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# Is mn < 11? (1) m + n = 7 (2) 5 ≥ m ≥ 3 and 4 ≥ n ≥ 2

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Math Expert
Joined: 02 Sep 2009
Posts: 50627
Is mn < 11? (1) m + n = 7 (2) 5 ≥ m ≥ 3 and 4 ≥ n ≥ 2  [#permalink]

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18 Jul 2018, 23:06
00:00

Difficulty:

35% (medium)

Question Stats:

69% (00:49) correct 31% (00:56) wrong based on 25 sessions

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Is mn < 11?

(1) m + n = 7

(2) 5 ≥ m ≥ 3 and 4 ≥ n ≥ 2

_________________
Math Expert
Joined: 02 Aug 2009
Posts: 7036
Re: Is mn < 11? (1) m + n = 7 (2) 5 ≥ m ≥ 3 and 4 ≥ n ≥ 2  [#permalink]

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18 Jul 2018, 23:44
Bunuel wrote:
Is mn < 11?

(1) m + n = 7
if m=4 and n=3....mn=4*3=12>11........so not <11
m=0 and n=7.....mn=0<11...................yes
insuff

(2) 5 ≥ m ≥ 3 and 4 ≥ n ≥ 2

max value...5*4=20 so not <11
least value...3*2=6 s0 >11
insuff

combined
5*2=10
4*3=12
insuff
ofcourse m and n need not be integers ...
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: Is mn < 11? (1) m + n = 7 (2) 5 ≥ m ≥ 3 and 4 ≥ n ≥ 2  [#permalink]

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19 Jul 2018, 01:31
Bunuel wrote:
Is mn < 11?

(1) m + n = 7

(2) 5 ≥ m ≥ 3 and 4 ≥ n ≥ 2

Statement 1:
Insufficient

Statement 2:
Max value of m = 5*4 = 20 and Minimum value of m = 3*2 = 6.
Insufficient

1&2:
3+4 = 7 also 3*4 = 12 > 11. False
5+2 = 7 also 5*2 = 10 < 11. True
Insufficient
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Re: Is mn < 11? (1) m + n = 7 (2) 5 ≥ m ≥ 3 and 4 ≥ n ≥ 2 &nbs [#permalink] 19 Jul 2018, 01:31
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