SHOW ALL WORKING OUT PLEASE!.
Ricky is thinking of a positive integer. If he subtracts 2 from the number it is divisible by 8. If he subtracts 6 from the number it is divisible by 3. If he subtracts 7 from the number it is divisible by 7.
What number is Ricky thinking of?
Ricky is thinking of a positive integer. If he subtracts 2 from the number it is divisible by 8. If he subtracts 6 from the number it is divisible by 3. If he subtracts 7 from the number it is divisible by 7.
What number is Ricky thinking of?
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"If he subtracts 6 from the number it is divisible by 3."
• Because 6 is also divisible by 3, the original number must be divisible by 3. (Therefore it's a multiple of 3.)
"If he subtracts 7 from the number it is divisible by 7."
• Similarly, the original number must be divisible by 7. (Therefore it's a multiple of 7.)
So, we're looking for a number divisible by both 3 and 7, therefore it's a multiple of 21.
Going through the multiples of 21:
• 21
• 42 … Bingo! 42 - 2 = 40, which is divisible by 8.
• 63
• 84
• 105
• 126
• 147
• 168
• 189
• 210 … Bingo again! 210 - 2 = 208, which is divisible by 8.
The numbers turn out to be 42*1, 42*5, 42*9, 42*13 ...
SOLUTION: Basically, any numbers in the sequence 42(4n - 3), where n is a positive integer, will work. Ricky might be thinking of just one, or several, or an endless sequence of such numbers.
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Just in case Ricky's dreaming of interplanetary travel … try n = 1,000,000
42(4n - 3) = 42 * 3,999,997 = 167,999,874
Subtract 2, then divide by 8:
167,999,872 / 8 = 20,999,984
Yep!
Bonus – two links for Douglas Adams aficionados:
http://www.youtube.com/watch?v=tAgqCLtYm…
http://en.wikipedia.org/wiki/42_(Hitchhi…
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• Because 6 is also divisible by 3, the original number must be divisible by 3. (Therefore it's a multiple of 3.)
"If he subtracts 7 from the number it is divisible by 7."
• Similarly, the original number must be divisible by 7. (Therefore it's a multiple of 7.)
So, we're looking for a number divisible by both 3 and 7, therefore it's a multiple of 21.
Going through the multiples of 21:
• 21
• 42 … Bingo! 42 - 2 = 40, which is divisible by 8.
• 63
• 84
• 105
• 126
• 147
• 168
• 189
• 210 … Bingo again! 210 - 2 = 208, which is divisible by 8.
The numbers turn out to be 42*1, 42*5, 42*9, 42*13 ...
SOLUTION: Basically, any numbers in the sequence 42(4n - 3), where n is a positive integer, will work. Ricky might be thinking of just one, or several, or an endless sequence of such numbers.
–––––––––––––––––––––––––––––
42(4n - 3) = 42 * 3,999,997 = 167,999,874
Subtract 2, then divide by 8:
167,999,872 / 8 = 20,999,984
Yep!
Bonus – two links for Douglas Adams aficionados:
http://www.youtube.com/watch?v=tAgqCLtYm…
http://en.wikipedia.org/wiki/42_(Hitchhi…
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If he subtracts 6, he gets a multiple of three. Because 6 is already a multiple of 3, the number is also divisible by 3. If he subtracts 7, it is divisible by 7. That means the number is also divisible by 7. Since it is divisble by 3 and 7, it is a multiple of 21. If you subtract an even number from an odd number, you get an odd number. If you subtract even from even, it is even. Since you subtract 2 (an even number) from the number to get a multiple of 8. That means the number is also even, meaning it must be divisible by 2. Since it is a multiple of 2 and 21, it is also a multiple of 42. If you subtract 2 from 42, you get 40, which is a multiple of 8. Ricky is thinking of the number 42.