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# How many digits are in the number 50^8 × 8^3 × 11^2?

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Math Expert
Joined: 02 Sep 2009
Posts: 51218
How many digits are in the number 50^8 × 8^3 × 11^2?  [#permalink]

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28 Apr 2016, 00:09
00:00

Difficulty:

65% (hard)

Question Stats:

57% (01:14) correct 43% (01:22) wrong based on 143 sessions

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How many digits are in the number 50^8 × 8^3 × 11^2?

A. 22
B. 20
C. 19
D. 18
E. 17

_________________
Math Expert
Joined: 02 Aug 2009
Posts: 7107
Re: How many digits are in the number 50^8 × 8^3 × 11^2?  [#permalink]

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28 Apr 2016, 01:29
1
1
Bunuel wrote:
How many digits are in the number 50^8 × 8^3 × 11^2?

A. 22
B. 20
C. 19
D. 18
E. 17

As we can see 5s and 2s in the term, lets get it in terms of 10s..

$$50^8 × 8^3 × 11^2 = (5^2)^8*2^8*2^{3*3}*11^2 = 5^{16}*2^{17}*11^2 = 10^{16}*2*121$$
so 3 digits from 2*121 and 16 trailing zeroes from $$10^{16}$$..
total = 3+16 = 19
C
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: How many digits are in the number 50^8 × 8^3 × 11^2?  [#permalink]

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28 Apr 2016, 23:45
1
1
Bunuel wrote:
How many digits are in the number 50^8 × 8^3 × 11^2?

A. 22
B. 20
C. 19
D. 18
E. 17

This might look to be a difficult question on the first glance.
Whenever you are asked to find the number of digits, try to bring the number in multiples of 10. This way, we can wasily calculate the umber of 0's through the powers of 10

50^8 × 8^3 × 11^2 = (5^2*2)^8*2^9*11^2 = 5^16*2^17*11^2 = 2*11^2*10^16 = 242*10^16
Hence we would have 16 trailing 0's and the three digits from 242
Total digits = 3 + 16 = 19

Correct Option: C
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Posts: 9165
Re: How many digits are in the number 50^8 × 8^3 × 11^2?  [#permalink]

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01 Nov 2018, 23:21
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Re: How many digits are in the number 50^8 × 8^3 × 11^2? &nbs [#permalink] 01 Nov 2018, 23:21
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