document.write( "Question 201841: if a = 4b + 26 and b is a positive integer. the a could be divisible by all of the following except\r
\n" ); document.write( "\n" ); document.write( "a)2 b) 4 c) 5 d)6 e) 7 \n" ); document.write( "

Algebra.Com's Answer #152084 by jim_thompson5910(35256) $\"\"$ $\"About$

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The previous solution is dead on in saying that the only number that \"a\" is NOT divisible is 4. Here's another way to look at it:\r
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\n" ); document.write( "\n" ); document.write( "Recall that $\"a=4b\"$ , means that \"a\" is divisible by 4 (ie \"a\" is a multiple of 4). However, once we add 26 on, we get $\"a=4b%2B26\"$ which can be rewritten as $\"a=4b%2B24%2B2\"$ and $\"a=4%28b%2B6%29%2B2\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let p=b+6 (\"p\" is automatically an integer since \"b\" is). So we then get: $\"a=4p%2B2\"$ which tells us that for ANY value of \"p\", $\"a%2Fp\"$ will result in a remainder of 2. This means that \"a\" is NOT divisible by 4 (since a non-zero remainder results every time).\r
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\n" ); document.write( "\n" ); document.write( "So the answer is once again B) 4 \n" ); document.write( "

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