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Re: If a and b are positive numbers, is a < b?
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17 Jun 2017, 03:45
Given a and b are positive numbers, we need to find out if a < b?
(1) a < b/2 + 2 Equation can be re-written as a-2 < b/2 For values a = b = 10 statement a<b is false as a=b Similarly, for values a = 3,b=3.2 statement a<b is true Hence, not sufficient.
(2) a < b/2 - 2 Equations can be rewritten as a+2 < b/2 If a=b=any value, the equation a+2 < b/2 will not stand. If a>b for any positive number, the equation a+2 < b/2 will not stand. Only when a<b, this statement stands.
Hence this statement alone is sufficient.(Option B)
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Re: If a and b are positive numbers, is a < b?
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17 Jun 2017, 08:38
Top Contributor
bkpolymers1617 wrote:
If a and b are positive numbers, is a < b?
(1) a < b/2 + 2 (2) a < b/2 - 2
Target question:Is a < b?
Given: a and b are positive numbers
Statement 1: a < b/2 + 2 This statement doesn't FEEL sufficient, so I'll TEST some values. There are several values of a and b that satisfy statement 1. Here are two: Case a: a = 0 and b = 2, in which case a < b Case b: a = 2.5 and b = 2, in which case a > b Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: a < b/2 - 2 Since b is POSITIVE, we know that b/2 < b We can also say that b/2 - 2 < b/2 We can COMBINE these inequalities to get: a < b/2 - 2 < b/2 < b If we ignore the middle parts, we see that a < b Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Re: If a and b are positive numbers, is a < b?
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15 Oct 2018, 07:17
Bunuel wrote:
If a and b are positive numbers, is a < b?
(1) a < b/2 + 2. If b = 2 and a = 2, then answer is NO but if b = 4 and a = 1, then the answer is YES. Not sufficient.
(2) a < b/2 - 2. Notice that b/2 is less than b, so b/2 - 2 is even less. So, even if b/2 - 2 is greater than a, then so must be b alone. Sufficient.
Answer: B.
Dear brunel Any tips in deciding the numbers to test the inequalities? i am taking too much in agreeing on the numbers to test the DS questions. thanks in advance
gmatclubot
Re: If a and b are positive numbers, is a < b?
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15 Oct 2018, 07:17