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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?
  1. No woman in the group who had a graduate degree was unemployed
  2. Less than half of the women in the group were employed and had a graduate degree
  3. 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
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
In a certain group of women, 70 percent of the women were employed and...
Given:
  • The Women in the group are divided into groups based on 2 parameters:
    • Employment (Employed, Unemployed)
    • Education (Have a Graduate Degree, Don’t have Graduate Degree)
  • So, the given information can be represented in a table as follows:
  • Now, % of women Unemployed = 100% - 70% = 30%
  • And, % of Women with Graduate Degree = 100% - 25% = 75%
To find: Which of the 3 statements cannot be true?
  • That is, which of the 3 statements are definitely false
Approach:
  1. We’ll evaluate the 3 statements one by one to evaluate which of them are definitely false.
Working Out:
  • Evaluating Statement I
  • No woman in the group who had a graduate degree was unemployed
    • Let the Women with Graduate Degree who are Unemployed be X, and let the Women with Graduate Degree who are Employed be Y.
    • As per this Statement, X = 0%
  • Now, the maximum possible value of Y is 70% (happens when ALL employed women have graduate degrees)
  • So, the minimum possible value of X is 5% (since the sum of Y and X is 75%)
  • Therefore, Statement I is definitely false.
  • Evaluating Statement II
  • Less than half of the women in the group were employed and had a graduate degree
    • Again, Let the women who were employed and had Graduate Degree be Y
    • As per this Statement, Y < 50%
Remember that the question is asking if a Statement is definitely false (that is, false for all possible values of Y)
  • In our analysis of Statement I above, we saw that the maximum possible value of Y is 70%
    • Therefore, for the maximum value of Y, Statement II is false
    • But we cannot say at this point if Statement II is definitely false (that is, false for all possible values of Y)
  • So, let’s now evaluate is also false for the minimum value of Y.
    • The maximum number of Employed Women without Graduate Degree is 25% (happens when ALL women without Graduate Degree are Employed)
​
  • So, the minimum value of Y is 70% - 25% = 45%
  • We observe that for the minimum value of Y, Statement II is true.
  • Thus, Statement II is true for some values of Y and false for other values of Y.
     
  • So, Statement II is not definitely false.
 
  • Evaluating Statement III
  • The number of unemployed women with a graduate degree was 50 percent greater than the number of employed women without a graduate degree
    • Let the Women with Graduate Degree who are Unemployed be X, and let the Women without Graduate Degree who are Employed be Z.
    • As per Statement III, X = 1.5Z
  • Note that this Statement will be definitely false if no valid pair of (X,Z) satisfies the equation X = 1.5Z
  • We will first find the values of X and Z that will satisfy this equation as well as the table above. Then, we will check if these values are acceptable.
  • So, the equation that we can write to relate X and Z is:
    • X = 75% - (70% - Z)
      • = 5% + Z
    • Let’s now substitute X = 1.5Z in this equation:
      • 1.5Z = 5% + Z
      • So, 0.5Z = 5%
      • Therefore, Z = 10%
      • Corresponding value of X = 1.5*10% = 15%
         
  • So, X = 1.5Z is satisfied by X = 15% and Z = 10%
  • We now need to check if these values of X and Z are acceptable
    • The minimum possible value of Z is 0%.
    • In this case, the table will look as under:
The maximum possible value of Z is 25%. In this case, the table will look as under:
  • So, the values of Z range from 0% to 25% and correspondingly, the values of X range from 5% to 30%
  • So, the values X = 15% and Z = 10% do indeed fall in the acceptable range of values of X and Z.
  • So, Statement III is true for one particular pair of X and Z
  • Therefore, Statement III is not definitely false
 
  • Getting to the answer
    • We’ve seen above that out of Statements I, II and III, only Statement I is definitely false.
Looking at the answer choices, we see that the correct answer is Option A
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Most Upvoted Answer
In a certain group of women, 70 percent of the women were employed and...
Cannot Be True Statements:
1. No woman in the group who had a graduate degree was unemployed.
2. Less than half of the women in the group were employed and had a graduate degree.
3. The number of unemployed women with a graduate degree was 50 percent greater than the number of employed women without a graduate degree.

Explanation:
To determine which statement cannot be true, let's analyze each statement one by one.

Statement 1: No woman in the group who had a graduate degree was unemployed.
- Since 70 percent of the women in the group were employed, it is possible that some of them have graduate degrees.
- However, the statement says that no woman with a graduate degree was unemployed.
- This statement cannot be true because it is possible for some women with graduate degrees to be unemployed.

Statement 2: Less than half of the women in the group were employed and had a graduate degree.
- The statement implies that the number of women with both employment and a graduate degree is less than half of the total group.
- Since 70 percent of the women in the group were employed, it is possible that more than half of them have employment without a graduate degree.
- Therefore, this statement can be true.

Statement 3: The number of unemployed women with a graduate degree was 50 percent greater than the number of employed women without a graduate degree.
- Let's assume there are 100 women in the group.
- 70 percent of them are employed, which means 70 women are employed.
- Since 25 percent of them do not have a graduate degree, 25 percent of 70 women or 17.5 women do not have a graduate degree and are employed.
- If the number of unemployed women with a graduate degree is 50 percent greater than the number of employed women without a graduate degree, it would mean there are 26.25 unemployed women with a graduate degree.
- However, since the number of women cannot be in decimals, this statement cannot be true.

Conclusion:
Based on the analysis, the statement that cannot be true is statement 1: No woman in the group who had a graduate degree was unemployed.
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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? No woman in the group who had a graduate degree was unemployed Less than half of the women in the group were employed and had a graduate degree The number of unemployed women with a graduate degree was 50 percent greater than the number of employed women without a graduate degreea)I onlyb)II onlyc)III onlyd)I and III onlye)II and III onlyCorrect answer is option 'A'. Can you explain this answer?
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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? No woman in the group who had a graduate degree was unemployed Less than half of the women in the group were employed and had a graduate degree The number of unemployed women with a graduate degree was 50 percent greater than the number of employed women without a graduate degreea)I onlyb)II onlyc)III onlyd)I and III onlye)II and III onlyCorrect answer is option 'A'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about 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? No woman in the group who had a graduate degree was unemployed Less than half of the women in the group were employed and had a graduate degree The number of unemployed women with a graduate degree was 50 percent greater than the number of employed women without a graduate degreea)I onlyb)II onlyc)III onlyd)I and III onlye)II and III onlyCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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? No woman in the group who had a graduate degree was unemployed Less than half of the women in the group were employed and had a graduate degree The number of unemployed women with a graduate degree was 50 percent greater than the number of employed women without a graduate degreea)I onlyb)II onlyc)III onlyd)I and III onlye)II and III onlyCorrect answer is option 'A'. Can you explain this answer?.
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