Bunuel wrote:
The variables a and b represent the hundreds digits of the two numbers in the inequality \(1a35 < 1b45\). What is the value of 1a35 ?
(1) \(a ≤ b < 2\)
(2) \(2 – (a + b) > 0\)
Given: The variables a and b represent the hundreds digits of the two numbers in the inequality 1a35 < 1b45 Target question: What is the value of 1a35 ? Statement 1: a ≤ b < 2 There are several values of a and b that satisfy statement 1 (and the given information). Here are two:
Case a: a = 0 and b = 0. In this case, the answer to the target question is
1a35 = 1035Case b: a = 1 and b = 1. In this case, the answer to the target question is
1a35 = 1135Since we can’t answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: 2 – (a + b) > 0Add (a + b) to both sides of the inequality to get:
2 > a + b There are exactly two pairs of values of a and b that satisfy the inequality
2 > a + b (and the given information). They are:
Case a: a = 0 and b = 0. In this case, the answer to the target question is
1a35 = 1035Case b: a = 0 and b = 1. In this case, the answer to the target question is
1a35 = 1035Notice that the answer to the target question is the same in both cases:
1a35 = 1035Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: B
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I believe there would be another case for 2nd statement.
In that case statement 2 would be insufficient as well.
I am yet to check the statements combined. I will do that edit shortly.