Data Sufficiency

The product of positive integers m and n is 36. What is the value of m + n?

(1) m is evenly divisible by 9.

(2) n is evenly divisible by 2.

what does evenly divisible mean.Does it mean that the quotient is even or it means that the number is completely divisible

when A is evenly divisible by B means remainder is 0 or A is multiple of B.

For ex 9 is evenly divisible by 3.

Given,

m*n=36

m+n=?

stmt1,

m=9a

No info abt n

Insuff


stmt2,

n=9b

No info abt m

Insuff

combining 1 and 2,

m*n=9a*2b=36

m=9,n=4,m+n=13

m=18,n=2,m+n=20

Insuff

Pick E

mn= 36 = 2 x 18, 3, x 12 , 4 x 9 , 6 x6

m + n = ?

statement 1)

m is evenly divisible by 9 means that m/9 leaves no remainder...

so m = 9 or 18
so the sum could be 18 + 2 = 20 or 4 + 9 = 13

insufficient...

statement 2)
n is even...
almost all the combinations have one number even... so the sum will be different... insufficient...

together...

m is divisble by 9 and n by 2
sum could be 18 + 2 = 20 or 4 + 9 = 13
since we have 2 diff sums again...
insufficient..

PIck E

I think the quickest way is to do this:

breakdown 36 into number components: 3 x 2 x 2 x 3

I) m can be 9 (n = 4, from 2x2)or 18 (n=2) - more than 2 choices therefore insufficient
II) n can be 2 or [2 x any of the other numbers] - more than 2 choices therefore insufficient

combined:

m can be 9, n can be 4
or
m can be 18, n can be 2

therefore, E

mrinal2100 wrote:The product of positive integers m and n is 36. What is the value of m + n?

(1) m is evenly divisible by 9.

(2) n is evenly divisible by 2.

what does evenly divisible mean.Does it mean that the quotient is even or it means that the number is completely divisible