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Several friends in a dinner group decide to contribute equally...

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Several friends in a dinner group decide to contribute equally...

by swerve » Tue Jan 14, 2020 11:25 am
Several friends in a dinner group decide to contribute equally to the 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

Source: Manhattan Prep
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Source: — Data Sufficiency |
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Re: Several friends in a dinner group decide to contribute equally...

by deloitte247 » Sat Jan 18, 2020 6:52 pm
Let the total number of friends in the dinner group = x
Let one contribution = y
Total contributions for gift = x * y = $36
Question: How many people are in the group? i.e we want to find the value of x.
From the contribution; xy = 36; x = 36/y
Statement 1: The number of people in the group is equal to the size of each person's contribution in dollar.
i.e x=y and y=x
From the calculation, xy = 36 (substitute y with x because y=x and x=y)
Therefore, x * x = 36 $$x^2=36,\ and\ x=\sqrt{36}=6$$
Based on this, state,emt 1 is SUFFICIENT.

Statement 2: If 3 more people joined the group, each person's individual contribution would fall by $2.
3 people joined the group => x + 3
Individual contribution => y - 2
Total contribution for gift = (x+3)(y-2) = $36
xy - 2x + 3y - 6 = 36
subsitute xy with 36 because xy=36 from the question stem
36 - 2x + 3y - 6 = 36
- 2x + 3y = 6
from xy=36; y=36/x
Therefore,
$$-2x+3\left(\frac{36}{x}\right)=6$$
$$-2x+\frac{108}{x}=6$$
$$-2x^2-6x+108=0$$
Divide through by -2
$$x^2+3x-54=0$$
(x - 6)(x + 9) = 0
x=6 or x=-9
Since contribution cannot be negative, then x=6.
Therefore, statement 2 is SUFFICIENT. Hence, each statement alone is sufficient, the correct answer is option D.
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