At the beginning of 2007, a company had x employees. To handle

Question

At the beginning of 2007, a company had  x  employees. To handle an increasing workload, it recruited  p\%  additional employees during the year. However, in 2008, due to the financial crisis, the company was compelled to lay off  q\%  of its workforce. As a result, the total number of employees returned to  x .
 
Select for  p  and for  q  values that are jointly consistent with the information provided. Make only two selections, one in each column.

Bunuel · Answer

Official Solution: The number of employees after p\% increase and q\% decrease would be x(1 + \frac{p}{100})(1 - \frac{q}{100}) . Since at the end the company had the same number of employees, we get: x(1 + \frac{p}{100})(1 - \frac{q}{100})=x (1 + \frac{p}{100})(1 - \frac{q}{100})=1 (\frac{100+p}{100})(\frac{100-q}{100})=1 (100+p)(100-q)=100*100 Now, we need to find the values of p and q that satisfy this equation. Notice that the right-hand side, 100 * 100 = 10^4 , has only 2 and 5 as its prime factors. Thus, the left-hand side must also have only these primes. Substituting different values of p from the options for 100 + p , we get: 110, 115, 120, 125, 150, and 175.. Only 125 does not have primes other than 2 and 5. Hence, p must be 25. Increasing something by 25\% needs to be decreased by 20\% to bring it back to the original value, making q equal to 20. Correct answer: p "25" q "20" GMAT-Club-Forum-z53apl9i.png

Bismuth83 · Answer

1. Let's model the question. The company starts off with x employees.

2. Then in 2007 it added p% employees. So, there was a total number of  x + x * p\% .

3. In 2008 they layed off q%. So, the total number of employees was  (x + x * p\%) - (x + x * p\%) * q\% .

4. It is known that the final value is x. That means we have the following equation:  x = (x + x * p\%) - (x + x * p\%) * q\% .

5. Let's simplify  x = (x + x * p\%) - (x + x * p\%) * q\% \rightarrow 0 = x * p\% - x * q\% - x * p\% * q\% = x(p\% - q\% - p\% * q\%) .

6. x is not zero, so  0 = p\% - q\% - p\% * q\% \rightarrow p\%(1 - q\%) = q\% \rightarrow p\% = \frac{q\%}{1 - q\%} .

7. Let's plug in the values for q and see what p we get:

- q = 10.  \frac{10\%}{1 - 10\%} = \frac{0.1}{1 - 0.1} \approx 0.111 = 11.1\% , 11.1   isn't an answer choice for p.  
 - q = 15.  \frac{15\%}{1 - 15\%} = \frac{0.15}{1 - 0.15} \approx 0.176 = 17.6\% , 17.6   isn't an answer choice for p.   
 - q = 20.  \frac{20\%}{1 - 20\%} = \frac{0.2}{1 - 0.2} = 0.25 = 25\% , 25   is an answer choice for p.   
 - q = 25.  \frac{25\%}{1 - 25\%} = \frac{0.25}{1 - 0.25} \approx 0.333 = 33.3\% , 33.3   isn't an answer choice for p.   
 - q = 50.  \frac{50\%}{1 - 50\%} = \frac{0.5}{1 - 0.5} = 1 = 100\% , 100   isn't an answer choice for p.   
 - q = 75.  \frac{75\%}{1 - 75\%} = \frac{0.75}{1 - 0.75} = 3 = 300\% , 300   isn't an answer choice for p.

8. Our answer will be:   p - 25 and q - 20  .

GMATGuruNY · Answer

Consider the following case:
Let the original number of employees = 10
If p=100 -- implying an increase of 100% -- the number of employees doubles to 20.
If q=50 -- implying a decrease of 50% -- the number of employees decreases by 1/2 back down to 10.
Notice that, to return to the original number of employees, the value of p must be greater than the value of q.
Implication:
p is likely to be one of the three greatest answer choices, with q one of the three smallest.

p --> an increase of 25%, 50% or 75% implies the following: 
 25% increase --> 125% of the original value --> multiply by  \frac{125}{100} = \frac{5}{4}  
50% increase --> 150% of the original value --> multiply by  \frac{150}{100} = \frac{3}{2} 
75% increase --> 175% of the original value --> multiply by  \frac{175}{100} = \frac{7}{4}

q --> a decrease of 10%, 15% or 20% implies the following: 
10% decrease --> 90% remains --> multiply by  \frac{90}{100} = \frac{9}{10} 
15% decrease --> 85% remains --> multiply by  \frac{85}{100} = \frac{17}{20} 
 20% decrease --> 80% remains --> multiply by  \frac{80}{100} = \frac{4}{5}

For the number of employees to return to the original value of x, the fractions implied by p and q must be RECIPROCALS, as the blue options above will make clear:
  x * \frac{5}{4} * \frac{4}{5} = x

Thus:
p=25% and q=20%

Purnank · Answer

Just assuming x = 100 then doing increase and decrease by using options evaluations will be effective here.

like at start it will increase then decreases with same number. means when we calculate in % it will always be higher value for p than q

so p and q will not be 10 and 75. and now evaluating remaining options you will notice for p = 25 and q = 20 only satisfies.

100 --- (+25%) ---- 125 ---- (-20%) ----- 100

At the beginning of 2007, a company had x employees. To handle

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

GMAT Two-part Analysis (TPA) Questions

At the beginning of 2007, a company had x employees. To handle

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