Each of the dogs enrolled in an obidience course either passed or fail

Question

Each of the dogs enrolled in an obedience course either passed or failed. What percent of the dogs enrolled in the course passed?

(1) Of the female dogs enrolled, 70 percent passed.
(2) Of the male dogs enrolled, 63 percent passed.

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gmatophobia · Answer

We can use a 2 × 2 matrix to plot the data, as shown below

Male  Female      Pass          Fail            m  x - m  x

Statement 1

(1) Of the female dogs enrolled, 70 percent passed.

Male  Female      Pass    0.7(x-m)  ?    Fail            m  x-m  x

We have no information on male dogs. Hence, this statement alone is not sufficient. Eliminate A and D

Statement 2

(2) Of the male dogs enrolled, 63 percent passed.

Male  Female      Pass  0.63*x    ?    Fail            m  x-m  x

We have no information on female dogs. Hence, this statement alone is not sufficient. Eliminate B

Combined

Male  Female      Pass  0.63*x  0.7(x-m)  ?    Fail            m  x-m  x

Number of dogs passed = 0.63x + 0.7x - 0.7m

Percentage =  \frac{0.63x + 0.7x - 0.7m}{x} = 1.33 - 0.7 \frac{m}{x}

The statements combined do not help us get the ratio  \frac{m}{x} . Hence, the statements combined are not sufficient either.

Option E

GMATinsight · Answer

There are only 4 possible categories here
(1) Male Passed
(2) Female Passed
(3) Male Failed
(4) Female Failed

Also, (1) + (2) + (3) + (4) = 100 (percent)

Question: (2) + (4) = ?

Statement 1  : 0.7*   = (2)
but we have no information about their actual number as percentage of total dogs hence
 NOT SUFFICIENT

Statement 2  : 0.63*   = (1)
but we have no information about their actual number as percentage of total dogs hence
 NOT SUFFICIENT

Combining the statements
We still have no information about the total percentage of male or female dog hence
 NOT SUFFICIENT

Answer: Option E

Kinshook · Answer

@joaquincolladoGiven: Each of the dogs enrolled in an obidience course either passed or failed.
Asked: What percent of the dogs enrolled in the course passed?

(1) Of the female dogs enrolled, 70 percent passed.
 
    Passed  Failed  Total  
  Male dogs        
  Female dogs  .7x%  .3x%  x%  
  Total dogs       100%  
 
From the above information, it can not be ascertained what percent of the dogs enrolled in the course passed.
NOT SUFFICIENT

(2) Of the male dogs enrolled, 63 percent passed. 
    Passed  Failed  Total  
  Male dogs  .63y%  .37y%  y%  
  Female dogs        
  Total dogs       100%  
 
From the above information, it can not be ascertained what percent of the dogs enrolled in the course passed.
NOT SUFFICIENT

(1) + (2) 
(1) Of the female dogs enrolled, 70 percent passed.
(2) Of the male dogs enrolled, 63 percent passed.
 
    Passed  Failed  Total  
  Male dogs  .63y%  .37y%  y%=100-x%  
  Female dogs  .7x%  .3x%  x%  
  Total dogs       100%

The percentage of dogs who passed the course = .63y% + .7x% = .63(100-x%) + .7x% = 63% + 0.07x%
Since the value of x is unknown
NOT SUFFICIENT

IMO E

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Each of the dogs enrolled in an obidience course either passed or fail

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	Passed	Failed	Total
Male dogs
Female dogs	.7x%	.3x%	x%
Total dogs			100%

GMAT Data Sufficiency (DS) Questions

Each of the dogs enrolled in an obidience course either passed or fail

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