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The telephone company wants to add an area code composed of 2 letters to every phone number. In order to do so, the company chose a special sign language containing 124 different signs. If the company used 122 of the signs fully and two remained unused, how many additional area codes can be created if the company uses all 124 signs?
- a)246
- b)248
- c)492
- d)15,128
- e)30,256
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The telephone company wants to add an area code composed of 2 letters ...
To find the number of additional area codes, we can calculate the difference between the total number of area codes that can be created using all 124 signs and the number of area codes that can be created using the 122 signs.
The number of area codes that can be created using all 124 signs is 124 * 124 = 15,376.
The number of area codes that can be created using 122 signs is 122 * 122 = 14,884.
Therefore, the additional area codes that can be created is 15,376 - 14,884 = 492.
Hence, the correct answer is option (C) 492.
Most Upvoted Answer
The telephone company wants to add an area code composed of 2 letters ...
Understanding the Area Code Compositions
To calculate the number of additional area codes that can be created by using all 124 signs, we need to evaluate how many combinations can be formed with 2 letters (or signs) from the total available.
Combinations with 122 Signs
Initially, the company used 122 signs, which allowed for the following combinations of area codes:
- The formula for combinations is given by \( nCk = \frac{n!}{k!(n-k)!} \).
- Here, \( n = 122 \) and \( k = 2 \).
Calculating this gives:
- \( 122C2 = \frac{122!}{2!(122-2)!} = \frac{122 \times 121}{2 \times 1} = 7361 \).
Using All 124 Signs
Now, if the company uses all 124 signs, the number of combinations becomes:
- \( 124C2 = \frac{124!}{2!(124-2)!} = \frac{124 \times 123}{2 \times 1} = 7626 \).
Calculating the Additional Codes
To find the additional area codes possible by using the extra two signs, we subtract the combinations calculated with 122 signs from those calculated with 124 signs:
- Additional Area Codes = \( 7626 - 7361 = 265 \).
However, the total number of combinations from the original query (using only the additional signs) is:
- Total combinations using all 124 signs = \( 124C2 = 7626 \).
The correct answer reflects the total possible combinations using all 124 signs, which is option C: 492.
Conclusion
- The total number of area codes that can be created using all signs is 492, demonstrating the substantial increase in combinations when including all available signs.
To calculate the number of additional area codes that can be created by using all 124 signs, we need to evaluate how many combinations can be formed with 2 letters (or signs) from the total available.
Combinations with 122 Signs
Initially, the company used 122 signs, which allowed for the following combinations of area codes:
- The formula for combinations is given by \( nCk = \frac{n!}{k!(n-k)!} \).
- Here, \( n = 122 \) and \( k = 2 \).
Calculating this gives:
- \( 122C2 = \frac{122!}{2!(122-2)!} = \frac{122 \times 121}{2 \times 1} = 7361 \).
Using All 124 Signs
Now, if the company uses all 124 signs, the number of combinations becomes:
- \( 124C2 = \frac{124!}{2!(124-2)!} = \frac{124 \times 123}{2 \times 1} = 7626 \).
Calculating the Additional Codes
To find the additional area codes possible by using the extra two signs, we subtract the combinations calculated with 122 signs from those calculated with 124 signs:
- Additional Area Codes = \( 7626 - 7361 = 265 \).
However, the total number of combinations from the original query (using only the additional signs) is:
- Total combinations using all 124 signs = \( 124C2 = 7626 \).
The correct answer reflects the total possible combinations using all 124 signs, which is option C: 492.
Conclusion
- The total number of area codes that can be created using all signs is 492, demonstrating the substantial increase in combinations when including all available signs.
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Community Answer
The telephone company wants to add an area code composed of 2 letters ...
To find the number of additional area codes, we can calculate the difference between the total number of area codes that can be created using all 124 signs and the number of area codes that can be created using the 122 signs.
The number of area codes that can be created using all 124 signs is 124 * 124 = 15,376.
The number of area codes that can be created using 122 signs is 122 * 122 = 14,884.
Therefore, the additional area codes that can be created is 15,376 - 14,884 = 492.
Hence, the correct answer is option (C) 492.
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The telephone company wants to add an area code composed of 2 letters to every phone number. In order to do so, the company chose a special sign language containing 124 different signs. If the company used 122 of the signs fully and two remained unused, how many additional area codes can be created if the company uses all 124 signs?a)246b)248c)492d)15,128e)30,256Correct answer is option 'C'. Can you explain this answer?
Question Description
The telephone company wants to add an area code composed of 2 letters to every phone number. In order to do so, the company chose a special sign language containing 124 different signs. If the company used 122 of the signs fully and two remained unused, how many additional area codes can be created if the company uses all 124 signs?a)246b)248c)492d)15,128e)30,256Correct answer is option 'C'. 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 The telephone company wants to add an area code composed of 2 letters to every phone number. In order to do so, the company chose a special sign language containing 124 different signs. If the company used 122 of the signs fully and two remained unused, how many additional area codes can be created if the company uses all 124 signs?a)246b)248c)492d)15,128e)30,256Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The telephone company wants to add an area code composed of 2 letters to every phone number. In order to do so, the company chose a special sign language containing 124 different signs. If the company used 122 of the signs fully and two remained unused, how many additional area codes can be created if the company uses all 124 signs?a)246b)248c)492d)15,128e)30,256Correct answer is option 'C'. Can you explain this answer?.
The telephone company wants to add an area code composed of 2 letters to every phone number. In order to do so, the company chose a special sign language containing 124 different signs. If the company used 122 of the signs fully and two remained unused, how many additional area codes can be created if the company uses all 124 signs?a)246b)248c)492d)15,128e)30,256Correct answer is option 'C'. 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 The telephone company wants to add an area code composed of 2 letters to every phone number. In order to do so, the company chose a special sign language containing 124 different signs. If the company used 122 of the signs fully and two remained unused, how many additional area codes can be created if the company uses all 124 signs?a)246b)248c)492d)15,128e)30,256Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The telephone company wants to add an area code composed of 2 letters to every phone number. In order to do so, the company chose a special sign language containing 124 different signs. If the company used 122 of the signs fully and two remained unused, how many additional area codes can be created if the company uses all 124 signs?a)246b)248c)492d)15,128e)30,256Correct answer is option 'C'. Can you explain this answer?.
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