NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 13:16 It is currently 26 Apr 2024, 13:16
Decision Tracker
My Rewards
New posts
New comers' posts

Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

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

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92948
Own Kudos [?]: 619228 [21]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
The number of digits in the number (4^11)(5^25) = ? [#permalink] New post   28 Oct 2019, 21:23
1
Kudos
20
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

45% (medium)

Question Stats:

59% (01:11) correct 41% (01:34) wrong based on 233 sessions
Hide Show timer Statistics

Competition Mode Question



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

(A) 22
(B) 23
(C) 24
(D) 25
(E) 26
ShowHide Answer
Official Answer
D
Most Helpful Reply
User avatar
G
anbknaga
Manager
Manager
Joined: 27 Aug 2018
Posts: 95
Own Kudos [?]: 81 [8]
Given Kudos: 52
Location: India
Concentration: Operations, Healthcare
Schools: ISB '21 (D) Great Lakes '21 (WD)
GMAT 1: 650 Q48 V31
WE:Operations (Health Care)
Send PM
Reviews Badge
Re: The number of digits in the number (4^11)(5^25) = ? [#permalink] New post   28 Oct 2019, 23:22
5
Kudos
3
Bookmarks
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.
General Discussion
User avatar
B
Peddi
Intern
Intern
Joined: 20 Jul 2019
Posts: 47
Own Kudos [?]: 27 [1]
Given Kudos: 59
Send PM
Re: The number of digits in the number (4^11)(5^25) = ? [#permalink] New post   28 Oct 2019, 21:40
1
Kudos
4^11*5^25=2^22*5^22*125=10^22*5^3=125*10^22, no of digits=3+22=25

Posted from my mobile device
User avatar
D
eakabuah
Retired Moderator
Joined: 18 May 2019
Posts: 785
Own Kudos [?]: 1040 [2]
Given Kudos: 101
Send PM
GMAT ToolKit User
Re: The number of digits in the number (4^11)(5^25) = ? [#permalink] New post   28 Oct 2019, 21:49
1
Kudos
1
Bookmarks
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

The answer is therefore E.
User avatar
B
kk47
Intern
Intern
Joined: 21 Sep 2016
Posts: 26
Own Kudos [?]: 21 [1]
Given Kudos: 187
GMAT 1: 610 Q47 V27
Send PM
Re: The number of digits in the number (4^11)(5^25) = ? [#permalink] New post   29 Oct 2019, 00:18
1
Kudos
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.

Therefore, answer is 25.

Posted from my mobile device
avatar
S
vg18
Manager
Manager
Joined: 30 Nov 2017
Posts: 62
Own Kudos [?]: 79 [0]
Given Kudos: 95
GMAT 1: 690 Q49 V35
Send PM
Re: The number of digits in the number (4^11)(5^25) = ? [#permalink] New post   29 Oct 2019, 00:25
125 followed by 22 zeros: Total: 25 digits
User avatar
L
unraveled
CEO
CEO
Joined: 07 Mar 2019
Posts: 2555
Own Kudos [?]: 1813 [1]
Given Kudos: 763
Location: India
WE:Sales (Energy and Utilities)
Send PM
Re: The number of digits in the number (4^11)(5^25) = ? [#permalink] New post   29 Oct 2019, 00:34
1
Kudos
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

Answer D.
User avatar
D
lacktutor
Director
Director
Joined: 25 Jul 2018
Posts: 668
Own Kudos [?]: 1119 [2]
Given Kudos: 69
Send PM
Re: The number of digits in the number (4^11)(5^25) = ? [#permalink] New post   29 Oct 2019, 00:38
2
Kudos
\(4^{11}*5^{25}\)= \(2^{22}*5^{25}\)=

\(5^{3}*5^{22}*2^{22}\)= \(5^{3}*10^{22}\)

—> \(5^{3}\)= 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

The answer is D

Posted from my mobile device
avatar
Tahia50
Intern
Intern
Joined: 29 Oct 2019
Posts: 1
Own Kudos [?]: 1 [1]
Given Kudos: 0
Send PM
Re: The number of digits in the number (4^11)(5^25) = ? [#permalink] New post   29 Oct 2019, 04:44
1
Kudos
(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
avatar
B
Kalubalu
Intern
Intern
Joined: 15 Aug 2017
Posts: 20
Own Kudos [?]: 10 [1]
Given Kudos: 4
Send PM
Re: The number of digits in the number (4^11)(5^25) = ? [#permalink] New post   29 Oct 2019, 06:36
1
Kudos
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
User avatar
L
CareerGeek
VP
VP
Joined: 20 Jul 2017
Posts: 1300
Own Kudos [?]: 3451 [1]
Given Kudos: 162
Location: India
Concentration: Entrepreneurship, Marketing
GMAT 1: 690 Q51 V30
WE:Education (Education)
Send PM
Re: The number of digits in the number (4^11)(5^25) = ? [#permalink] New post   29 Oct 2019, 06:51
1
Kudos
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

