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m and n are positive integers. What is the value of m?

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m and n are positive integers. What is the value of m?  [#permalink]

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09 Mar 2016, 12:23
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65% (hard)

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65% (02:48) correct 35% (02:38) wrong based on 199 sessions

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m and n are positive integers. What is the value of m?

(1) n > |12 - m|
(2) 3m + 4n = 45

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Re: m and n are positive integers. What is the value of m?  [#permalink]

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11 Mar 2016, 02:55
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St1: n > |12 - m| --> not sufficient as we can have many values for m

St2: 3m + 4n = 45
3(3) + 4(9) = 45
3(7) + 4(6) = 45
3(11) + 4(3) = 45
We have 3 different values for m. So not sufficient

Combining St1 and St2, we have
6 > |12 - 7| --> Value of m can be 7
3 > |12 - 11| --> Value of m can be 11
We do not get a unique value of m and hence not sufficient.

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Re: m and n are positive integers. What is the value of m?  [#permalink]

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16 Mar 2016, 06:47
m and n are positive integers. What is the value of m?

(1) n > |12 - m|
If 12-m>0 => m<12 => n>(12-m) => n+m>12
If 12-m<0 => m>12 => n>-(12-m) => m-n<12
Single value of m cannot be estimated with the above information. INSUFFICIENT.

(2) 3m + 4n = 45
Single value of m cannot be estimated with the above inf. INSUFFICIENT.

combining 1 and 2
It is clear from the graph that there exist multiple values of m satisfying both the conditions. Hence single value of m cannot be obtained even after combining both the statements.
Hence E.

Thanks.
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m and n are positive integers. What is the value of m?  [#permalink]

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05 Aug 2018, 19:42
Bunuel wrote:
m and n are positive integers. What is the value of m?

(1) n > |12 - m|
(2) 3m + 4n = 45

GIVEN: m and n are positive non zero integers

(1) n and m can be many different values. Not Sufficient

(2) 45 is divisible by 3, but not by 4. So find the LCM of 3 and 4 which = 12. So n can only be values that lead to multiple of 12.
So n = 3, 6, or 9

If n = 3, m = 11
If n = 6, m = 7
If n = 9, m = 3

Not Sufficient

(1) + (2) n = 3 and m = 11 satisfies both statements. n = 6 and m = 7 satisfies both statements.

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m and n are positive integers. What is the value of m?  [#permalink]

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18 Aug 2018, 04:56
@MikeScarn;

[b](2) 45 is divisible by 3, but not by 4. So find the LCM of 3 and 4 which = 12. So n can only be values that lead to multiple of 12.
So n = 3, 6, or 9
[/b] - i dont know this concept, but looks very handy..can you pleasse explain? Also are there any corollaries of this that u can tell.
m and n are positive integers. What is the value of m?   [#permalink] 18 Aug 2018, 04:56
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