Average height of the adults is 170cm

Let number of men and women be 1u each (since same number)

Total height of all men = 180u cm

Total height of all the adults = 170cm x 2u
= 340u cm

Total height of women
= 340u cm - 180u cm
= 160u cm

Average height of women
= 160u cm ÷ 1u = 160cm

So for the second question, the option is true.


You can also think about it this way :

Since there are equal number of men and women, some of the men's height must be 'donated' to the women to 'even out' to 170cm per person.

Since the average of the men is 180cm, we can say on average, each man 'donates' 10cm to the women.

As there are equal number of men and women, each woman can be paired with 1 man. Each woman 'receives' 10cm from 1 man to reach the average of 170cm for all the adults.


So the average height of the women would be 160cm (170cm - 10cm)

As for the first question, it may be true or false.


Examples of a case where it's true:

① All the men are 180cm and all the women are 160cm tall.

①All the men are 180cm tall except two, who are 185cm and 175cm tall. Their average is still 180cm.
All the women are 160cm tall except 3 , who are 158cm,157cm and 165cm tall. Their average is still 160cm.

Examples of cases where it's false :

① All men are 180cm tall except 3, who are 195cm tall, 196cm tall and 149cm tall. Their average is still going to be 180cm.
All the women are 160cm tall. So not all the men are taller than all the women.

But the question has no info on their individual heights so it's not possible to tell