Recently mary gave a birthday party for her daughter...

[furtadovinod]

Here is the link to the original post....

http://www.manhattangmat.com/forums/recently-mary-gave-a-birthday-party-for-her-daughter-at-t6096.html

I got this question during my CAT 1 and I also chose E. At that time I did think that A is a possible answer because I could set the no. of boys to 8. The issue I have with the answer explanation is that there are too many ifs or possibilities. As an example, what if the two statements were

(1) Exactly thirty children attended the party.

(2) 12 boys attended the party.

By the logic given the answer would be (D), but the answers would be totally different.

[esledge]

Here's the text of the original question, so people won't have to go back and forth between posts:

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?

(1) Exactly thirty children attended the party.

(2) Fewer than half the children had strawberry ice cream.

I answered the original question (see link above), and still maintain that (1) is sufficient, so the answer cannot be E. I'm going to recommend a revision to this one:

The intent of the question would be clearer with this wording: "What is the maximum number of girls who could have eaten some chocolate ice cream?"

This is an important distinction: we don't need to know how many girls actually did eat chocolate ice cream.

If Total = y + 8 + 9 + x, where y = boys who ate strawberry and x = girls who ate chocolate, then x = Total - y - 17. We would clearly need both Total and y to determine an exact value for x. I think this is why people are arguing that the answer is E.

However, we don't need x, but rather the maximum possible value for x. This changes how we must look at the statements.

(1) Total = 30, but what is y? To maximize x, minimize y. We have no info on y, other than the implied constraint that a negative number of people is nonsensical. The minimum y is thus 0. Maximum x = 30 - 0 - 17 = 13.

(2) Number of strawberry ice cream-eaters is less than half the total. So, y + 9 < Total/2. If we knew the Total, this would give is a maximum for y, but we care about minimizing y. The minimum y would still be 0. However, we still need the Total.

Maximum x = Total - 0 - 17 = unknown (it depends on the Total).

As an example, what if the two statements were

(1) Exactly thirty children attended the party.

(2) 12 boys attended the party.

By the logic given the answer would be (D), but the answers would be totally different.

In this example, the answer would still be (A).

Statement (1) gives the total, and allows the possibility that y can be as low as 0. Thus, maximum x = 30 - 0 - 17 = 13.

While statement (2) implies an exact value for y (y = 12-8 = 4 = max y = min y), the maximum possible value for x still depends on the total (not given in (2)).

[furtadovinod]

Here's the text of the original question, so people won't have to go back and forth between posts:

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?

(1) Exactly thirty children attended the party.

(2) Fewer than half the children had strawberry ice cream.

I answered the original question (see link above), and still maintain that (1) is sufficient, so the answer cannot be E. I'm going to recommend a revision to this one:

The intent of the question would be clearer with this wording: "What is the maximum number of girls who could have eaten some chocolate ice cream?"

This is an important distinction: we don't need to know how many girls actually did eat chocolate ice cream.

If Total = y + 8 + 9 + x, where y = boys who ate strawberry and x = girls who ate chocolate, then x = Total - y - 17. We would clearly need both Total and y to determine an exact value for x. I think this is why people are arguing that the answer is E.

However, we don't need x, but rather the maximum possible value for x. This changes how we must look at the statements.

(1) Total = 30, but what is y? To maximize x, minimize y. We have no info on y, other than the implied constraint that a negative number of people is nonsensical. The minimum y is thus 0. Maximum x = 30 - 0 - 17 = 13.

(2) Number of strawberry ice cream-eaters is less than half the total. So, y + 9 < Total/2. If we knew the Total, this would give is a maximum for y, but we care about minimizing y. The minimum y would still be 0. However, we still need the Total.

Maximum x = Total - 0 - 17 = unknown (it depends on the Total).

As an example, what if the two statements were

(1) Exactly thirty children attended the party.

(2) 12 boys attended the party.

By the logic given the answer would be (D), but the answers would be totally different.

In this example, the answer would still be (A).

Statement (1) gives the total, and allows the possibility that y can be as low as 0. Thus, maximum x = 30 - 0 - 17 = 13.

While statement (2) implies an exact value for y (y = 12-8 = 4 = max y = min y), the maximum possible value for x still depends on the total (not given in (2)).

Hi Emily,

Thanks for the detailed reply. It looks to me that you are not only changing the answer to the question but also changing the wording. The new wording (with could) seems less ambiguous. Anyways my query was put at the time of writing the exam and my thought process then. Its been sometime already since I gave that exam and hence , its possible that the new question could be less ambiguous.

[Ben Ku]

good luck!