If a > b, is (a + b) an integer?

Solution

Step 1: Analyse Question Stem

• a > b

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

• If a and b are integers, then a – b will be integer

o a + b will also be integer.
• If a = 1.4 and b = 0.4, then a – b = 1, which is an integer.

o a + b = 1.4 + 0.4 = 1.8 is not an integer.

• If a and b are integers, then a + 2b is an integer

o a + b is also an integer.
• If a = 0.8 and b = 0.1, then a + 2b = 1.0 is an integer

o a + b = 0.9, is not an integer.

Step 3: Analyse Statements by combining.

• If a and b are integers, then a + b is an integer.
• If a and b are non-integers, for example: \(a =\frac{5}{3}\) and \(b = \frac{-1}{3}\),

o In this case also, \(a - b = \frac{5}{3} - (-\frac{1}{3}) = 2\)(Integer) and a + 2b = \(\frac{5}{3}\) + \(2*(\frac{-1}{3})= 1\)(Integer)
o However, \(a + b = \frac{5}{3} + \frac{-1}{3} =\frac{4}{3}\), is a fraction