Hi All,
While this question becomes considerably easier IF you have your prime numbers memorized, even if you DON'T have them memorized, you can still get to the correct answer relatively quickly by doing some 'brute force' arithmetic and using the rules of division to avoid a lot of the implied 'math work.'
To start, we need to define how many integers are between 50 and 69, inclusive. This is an example of a 'fence post' problem - and if you recognize that, then you know that there are 69 - 50 + 1 = 20 total numbers. If you don't recognize that though, you can still 'group' the numbers....
50 - 59 = 10 numbers
60 - 69 = another 10 numbers
Total = 20 numbers
Next, we need to figure out the factors of 89. Since 89 is less than 100, the square-root of 89 is less than 10, so we just have to consider single-digit divisors... Since 89 is ODD, it's not divisible by any EVEN integers. Since it's digits add up to 17, it's not divisible by 3 or 9. Since it ends in a 9, it's not divisible by 5. All that's left is to try 7... which does NOT divide either. Thus, the only factors of 89 are 1 and 89.
After that, we have to determine how many of the 20 numbers have JUST TWO factors.
We can quickly eliminate all of the even numbers (they'll all have at least 4 factors).
We can also eliminate all of the multiples of 5 (they'll also have at least 4 factors).
So we're left with... 51, 53, 57, 59, 61, 63, 67 and 69
We can eliminate 51, 57, 63 and 69 with the 'rule of 3'
Now we're left with 53, 59, 61 and 67
This is 4 of the 20 numbers = 1/5 of the numbers. Based on the answer choices, the correct answer must be either B or C. Once you prove that ANY of those 4 numbers has just 2 factors, then you know what the correct answer must be...
Final Answer:
GMAT assassins aren't born, they're made,
Rich
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