In a certain game, a large bag is filled with blue, green, purple and red chips worth 1, 5, x and 11 points each, respectively. The purple chips are worth more than the green chips, but less than the red chips. A certain number of chips are then selected from the bag. If the product of the point values of the selected chips is 88,000, how many purple chips were selected?

Question: In a certain game, a large bag is filled with blue, green, purple and red chips worth 1, 5, x and 11 points each, respectively. The purple chips are worth more than the green chips, but less than the red chips. A certain number of chips are then selected from the bag. If the product of the point values of the selected chips is 88,000, how many purple chips were selected?

Solution:
Blue chip = 1 point
Green chip = 5 points
Purple chip = x points
Red chip = 11 points

Purple chips are worth more than green chips but less than red chips.
So, 5 < x < 11
Assuming x is an integer point value, possible values of x are:
6, 7, 8, 9, 10

Now, 88,000 = 88 × 1000
= 8 × 11 × 1000
= 2³ × 11 × 2³ × 5³
= 2⁶ × 5³ × 11

Green chips give factor 5 and red chips give factor 11. So, purple chips must supply the factor 2.
Among the possible values, only 8 = 2³ works properly.
88,000 = 8² × 5³ × 11

So, the number of purple chips selected is 2.

Correct Answer: খ) 2