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Recently Mary gave a birthday party for her daughter at which she served both chocolate and strawberry ice
cream. There were 8 boys who had chocolate ice cream, and nine girls who had strawberry. Everybody there
had some ice cream, but nobody tried both. What is the maximum possible number of girls who had some
chocolate ice cream?
Exactly thirty children attended the party.
Fewer than half the children had strawberry ice cream.
  • a)
    Statement ( 1 ) ALONE is sufficient but statement ( 2 ) alone is not sufficient.
  • b)
    Statemrnt ( 2 ) ALONE is sufficient but statement ( 1 ) is not sufficient
  • c)
    Both Stement TOGETHER are sufficient, but Neither statement  ALONE is sufficient
  • d)
    EACH stetement ALONE is sufficient
  • e)
    Statement ( 1 ) and ( 2 ) TOGETHER are NOT Sufficient.
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Recently Mary gave a birthday party for her daughter at which she serv...
Since there are two different classes into which we can divide the participants, we can solve this using a double-set matrix. The two classes into which we'll divide the participants are Boys/Girls along the top (as column labels), and Chocolate/Strawberry down the left (as row labels).
T
he problem gives us the following data to fill in the initial double-set matrix. We want to know if we can determine the maximum value of a, which represents the number of girls who ate chocolate ice cream.

(1) SUFFICIENT: Statement (1) tells us that exactly 30 children came to the party, so we'll fill in 30 for the grand total. Remember that we're trying to maximize a.
In order to maximize a, we must maximize b, the total number of chocolate eaters. Since 
b + d = 30, implying b = 30 - d, we must minimize d to maximize b. To minimize d we must minimize c. The minimum value for c is 0, since the question doesn't say that there were necessarily boys who had strawberry ice cream.
Now that we have an actual value for c, we can calculate forward to get the maximum possible value for a. If c = 0, since we know that c + 9 = d, then d = 9. Since b + d = 30, then b = 21. Given that 8 + a = b and b = 21, then a = 13, the maximum value we were looking for. Therefore statement (1) is sufficient to find the maximum number of girls who ate chocolate.
(2) INSUFFICIENT:  Knowing only that fewer than half of the people ate strawberry ice cream doesn't allow us to fill in any of the boxes with any concrete numbers.  Therefore statement (2) is insufficient.
The correct answer is A. 
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Most Upvoted Answer
Recently Mary gave a birthday party for her daughter at which she serv...
Understanding the Problem
To determine the maximum possible number of girls who had chocolate ice cream at the birthday party, let's analyze the given information.

Key Information
- Total children at the party: **30**
- Boys with chocolate ice cream: **8**
- Girls with strawberry ice cream: **9**
- No child had both flavors.
- Fewer than half had strawberry ice cream.

Analyzing the Statements

Statement (1): "There were 8 boys who had chocolate ice cream."
- This helps us establish that 8 boys consumed chocolate ice cream.
- The remaining boys (if any) must have had strawberry.
- This fact alone doesn't provide insight into how many girls had chocolate ice cream.

Statement (2): "Fewer than half the children had strawberry ice cream."
- If fewer than half of 30 children had strawberry ice cream, then at most **14 children** could have had strawberry.
- Since 9 girls had strawberry ice cream, it implies at least **5** children must have had chocolate (since 30 - 14 = 16, and 8 boys had chocolate).
- Therefore, at least **5** children could be girls having chocolate.

Combining the Statements
- From Statement (1), we know 8 boys had chocolate.
- From Statement (2), we know that fewer than 15 could have strawberry, allowing for more potential girls having chocolate.
- However, Statement (2) alone provides the maximum clarity on how many girls can have chocolate, as it restricts the number of children having strawberry.

Conclusion
- Thus, Statement (1) alone does not provide enough information about the girls having chocolate ice cream, while Statement (2) provides sufficient context to establish the maximum number of girls who can have chocolate ice cream.
The correct answer is **(a)**: "Statement (1) ALONE is sufficient but statement (2) alone is not sufficient."
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Recently Mary gave a birthday party for her daughter at which she served both chocolate and strawberry icecream. There were 8 boys who had chocolate ice cream, and nine girls who had strawberry. Everybody therehad some ice cream, but nobody tried both. What is the maximum possible number of girls who had somechocolate ice cream?Exactly thirty children attended the party.Fewer than half the children had strawberry ice cream.a)Statement ( 1 ) ALONE is sufficient but statement ( 2 ) alone is not sufficient.b)Statemrnt ( 2 ) ALONE is sufficient but statement ( 1 ) is not sufficientc)Both Stement TOGETHER are sufficient, but Neither statement ALONE is sufficientd)EACH stetement ALONE is sufficiente)Statement ( 1 ) and ( 2 ) TOGETHER are NOT Sufficient.Correct answer is option 'A'. Can you explain this answer?
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