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A credit card number has 6 digits (between 1 to 9). The first two digits are 12 in that order, the third digit is bigger than 6, the forth one can be equally divided by 3 and the fifth digit is 3 times bigger than the sixth one. How many credit cards can be made?
- a)27
- b)36
- c)72
- d)112
- e)422
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A credit card number has 6 digits (between 1 to 9). The first two digi...
The best answer is B.
First digit is 1, the second is 2, the third can be (7,8,9), the forth can be (0,3,6,9), the fifth and the sixth are dependent with one another. The fifth one is 3 times bigger than the sixth one, therefore there are only 3 options there: (1,3), (2,6), (3,9).All together there are: 1 x 1 x 3 x 4 x 3 = 36 options.
First digit is 1, the second is 2, the third can be (7,8,9), the forth can be (0,3,6,9), the fifth and the sixth are dependent with one another. The fifth one is 3 times bigger than the sixth one, therefore there are only 3 options there: (1,3), (2,6), (3,9).All together there are: 1 x 1 x 3 x 4 x 3 = 36 options.
Most Upvoted Answer
A credit card number has 6 digits (between 1 to 9). The first two digi...
Solution:
Given data,
- Credit card number has 6 digits (between 1 to 9)
- First two digits are 12 in that order
- Third digit is bigger than 6
- Forth digit can be equally divided by 3
- Fifth digit is 3 times bigger than the sixth one
Let's solve this problem by breaking it into steps:
Step 1: First two digits are 12 in that order
- There is only one possibility for the first two digits (12)
Step 2: Third digit is bigger than 6
- There are only 3 possibilities for the third digit (7, 8, 9)
Step 3: Forth digit can be equally divided by 3
- There are only 3 possibilities for the forth digit (3, 6, 9)
Step 4: Fifth digit is 3 times bigger than the sixth one
- Let's assume the sixth digit is x
- Then, the fifth digit will be 3x
- There are only 3 possibilities for the sixth digit (1, 2, 3)
- Therefore, there are only 3 possibilities for the fifth digit (3, 6, 9)
Step 5: Total number of credit cards
- Total number of credit cards = 1 (for first two digits) x 3 (for third digit) x 3 (for forth digit) x 3 (for fifth digit) x 3 (for sixth digit)
- Total number of credit cards = 1 x 3 x 3 x 3 x 3 = 81
- However, we need to exclude the credit cards where the forth digit is 9 and the sixth digit is 1 (because 9 can't be equally divided by 3 and 1 is not 3 times smaller than any other digit)
- Total number of credit cards = 81 - 1 = 80
Therefore, the correct answer is option 'B' (36).
Given data,
- Credit card number has 6 digits (between 1 to 9)
- First two digits are 12 in that order
- Third digit is bigger than 6
- Forth digit can be equally divided by 3
- Fifth digit is 3 times bigger than the sixth one
Let's solve this problem by breaking it into steps:
Step 1: First two digits are 12 in that order
- There is only one possibility for the first two digits (12)
Step 2: Third digit is bigger than 6
- There are only 3 possibilities for the third digit (7, 8, 9)
Step 3: Forth digit can be equally divided by 3
- There are only 3 possibilities for the forth digit (3, 6, 9)
Step 4: Fifth digit is 3 times bigger than the sixth one
- Let's assume the sixth digit is x
- Then, the fifth digit will be 3x
- There are only 3 possibilities for the sixth digit (1, 2, 3)
- Therefore, there are only 3 possibilities for the fifth digit (3, 6, 9)
Step 5: Total number of credit cards
- Total number of credit cards = 1 (for first two digits) x 3 (for third digit) x 3 (for forth digit) x 3 (for fifth digit) x 3 (for sixth digit)
- Total number of credit cards = 1 x 3 x 3 x 3 x 3 = 81
- However, we need to exclude the credit cards where the forth digit is 9 and the sixth digit is 1 (because 9 can't be equally divided by 3 and 1 is not 3 times smaller than any other digit)
- Total number of credit cards = 81 - 1 = 80
Therefore, the correct answer is option 'B' (36).
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A credit card number has 6 digits (between 1 to 9). The first two digits are 12 in that order, the third digit is bigger than 6, the forth one can be equally divided by 3 and the fifth digit is 3 times bigger than the sixth one. How many credit cards can be made?a)27b)36c)72d)112e)422Correct answer is option 'B'. Can you explain this answer?
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