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06 Aug 2026, 06:02
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At a bookstore promotion, each of five customers won a chance to receive a discount. For each customer, five sealed envelopes were prepared. The five envelopes prepared for any customer contained the discounts $10, $20, $30, $40, and $60, one discount per envelope. If each customer selected one of the five envelopes prepared for that customer, did any customer receive the $60 discount?
(1) The sum of the discounts received by the five customers was $150.
(2) No two customers received the same discount.
(1) The sum of the discounts received by the five customers was $150.
(2) No two customers received the same discount.
06 Aug 2026, 06:02
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Official Solution:
At a bookstore promotion, each of five customers won a chance to receive a discount. For each customer, five sealed envelopes were prepared. The five envelopes prepared for any customer contained the discounts $10, $20, $30, $40, and $60, one discount per envelope. If each customer selected one of the five envelopes prepared for that customer, did any customer receive the $60 discount?
(1) The sum of the discounts received by the five customers was $150.
Let’s check whether the sum of the discounts can be $150 both with and without any customer receiving the $60 discount.
• Without the $60 discount:
\(30 + 30 + 30 + 30 + 30 = 150\)
So it is possible that no customer received the $60 discount.
• With the $60 discount:
\(60 + 40 + 20 + 20 + 10 = 150\)
So it is also possible that at least one customer received the $60 discount.
Not sufficient.
(2) No two customers received the same discount.
There are five customers and five possible discount amounts:
$10, $20, $30, $40, and $60
If no two customers received the same discount, then the five customers must have received all five discount amounts. Therefore, one customer received the $60 discount.
Sufficient.
Answer: B
At a bookstore promotion, each of five customers won a chance to receive a discount. For each customer, five sealed envelopes were prepared. The five envelopes prepared for any customer contained the discounts $10, $20, $30, $40, and $60, one discount per envelope. If each customer selected one of the five envelopes prepared for that customer, did any customer receive the $60 discount?
(1) The sum of the discounts received by the five customers was $150.
Let’s check whether the sum of the discounts can be $150 both with and without any customer receiving the $60 discount.
• Without the $60 discount:
\(30 + 30 + 30 + 30 + 30 = 150\)
So it is possible that no customer received the $60 discount.
• With the $60 discount:
\(60 + 40 + 20 + 20 + 10 = 150\)
So it is also possible that at least one customer received the $60 discount.
Not sufficient.
(2) No two customers received the same discount.
There are five customers and five possible discount amounts:
$10, $20, $30, $40, and $60
If no two customers received the same discount, then the five customers must have received all five discount amounts. Therefore, one customer received the $60 discount.
Sufficient.
Answer: B
