Lets use the elimination method:

a) One number is greater than the other. If we don't know by how much it is different we can't determine the numbers. If the sum is 15 the two numbers can be 7 and 8 or 3 and 12, thus just knowing that one is larger than the other won't help us determine the identity of the numbers

b) The cube of one number is 8. This tells us that one of the numbers is 2 (2^3 = 8). We can then determine the second number by doing sum-2

c) The product of the two numbers is 8. Two numbers a and b when multiplied equal to 8 (a*b=8). One of the numbers (lets say a) can be expressed using the other number a=8/b. Then sum (which is just a number that would have been given to us) equals b+(8/b) .

The b can be expressed as b^2/b to add to 8/b and yield (b^2+8)/b = sum

Then since sum is a number we can multiply both sides of the equation by b to get: b^2+8 = sum*b

Subtract sum*b from both sides to get yourself a quadratic

b^2 - sum*b + 8 =0You can solve this for b and then figure out a

d) The difference between the two numbers ·is 2. This tells us that the two numbers can be expressed as x and x+2. Thus sum = x+ (x+2). We can determine x (one of the numbers) and then add 2 to determine the second number.

e) One number is half the other. If one number (a) is half of the other number (b), we then know that a=0.5b. Thus the total sum of a+b = 1b+0.5b =1.5b. Then the sum can be divided by 1.5 to determine b, and then do sum -b to determine the other number

Thus only A is not a sufficient qualifying statement to determine the values of the two numbers

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