Author 
Message 
TAGS:

Hide Tags

Retired Moderator
Joined: 27 Oct 2017
Posts: 1410
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)

What is the value of mn?
[#permalink]
Show Tags
07 Dec 2019, 18:56
Question Stats:
21% (01:36) correct 79% (01:21) wrong based on 82 sessions
HideShow timer Statistics
GMATBusters’ Quant Quiz Question 1 What is the value of mn? (1) \(5^m*3^n=45\) (2) \(9^{(m1)(n2)}=1\)
Official Answer and Stats are available only to registered users. Register/ Login.
_________________



Intern
Joined: 11 Dec 2018
Posts: 16
Location: United States (NC)

Re: What is the value of mn?
[#permalink]
Show Tags
07 Dec 2019, 19:18
Answer:A
1) Using prime factorization convert 45= 3^2*5
m=1 and n=2 gives mn=2
2) has multiple possibilites as 1=1^0 or 1^1



Intern
Joined: 18 May 2017
Posts: 4

Re: What is the value of mn?
[#permalink]
Show Tags
07 Dec 2019, 20:26
Required: value of m*n?
Statement 1: 5^m * 3^n = 45
For the above equation to be valid m has to take value 1 and n has to take value 2
Hence, Sufficient.
Statement 2: 9 ^ ((m1) * (n2)) = 1
9^0 = 1 (m1) * (n2) = 0 1. m equals 1 or (not sufficient) 2. n equals 2 or (not sufficient) 3. both (sufficient)
Hence, Not sufficient
Ans A.
Posted from my mobile device



Senior Manager
Joined: 25 Jul 2018
Posts: 491

Re: What is the value of mn?
[#permalink]
Show Tags
07 Dec 2019, 20:49
What is the value of mn?
(Statement1): \(5^{m}∗3^{n}=45\) if m=1, n=2 and \(5^{1}∗3^{2}=45\), then > m*n =1*2=2
> but in the question stem, it does not say whether m,n are positive integer. if n=0, then m will be equal to \(log_5\)45 (real number) > m*n will be equal to 0(zero) TWO values Insufficient (Statement2): \(9^{(m−1)(n−2)}=1\) \(9^{(m−1)(n−2)}=9^{0}\) (m−1)(n−2)=0
> In order (m−1)(n−2) be equal to 0, one of (m1) and (n2) is enough to equal to zero.
> (case1): if m=1,n=2 and (m−1)(n−2)=0, then m*n=1*2. > (case1): if m=1, n=3 and (11)(32)=0*1=0, then m*n=1*3=3 TWO values Insufficient
Taken together 1&2, In this equation (m−1)(n−2)=0: > if m=1, then \(5^{1}*3^{n}= 45\)> n= 2 (must) > m*n=2 > if n=2, then \(5^{m}*3^{2}= 45\)> m=1(must) > m*n=2
The value of m*n which is equal to 2 is UNIQUE Sufficient
The answer is C.



Intern
Joined: 18 Nov 2018
Posts: 39

Re: What is the value of mn?
[#permalink]
Show Tags
07 Dec 2019, 21:24
45 = 5 x 3^2 Making it 5^m x 3^n as m=1and 3=2
With statement 2. (M1)(n2)=0 Here either m =1 and n could be anything or n =2 and m could be anything. No distinct answers.
So answer is A
Posted from my mobile device



Intern
Joined: 07 Jul 2017
Posts: 15

Re: What is the value of mn?
[#permalink]
Show Tags
07 Dec 2019, 23:30
value of mn?
A) 5^m * 3^n =45
m has to be 1 n has to be 2 so mn=2.1=2 sufficient hence,A
B)9^(m1)(n2) =1
for 9^anything to be 1>>9^0 =1
m=1 n=2 mn=2.1=2 or m=1 n=50 mn=50.1=50
two different answers so not sufficient



Intern
Joined: 15 Apr 2017
Posts: 32

Re: What is the value of mn?
[#permalink]
Show Tags
08 Dec 2019, 00:10
Q: m*n=? (1) 3^n*5^m = 3^2*5^1 hence, n=2 and m=1 (Sufficient) (2) 9^(m1)(n2) = 1 hence, (m1)(n2) = 0 either m=1 or n=2 (Not Sufficient) Ans: A



