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An electronic safe has a key which is made up of 5 digits (not necessarily distinct). It is also known that the first digit is three times the last digit. The third digit is 3 less than the second digit and the fourth digit is 4 more than the second digit. Also there are 3 pairs of digits which add up to give 11. The 5 digit number which can open the electronic lock of the safe is______
Correct answer is '11'. Can you explain this answer?
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An electronic safe has a key which is made up of 5 digits (not necess...
A B C D E
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3E B B-3 B+4 E
3 0 7 ……… (I)
4 1 8 …… (II)
5 2 9 ……. (III)
3 1…(IV)
6 2….(V)
9 3…(VI)
In order to satisfy the other condition that pairs of digits add up to give 11. Based on inputs, out of the possible sets listed above, we can the ONLY possible set fulfilling given conditions formed by combining III and V giving us the unique code as 6 5 2 9 2
6 + 5=11=2+9=9+2.
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An electronic safe has a key which is made up of 5 digits (not necess...
Understanding the problem:
We are given a 5-digit key for an electronic safe. The key has the following properties:
1. The first digit is three times the last digit.
2. The third digit is 3 less than the second digit.
3. The fourth digit is 4 more than the second digit.
4. There are 3 pairs of digits that add up to give 11.
Solution:
Let's analyze each property of the key to find the possible values for each digit.
First property: First digit is three times the last digit.
Let's consider the last digit as 'x'. According to the first property, the first digit is three times 'x'. So the first digit is 3x.
Second property: Third digit is 3 less than the second digit.
According to the second property, the third digit is 3 less than the second digit. Let's consider the second digit as 'y'. So the third digit is y - 3.
Third property: Fourth digit is 4 more than the second digit.
According to the third property, the fourth digit is 4 more than the second digit. So the fourth digit is y + 4.
Fourth property: Three pairs of digits add up to give 11.
Let's consider the pairs of digits as (a, b), (c, d), and (e, f). According to the fourth property, a + b = 11, c + d = 11, and e + f = 11.
Finding the values of the digits:
Now, let's substitute the values we found for the first, second, and fourth digits into the equations for the pairs of digits.
- a + b = 11 (First pair of digits)
- c + d = 11 (Second pair of digits)
- e + f = 11 (Third pair of digits)
From the first property, we know that the first digit is 3x and the last digit is x. So we can write the equation as:
3x + x = 11
4x = 11
x = 11/4
Since the digits must be integers, x can only be 2.5, which is not possible. Therefore, there is no valid 5-digit number that satisfies all the given properties.
Hence, the answer to the problem is 'No valid combination exists'.
We are given a 5-digit key for an electronic safe. The key has the following properties:
1. The first digit is three times the last digit.
2. The third digit is 3 less than the second digit.
3. The fourth digit is 4 more than the second digit.
4. There are 3 pairs of digits that add up to give 11.
Solution:
Let's analyze each property of the key to find the possible values for each digit.
First property: First digit is three times the last digit.
Let's consider the last digit as 'x'. According to the first property, the first digit is three times 'x'. So the first digit is 3x.
Second property: Third digit is 3 less than the second digit.
According to the second property, the third digit is 3 less than the second digit. Let's consider the second digit as 'y'. So the third digit is y - 3.
Third property: Fourth digit is 4 more than the second digit.
According to the third property, the fourth digit is 4 more than the second digit. So the fourth digit is y + 4.
Fourth property: Three pairs of digits add up to give 11.
Let's consider the pairs of digits as (a, b), (c, d), and (e, f). According to the fourth property, a + b = 11, c + d = 11, and e + f = 11.
Finding the values of the digits:
Now, let's substitute the values we found for the first, second, and fourth digits into the equations for the pairs of digits.
- a + b = 11 (First pair of digits)
- c + d = 11 (Second pair of digits)
- e + f = 11 (Third pair of digits)
From the first property, we know that the first digit is 3x and the last digit is x. So we can write the equation as:
3x + x = 11
4x = 11
x = 11/4
Since the digits must be integers, x can only be 2.5, which is not possible. Therefore, there is no valid 5-digit number that satisfies all the given properties.
Hence, the answer to the problem is 'No valid combination exists'.
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An electronic safe has a key which is made up of 5 digits (not necessarily distinct). It is also known that the first digit is three times the last digit. The third digit is 3 less than the second digit and the fourth digit is 4 more than the second digit. Also there are 3 pairs of digits which add up to give 11. The 5 digit number which can open the electronic lock of the safe is______Correct answer is '11'. Can you explain this answer?
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An electronic safe has a key which is made up of 5 digits (not necessarily distinct). It is also known that the first digit is three times the last digit. The third digit is 3 less than the second digit and the fourth digit is 4 more than the second digit. Also there are 3 pairs of digits which add up to give 11. The 5 digit number which can open the electronic lock of the safe is______Correct answer is '11'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about An electronic safe has a key which is made up of 5 digits (not necessarily distinct). It is also known that the first digit is three times the last digit. The third digit is 3 less than the second digit and the fourth digit is 4 more than the second digit. Also there are 3 pairs of digits which add up to give 11. The 5 digit number which can open the electronic lock of the safe is______Correct answer is '11'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An electronic safe has a key which is made up of 5 digits (not necessarily distinct). It is also known that the first digit is three times the last digit. The third digit is 3 less than the second digit and the fourth digit is 4 more than the second digit. Also there are 3 pairs of digits which add up to give 11. The 5 digit number which can open the electronic lock of the safe is______Correct answer is '11'. Can you explain this answer?.
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