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# If 10^50-74 is written as an integer in base 10 notation

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If 10^50-74 is written as an integer in base 10 notation [#permalink]

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26 Aug 2010, 07:42
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If 10^50-74 is written as an integer in base 10 notation, what is the sum of the digits in that integer?

A. 424
B. 433
C. 440
D. 449
E. 467
[Reveal] Spoiler: OA

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26 Aug 2010, 08:25
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udaymathapati wrote:
If 10^{50}-74 is written as an integer in base 10 notation, what is the sum of the digits in
that integer?
A. 424
B. 433
C. 440
D. 449
E. 467

$$10^{50}$$ has 51 digits (1 followed by 50 zeros). $$10^{50}-74$$ has 50 digits: last 2 digits are 2 and 6 (26) and first 48 digits are 9's.

Like 1,000-74=926.

So the sum of the digits is $$9*48+2+6=440$$.

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26 Aug 2010, 18:58
Bunuel wrote:
udaymathapati wrote:
If 10^{50}-74 is written as an integer in base 10 notation, what is the sum of the digits in
that integer?
A. 424
B. 433
C. 440
D. 449
E. 467

$$10^{50}$$ has 51 digits (1 followed by 50 zeros). $$10^{50}-74$$ has 50 digits: last 2 digits are 2 and 6 (26) and first 48 digits are 9's.

Like 1,000-74=926.

So the sum of the digits is $$9*48+2+6=440$$.

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26 Aug 2010, 23:12
C for me too..Excellent expln by Bunnel. Thanks.

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19 Feb 2011, 14:03
The integer is going to have 48 9's.
Last 2 digits will be 26

48*9 + 2 + 6 = 432+8 = 440.

Ans: "C"
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Re: If 10^50-74 is written as an integer in base 10 notation [#permalink]

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23 Nov 2013, 12:05
I don't understand why in the question it is mentioned "in base 10 notation"

Maybe its because English is not my mother tongue but that instruction really confused me. I thought I was looking for a number like "ten to the power of something".

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Re: If 10^50-74 is written as an integer in base 10 notation [#permalink]

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23 Nov 2013, 13:07
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Lobro wrote:
I don't understand why in the question it is mentioned "in base 10 notation"

Maybe its because English is not my mother tongue but that instruction really confused me. I thought I was looking for a number like "ten to the power of something".

Based 10 notation, or decimal notation, is just a way of writing a number using 10 digits: 1, 2, 3, 4, 5, 6, 7, 8, and 0 (usual way), in contrast, for example, to binary numeral system (base-2 number system) notation.

Similar questions to practice:
the-sum-of-the-digits-of-64-279-what-is-the-141460.html
the-sum-of-all-the-digits-of-the-positive-integer-q-is-equal-126388.html
10-25-560-is-divisible-by-all-of-the-following-except-126300.html
if-10-50-74-is-written-as-an-integer-in-base-10-notation-51062.html

Hope this helps.
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Re: If 10^50-74 is written as an integer in base 10 notation [#permalink]

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04 Apr 2014, 01:26
100 - 74 = 26

The last 2 digits of the term would be 26; all else would be 9

99999999......26

Important rule:

Sum of ANY NUMBER added to 9 would give the SAME value of itself

For example; Consider number = 13

Sum of digits = 1+3 = 4

Adding 9 to 13 = 22 = 2+2 = 4

So the sum would always remain the same;

Back to our problem

99999999......26 = The sum of this number will add up to 2+6 = 8

From the options available, A & B can be discarded

9x1 = 9
9x2= 18
9x3= 27
9x4= 36
9x5= 45
9x6= 54
9x7= 63
9x8= 72 ........................................ 48th time
9x9= 81
9x10=90

99999999......26

$$10^{50}- 74$$ means 9 would be repeated 48 times; so last digit would be 2

Now we have 2+2+6 = 10 (Last digit is 0)

Only option C best fits = 440

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Re: If 10^50-74 is written as an integer in base 10 notation [#permalink]

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06 Oct 2017, 10:32
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Re: If 10^50-74 is written as an integer in base 10 notation   [#permalink] 06 Oct 2017, 10:32
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