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09 Dec 2019, 11:07
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Quote:
What is the value of mn?
(1) \(5^m∗3^n=45\)
(2) 9(m−1)(n−2)=1
(1) \(5^m∗3^n=45\)
(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) sufic
From (2) we know that they are integers ≠ 0, so from (1) mn=(1,2)=2.
Ans (C)
04 Jan 2020, 10:57
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gmatbusters
GMATBusters’ Quant Quiz Question -1
What is the value of mn?
(1) \(5^m*3^n=45\)
(2) \(9^{(m-1)(n-2)}=1\)
Asked: What is the value of mn?
(1) \(5^m*3^n=45\)
Since m & n may not be positive integers
NOT SUFFICIENT
(2) \(9^{(m-1)(n-2)}=1\)
(m-1)(n-2) = 0
Either m=1 or n=2 or both
NOT SUFFICIENT
(1) + (2)
(1) \(5^m*3^n=45\)
(2) \(9^{(m-1)(n-2)}=1\)
m = 1 or n=2 or both
If m=1
5^1*3^n=45
n=2
If n=2
5^m*3^2 = 45
m=1
m=1 & n=2
mn=2
SUFFICIENT
IMO C
12 Mar 2020, 11:29
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Sir, we factorise a number into prime factors.
In statement A, 15 is not a prime factor.
So, how did you eliminate A?
In statement A, 15 is not a prime factor.
So, how did you eliminate A?
Archit3110
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
#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
