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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # The number of digits in the number (4^11)(5^25) = ?

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Math Expert V
Joined: 02 Sep 2009
Posts: 59588
The number of digits in the number (4^11)(5^25) = ?  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 57% (01:04) correct 43% (01:06) wrong based on 72 sessions

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Competition Mode Question

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

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

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Manager  B
Joined: 20 Jul 2019
Posts: 55
Re: The number of digits in the number (4^11)(5^25) = ?  [#permalink]

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4^11*5^25=2^22*5^22*125=10^22*5^3=125*10^22, no of digits=3+22=25

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Director  P
Joined: 18 May 2019
Posts: 528
Re: The number of digits in the number (4^11)(5^25) = ?  [#permalink]

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To find the number of digits in 4^11 * 5^25

4^11=2^22
hence 4^11*5^25=2^22 * 5^22 * 5^3
But 2^22 * 5^22 = (2*5)^22=10^22
Therefore 2^22 * 5^22 * 5^3 = 10^22 * 5^3
but 10^a = a+1 digits
So, 10^22 = 22+1 = 23 digits
and 5^a = a digits
so 5^3 = 3 digits
Total digits = 23+3 = 26

Manager  G
Joined: 27 Aug 2018
Posts: 93
Location: India
Concentration: Operations, Healthcare
GMAT 1: 650 Q48 V31 WE: Operations (Health Care)
Re: The number of digits in the number (4^11)(5^25) = ?  [#permalink]

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2
1
To get the number of digits in any number:

1. Check the number of equal powers of 2's and 5's (i.e, $$2^x$$ and $$5^x$$). The powers should be same.
2. The remaining prime factors (including additional powers of 2 or 5 left out) should be multiplied to get a number.
3. Add the number of 0's from (1) and number of digits of the number from (2) to get the desired result.

(4^11)(5^25) can be written as (2^22)(5^25).

Step 1: The common powers of 2 and 5 are (2^22) and (5^22). This gives us 22 zeros
Step 2: The remaining prime factors and its powers are (5^3) = 125 which is 3 digits.

Step 3: Add no. of digits from 1 and 2 - (22+3 = 25)

Therefore, the answer is D 25.
Intern  B
Joined: 21 Sep 2016
Posts: 21
Re: The number of digits in the number (4^11)(5^25) = ?  [#permalink]

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4^11 x 5^25
= 2^22 x 5^25 (arranging 2s and 5s.....)
= 10^22 x 5^3 (.....to get 10s)
= 125 x 10^22

10^22 has 23 digits and multiplying it by 125 will add 2 digits more.

The factors will not add more digits as we have already merged 2s and 5s to 10s. In such questions we need to take care if the multiplication will add more digits, for e.g. 3 x 3 will yield a single digit number only whereas 3 x 5 will yield a double digit number.

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Intern  S
Joined: 30 Nov 2017
Posts: 47
GMAT 1: 690 Q49 V35 Re: The number of digits in the number (4^11)(5^25) = ?  [#permalink]

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125 followed by 22 zeros: Total: 25 digits
Senior Manager  P
Joined: 07 Mar 2019
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GMAT 1: 580 Q43 V27 WE: Sales (Energy and Utilities)
Re: The number of digits in the number (4^11)(5^25) = ?  [#permalink]

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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
$$(4^{11})(5^{25})$$ = $$((2^2)^{11})(5^{25})$$
$$(2^{22})(5^{25})$$
$$(2^{22})(5^{22})(5^3)$$
$$(10^{22})(5^3)$$
22 + 3 = 25 digits

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Senior Manager  G
Joined: 25 Jul 2018
Posts: 386
Re: The number of digits in the number (4^11)(5^25) = ?  [#permalink]

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$$4^{11}*5^{25}$$= $$2^{22}*5^{25}$$=

$$5^{3}*5^{22}*2^{22}$$= $$5^{3}*10^{22}$$

—> $$5^{3}$$= 125 is greater than $$10^{2}$$, but less than $$10^{3}$$.