Manager
Joined: 13 Apr 2019
Posts: 180
Location: India
GPA: 3.85

Re: What is the value of mn?
[#permalink]
Show Tags
08 Dec 2019, 00:16
Since it is not given that m and n are integers
1. This option give one value for m and n if they are integer We can also get other value for m and n , if they are not integer.
Thus 1 is not sufficient alone.
2. With 2 alone also we get that if value of m is 1, value of n can be anything. If value of n is 2, value of m can be anything.
So 2 alone is also not sufficient
Taken 1 and 2 together is sufficient. As through option 2 we get value of m is 1 or the value of n is 2; and correspondingly we get value of n or m from option 1
So answer is C



GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5748
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)

Re: What is the value of mn?
[#permalink]
Show Tags
Updated on: 08 Dec 2019, 20:15
value of m*n #1 45= 3^2*5^1 so m=1 and n=2 ; mn= 2 sufficient Or 15^1*3^1 mn =1 insufficient #2 9^(m−1)(n−2)=1 possible 9^0 so either m=1 or n=2 but value of m and n can be different if either of them is m=1 or n=2 or could be same as well m*n could vary insufficient From 1&2 M =1 n=2 IMO c
What is the value of mn?
(1) 5m∗3n=45
(2) 9^(m−1)(n−2)=1
Originally posted by Archit3110 on 08 Dec 2019, 00:50.
Last edited by Archit3110 on 08 Dec 2019, 20:15, edited 1 time in total.



Manager
Status: On the journey of achieving
Affiliations: Senior Manager, CA by profession, CFA(USA) Level 2
Joined: 06 Feb 2016
Posts: 207
Location: India
Concentration: Finance, Finance
GPA: 3.82
WE: Other (Commercial Banking)

Re: What is the value of mn?
[#permalink]
Show Tags
08 Dec 2019, 00:52
Let us look at each statements one by one
(1) 5^m∗3^n=45
Here only possible values of m and n which satisfies the equation are m = 1 and n =2 Hence statement 1 alone is sufficient
(2) 9^(m−1)(n−2)=1
As per the statement, the possible values of m and n are 1 m =1 and n=2 , Hence statement 2 alone is also sufficient
So Final Answer is Option D Each Statement Alone is sufficient



Math Expert
Joined: 02 Aug 2009
Posts: 8327

Re: What is the value of mn?
[#permalink]
Show Tags
08 Dec 2019, 01:04
What is the value of mn? Many would surely go wrong by answering A because you would be taking m and n as integers(1) \(5^m*3^n=45=5*3^2\) we can take mn=1*2=2, but you take m as 3, there will be some value of n that will satisfy the given equation. We do not have to find more values but knowing this is enough. (2) \(9^{(m1)(n2)}=1\) either m=1, n=2 or both Combined.. we know at least one of the two m=1 or n=2 is true. Substituting any of the value in statement I would also satisfy the other value, so m=1 and n=2, and mn =2 C
_________________



Senior Manager
Joined: 22 Feb 2018
Posts: 451

Re: What is the value of mn?
[#permalink]
Show Tags
08 Dec 2019, 02:06
What is the value of mn?
(1) 5^m∗3^n=45, 5^m∗3^n = 3^2∗5^1 so, m = 1 and n=2, mn= 2 Hence, sufficient.
(2) 9^(m−1)(n−2)=1 3^2(m1)(n2) = 1 3^(2m2)(2n4) = 1 3^(4mn4n8m+8) = 1 One equation with two variables can have multiple number possibilities for mn. Hence, insufficient.
Imo. A.



Intern
Joined: 18 Feb 2019
Posts: 23
Location: India
GMAT 1: 610 Q43 V31

Re: What is the value of mn?
[#permalink]
Show Tags
08 Dec 2019, 03:32
The answer is A.
Explanation:
FROM A: Given \(5^m*3^n=45\)
For equations with exponents on both sides, we can eliminate base if we can keep the bases same on both sides. This way, we can equate the exponents value of the common bases.
So, in our approach, we try to keep the base same here.
We can express 45 as \(3^2*5^1\)
\(5^m*3^n=3^2*5*1\)
Same integers value would have same exponents. This means, m = 1 (common base 5), and n=2 (common base 3).
Hence, from A, we can get the definite answer of m*n = 1*2 = 2. Eliminate BCE.
FROM B: We can express 1 as 9^0, which is equal to 1.
\(9^(m1)(n2)=9^0\)
This gives us, (m1)(n2)=0 (common base 9) Now, if product of two integers are equal to zero, either one of them, or both of them, are zero. So either m = 1, then we can't get value of n, or n = 2, then we can't get value of m, or both m1 = 0, and n2 = 0, and we get value of m and n.
So we are not getting definite answer of mn. Hence, we eliminate D.
So, the answer is A.



