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This problem trains for: SAT-I, AMC-8, GMAT, AMC-10.

The LCM of two numbers is 2722 and their GCF is 22. The numbers are in a ratio of 9:14. Which ones of the statements below are true?

The numbers are in the ratio:

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We factorize the LCM and the GCF to see what factors they have:

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Since their GCD is 22 then both numbers are multiples of 2 and of 11:

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Since the LCM has a factor of 4, one of the numbers must have a factor of 4. The other number can only have a factor of 2 since the GCF only has a 2. From the ratio of the numbers, it is clear that the larger number is the multiple of 4.

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The LCM of these numbers is already the desired one.

Therefore, the numbers are 198 and 308.

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The difference of these numbers is a multiple of 10:

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Neither one of the numbers can have 5 as a divisor since 5 is not a factor in the GCF.

From the above, it is clear that the solution to this problem is unique.