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21 Jan 2025, 01:30
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
69% (01:42) correct
31%
(01:37)
wrong
based on 111
sessions
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Bill runs a hot dog stand, and at the end of the day he has collected an assortment of $1, $5, and $10 bills. He discovers that the number of $1, $5, and $10 bills that he has is in the ratio of 10 : 5 : 1, respectively. How many $10 bills does he have?
(1) The dollar value of his $1 bills equals the dollar value of his $10 bills.
(2) Bill has a total of $225.
(1) The dollar value of his $1 bills equals the dollar value of his $10 bills.
(2) Bill has a total of $225.
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
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Data Sufficiency Forum
21 Jan 2025, 06:31
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Bill runs a hot dog stand, and at the end of the day he has collected an assortment of $1, $5, and $10 bills. He discovers that the number of $1, $5, and $10 bills that he has is in the ratio of 10 : 5 : 1, respectively. How many $10 bills does he have?
Let the constant for number of bills be x
Therefore, the number of $1 Bills = 10x, $2 Bills= 5x and $3 Bills = 1x
(1) The dollar value of his $1 bills equals the dollar value of his $10 bills.
This only gives us:
1*10x=10*1x
Hence insufficient
(2) Bill has a total of $225.
This gives us:
1*10x + 5*5x + 10*1x =225
45*x=225
x=5
Therefore Number of 10$ bills= 1*5= 5
Hence Sufficient
IMO Ans B
Let the constant for number of bills be x
Therefore, the number of $1 Bills = 10x, $2 Bills= 5x and $3 Bills = 1x
(1) The dollar value of his $1 bills equals the dollar value of his $10 bills.
This only gives us:
1*10x=10*1x
Hence insufficient
(2) Bill has a total of $225.
This gives us:
1*10x + 5*5x + 10*1x =225
45*x=225
x=5
Therefore Number of 10$ bills= 1*5= 5
Hence Sufficient
IMO Ans B
21 Jan 2025, 07:38
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Given:
- Bill has $1, $5, and $10 bills in the ratio 10:5:1.
- We need to find how many $10 bills Bill has.
Step 1: Define variables based on the ratio.
- Let the number of $1 bills be 10x.
- Let the number of $5 bills be 5x.
- Let the number of $10 bills be x.
Step 2: Analyze the statements.
(1) The dollar value of the $1 bills equals the dollar value of the $10 bills.
- The dollar value of the $1 bills = 10x * 1 = 10x.
- The dollar value of the $10 bills = x * 10 = 10x.
- This condition is always true for any value of x, so it doesn't provide new information to solve for x.
- Insufficient.
(2) Bill has a total of $225.
- The total value of all bills = (10x * 1) + (5x * 5) + (x * 10) = 10x + 25x + 10x = 45x.
- We are told the total value is $225: 45x = 225.
- Solving for x: x = 225 / 45 = 5.
Step 3: Conclusion.
- The number of $10 bills is x = 5.
Answer: 5
- Bill has $1, $5, and $10 bills in the ratio 10:5:1.
- We need to find how many $10 bills Bill has.
Step 1: Define variables based on the ratio.
- Let the number of $1 bills be 10x.
- Let the number of $5 bills be 5x.
- Let the number of $10 bills be x.
Step 2: Analyze the statements.
(1) The dollar value of the $1 bills equals the dollar value of the $10 bills.
- The dollar value of the $1 bills = 10x * 1 = 10x.
- The dollar value of the $10 bills = x * 10 = 10x.
- This condition is always true for any value of x, so it doesn't provide new information to solve for x.
- Insufficient.
(2) Bill has a total of $225.
- The total value of all bills = (10x * 1) + (5x * 5) + (x * 10) = 10x + 25x + 10x = 45x.
- We are told the total value is $225: 45x = 225.
- Solving for x: x = 225 / 45 = 5.
Step 3: Conclusion.
- The number of $10 bills is x = 5.
Answer: 5
