If |m/5| |(m+10)/10|, which of the following could be true?

Question

If |\frac{m}{5}| > |\frac{m+10}{10}| , which of the following could be true? A. 2 < m < 10 B. m > 10 C. 0 < m < 2 D. m = 5 E. 5 < m < 7

chetan2u · Answer

Use the options.   All options give you m as positive integers, so both m and m+10 should be positive.  
Therefore, remove the MOD without any problems.

|\frac{m}{5}| > |\frac{m+10}{10}|

\frac{m}{5} > \frac{m+10}{10}

2m>m+10......m>10

B

GMATinsight · Answer

To find teh critical value of m for  |\frac{m}{5}| > |\frac{m+10}{10}|

|\frac{m}{5}| = |\frac{m+10}{10}| 
i.e.  2m = m+10 
i.e.  m = 10

i.e. @m=10, the left hand side will be equal to right hand side of inequation.

Now, check with a value such as 15 i.e. beyond critical value
 \frac{m}{5} = 3  and  \frac{m+10}{10} = 2.5

i.e value of m must be greater than 10 for the  given inequation to be true

i.e.  m > 10

Answer: Option B

LaveenaPanchal · Answer

|m/5|>|m+10|/|10|
m^2/25 > (m+10)^2/100 (squaring both sides)
4m^2>m^2+20m+100 = 3m^2-20m-100>0
This boils down to (m-10)(3m+10)>0
M<-10/3 or m>10.
so Option B could be true.

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If |m/5| > |(m+10)/10|, which of the following could be true?

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