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What is the value of mn?

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Kinshook

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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

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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?

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

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29 Mar 2020, 05:04

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Quote:

GMATBusters’ Quant Quiz Question -1

What is the value of mn?

(1) \(5^m*3^n=45\)

(2) \(9^{(m-1)(n-2)}=1\)

HI VeritasKarishma, Bunuel, GMATBusters

Can you please show me how apart from m=1 & n=2 doesn't satisfy?

Any other values please.

GMATBusters

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29 Mar 2020, 05:12

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Please rephrase your question, I am unable to understand your doubt.

NandishSS

Quote:

GMATBusters’ Quant Quiz Question -1

What is the value of mn?

(1) \(5^m*3^n=45\)

(2) \(9^{(m-1)(n-2)}=1\)

HI VeritasKarishma, Bunuel, GMATBusters

Can you please show me how apart from m=1 & n=2 doesn't satisfy?

Any other values please.

Bunuel

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29 Mar 2020, 05:15

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NandishSS

Quote:

GMATBusters’ Quant Quiz Question -1

What is the value of mn?

(1) \(5^m*3^n=45\)

(2) \(9^{(m-1)(n-2)}=1\)

HI VeritasKarishma, Bunuel, GMATBusters

Can you please show me how apart from m=1 & n=2 doesn't satisfy?

Any other values please.

This is a copy of the following GMAT Club question: https://gmatclub.com/forum/new-tough-an ... l#p1029249 Below is an explanation for statement (1):
if \(x\) and \(y\) are integers then as \(75=3^1*5^2\) then \(x=1\) and \(y=2\) BUT if they are not, then for any value of \(x\) there will exist some non-integer \(y\) to satisfy given expression and vise-versa (for example if \(y=1\) then \(3^x*5^y=3^x*5=75\) --> \(3^x=25\) --> \(x=some \ irrational \ #\approx{2.9}\)). Not sufficient.

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29 Mar 2020, 05:19

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GMATBusters

Please rephrase your question, I am unable to understand your doubt.

NandishSS

Quote:

GMATBusters’ Quant Quiz Question -1

What is the value of mn?

(1) \(5^m*3^n=45\)

(2) \(9^{(m-1)(n-2)}=1\)

HI VeritasKarishma, Bunuel, GMATBusters

Can you please show me how apart from m=1 & n=2 doesn't satisfy?

Any other values please.

Can you show how A is not sufficient if m & n are positive. Any example .

\(5^m*3^n=45 ==> 5^m*3^n=5^1*3^2\)

I couldn't figureout anyother value than m=1 & n=2

Bunuel

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29 Mar 2020, 05:21

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NandishSS

Can you show how A is not sufficient if m & n are positive. Any example .

\(5^m*3^n=45 ==> 5^m*3^n=5^1*3^2\)

I couldn't figureout anyother value than m=1 & n=2

Already replied tho your question: https://gmatclub.com/forum/what-is-the- ... l#p2483882

GMATBusters

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29 Mar 2020, 05:22

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ST1 : \(5^2 = 25\)
\(5^3 = 125\)
hence there is a number m , such that 2<m<3 and \(5^m = 45\)

Similarly, \(3^3 = 27 \) and \( 3^4 = 81\)
hence there is a number n , such that 3<n<4 and \(3^n = 45\)

I hope it is clear now

NandishSS

Quote:

GMATBusters’ Quant Quiz Question -1

What is the value of mn?

(1) \(5^m*3^n=45\)

(2) \(9^{(m-1)(n-2)}=1\)

HI VeritasKarishma, Bunuel, GMATBusters

Can you please show me how apart from m=1 & n=2 doesn't satisfy?

Any other values please.

NandishSS

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29 Mar 2020, 05:26

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Thanks Bunuel, GMATBusters

It is Clear now

pranayeekarmakar

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06 Apr 2020, 11:49

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St1.
5^m . 3^n = 5.3^2
or 5^(m-1)= 3^(2-n)
or m-1=2-n
or m+n=3
so m=1 , n=2 or m=-3, n=5 so imsufficient

St2.
3^2(m-1) (n-2)=1
or 2(m-1) (n-2) = 0
so m=1 or n=2 or m=1 & n=2
so insufficient

St1 + St2

if m=1, n=3-1=2 so mn =2
if n=2 , m=1 so mn=2

sufficient hence C

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06 Apr 2020, 14:44

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Answer is C

(1) right off the bat, i noticed it doesn't say m and n are integers. This leaves the door wide open for odd combinations of numbers to make the statement true. INSUFFICIENT
(2) as long as m or n is 1 or 2 and the exponent equals 0, the other number can be anything. INSUFFICIENT

C -> (2) states that m or n has to be 1 or 2, and placing that condition on (1) forces the other number to a single value. SUFFICIENT

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Bunuel

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