Of the pupilsin the class,50%have black hair and 25%have blonde hair33%aregirls and 67%areboys.which of the following is definitely true...The blonde haired pupils are all boys....Some boys have black hair...Some blonde haired pupils are girls ...Some girls have blonde hair some have black hair
since 33% are girls, and 50% have black hair,
some boys have black hair.
Based on the given information, we can determine the following:
1. The percentage of pupils with black or blonde hair: 50% (black hair) + 25% (blonde hair) = 75%.
2. The percentage of boys and girls: 33% (girls) + 67% (boys) = 100%.
From this information, we can conclude the following:
1. The blonde-haired pupils are not necessarily all boys since 25% of the pupils have blonde hair. It is possible for some of the blonde-haired pupils to be girls as well.
2. Some boys have black hair, since 50% of the pupils have black hair.
3. Some blonde-haired pupils are girls. Since it is stated that 33% of the pupils are girls and the percentage of pupils with black or blonde hair is 75%, it means that at least some of the blonde-haired pupils must be girls.
4. Some girls have blonde hair and some have black hair. Since the total percentage of pupils with black or blonde hair is 75% and the percentage of girls is 33%, it means that some girls have black hair and some have blonde hair.
Therefore, all of the answer choices are definitely true.
To determine which statement is definitely true, let's analyze the given information step by step:
1. 50% of the pupils have black hair. This means that half of the class has black hair.
2. 25% of the pupils have blonde hair. This means that a quarter of the class has blonde hair.
3. 33% of the pupils are girls. This means that roughly one-third of the class consists of girls.
4. 67% of the pupils are boys. This means that approximately two-thirds of the class consists of boys.
Now let's evaluate each statement:
A. "The blonde-haired pupils are all boys" - This statement is NOT definitely true because only 25% of the pupils have blonde hair, and it doesn't necessarily mean they are all boys. This statement is not supported by the given information.
B. "Some boys have black hair" - This statement is definitely true. Since 50% of the pupils have black hair and two-thirds of the class consists of boys, it is certain that some boys will have black hair.
C. "Some blonde-haired pupils are girls" - This statement is also definitely true. Since 25% of the pupils have blonde hair and one-third of the class consists of girls, it is certain that some blonde-haired pupils will be girls.
D. "Some girls have blonde hair, some have black hair" - This statement is NOT definitely true, as it assumes that some girls must have both blonde and black hair. However, the given information does not provide any details regarding hair color combinations for individual pupils.
In conclusion, the statements that are definitely true are "Some boys have black hair" and "Some blonde-haired pupils are girls."