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38% (02:20) correct
62%
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A campus bookstore bought 60 notebooks for a total of 540 euros. All of the notebooks were sold during a three-week orientation period. The notebooks were sold for 14 euros each in week 1, 11 euros each in week 2, and 8 euros each in week 3. Was the number of notebooks sold in week 1 greater than the number sold in week 3?
(1) Fewer than 20 notebooks were sold in week 2.
(2) The bookstore’s total profit on the notebooks was less than 120 euros.
(1) Fewer than 20 notebooks were sold in week 2.
(2) The bookstore’s total profit on the notebooks was less than 120 euros.
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02 Apr 2026, 04:45
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GMAT Club Official Solution:
A campus bookstore bought 60 notebooks for a total of 540 euros. All of the notebooks were sold during a three-week orientation period. The notebooks were sold for 14 euros each in week 1, 11 euros each in week 2, and 8 euros each in week 3. Was the number of notebooks sold in week 1 greater than the number sold in week 3?
(1) Fewer than 20 notebooks were sold in week 2.
We know:
{week 1} + {week 2} + {week 3} = 60
But this statement gives information only about {week 2}. It still leaves many possible values for {week 1} and {week 3}.
Not sufficient.
(2) The bookstore’s total profit on the notebooks was less than 120 euros.
The total cost was 540 euros, so the total revenue was less than 540 + 120 = 660 euros.
Thus, the average selling price was less than 660/60 = 11 euros.
Now 11 euros is exactly the price in week 2, and it is exactly halfway between 14 euros (week 1) and 8 euros (week 3).
So, if the overall average selling price is less than 11 euros, then more notebooks must have been sold at 8 euros than at 14 euros, because only then would the average be pulled below 11 euros. Therefore,
{the number of notebooks sold in week 3 at 8 euros} > {the number of notebooks sold in week 1 at 14 euros}
So the answer to the question is no. Sufficient.
Answer: B.
A campus bookstore bought 60 notebooks for a total of 540 euros. All of the notebooks were sold during a three-week orientation period. The notebooks were sold for 14 euros each in week 1, 11 euros each in week 2, and 8 euros each in week 3. Was the number of notebooks sold in week 1 greater than the number sold in week 3?
(1) Fewer than 20 notebooks were sold in week 2.
We know:
{week 1} + {week 2} + {week 3} = 60
But this statement gives information only about {week 2}. It still leaves many possible values for {week 1} and {week 3}.
Not sufficient.
(2) The bookstore’s total profit on the notebooks was less than 120 euros.
The total cost was 540 euros, so the total revenue was less than 540 + 120 = 660 euros.
Thus, the average selling price was less than 660/60 = 11 euros.
Now 11 euros is exactly the price in week 2, and it is exactly halfway between 14 euros (week 1) and 8 euros (week 3).
So, if the overall average selling price is less than 11 euros, then more notebooks must have been sold at 8 euros than at 14 euros, because only then would the average be pulled below 11 euros. Therefore,
{the number of notebooks sold in week 3 at 8 euros} > {the number of notebooks sold in week 1 at 14 euros}
So the answer to the question is no. Sufficient.
Answer: B.
General Discussion
30 Mar 2026, 22:50
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Cost per notebook: 540/ 60 = 9 euros each
Let w1, w2, w3 = notebooks sold in weeks 1, 2, 3.
Constraints:
w1 + w2 + w3 = 60
w1, w2, w3 ≥ 0 (integers)
Question: Is w1 > w3?
Profit equation:
Total profit = (14−9)w1 + (11−9)w2 + (8−9)w3
= 5w1 + 2w2 − w3
Since w3 = 60 − w1 − w2, profit becomes:
= 5w1 + 2w2 − (60 − w1 − w2)
= 6w1 + 3w2 − 60
Statement 1: w2 < 20
With w2 ranging 0–19, w1 and w3 can vary enormously.
A: w1 = 1, w2 = 1, w3 = 58 —— w1 < w3 —-No
B: w1 = 58, w2 = 1, w3 = 1 —- w1 > w3 —- Yes
Hence, Insufficient
Statement 2: Profit < 120
6w1 + 3w2 − 60 < 120
6w1 + 3w2 < 180
2w1 + w2 < 60
Since w1 + w2 + w3 = 60, we know w1 + w2 = 60 − w3, so:
2w1 + w2 < 60
w1 + (w1 + w2) < 60
w1 + (60 − w3) < 60
w1 < w3
This means the answer to the question is definitively No — w1 is not greater than w3. ——— sufficient
Ans B
Let w1, w2, w3 = notebooks sold in weeks 1, 2, 3.
Constraints:
w1 + w2 + w3 = 60
w1, w2, w3 ≥ 0 (integers)
Question: Is w1 > w3?
Profit equation:
Total profit = (14−9)w1 + (11−9)w2 + (8−9)w3
= 5w1 + 2w2 − w3
Since w3 = 60 − w1 − w2, profit becomes:
= 5w1 + 2w2 − (60 − w1 − w2)
= 6w1 + 3w2 − 60
Statement 1: w2 < 20
With w2 ranging 0–19, w1 and w3 can vary enormously.
A: w1 = 1, w2 = 1, w3 = 58 —— w1 < w3 —-No
B: w1 = 58, w2 = 1, w3 = 1 —- w1 > w3 —- Yes
Hence, Insufficient
Statement 2: Profit < 120
6w1 + 3w2 − 60 < 120
6w1 + 3w2 < 180
2w1 + w2 < 60
Since w1 + w2 + w3 = 60, we know w1 + w2 = 60 − w3, so:
2w1 + w2 < 60
w1 + (w1 + w2) < 60
w1 + (60 − w3) < 60
w1 < w3
This means the answer to the question is definitively No — w1 is not greater than w3. ——— sufficient
Ans B
