Last year, in Crossia, 25% of all babies were delivered in a private

Question

Last year, in Crossia, 25% of all babies were delivered in a private hospital, while 40% of all cesarean births occurred in a private hospital. Last year, in Crossia, what percentage of all births that took place in a private hospital were cesarean births?

(1) Last year, in Crossia, a total of 72,000 babies were delivered in a private hospital. 
(2) Last year, in Crossia, 20% of all births were caesareans.

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Dereno · Answer

Last year, Crossia 25% of all babies were delivered in a private hospital.

40% of ALL cesarean births occured in private hospital.

We need to find  : % of Cesarean births in Private hospitals

= number of cesarean births in private hospitals / Total number of Births in private hospitals

Total number of Births in private hospital = 25%* Total.

Ceaseran Births in private hospital = 40% * All caesarean births.

% of Cesarean births in Private hospitals = (40% * All caesarean births. )/(25%* Total).

Statement 1:

Last year, in Crossia, a total of 72,000 babies were delivered in a private hospital.

Total Babies delivered in Private hospitals = 72,000.

72000 = 25%* Total babies delievered in Crossia.

But, we need the number of Caesarean births in private hospitals.

Hence,  Insufficient. 
 
Statement 2:

Last year, in Crossia, 20% of all births were caesareans.

20% of all births were caesareans, which means 20% of Total births = Caesarean.

we know that:

% of Cesarean births in Private hospitals = (40% * All caesarean births. )/(25%* Total).

= (40% * 20% of Total birth) / (25% of Total Birth)

= 8/25

= 32%

Hence,  Sufficient .

Option B

ExpertsGlobal5 · Answer

Explanation:  
   
Let the total number of babies delivered be A.
Let the total number of babies delivered in a private hospital be P.
Let the total number of cesarean births be C.
Let the number of cesarean births in private hospitals be B.
Since 25% of all babies were delivered in a private hospital: P = 0.25A (Equation I)
Since 40% of all cesarean births occurred in a private hospital: B = 0.4C (Equation II)
We have to find the percentage of all births that took place in a private hospital were cesarean births, which can be expressed as: 
What percentage of P is B?
  We need to find whether the value of 100 x (B/P) can be determined.  
 
 Statement (1) 
 
A = 72,000
 
Using the value of A, from Equation I we can determine the value of P, however,   no information is provided regarding the value of B  . 
 
It is NOT possible to determine with certainty the value of 100 x (B/P).   Hence, Statement (1) is insufficient.  
 
 Statement (2) 
 
0.2A = C 
From Equation II, we get: B = 0.4C = 0.4(0.2)A (Equation III)
 
Dividing Equation III by Equation I, we get: B/P = 0.4(0.2)A/0.25A = (0.4)(0.2)/0.25
 
It is possible to determine with certainty the value of 100 x (B/P).   Hence, Statement (2) is sufficient.  
 
  B is the correct answer choice.

Stormik1 · Answer

this is one of the most difficult question of the overlapping sets I have encountered

agil31 · Answer

Try making a 2x2 matrix for this question. It makes it a whole lot simpler!

MarkGMATMentor · Answer

It's often easier and safer to visualize overlapping sets problems with a Venn diagram or table,  as  agil31  mentioned.

Let's see how the table approach works. Set up the table and fill in the information from the prompt:
    
 private 
 public 
 total 
 
  cesarean 
 40% of C 
  
 C% 
 
  non-cesarean

total 
 25% 
  
 100%

Note that it's important to specify that the 40% refers only to 40% of cesarean births, not 40% of all births. Since you don't know the total for cesarean births, let's indicate it with the variable C.

The question asks for the percentage of private hospital births that were cesarean. In other words, if we can solve for 40% of C, we can divide that number by 25% (total private hospital births) to find the percentage.

Statement 1: 
This gives us an actual number, while the question asks for a percentage. There's no way it can give us useful information about percentages in the table. The trap would be to solve for the total number of babies and think that provides useful information, but we still don't know C, which could be many different possibilities.  Not sufficient.

Statement 2: 
This statement gives us the value of C. From this we can calculate 40% of C, and then divide that by 25% to find the answer. There's no need to actually calculate.  Sufficient.

The answer is B.

A couple of takeaways here: 
 
  On DS questions, your focus should be on what you need to solve the question, NOT on actually calculating. It's easy to get confused here on percents vs. actual numbers.  
  Overlapping sets are often best solved with a Venn diagram or table to help you understand what you need.

Last year, in Crossia, 25% of all babies were delivered in a private

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	private	public	total
cesarean	40% of C		C%
non-cesarean
total	25%		100%

GMAT Data Sufficiency (DS) Questions

Last year, in Crossia, 25% of all babies were delivered in a private

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