A certain company defines its annual labor turnover rate as the number

Question

A certain company defines its  annual labor turnover rate  as the number of employees who left the company during the year divided by the average of the number of employees on the first day of the year and the number of employees on the last day of that year. Last year, the company had a labor turnover rate of exactly 25%.

Assuming that the information above is true, select for  Statement 1  and for  Statement 2  the statements such that if Statement 1 is true, then Statement 2 must be true, but it could be the case that Statement 2 is true and Statement 1 is false. Make only two selections, one in each column.

ID: 700205

KarishmaB · Accepted Answer

The turnover rate is 25% i.e. 1/4

So various scenarios are possible.

Beg of year - 4 people
1 left, 1 joined
End of year - 4 people

Beg of year - 9 people
2 left, 0 joined
End of year - 7 people

etc...

Why (D) and (E) work (ANSWER):

(D) 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.

Consider the 1st example above. The 4 who were at the beginning were the ones at the end too. That is all. It is certainly possible. One person joined and he was the one who left.

(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.

Has to be true because all and only those who were on the 1st day were on the last day too. No reductions. No extra people.

Why (B) and (E) do not work:

(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 as per the illutration above.

kkannan2 · Answer

Hi  KarishmaB  - what's your logic in picking numbers for this question? In other words, how did you know to test out the numbers that you did (4 employees at the company to start, 1 joins and 1 leaves and 9 employees at the company to start, 2 leave and 0 join)? I find it tough to pick numbers for such TPA questions and generally waste time on that. Any tips or suggestions would be appreciated! Thanks!

Gemmie · Answer

E_1​ : The number of employees on the first day of the year.
 E_2 ​: The number of employees on the last day of the year.
L: The number of employees who left the company during the year.

Turnover Rate=  L \div \frac{E_1​+E_2​​}{2}= 0.25

>>>  L = 0.125 * (E_1​+E_2​)

Requirements 
S1 ==> S2
But it cannot be S2 ==> S1

=> Statement 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.
 => Statement 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.

S1: If all and only those who were employees on the first day were employees on the last day:

No new employees joined the company during the year.

The number of employees who left equals the number of employees who joined, which is zero since no new employees joined.

So, E1=E2​, and everyone who left must have been among the initial employees. (i.e. S2)

S2: If the number of employees on the first day of the year was equal to the number on the last day of the year:

E1=E2

Given the turnover rate of 25%, we have: L=0.25×E1

But we cannot jump to S1. The company could have had new employees join and the same number (but a different set, which is a part of E1) leave, maintaining the total number equal.

KarishmaB · Answer

I want to keep the numbers small, simple but realistic. So 4 and 1 are the best options. They are easy to evaluate.
25 and 100 would lead to chaos.

Also, it is much easier to explain why certain options work and why others don't. But picking the options and checking in an exam setup will be hard. Such a question where looking for the first thread is hard should be bookmarked. Return to it if you have time. Penalty of an incorrect answer here would be negligible.

desertEagle · Answer

Kindly explain the meaning of the term "all and only those"

My understanding is that it means that "all and only those employees who were employees of company on first day of last year" means that only those employees who were employees of company.

My understanding is that it means that if a, b, c were employees the only possiblity for last day are "a" or "b" or "c" or "a and b" or "a and c" or "b and c" or "a, b and c". There is no mention of the word  number  . Why are you all equating all and those to number of employees

Bunuel · Answer

The phrase "all and only those" means that everyone who was an employee on the first day of last year remained an employee on the last day of the year, and no one else became an employee during that time.

In simpler terms:

"All" means every person who was an employee on the first day continued to be an employee on the last day. 
 "Only those" means no one else (who wasn’t an employee at the start) became an employee by the end of the year.

So, if a, b, and c were employees at the beginning, then the only people who could still be employees at the end of the year are a, b, and c, no one else.

This isn't about the "number" of employees changing, but rather about the specific individuals who were employees throughout the year.

imAman · Answer

Hi  KarishmaB ,

I chose the option E as St1 and Option B as St2. I know this is a wrong answer but I don't know why this is wrong.
Can you help me with this?

KarishmaB · Answer

Think about it: Say there were 100 people on the first day and 100 people on the last day. (Option (E) is true)

On the first day, the employees are E1 to E100.

Say 20 of these left - from E1 to E20. So now there are 80 employees (E21 to E100)
Say 25 new people joined (E101 to E125). So now there are 105 employees. (E21 to E125)
Now say 5 of these new people left (E121 to E125 left).

There are again 100 employees - from E21 to E120

Is (B) true?
(B) Exactly 25% of the employees working at the company on the first day of last year left the company last year.

No. Only 20% of the employees working at the company on the first day of last year left the company last year.

That is why (E) - (B) doesn't work.

NoeticImbecile · Answer

Hello, thank you for the solution. I have a question: in S1, 
"No new employees joined the company during the year.

The number of employees who left equals the number of employees who joined, which is zero since no new employees joined." In this case, shouldn't the turnover rate be zero as no one left the company

cheshire · Answer

You could have the same employees who joined also be the ones who left, which would still allow a 25% turnover rate while keeping the statements true.

