Bunuel wrote:
If a, b, and c are positive integers such that a < b < c, is a% of b% of c an integer?
(1) b = (a/100)^(-1)
(2) c = 100^b
Kudos for a correct solution.
Target question: Is a% of b% of c an integer? This is a great candidate for
rephrasing the target question. Aside: See our video with tips on rephrasing the target question (below)a% of b% of c is the same as (a/100)(b/100)(c), which equals abc/10,000
So, we can rephrase the target question as follows:
REPHRASED target question: Is abc/10,000 an integer? We can REPHRASE the target question even further...
RE-REPHRASED target question: Is abc a multiple of 10,000? Statement 1: b = (a/100)^-1 In other words, b = 100/a
There are several values of a, b and c that satisfy this condition. Here are two:
Case a: a = 1, b = 100 and c = 1000, in which case abc = 100,000. Here,
abc IS a multiple of 10,000Case b: a = 1, b = 100 and c = 101, in which case abc = 10,100. Here,
abc is NOT a multiple of 10,000Since we cannot answer the
RE-REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: c = 100^b IMPORTANT: We are told that a, b and c are POSITIVE INTEGERS and that a < b < c
So, we can be certain that b
> 2.
If b is greater than or equal to 2, then c (which equals 100^b) can equal 10,000 or 1,000,000 or 100,000,000 and so on.
Notice that ALL of these possible values of c are multiples of 10,000
So, if c is a multiple of 10,000, then
abc MUST be a multiple of 10,000Since we can answer the
RE-REPHRASED target question with certainty, statement 2 is SUFFICIENT
Answer: B
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