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The sum of three prime numbers is 100. If one of them exceeds another by 36, then one of the numbers is
- a)17
- b)29
- c)43
- d)None of the above
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The sum of three prime numbers is 100. If one of them exceeds another ...
Let the three prime numbers be x, y, y+36
x+y+y+36 = 100
x+2y = 64
2y is an even number always
We know that
Even + even = even or odd + odd = even
So x has to be even to satisfy x+2y = 64
The only even prime no is 2
Put x=2
2y = 62
Or y = 31
So the numbers are 2, 31, 67
Thus option D is the answer.
x+y+y+36 = 100
x+2y = 64
2y is an even number always
We know that
Even + even = even or odd + odd = even
So x has to be even to satisfy x+2y = 64
The only even prime no is 2
Put x=2
2y = 62
Or y = 31
So the numbers are 2, 31, 67
Thus option D is the answer.
Most Upvoted Answer
The sum of three prime numbers is 100. If one of them exceeds another ...
Let the three prime numbers be x, y, y+36
x+y+y+36 = 100
x+2y = 64
2y is an even number always
We know that
Even + even = even or odd + odd = even
So x has to be even to satisfy x+2y = 64
The only even prime no is 2
Put x=2
2y = 62
Or y = 31
So the numbers are 2, 31, 67
Thus option D is the answer.
x+y+y+36 = 100
x+2y = 64
2y is an even number always
We know that
Even + even = even or odd + odd = even
So x has to be even to satisfy x+2y = 64
The only even prime no is 2
Put x=2
2y = 62
Or y = 31
So the numbers are 2, 31, 67
Thus option D is the answer.
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Community Answer
The sum of three prime numbers is 100. If one of them exceeds another ...
Explanation:
First, let's assume the three prime numbers are x, x+36, and y. We know that their sum is 100. Therefore, we can write the equation:
x + (x+36) + y = 100
Simplify the equation:
2x + y = 64
Since x, x+36, and y are prime numbers, x must be an odd prime number (except for 2). The only odd prime number less than 36 is 29. Let's substitute x = 29 into the equation:
2(29) + y = 64
58 + y = 64
y = 6
Therefore, the three prime numbers are 29, 29+36, and 6, which are not among the options given. Hence, the correct answer is option 'D' - None of the above.
First, let's assume the three prime numbers are x, x+36, and y. We know that their sum is 100. Therefore, we can write the equation:
x + (x+36) + y = 100
Simplify the equation:
2x + y = 64
Since x, x+36, and y are prime numbers, x must be an odd prime number (except for 2). The only odd prime number less than 36 is 29. Let's substitute x = 29 into the equation:
2(29) + y = 64
58 + y = 64
y = 6
Therefore, the three prime numbers are 29, 29+36, and 6, which are not among the options given. Hence, the correct answer is option 'D' - None of the above.
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