An office building housed some tenants and service workers.

Question

An office building housed some tenants and service workers. In a certain month, 15 workers left the building. This left two tenants for each worker. Subsequently, forty-five tenants left. Now there were five workers left for each tenant. How many service workers lived in the building at the beginning?

(A) 30

(B) 35

(C) 40

(D) 45

(E) 50

(A) 30

(B) 35

(C) 40

(D) 45

(E) 50

CareerGeek · Accepted Answer

Tenants ———— workers
— t ———————w—— 
15 workers left the building
 — t —————— w-15 — 
This left two tenants for each worker. —> t = 2(w-15)
 —2(w-15)————w-15 — 
Subsequently, forty-five tenants left. 
 —2(w-15)-45 —— w-15 — 
Now there were five workers left for each tenant.
—> 5(2(w-15) - 45) = (w-15)
—> 10w - 375 = w - 15
—> 9w = 360
—> w = 40

IMO Option C

Pls Hit kudos if you like the solution

Posted from my mobile device

ScottTargetTestPrep · Answer

We can let t = the number of tenants and s = the number of service workers. After the first action, in which 15 workers left, the number of tenants was unchanged. There were now (s - 15) service workers, and this was half the number of tenants. We can create the equation:

1/2t = (s - 15)

t = 2(s - 15)

After the second action, the number of service workers was still (s - 15), but 45 tenants had left, so we have (t - 45). The new relationship between the two groups was that there were now 5 times as many workers as tenants, so we have:

s - 15 = 5(t - 45)

Substituting 5(t - 45) for s - 15 in the first equation, we have:

t = 2(5(t - 45))

t = 10t - 450

450 = 9t

50 = t

Now, substituting 50 for t in the first equation, we have:

50 = 2(s - 15)

25 = s - 15

40 = s

Answer: C

luisdicampo · Answer

Deconstructing the Question

Let  T  be the initial number of tenants and  W  be the initial number of service workers.

After 15 workers left, workers became  W-15  and there were 2 tenants per worker:

T = 2(W-15)

Then 45 tenants left, tenants became  T-45 , and there were 5 workers per tenant:

W-15 = 5(T-45)

We are asked for the initial number of workers  W .

Step-by-step

From the first condition:

T = 2(W-15) = 2W-30

Substitute into the second condition:

W-15 = 5((2W-30)-45)

Simplify inside:

(2W-30)-45 = 2W-75

So:

W-15 = 5(2W-75) = 10W-375

Move  W  terms:

-15 = 9W-375

Add 375 to both sides:

360 = 9W

W = \frac{360}{9} = 40

Answer: C

An office building housed some tenants and service workers.

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 Problem Solving (PS) Questions

An office building housed some tenants and service workers.

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