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31 Jul 2024, 08:45
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D
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Difficulty:
35%
(medium)
Question Stats:
68% (01:48) correct
32%
(01:35)
wrong
based on 137
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Customers can use a manufacturer's coupon and a store coupon to obtain a discount when buying soap powder in a certain store. In one week, 65% of customers used the store coupon when purchasing the soap powder, and 35% used the manufacturer's coupon. What percent of customers used both the manufacturer's coupon and the store coupon when purchasing the soap powder?
(1) 15% of customers used neither coupon when purchasing the soap powder
(2) 50% of customers used the store coupon but not the manufacturer's coupon when purchasing the soap powder
(1) 15% of customers used neither coupon when purchasing the soap powder
(2) 50% of customers used the store coupon but not the manufacturer's coupon when purchasing the soap powder
19 Sep 2024, 10:55
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Let:
S = percentage who used the store coupon (65%)
M = percentage who used the manufacturer's coupon (35%)
B = percentage who used both coupons (unknown, what we're trying to find)
Statement (1): 15% of customers used neither coupon when purchasing the soap powder
This means 85% used at least one coupon. We can represent this as:
S + M - B = 85% (because we need to subtract B to avoid double-counting)
Substituting the known values:
65% + 35% - B = 85%
100% - B = 85%
B = 15%
With this statement alone, we can determine the percentage who used both coupons.
Statement (1) is sufficient.
Statement (2): 50% of customers used the store coupon but not the manufacturer's coupon
This tells us that out of the 65% who used the store coupon, 50% didn't use the manufacturer's coupon.
This implies that 65% - 50% = 15% used both coupons.
With this statement alone, we can also determine the percentage who used both coupons.
Statement (2) is sufficient.
Therefore, the answer is D: Each statement alone is sufficient to answer the question.
S = percentage who used the store coupon (65%)
M = percentage who used the manufacturer's coupon (35%)
B = percentage who used both coupons (unknown, what we're trying to find)
Statement (1): 15% of customers used neither coupon when purchasing the soap powder
This means 85% used at least one coupon. We can represent this as:
S + M - B = 85% (because we need to subtract B to avoid double-counting)
Substituting the known values:
65% + 35% - B = 85%
100% - B = 85%
B = 15%
With this statement alone, we can determine the percentage who used both coupons.
Statement (1) is sufficient.
Statement (2): 50% of customers used the store coupon but not the manufacturer's coupon
This tells us that out of the 65% who used the store coupon, 50% didn't use the manufacturer's coupon.
This implies that 65% - 50% = 15% used both coupons.
With this statement alone, we can also determine the percentage who used both coupons.
Statement (2) is sufficient.
Therefore, the answer is D: Each statement alone is sufficient to answer the question.
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