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14 Jul 2026, 03:23
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Legallyblond
I am not sure of your question. (B) and (E) cannot be the answer. That is, if B is true, then it is NOT NECESSARY that (E) must be true too. (E) may or may not be true in that case.
In this example, I have shown that.
(B) Exactly 25% of the employees working at the company on the first day of last year left the company last year.
Beg of year - 100 people
25 of these 100 left, 70 joined and 5 of these left
End of year - 140 people
Turnover Rate = 30/120 = 25%
(E) Last year, the number of employees on the first day of the year was equal to the number of employees on the last day of the year.
Not true in this example. At the beg of the year, there were 100 people and at the end 140. So it is NOT NECESSARY that the number of employees on the first day of the year was equal to the number of employees on the last day of the year. They could be different. That is why (B) and (E) is not the answer.
14 Jul 2026, 10:56
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Hi Legallyblond,
You've actually got half of it nailed. Your 20% case correctly shows that E can be true while B is false, so E cannot force B. That's exactly why B is disqualified from being Statement 2 under E.
But your remaining doubt is about the other direction: you're assuming that if B is true, then E must be true (i.e., B could be Statement 1 with E as Statement 2). That's the step that quietly breaks.
Read exactly what B says: "Exactly 25% of the employees working at the company on the first day left." B only constrains the beginning group. It says nothing about people who were hired during the year and then also left. Those extra leavers still count toward the total number who left.
Look back at Karishma's counterexample - it's the very case that kills B => E:
- Start: 100 employees
- 25 of those 100 leave -> B is true (exactly 25% of the first-day group left)
- 70 new people are hired, and 5 of those newcomers also leave
- Total who left = 30, End = 100 - 25 + 70 - 5 = 140
- Turnover = 30 / ((100+140)/2) = 30/120 = 25% ✓
Here B is true, the 25% turnover holds - but Start (100) ≠ End (140), so E is false.
So B does not force E. Your intuition that "25 left the beginning group, so counts must balance" only holds if those 25 were the only leavers - but B never promises that. New hires can leave too, pushing the end count above the start.
That's why B pairs with neither column: it fails as Statement 1 (doesn't force E) and, from your own 20% case, fails as Statement 2.
Answer: Column 1 = All and only those who were employees at the company on the first day of last year were employees on the last day of last year. (option 4); Column 2 = Last year, the number of employees on the first day of the year was equal to the number of employees on the last day of the year. (option 5)
You've actually got half of it nailed. Your 20% case correctly shows that E can be true while B is false, so E cannot force B. That's exactly why B is disqualified from being Statement 2 under E.
But your remaining doubt is about the other direction: you're assuming that if B is true, then E must be true (i.e., B could be Statement 1 with E as Statement 2). That's the step that quietly breaks.
Read exactly what B says: "Exactly 25% of the employees working at the company on the first day left." B only constrains the beginning group. It says nothing about people who were hired during the year and then also left. Those extra leavers still count toward the total number who left.
Look back at Karishma's counterexample - it's the very case that kills B => E:
- Start: 100 employees
- 25 of those 100 leave -> B is true (exactly 25% of the first-day group left)
- 70 new people are hired, and 5 of those newcomers also leave
- Total who left = 30, End = 100 - 25 + 70 - 5 = 140
- Turnover = 30 / ((100+140)/2) = 30/120 = 25% ✓
Here B is true, the 25% turnover holds - but Start (100) ≠ End (140), so E is false.
So B does not force E. Your intuition that "25 left the beginning group, so counts must balance" only holds if those 25 were the only leavers - but B never promises that. New hires can leave too, pushing the end count above the start.
That's why B pairs with neither column: it fails as Statement 1 (doesn't force E) and, from your own 20% case, fails as Statement 2.
Answer: Column 1 = All and only those who were employees at the company on the first day of last year were employees on the last day of last year. (option 4); Column 2 = Last year, the number of employees on the first day of the year was equal to the number of employees on the last day of the year. (option 5)
Legallyblond
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