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Every member of Meg’s immediate family agrees to share equally the cos

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Every member of Meg’s immediate family agrees to share equally the cos  [#permalink]

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New post 14 Feb 2020, 00:55
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Every member of Meg’s immediate family agrees to share equally the cost of her wedding, which is $18,000 in total. How many people are in Meg’s immediate family?

(1) Everyone in Meg’s immediate family will pay $1,500.
(2) If 4 immediate family members do not contribute their share, each of the other family members will have to contribute $750 more than if everyone had contributed.

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Re: Every member of Meg’s immediate family agrees to share equally the cos  [#permalink]

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New post 14 Feb 2020, 01:19
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Question: Number of members in Meg's family = ?

Statement 1: Everyone in Meg’s immediate family will pay $1,500.

i.e. total members = Total expense / expense per person = 18000/1500 = 12
SUFFICIENT

Statement 2: If 4 immediate family members do not contribute their share, each of the other family members will have to contribute $750 more than if everyone had contributed.

i.e. 18000/x = 750 + [18000/(x-4)]
leaving us with unique value of x=12 i.e. number of family members hence

SUFFICIENT

Answert: Option D

Quote:
Every member of Meg’s immediate family agrees to share equally the cost of her wedding, which is $18,000 in total. How many people are in Meg’s immediate family?

(1) Everyone in Meg’s immediate family will pay $1,500.
(2) If 4 immediate family members do not contribute their share, each of the other family members will have to contribute $750 more than if everyone had contributed.

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Re: Every member of Meg’s immediate family agrees to share equally the cos  [#permalink]

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New post 14 Feb 2020, 01:31
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(1) $18,000/ $1,500 = 12 people
There are 12 people in Meg’s immediate family.
SUFFICIENT

(2) Let total no. of immediate family members = n, individual contribution = m, and n*m=18000, then 18000 = (n-4)(m+750)
--> 18000 = 18000 +750n -4m -3000

Multiplying both sides with n,
--> 0 = 750n^2 - 3000n - 4*18000
--> 0 = n^2 - 4n - 96
--> 0 = (n-12)(n+8)
n=12 (Yes) or n=-8 (N.A)
There are 12 people in Meg’s immediate family.
SUFFICIENT

FINAL ANSWER IS (D)

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Re: Every member of Meg’s immediate family agrees to share equally the cos  [#permalink]

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New post 14 Feb 2020, 03:47
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Quote:
Every member of Meg’s immediate family agrees to share equally the cost of her wedding, which is $18,000 in total. How many people are in Meg’s immediate family?

(1) Everyone in Meg’s immediate family will pay $1,500.
(2) If 4 immediate family members do not contribute their share, each of the other family members will have to contribute $750 more than if everyone had contributed.


"every member will share equally":
18000/n is how much each will contribute
n is the number of members

(1) sufic
18000/n=1500, n=18000/1500=12;

(2) sufic
18000/n-4=18000/n+750, 18k(n)-18k(n-4)=750(n)(n-4)…
18k(n-(n-4))=750(n)(n-4), 18000*4/750=n(n-4), n^2-4n-96=0…
(n-12)(n+8)=0…n>0…n=12

Ans (D)
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Re: Every member of Meg’s immediate family agrees to share equally the cos  [#permalink]

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New post 14 Feb 2020, 03:57
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Let total number of people in Meg's immediate family = T

Question is: Find T.

Option (1): Everyone in Meg’s immediate family will pay $1,500.

Since total expenditure is $18,000 and each member will pay $1,500, we can calculate 'T' using (18,000/1500) = 12
SUFFICIENT.

Option (2): If 4 immediate family members do not contribute their share, each of the other family members will have to contribute $750 more than if everyone had contributed.

Contribution of each individual can be calculated as, (Total Expenditure/Total People)

If 4 fewer people (i.e T - 4) contribute to the total expenditure, that means per person contribution will increase, i.e. Option (2) can be mathematically written as,

(18000/(T-4)) - (18000/T) = $750

Solving the above equation, we get (T^2 - 4T - 96 = 0)
Solving the quadratic, we get two values of T, i.e. T = 12, T = -8

Since, the number of people cannot be negative, we get T = 12.
SUFFICIENT.