Intern
Joined: 20 Sep 2015
Posts: 17
Location: India
WE: Research (Energy and Utilities)

Re: What is the value of mn?
[#permalink]
Show Tags
08 Dec 2019, 04:47
we need to find nm=?
(1) 5m∗3n=45= 3^2*5^1 comparing indices, we get m=1, n=2 hence mn=2 sufficient to answer.
(2) 9^(m−1)(n−2)=1 in this case (m1)(n1) = 0 so if (m1)=0 then (n1) may or may not equal to zero, giving different n values
similarly if (n1)=0 then (m1) may or may not equal to zero, hence may give different values of n. hence this is insufficient. answer is A.



Intern
Joined: 31 Aug 2019
Posts: 7

Re: What is the value of mn?
[#permalink]
Show Tags
08 Dec 2019, 06:31
Since that m and n are integers is not given, we can't conlude anything from the first equation. Given the second equation, we know that either m = 1 or n = 2. Combined with (1), each case returns the same pair of (m, n) > mn = 2, but it takes both equations to come to this



Intern
Joined: 02 Sep 2019
Posts: 10

Re: What is the value of mn?
[#permalink]
Show Tags
Updated on: 08 Dec 2019, 22:03
(1) (5^m)∗(3^n) = 45 …(i) 45 = 3^2*5^1 …(ii) From the above two, we get m=1, n=2. Also, for m=0, we will get 3^n = 45 for some real value of n. Therefore, we do not have a unique solution.
(2) 9^{(m1)(n2)} = 1 …(i) 9^{(m1)(n2)} = 9^0 …(ii) Comaparing (i) and (ii), we get (m1)(n2) = 0 Therefore, either m1 = 0 or n2 = 0 For m=1, n can take any real value and still satisfy (i). Therefore, we do not have a unique solution. Similarly, for n=2, m can take any real value and still satisfy (ii). Therefore, we do not have a unique solution.
Combining statements 1 and 2 we get m = 1 and n = 2 which is a unique solution. Therefore, Choice C is the answer.
Originally posted by jhavyom on 08 Dec 2019, 06:39.
Last edited by jhavyom on 08 Dec 2019, 22:03, edited 1 time in total.



Intern
Joined: 17 Aug 2019
Posts: 1

Re: What is the value of mn?
[#permalink]
Show Tags
08 Dec 2019, 08:54
What is the value of mn?
(1) 5m∗3n=455m∗3n=45
(2) 9(m−1)(n−2)=1
Let's assess option 1. the Prime Factorization of 45 is 3^2 and 5. Hence, we can find the unique solution for m and n. Now need to check for option 2
Option 2, result of any numbers raised to the power of 0 is zero. From here, (m1)(n2) = 0 However, there are many solutions possible. (E.g. m=1 and n=3 or m=2 and n=2). Hence, this option only is not sufficient to answer
In conclusion, option 1 only is suffice to answer, but option 2 only is not sufficient (A)



Intern
Joined: 08 Apr 2017
Posts: 3

Re: What is the value of mn?
[#permalink]
Show Tags
08 Dec 2019, 12:35
ANSC, Statement A will be sufficient if m and n are integer.



Intern
Joined: 09 Dec 2019
Posts: 10

Re: What is the value of mn?
[#permalink]
Show Tags
09 Dec 2019, 04:57
(1) (5^m)∗(3^n) = 45 Since m and n are not integers, they can take any real value. Not sufficient.
(2) 9^{(m1)(n2)} = 1 9^{(m1)(n2)} = 9^0 From the above two equations, (m1)(n2) = 0 Therefore, either m1 = 0 or n2 = 0 For m=1, n can take any real value. For n=2, m can take any real value.
Combining (1) and (2) m = 1, n = 2 Unique solution. C is the answer.



VP
Joined: 24 Nov 2016
Posts: 1139
Location: United States

Re: What is the value of mn?
[#permalink]
Show Tags
09 Dec 2019, 11:07
Quote: What is the value of mn?
(1) \(5^m∗3^n=45\)
(2) 9(m−1)(n−2)=1 (1) \(5^m∗3^n=45\) insufic\(5^m∗3^n=5*3^2…(m,n)=(1,2;ln(45)/ln(5),0;0,ln(45)/ln(3)\) (2) \(9^{(m−1)(n−2)}=1\) insufic(m,n)=(1,any;any,2) (1)&(2) suficFrom (2) we know that they are integers ≠ 0, so from (1) mn=(1,2)=2. Ans (C)




Re: What is the value of mn?
[#permalink]
09 Dec 2019, 11:07



Go to page
1 2
Next
[ 21 posts ]