Posted from my mobile device
User avatar
L
Abhishek009
Board of Directors
Joined: 11 Jun 2011
Status:QA & VA Forum Moderator
Posts: 6072
Own Kudos [?]: 4690 [1]
Given Kudos: 463
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Send PM
GMAT ToolKit User
Re: The number of digits in the number (4^11)(5^25) = ? [#permalink] New post   29 Oct 2019, 07:42
1
Kudos
\(4^{11}*5^{25}\)

\(= 2^{22}*5^{25}\)

\(= 2^{22}*5^{22}*5^3\)

\(= 10^{22}*5^3\)

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
avatar
B
rahulswimmer
Intern
Intern
Joined: 30 Sep 2017
Posts: 15
Own Kudos [?]: 10 [0]
Given Kudos: 0
Send PM
Re: The number of digits in the number (4^11)(5^25) = ? [#permalink] New post   29 Oct 2019, 07:48
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
User avatar
D
thangvietnam
Director
Director
Joined: 29 Jun 2017
Posts: 778
Own Kudos [?]: 396 [1]
Given Kudos: 2198
Send PM
Re: The number of digits in the number (4^11)(5^25) = ? [#permalink] New post   29 Oct 2019, 08:08
1
Kudos
= 2^22 *5^22 * 5^3
= 625*10^22
answer is d
User avatar
L
Archit3110
GMAT Club Legend
GMAT Club Legend
Joined: 18 Aug 2017
Status:You learn more from failure than from success.
Posts: 8020
Own Kudos [?]: 4098 [1]
Given Kudos: 242
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1:
545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy and Utilities)
Send PM
GMAT ToolKit User CAT Tests
Re: The number of digits in the number (4^11)(5^25) = ? [#permalink] New post   29 Oct 2019, 08:35
1
Kudos
((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
User avatar
L
ShankSouljaBoi
Director
Director
Joined: 21 Jun 2017
Posts: 638
Own Kudos [?]: 531 [1]
Given Kudos: 4092
Location: India
Concentration: Finance, Economics
Schools: Rotman '23 (D) IIMA PGPX'22 (D) Desautels '23 (D) Schulich Sept '23 (D) WBS (D) IIML IPMX'25 (A)
GMAT 1: 660 Q49 V31
GMAT 2: 620 Q47 V30
GMAT 3: 650 Q48 V31
GPA: 3.1
WE:Corporate Finance (Non-Profit and Government)
Send PM
Reviews Badge
Re: The number of digits in the number (4^11)(5^25) = ? [#permalink] New post   29 Oct 2019, 08:59
1
Kudos
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.
avatar
P
chaitralirr
Senior Manager
Senior Manager
Joined: 17 Mar 2019
Posts: 364
Own Kudos [?]: 281 [1]
Given Kudos: 35
Location: India
Concentration: Healthcare, General Management
Schools:
GPA: 3.75
WE:Pharmaceuticals (Health Care)
Send PM
Re: The number of digits in the number (4^11)(5^25) = ? [#permalink] New post   29 Oct 2019, 10:58
1
Kudos
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
User avatar
G
Mohammadmo
Senior Manager
Senior Manager
Joined: 29 Jun 2019
Posts: 358
Own Kudos [?]: 215 [1]
Given Kudos: 16
Send PM
Re: The number of digits in the number (4^11)(5^25) = ? [#permalink] New post   29 Oct 2019, 14:33
1
Kudos
2²² × 5²² × 5³=
10²² ×5³= 125×10²²
3+22=25
Option D

Posted from my mobile device
User avatar
G
BelalHossain046
Manager
Manager
Joined: 11 Feb 2013
Posts: 202
Own Kudos [?]: 305 [1]
Given Kudos: 60
Location: United States (TX)
Concentration: Finance
GMAT 1: 490 Q44 V15
GMAT 2: 690 Q47 V38
GRE 1: Q165 V155
GPA: 3.05
WE:Analyst (Commercial Banking)
Send PM
GMAT ToolKit User
Re: The number of digits in the number (4^11)(5^25) = ? [#permalink] New post   29 Oct 2019, 19:09
1
Kudos
My answer: D

2^22 *5^22*5^3
=5^3*10^22
=125 and 22 zeros.
So, total 25 digits.
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32688
Own Kudos [?]: 822 [0]
Given Kudos: 0
Send PM
Re: The number of digits in the number (4^11)(5^25) = ? [#permalink] New post   04 Jan 2024, 04:16
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
gmatclubot
Re: The number of digits in the number (4^11)(5^25) = ? [#permalink]
04 Jan 2024, 04:16
Moderators:
Bunuel
Math Expert
92948 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions