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What is the sum of the digits of the number (2^{2018})(5^{2019})(3^2)?

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Math Revolution GMAT Instructor
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What is the sum of the digits of the number (2^{2018})(5^{2019})(3^2)?  [#permalink]

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New post 07 Feb 2019, 17:31
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A
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Difficulty:

  25% (medium)

Question Stats:

73% (01:25) correct 27% (00:58) wrong based on 22 sessions

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[GMAT math practice question]

What is the sum of the digits of the number \((2^{2018})(5^{2019})(3^2)\)?

\(A. 4\)
\(B. 5\)
\(C. 6\)
\(D. 7\)
\(E. 9\)

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Re: What is the sum of the digits of the number (2^{2018})(5^{2019})(3^2)?  [#permalink]

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New post 07 Feb 2019, 18:22
(2^2018)(5^2019)(3^2)
=(2^2018*5^2018)*5*9
= 45000000000000...... 2018 times

Sum of the digits is 4+5=9

MathRevolution

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What is the sum of the digits of the number (2^{2018})(5^{2019})(3^2)?  [#permalink]

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New post 07 Feb 2019, 18:40
MathRevolution wrote:
[GMAT math practice question]

What is the sum of the digits of the number \((2^{2018})(5^{2019})(3^2)\)?

\(A. 4\)
\(B. 5\)
\(C. 6\)
\(D. 7\)
\(E. 9\)


So \(2^{2018} * 2^{2019} * 3^2\)

can be written as \(10^{2018} * 45\)

Sum will be 9.

E
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Re: What is the sum of the digits of the number (2^{2018})(5^{2019})(3^2)?  [#permalink]

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New post 08 Feb 2019, 03:13
1
MathRevolution wrote:
[GMAT math practice question]

What is the sum of the digits of the number \((2^{2018})(5^{2019})(3^2)\)?

\(A. 4\)
\(B. 5\)
\(C. 6\)
\(D. 7\)
\(E. 9\)



Keyword:Sum of digits (Not remainder)

Approach...We cant go ahead and do calculation .Of course we might require a calculator and still it will be an Achille's task.

So try seeing something more in the questions..Ooh yes..I notice 2 and 5 as based and 2018 as lower base...Now
my line of thinking would be to bring 5*2 as base and put the power as 2018 .

Reason we would get zeros and zeros later and adding up zeros would be a cake walk.

So,

(2*5)^2018 * 5*3^2 = 10^2018 * 45= 45 followed by 2018 zeros.

So sum of digits is 9


Hope it helps!!
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Re: What is the sum of the digits of the number (2^{2018})(5^{2019})(3^2)?  [#permalink]

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New post 10 Feb 2019, 17:11
=>

\((2^{2018})(5^{2019})(3^2)\)
\(= (2^{2018})(5^{2019})(5^1)(3^2)\)
\(= (10^{2018})(5)(9)\)
\(= (45)(10^{2018})\)
\(= 450000…0\)

The sum of the digits is
\(4 + 5 + 0 + 0 + 0 + … + 0 = 9\)

Therefore, the answer is E.
Answer: E
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Re: What is the sum of the digits of the number (2^{2018})(5^{2019})(3^2)?  [#permalink]

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New post 11 Feb 2019, 00:12
MathRevolution wrote:
[GMAT math practice question]

What is the sum of the digits of the number \((2^{2018})(5^{2019})(3^2)\)?

\(A. 4\)
\(B. 5\)
\(C. 6\)
\(D. 7\)
\(E. 9\)



\((2^{2018})(5^{2019})(3^2)\)

can be written as
10^2018 * 45
sum of digits = 9
IMO E
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Re: What is the sum of the digits of the number (2^{2018})(5^{2019})(3^2)?   [#permalink] 11 Feb 2019, 00:12
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