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27 Oct 2021, 07:30
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Difficulty:
65%
(hard)
Question Stats:
53% (01:57) correct
47%
(02:10)
wrong
based on 89
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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) \(2 – (a + b) > 0\)
(1) \(a ≤ b < 2\)
(2) \(2 – (a + b) > 0\)
27 Oct 2021, 10:24
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Bunuel
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 = 1035
Case b: a = 1 and b = 1. In this case, the answer to the target question is 1a35 = 1135
Since we can’t answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: 2 – (a + b) > 0
Add (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 = 1035
Case b: a = 0 and b = 1. In this case, the answer to the target question is 1a35 = 1035
Notice that the answer to the target question is the same in both cases: 1a35 = 1035
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer: B
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27 Oct 2021, 10:47
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BrentGMATPrepNow
I believe there would be another case for 2nd statement.
a= 1 and b= 0, since a + b < 2
In that case statement 2 would be insufficient as well.
I am yet to check the statements combined. I will do that edit shortly.
Posted from my mobile device
