183

$$10^{20}$$ has 21 digits: 1 followed by 20 zeros;
$$10^{20}-16$$ has 20 digits: 18 9's and 84 in the end;

So, the sum of the digits of $$10^{20}-16$$ equals to 18*9+8+4=174.

D can't be the answer. once we subtract 16 from 10^20 we have only 19 numbers left. among 19 numbers 17 are nine and last two are 8 and 4.
therefor sum is 17*9+8+4=165
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04 May 2014, 14:15
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OA is wrong
C is the right ans
because on subtracting 16 from 10^20, we have only 19 nos left.
17 are 9 and last two are 8 and 4.
so sum= 17*9+8+4=165
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05 May 2014, 01:59
daboo343 wrote:
Bunuel wrote:
topmbaseeker wrote:
What is the sum of digits in decimal notation of number $$10^{20} - 16$$ ?

(A) 158
(B) 162
(C) 165
(D) 174
(E) 183

Source: GMAT Club Tests - hardest GMAT questions

What is the sum of the digits in decimal notation of number $$10^{20}-16$$?

A. 158
B. 162
C. 165
D. 174
E. 183

$$10^{20}$$ has 21 digits: 1 followed by 20 zeros;
$$10^{20}-16$$ has 20 digits: 18 9's and 84 in the end;

So, the sum of the digits of $$10^{20}-16$$ equals to 18*9+8+4=174.

D can't be the answer. once we subtract 16 from 10^20 we have only 19 numbers left. among 19 numbers 17 are nine and last two are 8 and 4.
therefor sum is 17*9+8+4=165

Nope.

$$10^{20}$$ has 21 digits: 1 followed by 20 zeros: 100,000,000,000,000,000,000

$$10^{20}-16$$ has 20 digits: 18 9's and 84 in the end: 99,999,999,999,999,999,984.
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# m16#36

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