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If the numbers (4X + 17) and (7X + 33) are not co-prime then, which of the following is the common factor? (X is a natural number) 
  • a)
    11
  • b)
    13
  • c)
    17
  • d)
    23
Correct answer is option 'B'. Can you explain this answer?
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If the numbers (4X + 17) and (7X + 33) are not co-prime then, which of...
Solution: Let the common factor be denoted by f. Both (4X + 17) and (7X + 33) are divisible by f. 4(7X + 33) and 7(4X +17) are also divisible by f. 4(7X + 33) - 7(4X + 17) will also be divisible by f. 4(7X + 33) - 7(4X + 17) = 132 - 119 = 13
13 is divisible by f. f= 1 or 13
4X + 17 and 7X + 33 are not coprime, f = 13 Hence, option 2.
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Most Upvoted Answer
If the numbers (4X + 17) and (7X + 33) are not co-prime then, which of...
Explanation:

To find the common factor between the given two numbers, we need to factorize each number separately.

Given Numbers:
1) (4X + 17)
2) (7X + 33)

1) Factorization of (4X + 17):
To factorize (4X + 17), we need to find the factors of 17.

Factors of 17: 1, 17

Since we cannot factorize 17 any further, the factorization of (4X + 17) is 1 * (4X + 17).

2) Factorization of (7X + 33):
To factorize (7X + 33), we need to find the factors of 33.

Factors of 33: 1, 3, 11, 33

Since we cannot factorize 33 any further, the factorization of (7X + 33) is 1 * (7X + 33).

Common Factor:
To find the common factor between the two numbers, we need to find the factors that are common to both factorizations.

The common factor between the two numbers is the common factor between 1 * (4X + 17) and 1 * (7X + 33).

The common factor is 1.

Conclusion:
Since the common factor between the given two numbers is 1, which is not a valid option in the given answer choices, we can conclude that the given two numbers (4X + 17) and (7X + 33) are co-prime.

Therefore, none of the options (a) 11, (b) 13, (c) 17, or (d) 23 are the common factor.
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Directions: Study the given information and answer the following question.A car servicing company has ten LED boards which are fitted on a wall. Each of them displays the digits from 0-9. They are programmed in such a way that when any car enters the workshop for service, the registration number on the cars number plate will appear on the wall as the digits on the wall-mounted LED boards shall glow to show a 4-digit number. On Monday, 4 cars of different colours, i.e. red, white, black and grey, entered the workshop. Due to faulty software, the only thing that got noted down was the number of times each LED board glowed in total after the 4 cars entered. Hence, the following data was collected.Further, software provided the following data:(1) The registration number of each car has a factor 5.(2) Except the white car, all the other cars have at least three different digits.(3) The registration number of black car has the highest value numerically.(4) The registration number of red car has four different digits, three of which are not present in the registration numbers of any of the other 3 cars.(5) The difference between the registration numbers of red car and grey car has a maximum value of 600 and a minimum value of 500.(6) The registration number of white car is exactly a factor of the registration number of black car.(7) The sum of the digits of registration number of white car is 8.What is the registration number of white car? Correct answer is '1115'. Can you explain this answer?

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If the numbers (4X + 17) and (7X + 33) are not co-prime then, which of the following is the common factor? (X is a natural number)a)11b)13c)17d)23Correct answer is option 'B'. Can you explain this answer?
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