The mean mass of a sweet in a bag of 20 sweets must be greater than 10 grams but not greater than 10.5 grams. A bag is being filled with sweets. The mean mass of the first 16 sweets is exactly 9.5 grams. Four more sweets, each of mass x grams, are added to the bag to bring the mean mass of the 20 sweets into the correct range. What is the complete range of possible values of x ?/

Answer:

20) A

We can find the total mass of the first 16 sweets.

Total mass of 16 sweets = 16 x 9.5 = 152 g

Then 4 more sweets, each of mass ‘x’ were added.

Mass of the 4 sweets = 4x

Total mass of 20 sweets = 152 + 4x

Average mass = (152 + 4x) ÷ 20

Now substitute values given in the option into the equation.

Option A:
If x = 12,
Average mass = 10g
If x = 14.5,
Average mass = 10.5 g
So x must be greater than 12 but less than or equal to 14.5
So A is correct.

Option B is wrong because it says (x < 14.5). ‘x’ can be lesser than OR equal to 14.5, which is why option A is correct.

Option C is wrong because it says (12 ≤ x). ‘x’ cannot be equal to 12 as mean mass of a sweet MUST be greater than 10 g.

Options D, E and F are just completely wrong.