NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 07:25 It is currently 26 Apr 2024, 07:25
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

What is the value of 0.1 + 0.1^(1/m) + 0.1^(1/n) ?

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
D
KSBGC
VP
VP
Joined: 31 Oct 2013
Posts: 1260
Own Kudos [?]: 1155 [2]
Given Kudos: 635
Concentration: Accounting, Finance
GPA: 3.68
WE:Analyst (Accounting)
Send PM
What is the value of 0.1 + 0.1^(1/m) + 0.1^(1/n) ? [#permalink] New post   Updated on: 27 Feb 2023, 10:20
2
Bookmarks
00:00
A
B
C
D
E

Difficulty:

75% (hard)

Question Stats:

51% (02:08) correct 49% (01:58) wrong based on 126 sessions
Hide Show timer Statistics
What is the value of \(0.1 + 0.1^{\frac{1}{m}} + 0.1^{\frac{1}{n}}\)?


(1) \(\frac{1}{m}+ \frac{1}{n} = \frac{4}{3}\)

(2) mn = 3.
ShowHide Answer
Official Answer
C

Originally posted by KSBGC on 05 Mar 2019, 16:08.
Last edited by Bunuel on 27 Feb 2023, 10:20, edited 2 times in total.
Renamed the topic and edited the question.
User avatar
P
ocelot22
Manager
Manager
Joined: 16 Oct 2011
Posts: 171
Own Kudos [?]: 125 [1]
Given Kudos: 545
GMAT 1: 640 Q38 V40
GMAT 2: 650 Q44 V36
GMAT 3: 570 Q31 V38
GMAT 4: 720 Q49 V40
GPA: 3.75
Send PM
Reviews Badge
Re: What is the value of 0.1 + 0.1^(1/m) + 0.1^(1/n) ? [#permalink] New post   06 Mar 2019, 07:18
1
Kudos
Poorvi55 wrote:
Can someone please explain this in detail!?

Posted from my mobile device


IF YOU FIND MY SOLUTION HELPFUL, PLEASE GIVE ME KUDOS

What is the value of .1 +.1^1/m +.1^1/n

We need to know the values of m and n to evaluate the above expression

(1) 1/m +1/n = 4/3. We can several combinations of values for m and n that will give us different values for our expression

let 1/m = 1/3 and let 1/n =1, then our expression becomes .1+.1^1/3 + .1 = .2 +.1^1/3

Let 1/m =2/3 and let 1/n =2/3, then our expression becomes .1 +.1^2/3 +.1^2/3

Since we get two different values for our expression we can mark NS

(2) mn = 3

Let m =1 and n =3. Then our expression becomes .1 + .1^1 + .1^3 = .1+.1 + .001 = .201

Let m = 3/2 and n =2. Then our expression becomes .1 + .1^3/2 + .1^2 = .11 + .1^3/2

Since we get two different values for our expression we can mark NS

(1) and (2). This gives us two equations that we can use to solve for m and n. From (2) m =3/n. We can substitute into (1) to get 1/(3/n) + 1/n =4/3.

This is 1 variable in 1 equation, so we can solve for n, which allows us to solve for m. Sufficient.
User avatar
B
anmolgmat14
Intern
Intern
Joined: 12 Feb 2019
Posts: 10
Own Kudos [?]: 2 [1]
Given Kudos: 17
Send PM
Re: What is the value of 0.1 + 0.1^(1/m) + 0.1^(1/n) ? [#permalink] New post   11 Jun 2019, 08:31
1
Kudos
If we Consider statement 1,
adding both the terms gives us the equation M+N/MN=4/3

Doesn't it tells us that M+N=4
&
MN=3
User avatar
G
SaquibHGMATWhiz
GMATWhiz Representative
Joined: 23 May 2022
Posts: 640
Own Kudos [?]: 429 [1]
Given Kudos: 6
Location: India
GMAT 1: 760 Q51 V40
Send PM
Re: What is the value of 0.1 + 0.1^(1/m) + 0.1^(1/n) ? [#permalink] New post   28 Feb 2023, 01:43
1
Kudos
Expert Reply
KSBGC wrote:
What is the value of \(0.1 + 0.1^{\frac{1}{m}} + 0.1^{\frac{1}{n}}\)?


(1) \(\frac{1}{m}+ \frac{1}{n} = \frac{4}{3}\)

(2) mn = 3.

