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Susan invited 13 of her friends for her birthday party and created return gift hampers comprising one each of $3, $4, and $5 gift certificates. One of her friends did not turn up and Susan decided to rework her gift hampers such that each of the 12 friends who turned up got $13 worth gift certificates. How many gift hampers did not contain $5 gift certificates in the new configuration?
- a)5
- b)2
- c)9
- d)3
- e)7
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Susan invited 13 of her friends for her birthday party and created ret...
Key Data:
Total dollar value of all gift certificates in the initial configuration : 13 hampers × 12 dollars = $156
Total dollar value of all gift certificates in the new configuration = 12 hampers × 13 dollars = $156
No change in total value of gift certificates.
Total dollar value of all gift certificates in the new configuration = 12 hampers × 13 dollars = $156
No change in total value of gift certificates.
Susan started with 13 hampers.
So, she has 13 of $3, 13 of $4, and 13 of $5 certificates.
So, she has 13 of $3, 13 of $4, and 13 of $5 certificates.
Key Question: What are the possible combination of certificates in the new hampers?
In the new configuration, $13 can be achieved as follows: {3, 3, 3, 4}, {4, 4, 5}, and {5, 5, 3}
The hampers that contain the configuration {3, 3, 3, 4} will not have $5 certificates.
The hampers that contain the configuration {3, 3, 3, 4} will not have $5 certificates.
Assign Variables and Frame Linear Equations
Let Susan make x hampers of {3, 3, 3, 4}, y hampers of {4, 4, 5}, and z hampers of {5, 5, 3}.
The answer to ‘x’ is the answer to the question.
The answer to ‘x’ is the answer to the question.
Number of $3 certificates will be 3x + z = 13 ....(1)
Number of $4 certificates will be x + 2y = 13 ....(2)
Number of $5 certificates will be y + 2z = 13 ....(3)
Number of $4 certificates will be x + 2y = 13 ....(2)
Number of $5 certificates will be y + 2z = 13 ....(3)
Solve the 3 Equations
Multiply (3) by 2: 2y + 4z = 26
Subtract (2) from (3) × 2
2y + 4z = 26
-x - 2y = -13
------------------
4z – x = 13 ....(4)
------------------
Subtract (2) from (3) × 2
2y + 4z = 26
-x - 2y = -13
------------------
4z – x = 13 ....(4)
------------------
Multiply (1) by 4: 12x + 4z = 52
Subtract (4) and (1) × 4
12x + 4z = 52
-4z + x = -13
----------------
13x = 39
-----------------
Or x = 3
Subtract (4) and (1) × 4
12x + 4z = 52
-4z + x = -13
----------------
13x = 39
-----------------
Or x = 3
'x' is the number of gift hampers without $5 certificates.
As x = 3, three gift hampers did not contain $5 gift certificates.
As x = 3, three gift hampers did not contain $5 gift certificates.
Choice D is the correct answer.
Most Upvoted Answer
Susan invited 13 of her friends for her birthday party and created ret...
Given information:
- 13 friends were invited to Susan's birthday party.
- Each return gift hamper originally contained $3, $4, and $5 gift certificates.
- One friend did not turn up, so Susan reworked the gift hampers for the 12 friends who attended.
- Each of the 12 friends who turned up received $13 worth of gift certificates in the new configuration.
Solution:
- Original Configuration:
- Total value of each gift hamper = $3 + $4 + $5 = $12
- Total value of 13 gift hampers = 13 * $12 = $156
- New Configuration:
- Total value of each gift hamper = $13
- Total value of 12 gift hampers = 12 * $13 = $156
- Calculating the number of $5 gift certificates in the new configuration:
- Each gift hamper in the new configuration has a total value of $13, which includes $3 and $4 gift certificates.
- Therefore, the number of $5 gift certificates in each gift hamper is calculated as: $13 - $3 - $4 = $6
- Number of gift hampers that did not contain $5 gift certificates = $6/$5 = 1.2
- Since we cannot have a fraction of a gift certificate, the number of gift hampers that did not contain $5 gift certificates is 1.
- Conclusion:
- The number of gift hampers that did not contain $5 gift certificates in the new configuration is 1.
Therefore, the correct answer is option D
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Susan invited 13 of her friends for her birthday party and created return gift hampers comprising one each of $3, $4, and $5 gift certificates. One of her friends did not turn up and Susan decided to rework her gift hampers such that each of the 12 friends who turned up got $13 worth gift certificates. How many gift hampers did not contain $5 gift certificates in the new configuration?a)5b)2c)9d)3e)7Correct answer is option 'D'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Susan invited 13 of her friends for her birthday party and created return gift hampers comprising one each of $3, $4, and $5 gift certificates. One of her friends did not turn up and Susan decided to rework her gift hampers such that each of the 12 friends who turned up got $13 worth gift certificates. How many gift hampers did not contain $5 gift certificates in the new configuration?a)5b)2c)9d)3e)7Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Susan invited 13 of her friends for her birthday party and created return gift hampers comprising one each of $3, $4, and $5 gift certificates. One of her friends did not turn up and Susan decided to rework her gift hampers such that each of the 12 friends who turned up got $13 worth gift certificates. How many gift hampers did not contain $5 gift certificates in the new configuration?a)5b)2c)9d)3e)7Correct answer is option 'D'. Can you explain this answer?.
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