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Difficulty:
85%
(hard)
Question Stats:
41% (02:01) correct
59%
(02:00)
wrong
based on 73
sessions
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If a > b, is (a + b) an integer?
Statement 1: (a - b) is an integer
Statement 2: a + 2b is an integer
Updated on: 22 Mar 2020, 12:02
Originally posted by GMATWhizTeam on 22 Mar 2020, 09:54.
Last edited by GMATWhizTeam on 22 Mar 2020, 12:02, edited 1 time in total.
Last edited by GMATWhizTeam on 22 Mar 2020, 12:02, edited 1 time in total.
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Solution
Step 1: Analyse Question Stem
- • a > b
Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE
Statement 1: (a - b) is an integer.
- • If a and b are integers, then a – b will be integer
- o a + b will also be integer.
- o a + b = 1.4 + 0.4 = 1.8 is not an integer.
Hence, statement 1 is not sufficient, we can eliminate answer options A and D
Statement 2: a + 2b is an integer.
- • If a and b are integers, then a + 2b is an integer
- o a + b is also an integer.
- o a + b = 0.9, is not an integer.
Hence, statement 2 is also not sufficient, we can eliminate answer options B.
Step 3: Analyse Statements by combining.
From statement 1: a – b is an integer
From statement 2: a + 2b is an integer
By combining the two,
- • 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
