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A group consisting of several families visited an amusement

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jjjinapinch Senior | Next Rank: 100 Posts Default Avatar
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A group consisting of several families visited an amusement

Post Tue Aug 08, 2017 7:41 am
A group consisting of several families visited an amusement park where the regular admission fees were ¥5,500 for each adult and ¥4,800 for each child. Because there were at least 10 people in the group, each paid an admission fee that was 10% less that the regular admission fee. How many children were in the group?

(1) The total of the admission fees paid for the adults in the group was ¥29,700
(2) The total of the admission fees paid for the children in the group was ¥4,860 more than the total of the admission fees paid for the adults in the group.

Official Guide question
Answer: C

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Post Fri Dec 08, 2017 7:36 am
jjjinapinch wrote:
A group consisting of several families visited an amusement park where the regular admission fees were ¥5,500 for each adult and ¥4,800 for each child. Because there were at least 10 people in the group, each paid an admission fee that was 10% less that the regular admission fee. How many children were in the group?

(1) The total of the admission fees paid for the adults in the group was ¥29,700
(2) The total of the admission fees paid for the children in the group was ¥4,860 more than the total of the admission fees paid for the adults in the group.
We are given that at an amusement park, regular admission fees were ¥5,500 for each adult and ¥4,800 for each child. However, a particular group paid 10% less than the regular admission fee. Thus, the admission fee per adult was 5,500 x 0.9 = 4,950 yen and per child was 4,800 x 0.9 = 4,320 yen. We need to determine the number of children in the group.

Statement One Alone:

The total of the admission fees paid for the adults in the group was ¥29,700.

If we let the number of adults = A, we can create the following equation:

4,950A = 29,700

A = 6

However, since we do not know the number of children, statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

The total of the admission fees paid for the children in the group was ¥4,860 more than the total of the admission fees paid for the adults in the group.

If we let C = the number of children, we can create the following equation:

4,320C = 4,860 + 4,950A

We see that we do not have enough information to determine C. We can eliminate answer choice B.

Statements One and Two Together:

Using the information from statements one and two, we know that A = 6 and 4,320C = 4,860 + 4,950A. We can see that if we substitute 6 for A in 4,320C = 4,860 + 4,950A, we can determine the value of C. The two statements together are sufficient.

Answer: C

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Post Thu Aug 10, 2017 11:09 am
Hi jjjinapinch,

We're told that admission fees at a park were ¥5,500 for each adult and ¥4,800 for each child and that because there were at least 10 people in the group, each paid an admission fee that was 10% less that the regular admission fee (meaning that each adult fee was 4950 yen and each child fee was 4320 yen). We're asked for the number of children in the group. While this question is wordy, it's built around a series of standard Algebra concepts.

1) The total of the admission fees paid for the adults in the group was ¥29,700

With the information in Fact 1, we can determine the number of adults in the group (using the following equation):
4950(A) = 29,700
A = 29,700/4950 = 6 adults
However, we do not know the number of children in the group.
Fact 1 is INSUFFICIENT

2) The total of the admission fees paid for the children in the group was ¥4,860 more than the total of the admission fees paid for the adults in the group.

With the information in Fact 2, we can create the following equation):
4320(C) = 4950(A) + 4860
While this equation is 'thick', it's still two variables and just one equation; since the numbers involved don't include anything too strange (weird decimals or primes, for example) there are likely to be multiple solutions.
Fact 2 is INSUFFICIENT

Combined, we know:
A = 6
4320(C) = 4950(A) + 4860
With the value of A, we can 'plug in' and solve for C.
Combined, SUFFICIENT

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

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