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

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Manager
Joined: 18 Jun 2011
Posts: 52
The product of positive integers m and n is 36. What is the  [#permalink]

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18 Jun 2011, 03:28
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Difficulty:

35% (medium)

Question Stats:

65% (01:30) correct 35% (01:20) wrong based on 307 sessions

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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.
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Joined: 20 Dec 2010
Posts: 1795
Re: D.S - 700 level question  [#permalink]

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18 Jun 2011, 03:43
guygmat 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.

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"
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Re: D.S - 700 level question  [#permalink]

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23 Jun 2011, 03:18
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.
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Re: D.S - 700 level question  [#permalink]

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23 Jun 2011, 21:58
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.

Intern
Joined: 24 Jun 2011
Posts: 1
Re: D.S - 700 level question  [#permalink]

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24 Jun 2011, 04:29
1
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.
Manager
Joined: 20 Jul 2011
Posts: 103
GMAT Date: 10-21-2011
Re: D.S - 700 level question  [#permalink]

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05 Sep 2011, 08:51
1
Quote:
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.

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.

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Re: D.S - 700 level question  [#permalink]

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05 Sep 2011, 22:22
Plug-in numbers 9*4 , 18*2
+1 for E
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Manager
Joined: 08 Sep 2011
Posts: 58
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Re: D.S - 700 level question  [#permalink]

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09 Sep 2011, 07:35
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
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Re: The product of positive integers m and n is 36. What is the  [#permalink]

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15 Sep 2015, 08:17
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.

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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Re: The product of positive integers m and n is 36. What is the  [#permalink]

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19 Sep 2015, 02:10
1
what does evenly divisible means?
if m is evenly divisible by 9, doesn't that mean that m can only be 18 and 36?
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Posts: 52906
Re: The product of positive integers m and n is 36. What is the  [#permalink]

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20 Sep 2015, 07:31
1
saroshgilani wrote:
what does evenly divisible means?
if m is evenly divisible by 9, doesn't that mean that m can only be 18 and 36?

Evenly divisible simply means divisible, so divisible without a remainder.
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Re: The product of positive integers m and n is 36. What is the  [#permalink]

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20 Sep 2015, 12:08
Bunuel wrote:
saroshgilani wrote:
what does evenly divisible means?
if m is evenly divisible by 9, doesn't that mean that m can only be 18 and 36?

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

thank you Bunuel....
this explains a lot of questions....
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Re: The product of positive integers m and n is 36. What is the  [#permalink]

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10 Oct 2018, 10:14
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
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Re: The product of positive integers m and n is 36. What is the  [#permalink]

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05 Feb 2019, 03:18
guygmat 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.

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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Re: The product of positive integers m and n is 36. What is the   [#permalink] 05 Feb 2019, 03:18
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# The product of positive integers m and n is 36. What is the

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