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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
Joined: 16 Aug 2015
Posts: 8456
GMAT 1: 760 Q51 V42
GPA: 3.82
What is the sum of the digits of the number (2^{2018})(5^{2019})(3^2)?  [#permalink]

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07 Feb 2019, 18:31
00:00

Difficulty:

35% (medium)

Question Stats:

59% (01:19) correct 41% (01:16) wrong based on 37 sessions

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[GMAT math practice question]

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

$$A. 4$$
$$B. 5$$
$$C. 6$$
$$D. 7$$
$$E. 9$$

_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Manager Joined: 29 Dec 2018 Posts: 63 Location: India Re: What is the sum of the digits of the number (2^{2018})(5^{2019})(3^2)? [#permalink] ### Show Tags 07 Feb 2019, 19:22 (2^2018)(5^2019)(3^2) =(2^2018*5^2018)*5*9 = 45000000000000...... 2018 times Sum of the digits is 4+5=9 MathRevolution Kudos if you like the approach Posted from my mobile device Director Joined: 09 Mar 2018 Posts: 988 Location: India What is the sum of the digits of the number (2^{2018})(5^{2019})(3^2)? [#permalink] ### Show Tags 07 Feb 2019, 19:40 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 _________________ If you notice any discrepancy in my reasoning, please let me know. Lets improve together. Quote which i can relate to. Many of life's failures happen with people who do not realize how close they were to success when they gave up. Senior Manager Joined: 09 Jun 2014 Posts: 345 Location: India Concentration: General Management, Operations Re: What is the sum of the digits of the number (2^{2018})(5^{2019})(3^2)? [#permalink] ### Show Tags 08 Feb 2019, 04:13 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!! Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8456 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: What is the sum of the digits of the number (2^{2018})(5^{2019})(3^2)? [#permalink] ### Show Tags 10 Feb 2019, 18:11 => $$(2^{2018})(5^{2019})(3^2)$$ $$= (2^{2018})(5^{2019})(5^1)(3^2)$$ $$= (10^{2018})(5)(9)$$ $$= (45)(10^{2018})$$ $$= 450000…0$$ The sum of the digits is $$4 + 5 + 0 + 0 + 0 + … + 0 = 9$$ Therefore, the answer is E. Answer: E _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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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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11 Feb 2019, 01:12
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
Re: What is the sum of the digits of the number (2^{2018})(5^{2019})(3^2)?   [#permalink] 11 Feb 2019, 01:12
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