bhandariavi wrote:

What is the probability of creating a three digit number with exactly two consecutive primes as digits?

a) 3/100

b) 9/250

c) 9/125

d) 21/250

e) 51/500

I got this question in this forum unanswered properly and without any OA. Got stuck many times when i try to solve this.

Can anyone help me with this cumbersome problem?

This is not a good question. There's no way to tell even what it means, the wording is so poor. The answer choices also make no sense. There are 900 three-digit numbers, so it has to be possible to write the answer as x/900, where x is an integer (x is the number of things with the property we want). No matter what x is, you'll never be able to cancel the fraction x/900 down to any of the answer choices besides A; the denominators in answers B, C, D and E are not factors of 900. Still, no matter how I interpret the question (and I can see several possible legitimate interpretations), the answer is not 3/100. Because the answer choices *can* all be arrived at by canceling a fraction of the form x/1000, I'm guessing the question is not intended to be about 'three digit numbers' at all; instead I imagine it means to ask about numbers from 0 to 999, inclusive. That's not at all clear from the wording.

Then I have no idea just what the phrase "with exactly two consecutive primes as digits" means - this is open to different legitimate interpretations. I assume a number like 302 is one 'with exactly two consecutive primes as digits', since it contains 2 and 3, whereas 325 is not, since it has three consecutive primes as digits. But what about a number like 322? This again contains exactly one pair of consecutive primes, but does not contain exactly two primes. Do we count it? Or perhaps the question means that our number has exactly two consecutive primes as digits and no other digits? So that the only numbers we should count are those like 233, 322, 355, 535, etc? The wording is so ambiguous that solving the question is really testing you psychic abilities - can you guess what the question designer was thinking - and not your GMAT Quant abilities. Just skip it.

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