VJesus12 wrote: ↑

Fri Dec 10, 2021 8:41 am

Paula and Sandy were among those people who sold raffle tickets to raise money for Club \(X.\) If Paula and Sandy sold a total of \(100\) of the tickets, how many of the tickets did Paula sell?

(1) Sandy sold \(\dfrac23\) as many of the raffle tickets as Paula did.
(2) Sandy sold \(8\) percent of all the raffle tickets sold for Club \(X.\)

Answer: A

Source: Official Guide

Target question: How many of the tickets did Paula sell?

Given: Paula and Sandy sold a total of 100 of the tickets
Let x = number of tickets that Paula sold
This means 100-x = number of tickets that Sandy sold

Statement 1: Sandy sold 2/3 as many of the raffle tickets as Paula did.
We can write: (# of tickets Sandy sold) = (2/3)(# of tickets Paula sold)
Or... 100-x = (2/3)x
Eliminate the fractions by multiplying both sides by 3 to get: 300 - 3x = 2x

ASIDE: At this point, we should recognize that we CAN solve this equation for x, which means we CAN answer the target question with certainty. But for "fun" let's finish the math...

Add 3x to both sides to get: 300 = 5x
Solve: x = 60
In other words, Paula sold 60 tickets
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: Sandy sold 8 percent of all the raffle tickets sold for Club X.
We don't know how many tickets were sold for Club X. All we know is that Paula and Sandy sold a total of 100 tickets.
Since we don't know how many tickets were sold for Club X, we can't determine the number of tickets Sandy sold.
If we can't determine the number of tickets Sandy sold, then we can't determine the number of tickets Paula sold.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer:A