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

"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)

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).

#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

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.

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.

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

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

OA:D

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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