Multiple choice

Yes No Not sure Program A 520 380 300 Program B 530 300 370 The table shows the number of employees who responded yes, no, or don't know when asked whether they participated in Training Programs A and B this year. If a total of 1,200 employees responded to the question about both programs, what was the number of employees who did not respond yes to participating in either of the two programs? 1) The number of employees who responded yes to participating in both Program A and Program B was 420. 2) The number of employees who responded don't know to participating in both Program A and Program B was 150.

  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

  4. EACH statement ALONE is sufficient.

  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total = 1200. We need to find those who did not answer 'yes' to either. This is 1200 - (YesA + YesB - BothYes). Statement 1 gives BothYes = 420. We know YesA=520, YesB=530. So we can calculate the union. Statement 1 is sufficient.

AI explanation

To find the number of employees who did not respond yes to either program, you must subtract the total number of unique employees who responded yes from the total pool of 1200. Statement 1 provides the overlap of 420 employees who responded yes to both programs. Using the inclusion-exclusion principle, you can find the total unique yes responses by adding the yes responses for Program A (520) and Program B (530), then subtracting the 420 overlap to get 630 unique yes responses. Subtracting this 630 from 1200 gives 570 employees, proving statement 1 is sufficient while statement 2 alone is not.

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