In a certain group of women, 70 percent of the women were employed and

Question

In a certain group of women, 70 percent of the women were employed and 25 percent did not have a graduate degree. Which of the following statements cannot be true?

I. No woman in the group who had a graduate degree was unemployed
II. Less than half of the women in the group were employed and had a graduate degree
III. The number of unemployed women with a graduate degree was 50 percent greater than the number of employed women without a graduate degree

A. I only
B. II only
C. III only
D. I and III only
E. II and III only

Source: e-GMAT Scholaranium

chetan2u · Answer

We can make a 2 by 2 ..
...........E.............UE..Total
G........a............... b.....75
NG.....c............... d......25
Total..70...........30.......100

We are looking for CANNOT be true..

I. No woman in the group who had a graduate degree was unemployed
 This means b=0 ,but a can be max 70, and this makes the least value if b as 5.
Cannot be true.

II. Less than half of the women in the group were employed and had a graduate degree
 This means a<50 . Possible, as max value of a will be when c is 0, so 70, and min value will be when c is max that is 25, so a = 70-25=45<50.
Can be true.

III. The number of unemployed women with a graduate degree was 50 percent greater than the number of employed women without a graduate degree.
 This means b=1.5c . Possible ..
a+b=75...a+c=70, so b-c=75-70=5 or 1.5c-c=5...c=10 and b =15.
Can be true.

Only I cannot be true

A

LeoN88 · Answer

chetan2u  Sir, this 2x2 matrix is really helpful:-

1. How did you know when to use?
2. Could you share few more sums like this?

Thank you.

chetan2u · Answer

Wherever you have a set of people/things that can be of 2 types.
Here 100 could be just G, just E, both or none.

parthanjha · Answer

I'm 99.9% sure the correct answer (none of the above) isn't in the options. Here's why -

E/UE = Employed, Unemployed. 
ND/D = No Degree, Degree

There are 70 E, 30 UE
And 25 ND, 75 D

Let all unemployed women have degrees. So 30 UE,D
Since 75 have degrees, 75-30 = 45 E,D
Since 70 are employed, 70-45 = 25 E, ND

This is a scenario where literally all the women who are unemployed have degrees and all the women with no degrees are employed.

Am I misunderstanding this or is the question wrong?

chetan2u · Answer

This is a CANNOT be true question, that is a particular statement will never be true. 
Please check your reasoning keeping the above in mind and ask query if any.

bumpbot · Answer

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In a certain group of women, 70 percent of the women were employed and

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In a certain group of women, 70 percent of the women were employed and

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