The difference of two natural numbers is 2 and their product is 224. Find the larger of the two numbers.

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Solution

The correct option is E
16

Let p and q be the numbers.

Their difference is 2, so we can write p - q = 2.

Their product is 224, so pq = 224.

From p - q = 2, I get p = q + 2.

Put this into pq = 224 and solve for q: (q + 2)q = 224

q $^{2}$ + 2q = 224

q $^{2}$ + 2q - 224 = 0

(q + 16)(q - 14) = 224

If q = -16, then p = -16 + 2 = -14.

If q = 14, then p = 14 + 2 = 16.

Since it is said that they are natural numbers, the pair that will be valid is: 14 and 16

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