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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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Re: m16#36 [#permalink]
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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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Re: m16#36 [#permalink]
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06 Oct 2009, 22:11
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The above answer is wrong. 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 \(= 18*9 + 8 + 4 = 174\) . The correct answer is D.
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Re: m16#36 [#permalink]
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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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Re: m16#36 [#permalink]
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27 Apr 2010, 08:35
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106 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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Re: m16#36 [#permalink]
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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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Re: m16#36 [#permalink]
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12 May 2010, 17:55
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Well, \(10^216=84\) and \(10^316 = 984\). So, we see the exponent tells us the number of digits involved in our answer (2 in the former case, 3 in the latter). \(10^2^016=999...984\); two numbers are the 8 and the 4, whereas the other eighteen are 9s! \((18*9)+8+4=174\)
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Re: m16#36 [#permalink]
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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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Re: m16#36 [#permalink]
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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 Answer  D
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Re: m16#36 [#permalink]
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03 May 2012, 18:36
zz0vlb wrote: 106 always gives 4 in the units place ..the only answer choice that has 4 in the units place is D. If it was 10^216=10016=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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Re: m16#36 [#permalink]
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05 May 2012, 10:37
zz0vlb wrote: 106 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



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Re: m16#36 [#permalink]
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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 = (202)*9 + (8+4) = 174



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Re: m16#36 [#permalink]
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07 May 2013, 01:36
18*9+8+4=174 I will go with 'D'



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Re: m16#36 [#permalink]
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07 May 2013, 13:19
zz0vlb wrote: 106 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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Re: m16#36 [#permalink]
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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. Answer: D. 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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Re: m16#36 [#permalink]
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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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Re: m16#36 [#permalink]
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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. Answer: D. 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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