Sofia works at a museum gift shop for the same fixed number of hours

Question

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.

Bunuel · Accepted Answer

GMAT Club 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. (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, (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 (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 (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.

Adit_ · Answer

Too much data, lets condense it:

Last week:

Post = 4x (x = Postcards sold this week)
Hourly = 4xy (y = amount per postcard sold)

This week:

Post = x
Hourly = 9/hr + 3/postcard

______________________________

Statement 1:

Hourly = Postcards sold
Hence, you can simply add 9+3 = 12
Total wages = 12/hr or 12/Postcard sold. We still cant find anything about earning of last week.
Clearly INSUFFICIENT.

Statement 2:
This says y > 3
Again we cant compare between earnings of last week and this week.
INSUFFICIENT.

Combining the 2:
We have,

4xy(earnings last week):12x
Considering x to be postcards sold and since hours worked and postcards sold are equal this week we can keep it as x.

4xy:12x = y:3

But now we also know from statement 2 that y>3. Thus 4xy>12x
Hence answer is NO.
SUFFICIENT.

Answer:  Option C

dp1234 · Answer

Hours postcard Paid
Last week h 4x 4xp (let rate p for each postcard set)
This week h x 9h + 3x

So question is 9h+3x > 4xp ? yes/no type
To asses this we need h, x and p - reduced to one variable. 
Statement-1: h=x. Gives only h in terms of x. Dont know value or relation of P. Not sufficient. 
Statement-2: states P>3. Which gives RHS of inequality more than 12x. But h is not known in LHS. Not sufficient. 
Together- LHS=12x and RHS is more than 12x. Thus it answers, sufficient.

thisisakr · Answer

So Let the number of postcard sold be P this week 
Last week it was 4P

1. According to 1 
 The number of hours worked ‘h’ is equal to number of postcard ‘P’ sold this week 
 9h+3P —> 11 P. ( h=P)
 Last week postcard sold were 4P but we still don’t know at what price they were sold 
 Hence,  Insufficient

2. This says the Cost postcard sold last week was greater than 3. So it could be 3.1, 3.2... anything 
 So the total cost 4P * 3.1 something

But we don’t know the 9h+3n value so we can’t really predict

Hence  insufficient  
Together

From 1 we get total cost of this week as 11P
From 2 we get the total cost of last week as greater than 12P

Hence both together is  sufficient

Sofia works at a museum gift shop for the same fixed number of hours

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Sofia works at a museum gift shop for the same fixed number of hours

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