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If m and n are positive integers, is mn <= 6?

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If m and n are positive integers, is mn <= 6? [#permalink] New post   25 Mar 2020, 01:31
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If m and n are positive integers, is \(mn \leq 6\)?


(1) \(m + n = 5\)

(2) \(1 \leq m \leq 3\) and \(2 \leq n \leq 4\)
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A
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Re: If m and n are positive integers, is mn <= 6? [#permalink] New post   25 Mar 2020, 02:16
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Quote:
If m and n are positive integers, is mn≤6?


(1) m+n=5

(2) 1≤m≤3 and 2≤n≤4



statement 1:

m+n = 5
m,n can be: (1,4),(2,3),(3,2),(4,1)
mn is always \(\le 6\)
sufficient

statement 2:
m,n can be (1,2); mn \(\lt 6\)
m,n can be (3,4); mn \(\gt 6\)
not sufficient
Ans: A
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Re: If m and n are positive integers, is mn <= 6? [#permalink] New post   25 Mar 2020, 05:01
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(1) since m,n are positive integers, possible sets of (m,n) can be (1,4),(2,3),(3,2),(4,1). All these sets yield mn<=6
SUFFICIENT

(2) If (m,n)=(1,2), then mn<=6. However, if (m,n)=(3,4) then mn>6. We don't know which (m,n) is used
NOT SUFFICIENT

FINAL ANSWER IS (A)

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Re: If m and n are positive integers, is mn <= 6? [#permalink] New post   25 Mar 2020, 05:41
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Quote:
If m and n are positive integers, is mn≤6mn≤6?


(1) m+n=5m+n=5

(2) 1≤m≤31≤m≤3 and 2≤n≤4


(1) sufic

1≤m,n≤5: m+n=5
min: m=1, n=4: 4*1=4
max: m=2, n=3: 3*2=6
4≤mn≤6

(2) insufic

m=3, n=3: 3*3=9
m=3, n=2: 3*2=6

Ans (A)
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Re: If m and n are positive integers, is mn <= 6? [#permalink] New post   25 Mar 2020, 07:20
m, n are positive integeres i.e. > 0 integers

i) m+n = 5 => m,n can be (2,3; 3,2; 4,1; 1,4)
In any case mn wil be either 6 or 4
Sufficient

ii) m can be 3, n can be 3 or 4 => mn will be 9 or 12 i.e. > 6
m can be 1, n can be 3 => mn will be 3 less than 6

Not Sufficient

Answer - A
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Re: If m and n are positive integers, is mn <= 6? [#permalink] New post   25 Mar 2020, 11:44
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If m and n are positive integers, is mn≤6?

(1) m+n=5
1+4 = 5; m*n = 4
2+3 = 5; m*n = 6
3+2 = 5; m*n = 6
4+1 = 5; m*n = 4
All YES Cases.

SUFFICIENT.


(2) 1≤m≤3 and 2≤n≤4
m = 3 and n = 2; m*n = 6 YES
m = 3 and n = 4; m*n = 12 NO

INSUFFICIENT.

Answer A.
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Re: If m and n are positive integers, is mn <= 6? [#permalink] New post   25 Mar 2020, 11:55
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If m and n are positive integers, is mn≤6mn≤6?


(1) m+n=5

(2) 1≤m≤3 and 2≤n≤4

1) Since m and n are positive integers the values mn can take are 4 and 6 (1+4 or 2+3). Sufficient
2) mn can take any integer value divisible by 2, 3 and 4 starting from 2 to 12. Not sufficient.
A is the answer.
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Re: If m and n are positive integers, is mn <= 6? [#permalink] New post   25 Mar 2020, 22:04
If m and n are positive integers, is mn≤6mn≤6?

We have to find if mXn is equal to or less than 6

(1) m+n=5m+n=5

(2) 1≤m≤3 and 2≤n≤4

Statement 1

m+n=5

so either m can be 3, 2, 1 or 4 and n can be 3, 2, 1 or 4 either way 2X3 =6 or 4X1 = 4 all values are either less than 6 or equal to 6.

Hence statement 1 is sufficient

Statement 2:

1≤m≤3 and 2≤n≤4

similarly if m=1 and n=4 then 4X1= 4 less than 6
m=2 and n=3 then 2X3=Equal to 6

Hence statement 2 is also sufficient

IMO D
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Re: If m and n are positive integers, is mn <= 6? [#permalink] New post   07 Jul 2021, 18:00
Interesting question. Getting statement 2 quickly out of the way can allow you to really think about statement 1. It's simply not possible to get above 6 if both POSITIVE INTEGERS equal to 5.
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Re: If m and n are positive integers, is mn <= 6? [#permalink]
07 Jul 2021, 18:00
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