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26 May 2017, 04:43
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30%~35% of the employees in a certain company have cell phones. Do at least half of the employees in the company with cell phones own their houses?
(1) 70%~75% of the employees in the Company own their houses
(2) 40%~45% of the employees in the Company with their houses have cell phones
(1) 70%~75% of the employees in the Company own their houses
(2) 40%~45% of the employees in the Company with their houses have cell phones
26 May 2017, 04:43
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Official Solution:
If you take the 1st step of the variable approach and modify the original condition and the question, this is the 2 by 2 question, which is the most common type of question in the current GMAT math, as shown below.
100% Have a cell phone
(30%~35%) Not have a cell phone
(65%~70%) Own a house x% a% Not own a house y% b%
As shown above, x+y=30~35 and a+b=65~70, then you have 4 variables (x, y, a, b) and 2 equations (x+y=30~35 and a+b=65~70). In order to match the number of variables to the number of equations, there must be 2 equations. Therefore, C is most likely to be the answer. By solving con 1) and con 2),
100% Have a cell phone
(30%~35%) Not have a cell phone
(65%~70%) Own a house
(70%~75%) 70%(40%)~75%(45%) =28%~33.75% a% Not own a house
(25%~30%) y% b%
As shown in the table above, you get \(\frac{28\%}{35\%} \sim \frac{30\%}{33.75\%} = 80\% \sim 89\%\), then at least 50%, hence yes, it is sufficient. The answer is C.
Answer: C
If you take the 1st step of the variable approach and modify the original condition and the question, this is the 2 by 2 question, which is the most common type of question in the current GMAT math, as shown below.
100% Have a cell phone
(30%~35%) Not have a cell phone
(65%~70%) Own a house x% a% Not own a house y% b%
As shown above, x+y=30~35 and a+b=65~70, then you have 4 variables (x, y, a, b) and 2 equations (x+y=30~35 and a+b=65~70). In order to match the number of variables to the number of equations, there must be 2 equations. Therefore, C is most likely to be the answer. By solving con 1) and con 2),
100% Have a cell phone
(30%~35%) Not have a cell phone
(65%~70%) Own a house
(70%~75%) 70%(40%)~75%(45%) =28%~33.75% a% Not own a house
(25%~30%) y% b%
As shown in the table above, you get \(\frac{28\%}{35\%} \sim \frac{30\%}{33.75\%} = 80\% \sim 89\%\), then at least 50%, hence yes, it is sufficient. The answer is C.
Answer: C
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