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# Is m > 5 ? (1) (m - 10)(m - 5) > 0 (2) m > 0

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Math Expert
Joined: 02 Sep 2009
Posts: 58381
Is m > 5 ? (1) (m - 10)(m - 5) > 0 (2) m > 0  [#permalink]

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17 Jun 2018, 04:35
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Difficulty:

45% (medium)

Question Stats:

55% (01:11) correct 45% (01:02) wrong based on 86 sessions

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Is m > 5 ?

(1) (m - 10)(m - 5) > 0
(2) m > 0

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Joined: 09 Oct 2017
Posts: 1
Re: Is m > 5 ? (1) (m - 10)(m - 5) > 0 (2) m > 0  [#permalink]

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17 Jun 2018, 05:11
Option C ,

Statement 1 - M can be negative or positive = positive result --- Not Sufficient
Statement 2 - NS : It can take any positive value
Combining - Only positive value can be obtained when m>5 and m>10. --Sufficient
Intern
Joined: 05 Mar 2017
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Re: Is m > 5 ? (1) (m - 10)(m - 5) > 0 (2) m > 0  [#permalink]

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17 Jun 2018, 05:24
1
option E

Statement 1: Take m=1,11 .Both will satisfy the equation.So insufficient.
Statement 2: doesn't give any information alone.

After combining also we can get two different value .Example M=1 and M=11 .so again insufficient.
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Re: Is m > 5 ? (1) (m - 10)(m - 5) > 0 (2) m > 0  [#permalink]

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17 Jun 2018, 05:30
According to Statement 1, m<5 or m>10. Thus, insufficient.

According to statement 2, m>0. Still we don't know whether ot is greater than 5. Thus, insufficient.

Combining both we know, it is a positive value. Thus, m could be less than 5 but greater than 0 or could be greater than 10. We still don't know whether it is greater than 5 as there are two possibilities. Again insufficent.

Thus, I would go with E.
Math Expert
Joined: 02 Aug 2009
Posts: 7959
Re: Is m > 5 ? (1) (m - 10)(m - 5) > 0 (2) m > 0  [#permalink]

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17 Jun 2018, 07:38
Bunuel wrote:
Is m > 5 ?

(1) (m - 10)(m - 5) > 0
(2) m > 0

1) (m-10)(m-5)>0
This equation should immediately tell you that m between 5 and 10 inclusive will give you answer NO, otherwise yes..
WHY so?
For equation to hold true, both m-10 and m-5 should be of same sign..
a) when m<5, both m-10 and m-5 are negative so negative*negative=positive
b) when m>10, both m-10 and m-5 are positive, so positive*positive=positive
c) 5<m<10, m-10 is negative and m-5 is positive, so positive*negative=negative
Insufficient
2) m>0
m can be 1,2 or 9,10
Insufficient

Combined..
m can be 1,2,3,4 or >10
Again insufficient

E
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Re: Is m > 5 ? (1) (m - 10)(m - 5) > 0 (2) m > 0  [#permalink]

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23 Jun 2018, 22:00
Hello, vaibhavkapoor100

Statement 1 - M can be negative or positive = positive result --- Not Sufficient
Statement 2 - NS : It can take any positive value
Combining - Only positive value can be obtained when m>5 and m>10. --Sufficient

We can't find the conclusion by combining both options.
If we put a value such as 2, 3, 4(positive & <5) & 11, 12(positive & >5) we will get the desired result which satisfies both the statements.
So, both the options are not sufficient to answer the question.

Hop it helps.
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Re: Is m > 5 ? (1) (m - 10)(m - 5) > 0 (2) m > 0  [#permalink]

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28 Feb 2019, 05:33
When i solve equation 1.
I get values of m as:
m-5>0
m-10>0
In either case, M>5
Shouldnt this be sufficient ?
m^2-5m-10m+50
m(m-5) -10(m-5)??
Math Expert
Joined: 02 Aug 2009
Posts: 7959
Re: Is m > 5 ? (1) (m - 10)(m - 5) > 0 (2) m > 0  [#permalink]

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28 Feb 2019, 05:50
1
hsn81960 wrote:
When i solve equation 1.
I get values of m as:
m-5>0
m-10>0
In either case, M>5
Shouldnt this be sufficient ?
m^2-5m-10m+50
m(m-5) -10(m-5)??

You are reading statement I wrongly..
(m-5)(m-10)>0 means both m-5 and m-10 have same sign..
Both are negative ...
m-5<0, that is m<5 and m-10<0, that is m<10...so m<5
Both are positive..
m-5>0, that is m>5 and m-10>0, that is m>10...so m>10..

So the range is m<5 and m>10..
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Re: Is m > 5 ? (1) (m - 10)(m - 5) > 0 (2) m > 0  [#permalink]

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28 Feb 2019, 07:08
Re: Is m > 5 ? (1) (m - 10)(m - 5) > 0 (2) m > 0   [#permalink] 28 Feb 2019, 07:08
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