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31 Aug 2020, 23:45
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$1 bills: 1
$20 bills: 16
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
44% (03:03) correct
56%
(02:41)
wrong
based on 397
sessions
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Percival has a total of 26 bills, consisting of a combination of $1, $5, $10, and $20 bills.
If the total value of these bills is $386, and Percival has at least one bill of each denomination, select for $1 bills the possible number of $1 bills Percival could have, and for $20 bills the possible number of $20 bills Percival could have that are jointly consistent with the information provided. Make only two selections, one in each column
If the total value of these bills is $386, and Percival has at least one bill of each denomination, select for $1 bills the possible number of $1 bills Percival could have, and for $20 bills the possible number of $20 bills Percival could have that are jointly consistent with the information provided. Make only two selections, one in each column
| $1 bills | $20 bills | |
| 1 | ||
| 6 | ||
| 10 | ||
| 12 | ||
| 16 | ||
| 18 |
ShowHide Answer
Official Answer
$1 bills: 1
$20 bills: 16
21 Dec 2024, 15:19
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Bunuel
Official Solution:
Let's analyze the provided options and determine how many $20 bills Percival could have.
• Percival cannot have 18 $20 bills, as that would amount to $360, leaving only $26 to be distributed among the remaining 8 bills consisting of $1, $5, and $10 denominations. Since the sum of $5 and $10 bills will always end with a units digit of 0 or 5, there can only be 1 or 6 $1 bills to make the total units digit equal 6. If there were 1 $1 bill, the remaining 7 bills of $5 and $10 denominations would exceed $25. Conversely, if there were 6 $1 bills, the remaining 2 bills of $5 and $10 denominations would total less than $20. Thus, 18 $20 bills is not possible.
• He also cannot have 12 $20 bills because, in that case, the total from the $20 bills would be $240. The remaining 14 bills, even if all were $10 bills, would amount to only $140, resulting in a total of $380, which is less than $386.
• Therefore, from the options, Percival must have 16 $20 bills, which amounts to $320.
This leaves $66 to be distributed among the remaining 10 bills consisting of $1, $5, and $10 denominations. Since the sum of $5 and $10 bills will always end with a units digit of 0 or 5, there can only be 1 or 6 $1 bills to make the total units digit equal 6.
• If there were 6 $1 bills, they would amount to $6, leaving $60 to be accounted for by the remaining 4 bills. However, even if all 4 bills were $10 bills, this would only amount to $40, which is less than $60.
• Therefore, there must be exactly 1 $1 bill.
Correct answer:
$1 bills "1"
$20 bills "16"
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General Discussion
01 Jan 2025, 16:42
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1. Let's rephrase the question using the information that Percival has 1 of each bill (there is $386 - $1 - $5 - $10 - $20 = $350 left). Find the number of possible $1 and $20 bills that match the answer choices, when the amount of money is $350 and there are 26 - 4 = 22 bills. The answer choices would then be: 0, 5, 9, 11, 15, and 17.
2. The maximum number of $20 bills we can have is 17, and the nearest answer choice to that is 17. This would make up $340 of $350 with 5 bills left, which is impossible to cover.
3. The next number of $20 bills we can have is 15. This would make up $300 of $350 with 7 bills left, which can be covered with 0 $1 bills, 3 $10 bills, and 4 $5 bills.
4. This means that altogether, we used 0 + 1 = 1 $1 bill, 4 + 1 = 5 $5 bills, 3 + 1 = 4 $10 bills, and 15 + 1 = 16 $20 bills.
5. Our answer will be: $1 bills - 1 and $20 bills - 16.
2. The maximum number of $20 bills we can have is 17, and the nearest answer choice to that is 17. This would make up $340 of $350 with 5 bills left, which is impossible to cover.
3. The next number of $20 bills we can have is 15. This would make up $300 of $350 with 7 bills left, which can be covered with 0 $1 bills, 3 $10 bills, and 4 $5 bills.
4. This means that altogether, we used 0 + 1 = 1 $1 bill, 4 + 1 = 5 $5 bills, 3 + 1 = 4 $10 bills, and 15 + 1 = 16 $20 bills.
5. Our answer will be: $1 bills - 1 and $20 bills - 16.