—> well, $$125*10^{22}$$= approximately greater than $$10^{24}$$, but cannot be equal to $$10^{25}$$.

—> $$10^{24}$$ — the number of digits in the number is 25

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

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(4^11) (5^25) can be broken into (4^11) * (5^22) * (5^3)

4 * (5^2) = 100, which means with 4^11 and 5^22 we get 100^11 and the remaining 5^3 = 125.
1st part: 100^11 or 10^22 (22 zeros)
2nd part: 125(3 digits)
So, the number is 125 * 10^22 and the answer is D) 25
Intern  B
Joined: 15 Aug 2017
Posts: 24
Re: The number of digits in the number (4^11)(5^25) = ?  [#permalink]

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

$$4^{11} = (2^2)^{11} = 2^{22}$$

This means there are 22 $$(5 * 2)$$ pairs, leave $$5^3$$

$$5^3 = 125$$, 3 digits plus the 22 digits in the 5*2 pair equates to 25 digits

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

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4^11*5^25 = 2^22*5^25
= (2*5)^22*5^3
= 125*10^22

Number of digits = 3 + 22 = 25

IMO Option D

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

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

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

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

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

10^22 - Will have 22 digits
5^3 = 125 , Will have 3 digits

SO, We have 22 + 3 = 25 Digits, Answer must be (D) 25
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Intern  B
Joined: 30 Sep 2017
Posts: 14
Re: The number of digits in the number (4^11)(5^25) = ?  [#permalink]

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Digit with highest power becomes the base number. Other digits with their respective powers are not going to mutate the base number length.

Max(11,25) + 1
= 26
Director  P
Joined: 29 Jun 2017
Posts: 927
Re: The number of digits in the number (4^11)(5^25) = ?  [#permalink]

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1
= 2^22 *5^22 * 5^3
= 625*10^22
GMAT Club Legend  V
Joined: 18 Aug 2017
Posts: 5436
Location: India
Concentration: Sustainability, Marketing
GPA: 4
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Re: The number of digits in the number (4^11)(5^25) = ?  [#permalink]

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1
((4^11)(5^25)
can be solveed
4^11*5^11*5^13
20^11*5^13
2^11*10^11*5^13
10^11 * 10^11 * 5^2
10^22 * 5^2
so we have 1 ; 1 ; 0 ; 22 ; 2 ; 1 and 5; 1
total 1+22+1+1 = 25 digits
IMO D

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

(A) 22
(B) 23
(C) 24
(D) 25
(E) 26
Senior Manager  G
Joined: 21 Jun 2017
Posts: 327
Location: India
Concentration: Finance, Economics
Schools: IIM
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Re: The number of digits in the number (4^11)(5^25) = ?  [#permalink]

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D 25 ---> 2^22*5^22*5^3 = 10^22* 5^3 = 125* 10^22 . So we have 22 zeros and thre digits in 125 . Total digits = 3 + 22 = 25.
Manager  G
Joined: 17 Mar 2019
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Re: The number of digits in the number (4^11)(5^25) = ?  [#permalink]

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The number of digits in the number (411)(525)= ?

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

211. 211. 525= (2^11 *5^11) * (2^11 *5^11)* 5^3= 10^11*10^11*125= 10^22*125

=25 DIGITS.

IMO D
Senior Manager  G
Joined: 29 Jun 2019
Posts: 470
Re: The number of digits in the number (4^11)(5^25) = ?  [#permalink]

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1
2²² × 5²² × 5³=
10²² ×5³= 125×10²²
3+22=25
Option D

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

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1

2^22 *5^22*5^3
=5^3*10^22
=125 and 22 zeros.
So, total 25 digits. Re: The number of digits in the number (4^11)(5^25) = ?   [#permalink] 29 Oct 2019, 19:09
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