At the beginning of 2023, a fitness club had 800 active members.

Question

At the beginning of 2023, a fitness club had 800 active members. During 2023, some of the members who had been active at the beginning of the year canceled their memberships and did not rejoin, and every new member who joined during 2023 remained active through the end of the year. If x percent of the members active at the beginning of 2023 canceled their memberships and did not rejoin, and if the number of active members at the end of 2023 was y percent greater than the number active at the beginning of 2023, how many new members joined the club during 2023?

(1) x - y = 7
(2) x + y = 35

M47-182

Bunuel · Accepted Answer

GMAT Club Official Solution:

At the beginning of 2023, a fitness club had 800 active members. During 2023, some of the members who had been active at the beginning of the year canceled their memberships and did not rejoin, and every new member who joined during 2023 remained active through the end of the year. If x percent of the members active at the beginning of 2023 canceled their memberships and did not rejoin, and if the number of active members at the end of 2023 was y percent greater than the number active at the beginning of 2023, how many new members joined the club during 2023?

At the beginning of 2023, the club had 800 active members.

x percent of those members canceled and did not rejoin, so the number of such members was:

800 * x/100 = 8x

At the end of 2023, the club had y percent more active members than it had at the beginning of the year, so the net increase was:

800 * y/100 = 8y

The new members had to replace the 8x members who canceled and also account for the net increase of 8y members.

So the number of new members who joined was:

8x + 8y = 8(x + y)

The question asks for 8(x + y).

(1) x - y = 7

This gives only the difference between x and y, not their sum.

For example, x = 17 and y = 10 gives x + y = 27.

But x = 21 and y = 14 gives x + y = 35.

So the number of new members is not fixed.

Not sufficient.

(2) x + y = 35

So:

8(x + y) = 8 * 35 = 280

Sufficient.

Answer: B.

BongBideshini · Answer

Let (N) be the number of new members who joined
Beginning members = 800.
Canceled members = 800x/100 = 8x
End-of-year members = 800 + 800y/100 = 800 + 8y
800 - 8x + N = 800 + 8y
N = 8(x+y)

Statement (1) 
x-y=7
This does not determine (x+y)
 Not sufficient.

Statement (2)

x+y=35
N=8(x+y)=8(35)=280
 Sufficient.

Answer: B

SS990 · Answer

Given: 800 people at the start of the year. x% of people left, did not rejoin. in the end y% increased from year start
deduction: n = 800(100+y/100)-800(100-x/100)
n=8(100+y)-8(100-x) = 8(y+x)

To find: no. of new people who joined during the year

1) x-y=7 insufficient, since we dont dont x,y or x+y needed to solve for n
2) x+y=35 sufficient, since we can find from deduced equation. Hence B is the answer

TheAdmissionHub · Answer

When the problem contains a lot of information, it is helpful to translate the information into equations and identify exactly which quantity we need to find before evaluating the statements.

Members at the beginning of 2023:  800

Members who canceled their membership during 2023:  \frac{x}{100} * (Beginning     members) = \frac{x}{100} * 800 = 8x

Members at the end of 2023:
  (Beginning     members) + \frac{y}{100} * (Beginning     members) = 800 + \frac{y}{100} * 800 = 800 + 8y

Let  N  be the number of new members hat joined the club during 2023. We can set up the following equation:

(Beginning     members) - (Canceled     members) + (New     members) = (Members     at     the     end)

800 - 8x + N = 800 + 8y

N = 8x + 8y

N = 8*(x+y)

Therefore, to determine  N  we only need to know the value of  x+y .

Statement (1):    x-y=7  
We don't have any information about the sum  x+y .
 Not sufficient

Statement (2):      x+y=35   
 We have the result of the sum  x+y , so we can find  N . 
 Sufficient

Answer: B

At the beginning of 2023, a fitness club had 800 active members.

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 Data Sufficiency (DS) Questions

At the beginning of 2023, a fitness club had 800 active members.

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