A foot race had 36 teams of a dozen runners each...

LUANDATO wrote:A foot race had 36 teams of a dozen runners each. By noon, 4/9 of the teams had finished the race, and 70 percent of the remaining teams finished the race by one o' clock. How many teams had not finished the race by one o' clock?

A. 1
B. 2
C. 4
D. 6
E. 8

Since 4/9 of the 36 teams finished by noon, the number of teams finished by noon = (4/9)(36) = 16.
Remaining teams = (total teams in the race) - (teams finished by noon) = 36-16 = 20.
Since 70% of the 20 remaining teams finished by 1pm, the number of teams finished between noon and 1pm = (70/100)(20) = 14.
Thus:
Number of teams not finished by 1pm = (total teams in the race) - (teams finished by noon) - (teams finished between noon and 1pm) = 36 - 16 - 14 = 6.

The correct answer is D.

A foot race had 36 teams of a dozen runners each. By noon, 4/9 of the teams had finished the race, and 70 percent of the remaining teams finished the race by one o' clock. How many teams had not finished the race by one o' clock?

A. 1
B. 2
C. 4
D. 6
E. 8

The OA is D.

I don't understand why D is the correct answer. Can any expert explain this PS question please? Thanks.

Hi LUANDATO,
Lets take a look at your question.

Total teams = 36

The question states that "By noon, 4/9 of the teams had finished the race".
Let's find the number of teams that finished the race by noon.

$$=36\times\frac{4}{9}=4\times4=16$$
16 teams had finished the race by noon.

Remaining Teams = 36 - 16 = 20

Next , the question states that " 70 percent of the remaining teams finished the race by one o' clock."
Let's find the number of teams that finished the race by one o' clock.

$$=20\times70\%$$
$$=20\times\frac{70}{100}$$
$$=2\times7=14$$

14 teams finished the race by one o' clock.

We need to find the number of teams that had not finished the race by one o' clock.

$$20\ -\ 14\ =\ 6$$

It means, 6 teams had not finished the race by one o' clock.

Therefore, Option D is correct.

Hope this helps.
I am available if you'd like any follow up.