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PostPosted: Fri Aug 10, 2018 6:32 pm 
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Joined: Mon Apr 11, 2016 6:45 am
Posts: 13
Can anyone help with the question please?

a) Take an even number. If you multiply it by 4, then you get the number P. If you half it then you get the number Q. P-Q is always a multiple of seven.
For example, if we choose 10, then P=40 and Q=5. 40-5=35, which is a multiple of seven. Explain why regardless of which even number you start with, you will always get a multiple of seven.

Many thanks


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PostPosted: Fri Aug 10, 2018 6:57 pm 
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Joined: Mon Feb 12, 2007 1:21 pm
Posts: 15770
Ahins wrote:
Take an even number. If you multiply it by 4, then you get the number P. If you half it then you get the number Q. P-Q is always a multiple of seven.
For example, if we choose 10, then P=40 and Q=5. 40-5=35, which is a multiple of seven. Explain why regardless of which even number you start with, you will always get a multiple of seven.


This is a totally inappropriate 11+ question: which school is this?

Take a general even number 2n

P = 4 x 2n = 8n
Q = 2n divided by 2 = n

P - Q = 8n - n = 7n hence always a multiple of 7.


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PostPosted: Fri Aug 10, 2018 10:16 pm 
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Joined: Mon Apr 11, 2016 6:45 am
Posts: 13
Thank you very much. Actually I do not think it is an 11+ question. I came across it from a few questions which I have collated over a period of time from different sources.Thanks for the quick response. Makes sense. Thanks so much.

Regards


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