What percentage of families in the state have annual incomes over $50

Question

What percentage of families in the state have annual incomes over $50,000 and have a net worth over $500,000?

(1) 65% of all the families in the state have an annual income over $50,000.
(2) 20% of the families in the state with an annual income over $50,000 have a net worth above $500,000.

Kudos for a correct  solution .

GMATinsight · Answer

These questions are best solved by using the Double Matrix or venn-Diagram so here are both.

Answer: Option C

ENGRTOMBA2018 · Answer

Bunuel : the title of the topic does not pertain to the actual question. As for the question, refer to the attached image for the solution. AI: Families with annual income >50,000 NAI: fFamilies with annual income <50,000 NW: families with net worth >500,000 NNW: families with net worth <500,000 need to find = X (in the attached figure) As this is a percentage question, assume total families =100 and follow the solution in the attached image. Statement 1, provides us the information about families that have annual income > 50,000. This does not help in finding the percentage of families out of these 65% who also have net worth > 50000. Thus this statement is not sufficient. Statement 2, Tells us that X=0.2Y (in the attached figure) but we do not have another equation to solve for both x and y. Thus this statement is not sufficient. Combining, we see X=0.2Y and Y =65. Thus value of X can be found. ----> C is the correct answer. C is the correct answer.

Bunuel · Answer

800score Official Solution:

(C) Statement (1) alone is not sufficient, because it only gives us the percentage of families in the state with the required annual income, but gives no information regarding the net worth.

Statement (2) is not sufficient because, although it tells you about the percentage of families that satisfy the question, it does not give you the percentage of families in the state that have an annual income of $50,000.

Statements (1) and (2) COMBINED are sufficient. 20% of the 65% are families who both have annual incomes over $50,000 AND have a net worth above $500,000. To find out the percentage of people with both traits, multiply the two independent variables. The two statements give these two variables.

Remember, however, that for these questions you do not need to solve for an answer; you simply need to establish whether or not you have sufficient information to do so.

pierjoejoe · Answer

High networth 
 Low net worth

high income 
 a 
 b

low income 
 c 
 d

total

we want \frac{a}{tot}

(1) a+b = 65% tot 
NS

High networth 
 Low net worth

high income 
 a 
 b 
 65% tot  
 
  low income 
 c 
 d 
 35% tot

total

(2)  20% of the families in the state with an annual income over $50,000--> 20%(a+b) have a net worth above $500,000 = a 
    
 High networth 
 Low net worth

high income 
 20%(a+b) 
  
 a+b 
 
  low income 
 c 
 d

total

20%(a+b) = a 
0.2a + 0.2b = a
0.2b = 0.8a

b = 4a

a = 4/5 (a+b) 
NS

(1)(2)
    
 High networth 
 Low net worth

high income 
 20%(a+b) 
 80%(a+b) 
 65%(a+b) 
 
  low income 
 c 
 d

total

a+b = 65% tot 
a = 4/5 (a+b)

we can solve and find a

a5/4 = (a+b) = 65% tot 
a5/4 = 65% tot 
a = 65% 4/5 tot =0.52 tot Sufficient

What percentage of families in the state have annual incomes over $50

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	High networth	Low net worth
high income	a	b	65% tot
low income	c	d	35% tot
			total

GMAT Data Sufficiency (DS) Questions

What percentage of families in the state have annual incomes over $50

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