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Intern  B
Joined: 10 Dec 2013
Posts: 4
GMAT 1: 510 Q37 V23 The number of digits in the number (4^11)(5^25) = ?  [#permalink]

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10 00:00

Difficulty:   45% (medium)

Question Stats: 64% (01:18) correct 36% (01:39) wrong based on 182 sessions

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The number of digits in the number (4^11)(5^25) = ?

A) 22
B) 23
C) 24
D) 25
E) 26

Originally posted by amithy on 18 Sep 2015, 05:11.
Last edited by Bunuel on 18 Sep 2015, 05:24, edited 1 time in total.
RENAMED THE TOPIC.
Manager  Joined: 29 Jul 2015
Posts: 155
Re: The number of digits in the number (4^11)(5^25) = ?  [#permalink]

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amithyarli wrote:
The number of digits in the number (4^11)(5^25) = ?

A) 22
B) 23
C) 24
D) 25
E) 26

$$4^{11} * 5^{25}$$

= $$2^{22} * 5^{25}$$

= $$2^{22} * 5^{22}*5^3$$

= $$5^3*10^{22}$$

= $$125 * 10^{22}$$

There are 3 digits in 125 and 22 0s after it.
Total digits = 22 + 3 =25

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Director  V
Joined: 04 Dec 2015
Posts: 745
Location: India
Concentration: Technology, Strategy
WE: Information Technology (Consulting)
Re: The number of digits in the number (4^11)(5^25) = ?  [#permalink]

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amithyarli wrote:
The number of digits in the number (4^11)(5^25) = ?

A) 22
B) 23
C) 24
D) 25
E) 26

$$(4^{11})(5^{25})$$

$$(2{^2})^{11}(5^{25})$$

$$(2^{22})(5^{25})$$

$$(2^{22} * 5^{22}) 5^3$$

$$(10^{22}) 125$$

$$(10^{22})$$ will have $$22$$ digits.

$$125$$ has $$3$$ digits.

Total number of digits $$=> 22 + 3 = 25$$ digits.

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Re: The number of digits in the number (4^11)(5^25) = ?  [#permalink]

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_________________ Re: The number of digits in the number (4^11)(5^25) = ?   [#permalink] 04 Nov 2018, 07:29
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