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

Question

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.

fluke · Answer

The best way is to write all combinations and work:

1,36
2,18
3,12
4,9
6,6

2,18 & 4,9 stand out.
m=18,n=2; m+n=20
OR
m=9,n=4; m+n=13

Both these sets qualify and thus both statements together NOT SUFFICIENT.

Ans: "E"

amit2k9 · Answer

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.

Spidy001 · Answer

1. Not sufficient

m = 9 18 27 36...

n =4 2 1...

2. Not sufficient

n = 2 4 6 8 10 12 ...18 ...26

m =18 9 6 ...... respectively

together,

m is multiple of 9 and n is multiple of 2

m 9 18 
 n 4 2 respectively.
 Not sufficient.

Answer is E.

mdn203 · Answer

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.

gmatopoeia · Answer

m*n=36
m+n=?

Prime factors of 36: 3, 3, 2, 2

From Statement 1 
possible values of m: 9, 18 and 36
Insufficient

From Statement 2 
posible values of n: 2, 4, 6, 18, 12, 36
Insufficient

Statement 1 + 2 
m*n=36 
--> m=9, n=4, or
--> m=18, n=2
Insufficient.

Answer: E

nageshshiv · Answer

Plug-in numbers 9*4 , 18*2 
+1 for E

Bowtie · Answer

not sure if this is 700 level, but answer is e.

statement 1: 9, 18 and 36 are all factors of 36 and divisbile by 9, insuff

Statement 2: could be 2, 6, 12, 18, 36 so insuff

Statement 1&2: could be 18 and 2 or 9 and 4. so insuff

i am sure fluke did a better job explaining

MathRevolution · Answer

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem.
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.

saroshgilani · Answer

what does evenly divisible means?
if m is evenly divisible by 9, doesn't that mean that m can only be 18 and 36?

Bunuel · Answer

Evenly divisible simply means divisible, so divisible without a remainder.

saroshgilani · Answer

thank you  Bunuel ....
this explains a lot of questions....

ArjunJag1328 · Answer

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

KanishkM · Answer

Take some time , Dont Rush

m and n = 36
9 * 4 
18 * 2 
36 * 1

(1) m is evenly divisible by 9.
18 * 2 
36 * 1

2 cases insufficient

(2) n is evenly divisible by 2
9 * 4 
18 * 2

2 cases insufficient

Combine 
18 * 2 
9 * 4

2 cases insufficient

E

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

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

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