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This was the question (but does not look to be GMAT since it has 4 answer choices). One third, one fourth, one fifth and one-seventh of the human population of Island X, which has fewer than 5000 human inhabitants, are all whole numbers and their sum is exactly the population of Island Y. What is the population of Island Y? A.4200 B.4279 C.4581 D. None of these Can anyone solve this math in details?
if x is the population of island_X then x < 5000
next the fractions are whole numbers
i.e. (1/3)x, (1/4)x, (1/5)x, (1/7)x are whole numbers.
we can take LCM of denominators to say x/420 is a whole number
now say x = 420*T for some whole number T
then; (1/3 * 420*T) + (1/4 * 420*T) + (1/5 * 420*T) + (1/7 * 420*T) = Population of Island_Y
solving this will yield 389*T = Population of Island Y
we can check from answer options which number represents 389*T
B) 4279 = 389 * 11 satisfies the ask