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If a and b are positive integers, what is the value of the product ab ?

(1) The least common multiple of a and b is 48

(2) The greatest common factor of a and b is 4

Target question:What is the value of the product ab?

Statement 1: The least common multiple of a and b is 48 Let's TEST some numbers. There are several values of a and b that satisfy statement 1. Here are two: Case a: a = 1 and b = 48. In this case, ab = (1)(48) = 48 Case b: a = 2 and b = 48. In this case, ab = (2)(48) = 96 Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The greatest common factor (aka divisor) of a and b is 4 Let's TEST some numbers (again). There are several values of a and b that satisfy statement 2. Here are two: Case a: a = 8 and b = 4. In this case, ab = (8)(4) = 32 Case b: a = 4 and b = 4. In this case, ab = (4)(4) = 16 Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined --------ASIDE---------------------- There's a nice rule that says: (greatest common divisor of x and y)(least common multiple of x and y) = xy Example: x = 10 and y = 15 Greatest common divisor of 10 and 15 = 5 Least common multiple of 10 and 15 = 30 Notice that these values satisfy the above rule, since (5)(30) = (10)(15) --------BACK TO THE QUESTION! ----------------------

When we apply the above rule, we get: (4)(48) = ab So, ab = 192 Since we can answer the target question with certainty, the combined statements are SUFFICIENT