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17 Jul 2022, 10:15
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D
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Difficulty:
55%
(hard)
Question Stats:
65% (02:27) correct
35%
(02:30)
wrong
based on 299
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The currencies of three countries are called credits, units, and bells. If 12 credits can be exchanged for a total of exactly 8 units and 5 bells, what is the smallest integer number of units that can be exchanged for an integer number of bells, with no change left over?
(1) 15 credits can be exchanged for 4 units and 25 bells, with no change left over.
(2) 25 bells can be exchanged for 8 units, with no change left over.
Are You Up For the Challenge: 700 Level Questions
(1) 15 credits can be exchanged for 4 units and 25 bells, with no change left over.
(2) 25 bells can be exchanged for 8 units, with no change left over.
Are You Up For the Challenge: 700 Level Questions
18 Jul 2022, 06:46
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Let's denote the credits as C, units as U, and bells as B.
The question stem gives us the info that 12C = 8U + 5B ... (1)
Statement 1
15 credits can be exchanged for 4 units and 25 bells, with no change left over.
So, we can exchange 25 B for 8 U. Statement 1 is sufficient and we eliminate options B, C, and E.
Statement 2
25 bells can be exchanged for 8 units, with no change left over
This statement directly gives us the answer. So statement 2 is sufficient.
So the answer is D.
The question stem gives us the info that 12C = 8U + 5B ... (1)
- We need to find out - the smallest integer number of units that can be exchanged for an integer number of bells, with no change left over
- This is nothing but the ratio of U:B
Statement 1
15 credits can be exchanged for 4 units and 25 bells, with no change left over.
- 15C = 4U + 25B ... (2)
We can equate C from this equation with equation (1) and get the ratio of U and B.
Although not needed we can do it after multiplying equations (1) by 5 and (2) by 4.
We have, 40U + 25B = 16U + 100B
Or, 24U = 75B
Or, 8U = 25B
So, we can exchange 25 B for 8 U. Statement 1 is sufficient and we eliminate options B, C, and E.
Statement 2
25 bells can be exchanged for 8 units, with no change left over
This statement directly gives us the answer. So statement 2 is sufficient.
So the answer is D.
17 Apr 2025, 13:02
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