Ratio

Let the total hours worked be 2x, 3x, 5x and 6x.

Total hours worked = 16x

Plugging in each of the answers

a) 16x = 80 => x = 5. The person who worked 6x satisfies the condition that one member worked on the project for 30hours (6x5)

b) 16x = 96 => x = 6. The person who worked 5x satisfies the condition that one member worked on the project for 30hours (5x6)

Keep doing so, and option (d) will result in x = 12, and 30 is not divisible by 12, hence (d)

Veronica wrote:4 staff members at a certain company worked on a project. The amounts of time that the four staff members worked on the project were in the ration 2 to 3 to 5 to 6. If one of the four staff members worked on the project for 30 hours, which of the following CANNOT be the total number of hours that the four staff members worked on the project?
a. 80; b. 96; c. 160; d. 192; e. 240

Thank you!

Assign 30 one by one to each number in the ration 2 to 3 to 5 to 6, and check the total of hours as under:

2:3:5:6 = 30:45:75:90; total of hours is (2 + 3 + 5 + 6) × 15 = 16 × 15 = 240, okayed

2:3:5:6 = 20:30:50:60; total of hours is (2 + 3 + 5 + 6) × 10 = 16 × 10 = 160, okayed

2:3:5:6 = 12:18:30:36; total of hours is (2 + 3 + 5 + 6) × 6 = 16 × 6 = 96, okayed

2:3:5:6 = 10:15:25:30; total of hours is (2 + 3 + 5 + 6) × 5 = 16 × 5 = 80, okayed

[spoiler]192 is the odd man, out

D[/spoiler]