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Several friends in a dinner group decide to contribute

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Several friends in a dinner group decide to contribute

by BTGmoderatorLU » Sat Dec 01, 2018 5:17 am

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Source: Manhattan Prep

Several friends in a dinner decide to contribute equally to purchase of a $36 gift. How many people are in the group?

1) The number of people in the group is equal to the size of each person's contribution, in dollars.
2) If three more people joined the group, each person's individual contribution would fall by $2.

The OA is D.
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Source: — Data Sufficiency |

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by ceilidh.erickson » Sat Dec 01, 2018 3:37 pm

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Here, we have a version of a rate problem:
($ contribution per person)(# of people) = total $ amount contributed

From the question stem, we're given that the total amount contributed is $36. Let:
c = $ contribution per person
n = number of people
(c)(n) = 36

Since the question is asking for the value of n, and we have the equation (c)(n) = 36, we'll simply need another equation to solve for the values of both variables.

1) The number of people in the group is equal to the size of each person's contribution, in dollars.

In other words, c = n. This gives us a 2nd equation, so we can solve:
(n)(n) = 36
n = 6
(We ignore the solution n = -6 since we can't have negative numbers of people)

Sufficient

2) If three more people joined the group, each person's individual contribution would fall by $2.

Translate: (c - 2)(n + 3) = 36

If we wanted to actually solve, we could isolate c in the first equation: c = 36/n
then plug it into the 2nd equation: ((36/n) - 2)(n + 3) = 36
From there, solving would create a rather complex quadratic. Don't actually solve it! Since this is DS, it's enough to know that 2 equations will be sufficient to solve for 2 values.

(n.b. as with statement 1, the quadratic will yield 2 potential solutions, but since we have to have a positive number of people, only one of those solutions will work, so it will be sufficient).

The answer is D.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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by ceilidh.erickson » Sat Dec 01, 2018 4:20 pm

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For similar variations on this type of word problem, see:
https://www.beatthegmat.com/impossible- ... tml#739205
https://www.beatthegmat.com/dollars-t273184.html#707179
https://www.beatthegmat.com/a-number-of ... tml#677091
https://www.manhattanprep.com/gmat/blog ... -equation/
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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