Question

Eleven apples are distributed among a girl and a boy. Then, which one of the following statements is true?
A. At least one of them will receive 7 apples
B. The girl receives at least 4 apples or the boy receives at least 9 apples
C. The girl receives at least 5 apples or the boy receives at least 8 apples
D. The girl receives at least 4 apples or the boy receives at least 8 apples

Answer 1

Hint:
 We are given that in a girl and a boy a total of 11 apples have to be distributed. We have 4 options in which we have to choose correctly, we look for possible counts. For Example, one in which the counter is possible then that statement is incorrect and the last possible will be the correct statement. So, we check each option one by one and reach the solution.

Complete step by step answer:
We are given that a total of 11 apples are distributed among a boy and a girl.
We are given the following option, we have to check which one is correct.
To choose the correct one we have to think of counterexamples that make other options invalid.
Now, we check each option and decide whether it is true or not.
Now, option A) at least one of them will receive 7 apples.
This option means that whatever the way we distribute either boy or girl one of them will surely get 7 apples.
But, if we share 4 with a girl and 5 with a boy then all 11 are distributed and yet have got 7.
So, option A) is incorrect.
Option B) A girl receives at least 4 apples or the boy receives at least 9 apples.
Now, we can see that if the girl receives say 3 apples then it means that states that the girl will receive at least 4 apples is wrong.
Since a girl has 3 apples so a boy will have $11-3=8$ Apples.
So it is clear as the boy has 8 apples
So the statement “boy has at least 9 apples” is wrong
So this option is wrong.
Option C) Girl receives at least 5 or the boy receives at least 8 apples.
As like above, if we consider girl get 4 apples then the statement “girl get at least 5 apples” is wrong
And since the girl has 4, so the boy will have $11-4=7$ apples.
So, the boy has 7 apples.
The other statement “boy has at least 8 apples is also incorrect.
So, Option A, B, and C are incorrect.Hence, Option D is our Option.

Note:
 Always remember that an easy way to cancel an option is to look for a possible counter.
Example: The word at least is the same $\ge $. It means the term is greater than or equal to that number. Similarly, the word at most is the same as $\le $. It means the term is less than or equal to that number.