Solution:
Pre Analysis:
  • We are asked the value of \(0.1 + 0.1^{\frac{1}{m}} + 0.1^{\frac{1}{n}}\)
  • This cannot be simplified in any way where any one statement will be sufficient
  • We need the value of both m and n to get the answer

Statement 1: \(\frac{1}{m}+ \frac{1}{n} = \frac{4}{3}\)
\(⇒\frac{n+m}{mn}=\frac{4}{3}\)
  • We cannot get the value of m and n from this
  • Thus, statement 1 alone is not sufficient and we can eliminate options A and D

Statement 2: mn = 3
  • We cannot get the value of m and n from this
  • Thus, statement 2 alone is also not sufficient and we can eliminate option B

Combining:
  • From statement 1, we have \(\frac{n+m}{mn}=\frac{4}{3}\)
    \(⇒\frac{n+m}{3}=\frac{4}{3}\) (from statement 2)
    \(⇒n+m=4\)
    \(⇒\frac{3}{m}+m=4\)
    \(⇒\frac{3+m^2}{m}=4\)
    \(⇒m^2-4m+3=0\)
  • The values of m are 3 and 1
  • When m = 3, \(n=\frac{3}{m}=\frac{3}{3}=1\)
  • When m = 1, \(n=\frac{3}{m}=\frac{3}{1}=3\)

  • When (m, n) = (3, 1), the value of \(0.1 + 0.1^{\frac{1}{3}} + 0.1^{\frac{1}{1}}=0.2+0.1^{\frac{1}{3}}\)
  • When (m, n) = (1, 3), the value of \(0.1 + 0.1^{\frac{1}{1}} + 0.1^{\frac{1}{3}}=0.2+0.1^{\frac{1}{3}}\)

Hence the right answer is Option C
User avatar
L
chetan2u
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11181
Own Kudos [?]: 31949 [1]
Given Kudos: 290
Send PM
Reviews Badge
Re: What is the value of 0.1 + 0.1^(1/m) + 0.1^(1/n) ? [#permalink] New post   05 Mar 2019, 19:54
Expert Reply
selim wrote:
What is the value of \(0.1 + 0.1^{1/m} + 0.1^{1/n}\)?

1) \(1/m + 1/n = 4/3\)

2) mn = 3.



\(0.1 + 0.1^{\frac{1}{m}} + 0.1^{\frac{1}{n}}=\frac{1}{10} + \frac{1}{10}^{\frac{1}{m}} + \frac{1}{10}^{\frac{1}{n}}=\frac{10^{m+n}+10^{m+1}+10^{n+1}}{10^{m+n+1}}\)
So, we require values of m and n..

When we combine statement 1 and statement 2, we get m and n as 1 and 3 in any order. When we substitute (m =3 and n=1) or (m=1 and n=3), we will get the same answer.
\(\frac{10^{m+n}+10^{m+1}+10^{n+1}}{10^{m+n+1}}=\frac{10^{1+3}+10^{1+1}+10^{3+1}}{10^{1+3+1}}=\frac{10^4+10^2+10^4}{10^5}=\frac{20100}{100000}=\frac{201}{1000}\)=0.201

C
avatar
B
Poorvi05
Intern
Intern
Joined: 11 Dec 2018
Posts: 49
Own Kudos [?]: 11 [0]
Given Kudos: 298
Send PM
Re: What is the value of 0.1 + 0.1^(1/m) + 0.1^(1/n) ? [#permalink] New post   06 Mar 2019, 07:03
Can someone please explain this in detail!?

Posted from my mobile device
avatar
B
FTGreco
Intern
Intern
Joined: 24 Feb 2019
Posts: 3
Own Kudos [?]: 5 [0]
Given Kudos: 3
Location: Brazil
Concentration: Strategy, General Management
GPA: 2.96
Send PM
Re: What is the value of 0.1 + 0.1^(1/m) + 0.1^(1/n) ? [#permalink] New post   11 Mar 2019, 12:50
KSBGC wrote:
What is the value of \(0.1 + 0.1^{\frac{1}{m}} + 0.1^{\frac{1}{n}}\)?


(1) \(\frac{1}{m}+ \frac{1}{n} = \frac{4}{3}\)

(2) mn = 3.



Since we have m and n as exponents in two separated terms from the equation, and those terms are being added together (so we cannot "merge" them like if they were being multiplied), we will need to figure out a way to find both \(m\) as well as \(n\).

(1) gives us one equation with 2 variables. This is not enough to solve for both of them, and thus is insufficient.

(2) gives us, again, one equation with 2 variables. Insufficient.

(1) + (2) gives us two equations for two variables, which can be solved. \(\frac{1}{m}+ \frac{1}{n} = \frac{m + n}{mn} = \frac{4}{3}\).
From this, \(m+n = 4\), and \(m = (4 - n)\).

\(m * n = 3\)

\((4 - n) * n = 3\)

\(n^2 - 4n + 3 = 0\)

\(n = 3\) or \(n = 1\).


If n = 3, m = 1. On the other hand, if n = 1, m = 3.

Now, since the terms to the power of \(\frac{1}{m}\) and \(\frac{1}{n}\) are both at the same base (\(0.1\)), it doesn't matter whether \((m,n) = (1,3)\) or \((m,n) = (3,1)\). Both will give the same final result, and this means that (1) and (2) together are sufficient.

Answer is C.
GMAT Club Bot
gmatclubot
Re: What is the value of 0.1 + 0.1^(1/m) + 0.1^(1/n) ? [#permalink]
11 Mar 2019, 12:50
Moderator:
Bunuel
Math Expert
92933 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