AliEjaz01 · Answer

Why not Option D and Option A. If Option D is correct then, definitely more people left the company than started work right? Since 0 people started work

Bunuel · Answer

Option D means that the people employed on the first day and the people employed on the last day are exactly the same set of individuals.

It does  not  mean that nobody started work during the year. People could have started work and then left before the last day. Therefore, starters are not necessarily zero, and you cannot conclude that more people left than started.

Nidhibatra · Answer

why isnt this the answer? If exactly 25% of the employees working at the company on the first day of last year left the company last year, then Last year, more people left the company than began work at the company. Solve this using eqns and you will find this to be true

Bunuel · Answer

Here is a simple counterexample that shows your implication is false.

Start of year: 100 employees
 Left during the year: 25 employees (so exactly 25% of the 100 left)
 Hired during the year: 25 employees
 End of year: 100 employees
Turnover is 25% (25 divided by the average of 100 and 100).
 
But “more left than began work” is false because 25 left and 25 began work.

Rickooreoisb · Answer

OFFICIAL ANSWER

Answer Explanation 
 Evaluate 
Note that because Statement 1 and Statement 2 must be chosen by determining whether a certain relationship between them holds—namely, that if Statement 1 is true, then Statement 2 must be true, but if Statement 2 is true, Statement 1 can be false—the two answer selections must be chosen together.
 
 Statement 1 and Statement 2 
We are told that a certain company “defines its annual labor turnover rate as the number of employees who left the company during the year divided by the average of the number of employees on the first day of the year and the number of employees on the last day of that year.” We are also told that the labor turnover rate last year was 25%.

To answer this question, Statement 1 must be such that if it is true, then the other (Statement 2) must be true, but the reverse may not hold (i.e., if Statement 2 is true, Statement 1 can be false).

Consider the fourth answer choice,  “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.”  If that is true, that means that 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. Notice that that is what the fifth answer choice says.

So, the fourth and fifth answer choices are likely candidates for the answer.

(Note that it may seem odd that the company would have exactly the same employees on the first and last day of the year, given that the company had a 25% annual turnover rate. But that turnover rate might occur if, for instance, the company hired some workers during the year for a short-term project, and all those workers who were hired at some point after the first day were no longer employed there on the last day.)

So, we’ve seen that if the fourth answer choice is true, the fifth answer choice must also be true. But does the fourth have to be true if the fifth is? No, because some people who were employees on the first of the year could have left during the year, and an equal number of employees were hired to replace them, all of whom remained employees on the last day of the year. That would result in the first and last days of the year having an equal number of employees, though not all the employees on the first day were employees on the last day.
 
 Final Selections 
 The correct answer for Statement 1 is 
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.
 The correct answer for Statement 2 is 
Last year, the number of employees on the first day was equal to the number of employees on the last day of the year.

Rickooreoisb · Answer

KarishmaB  - need help. I saw you pick this question in gmatclub video. However, can you also teach an approach on how to look at the options please

Rickooreoisb · Answer

Outcome of thinking :

On these GMAT logic questions, always look for:
Type Meaning
Identity Who is there
Quantity How many are there

Whenever you see:
one option talking about who
another talking about how many

Your brain should immediately test:
Does “who” force “how many”?

Almost always yes.
The reverse almost never holds.

That’s the pattern GMAT is exploiting here

__________________

Now coming to this question

🧠 Step 1 — Classify options by  type 
Always bucket the options:
   Type 
 What it controls 
 
   Who  
 Which people are employed (identity) 
 
   How many  
 Number of employees 
 
   Flows  
 Left, joined, percentages

In this problem:
 
  D  = who 
  E  = how many 
  A, B, C  = flows / percentages  
 
🧠 Step 2 — Find a  forcer  (Statement 1)
Test each option with this checklist:

A → no 
 B → no 
 C → no 
  D → yes (forces how many)  
 E → no (just gives a number)  
So only  D  can be Statement 1.
 
🧠 Step 3 — What does D force?
D = same people on both days
 Same people ⇒ same count
So  D ⇒ E 
 
🧠 Step 4 — Check one-way condition
Can E be true while D is false?
 Yes — same number, different people.
So:
D⇒EbutE⇏DD \Rightarrow E \quad	ext{but}\quad E 
Rightarrow DD⇒EbutE⇏D
That matches the rule.
 
✅ Final mental rule
 
That single idea solves this entire problem.

KarishmaB · Answer

Yes, I picked it up to show you the kind of questions you need to skip in your first run through the section. These iterative logic questions are a time sink. I have shown the analysis of 2 pairs of options above: https://gmatclub.com/forum/a-certain-co ... l#p3365621
Do we have the time to do it for about 10 pairs on average?

Rickooreoisb

KarishmaB - need help. I saw you pick this question in gmatclub video. However, can you also teach an approach on how to look at the options please

A certain company defines its annual labor turnover rate as the number

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

Statement 1	Statement 2
		Last year, more people left the company than began work at the company.
		Exactly 25% of the employees working at the company on the first day of last year left the company last year.
		More than 25% of the employees working at the company on the first day of last year left the company last year.
		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.
		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.

Type	What it controls
Who	Which people are employed (identity)
How many	Number of employees
Flows	Left, joined, percentages

GMAT Two-part Analysis (TPA) Questions

A certain company defines its annual labor turnover rate as the number

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards