Is m > n ? (1) m^2 + n^2 > 2mn (2) |m|n = m|n|

Solution

Step 1: Analyse Question Stem

Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE

• \(m^2 + n^2 -2mn > 0\)
• \((m-n)^2 > 0\)

o Here, we can’t say where m > n or not, because the power of m-n is 2, and even power of any number always gives us positive number.

• EIther m and n both will have same sign or at least one of them is zero.
• Case I: If m = 1 and n = 2,

o Then, |m|n = m|n| = 2, m < n
• Case II: If m = -1 and n = -2,

o Then |m|n = m|n| = -1, m > n
• We are getting different results
• We can’t answer the question with this information.

Step 3: Analyse Statements by combining.

• Case I: If m = 0 and n = 2, then |m|n = m|n| = 0

o 0 < 2, and m < n
• Case II: If m = 2 and n = 0, then |m|n = m|n| = 0

o 2 > 0 and m < n
• We are getting different results.