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.

the sets are 1*36;2*18;3*12;4*9 and 6*6. also the mirror images of these sets except 6*6.

thus 18,2 and 9,4 creep in.

E it is.

1. m is divisible by 9, hence m can be 9, 18, 36. (1) is not sufficient
2. n is divisible by 9, hence m can be 2, 4, 18. (2) is not sufficient.

m is divisible by 9, and n is divisible by 2: we have two pairs: (9,4) and (18,2). Not sufficient.

Hence E.

Plug-in numbers 9*4 , 18*2
+1 for E
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Remember equal number of variables and independent equations ensures a solution.

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.

In the original condition we have 2 variables (m,n) and 1 equation (mn=36) thus we need 1 more equation to match the number ov variables and equations. Since there is 1 each in 1) and 2), there is high probability that D is the answer.

In case of 1), (m,n)=(9,4),(18,2) the answer is not unique and therefore the condition is not sufficient.
In case of 2), ((m,n)=(9,4),(18,2) the answer is not not unique, and therefore the condition is not sufficient

Using both 1) & 2) together, (m,n)=(9,4),(18,2) the answer is not unique, and the condition is not sufficient.
Therefore the answer is E.

Normally for cases where we need 1 more equation, such as original conditions with 1 variable, or 2 variables and 1 equation, or 3 variables and 2 equations, we have 1 equation each in both 1) and 2). Therefore D has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) separately. Here, there is 59 % chance that D is the answer, while A or B has 38% chance. There is 3% chance that C or E is the answer for the case. Since D is most likely to be the answer according to DS definition, we solve the question assuming D would be our answer hence using 1) and 2) separately. Obviously there may be cases where the answer is A, B, C or E.
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Evenly divisible simply means divisible, so divisible without a remainder.
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M x N = 36, M + N = ?

St1: M/9 = {9,18,27,36}
Insufficient because we don't have any information about N

St2: N/2 = {2,4,6,8,10.....,36}
Same as St1 but here we don't have any information about M

St1 + St2:
Pick values from each statement and check it.
For eg:
9 x 4 = 36, 9 + 4 = 13
18 x 2 = 36, 18 + 2 = 20

Multiple values!!

Hence its E