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30 May 2026, 08:52
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Sofia works at a museum gift shop for the same fixed number of hours each week. This week, she was paid 9 euros per hour plus an additional 3 euros for each postcard set she sold. Last week, she was not paid an hourly wage and was paid only a different fixed amount for each postcard set she sold. If last week she sold 4 times as many postcard sets as she sold this week, did Sofia earn more money this week than last week?
(1) This week, the number of hours Sofia worked was equal to the number of postcard sets she sold.
(2) The amount Sofia was paid for each postcard set last week was greater than the amount Sofia was paid for each postcard set this week.
(1) This week, the number of hours Sofia worked was equal to the number of postcard sets she sold.
(2) The amount Sofia was paid for each postcard set last week was greater than the amount Sofia was paid for each postcard set this week.
30 May 2026, 08:52
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Official Solution:
Sofia works at a museum gift shop for the same fixed number of hours each week. This week, she was paid 9 euros per hour plus an additional 3 euros for each postcard set she sold. Last week, she was not paid an hourly wage and was paid only a different fixed amount for each postcard set she sold. If last week she sold 4 times as many postcard sets as she sold this week, did Sofia earn more money this week than last week?
(1) This week, the number of hours Sofia worked was equal to the number of postcard sets she sold.
Let \(s\) be the number of postcard sets Sofia sold this week. Statement (1) implies that the number of hours she worked this week is also \(s\). So this week’s pay is \(9s + 3s = 12s\).
Given that last week she sold 4 times as many postcard sets as she sold this week, she sold \(4s\) sets last week. But the pay per set last week is unknown, so last week’s pay could be less than, equal to, or greater than \(12s\). Not sufficient.
(2) The amount Sofia was paid for each postcard set last week was greater than the amount Sofia was paid for each postcard set this week.
Let last week’s pay per set be \(y\). Since this week’s pay per set is 3 euros, statement (2) gives \(y > 3\). But without knowing how many postcard sets she sold this week or how many hours she worked this week, we cannot compare her total earnings for the two weeks. Not sufficient.
(1) + (2): From statement (1), this week’s pay is \(12s\). Last week’s pay is \(4s * y\). So the question is whether \(12s > 4s * y\), which simplifies to: is \(3 > y\)? From statement (2), we know that \(y > 3\), so the answer to the question is No: last week’s pay is greater than this week’s pay. Sufficient.
Answer: C
Sofia works at a museum gift shop for the same fixed number of hours each week. This week, she was paid 9 euros per hour plus an additional 3 euros for each postcard set she sold. Last week, she was not paid an hourly wage and was paid only a different fixed amount for each postcard set she sold. If last week she sold 4 times as many postcard sets as she sold this week, did Sofia earn more money this week than last week?
(1) This week, the number of hours Sofia worked was equal to the number of postcard sets she sold.
Let \(s\) be the number of postcard sets Sofia sold this week. Statement (1) implies that the number of hours she worked this week is also \(s\). So this week’s pay is \(9s + 3s = 12s\).
Given that last week she sold 4 times as many postcard sets as she sold this week, she sold \(4s\) sets last week. But the pay per set last week is unknown, so last week’s pay could be less than, equal to, or greater than \(12s\). Not sufficient.
(2) The amount Sofia was paid for each postcard set last week was greater than the amount Sofia was paid for each postcard set this week.
Let last week’s pay per set be \(y\). Since this week’s pay per set is 3 euros, statement (2) gives \(y > 3\). But without knowing how many postcard sets she sold this week or how many hours she worked this week, we cannot compare her total earnings for the two weeks. Not sufficient.
(1) + (2): From statement (1), this week’s pay is \(12s\). Last week’s pay is \(4s * y\). So the question is whether \(12s > 4s * y\), which simplifies to: is \(3 > y\)? From statement (2), we know that \(y > 3\), so the answer to the question is No: last week’s pay is greater than this week’s pay. Sufficient.
Answer: C
