Quandaries and Queries hello i found a question on an IQ pop up similar and then found  almost the exact question on your site when trying to find an answer...   pop up problem:   John likes 400 but not 300; he likes 100 but not 99; he likes 3600 but not 3700. Which does he like?   900 1000 1100 1200   your site problem:   Question: John likes 400 but not 300; he likes 100 but not 99; he likes 2500 but not 2400.  Which does he like?   900 1000 1100 1200   ...and i was wondering if the change in the last two numbers of the problem change the reasoning used to find the answer on your site. thank you very much,   garrett Hi Garrett, In the solution to the previous question the prime factorization of each of the numbers was found, and after examining this factorization, two possible answers were given to the question. 1000 since the prime factorization of each of the numbers John liked had only 2's and 5' as prime factors. 900 since each of the numbers John liked were primes. Apply the same technique to the numbers in your problem. Find the prime factorization of the three numbers he likes and the three he does not like. Find a property that is true for the three he likes but is not true for the three he does not like? Now find the prime factorization for the four possible answers to the question. Is there one of them that satisfies the property you found? Penny Go to Math Central