Since, individually (1) and (2) are sufficient to solve the problem, the answer is Option (D).
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Re: Every member of Meg’s immediate family agrees to share equally the cos  [#permalink]

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New post 14 Feb 2020, 08:17
#1
Everyone in Meg’s immediate family will pay $1,500.
so total members ; 18000/1500 ; 12
sufficient
#2 If 4 immediate family members do not contribute their share, each of the other family members will have to contribute $750 more than if everyone had contributed
18000/(x-4) + 750 = 18000/x
we can find x
sufficient
IMO D



Every member of Meg’s immediate family agrees to share equally the cost of her wedding, which is $18,000 in total. How many people are in Meg’s immediate family?

(1) Everyone in Meg’s immediate family will pay $1,500.
(2) If 4 immediate family members do not contribute their share, each of the other family members will have to contribute $750 more than if everyone had contributed
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Re: Every member of Meg’s immediate family agrees to share equally the cos  [#permalink]

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New post 14 Feb 2020, 10:37
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Every member of Meg’s immediate family agrees to share equally the cost of her wedding, which is $18,000 in total. How many people are in Meg’s immediate family?
Let x be the total number of immediate family members. x = ?

(1) Everyone in Meg’s immediate family will pay $1,500.
\(\frac{18000}{1500} = x\)

SUFFICIENT.

(2) If 4 immediate family members do not contribute their share, each of the other family members will have to contribute $750 more than if everyone had contributed.
\(\frac{18000}{x} + 750 = \frac{18000}{x-4}\)

SUFFICIENT.

Answer D.
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Re: Every member of Meg’s immediate family agrees to share equally the cos  [#permalink]

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New post 14 Feb 2020, 10:52
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Every member of Meg’s immediate family agrees to share equally the cost of her wedding, which is $18,000 in total. How many people are in Meg’s immediate family?

(1) Everyone in Meg’s immediate family will pay $1,500.
(2) If 4 immediate family members do not contribute their share, each of the other family members will have to contribute $750 more than if everyone had contributed.

1) Since the total cost and cost per individual are known, we can find the desired value. sufficient.
2) We can write the equation as: \(\frac{18,000}{ (x -4)} \)- \(\frac{18,000}{x }\)=750 or, 18,000(4/x^2-4x)= 750 or, 120(4/x^2-4x) = 5 or, 24 *4 = x^2 - 4x or, x^2 -4x -96 =0 or, x^2 -12x+8x -96 =0. since the members of a family cannot be a negative number, so we can get only one value. sufficient.
D is the answer.
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Re: Every member of Meg’s immediate family agrees to share equally the cos  [#permalink]

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New post 14 Feb 2020, 11:11
1) $18000/$1500 gives you the number of people in the immediate family --> Sufficient

2) Let X be the number of people in the immediate family and $K be the each family member share

$18000/X = $K

If four members of the immediate family did not pay, then the share of each person goes up by $750.

$18000/(X-4) = $K+$750

So we have two unknown variables to solve in a single equation. --> In sufficient
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Re: Every member of Meg’s immediate family agrees to share equally the cos  [#permalink]

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New post 15 Feb 2020, 01:24
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Total =18,000
(1) Everyone in Meg’s immediate family will pay $1,500......so the total no.of people=18,000/1500=12.....SUFFICIENT
(2) If 4 immediate family members do not contribute their share, each of the other family members will have to contribute $750 more than if everyone had contributed.......let the total no.of people contributed..
then 18000/x + 750 = 18,000/(x-4).....we will get x=12...........SUFFICIENT

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Re: Every member of Meg’s immediate family agrees to share equally the cos  [#permalink]

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New post 16 Feb 2020, 13:26
1
P*C = 18000–> P=???

(Statement1): Everyone in Meg’s immediate family will pay $1,500.
—> P*1500= 18000
P= 12
Sufficient

(Statement2): If 4 immediate family members do not contribute their share, each of the other family members will have to contribute $750 more than if everyone had contributed.
(P—4)*(C+ 750) = 18000
P*C= 18000
—>\(375* P^{2} —1500P—36000=0\)
Got 2 values of P:
\(P_1= 12\) , \(P_2= —8 \)
—> P = 12
Sufficient

The answer is D

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Re: Every member of Meg’s immediate family agrees to share equally the cos   [#permalink] 16 Feb 2020, 13:26
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