document.write( "Question 626199: my daughter is in year 6 at school and has been given maths homework which i cant help her with i have 2 questions but need to be able to show workings out and be able to understand how we got the answer.\r
\n" ); document.write( "\n" ); document.write( "1) fatma is thinking of a 3 digit odd number. the hundreds digit is 3 times more than the units digit. the sum of the three digits is 4. what number is fatma thinking off\r
\n" ); document.write( "\n" ); document.write( "2)who am i, i have 3 digit i can only be divived by myself and one. the sum of my digits is 11 i am under 150 \n" ); document.write( "
Algebra.Com's Answer #852470 by n2(5)\"\" \"About 
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\n" ); document.write( "(2) who am i, i have 3 digits. i can only be divided by myself and one. the sum of my digits is 11 and i am under 150.
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document.write( "They want you find a 3-digit prime number between 100 and 150, with the sum of digits 11.\r\n" );
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document.write( "First of all, it is clear that the first digit of this number must be 1.\r\n" );
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document.write( "Hence, the sum of two remaining digits must be 10.\r\n" );
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document.write( "Next, the last (the ones) digits can not be even number, since, otherwise, the number in this interval is not a prime.\r\n" );
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document.write( "Also, it is clear that the last digit can not be 5, since, otherwise, the number is divisible by 5.\r\n" );
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document.write( "Taking this in account, we see that the last (= the ones) digit should be 1, or 3, or 7, or 9.\r\n" );
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document.write( "If the ones digit is 1, then the tens digit is 10-1 = 9, and the number itself is 191.\r\n" );
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document.write( "       This does not work, since 191 is greater than 150.\r\n" );
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document.write( "If the ones digit is 3, then the tens digit is 10-3 = 7, and the number itself is 173.\r\n" );
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document.write( "       This does not work, since 173 is greater than 150.\r\n" );
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document.write( "If the ones digit is 7, then the tens digit is 10-7 = 3, and the number itself is 137.\r\n" );
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document.write( "       This works, since 137 is a prime number (it is not divisible by 2, 3, 5, 7, 11,\r\n" );
document.write( "       and it is just enough to see that 137 is a prime).\r\n" );
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document.write( "If the ones digit is 9, then the tens digit is 10-9 = 1, and the number itself is 119.\r\n" );
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document.write( "       This does not work, since 119 = 7*17 is not a prime number.\r\n" );
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document.write( "Thus, we analyzed all possible cases and by the method of exclusion PROVED\r\n" );
document.write( "that there is one and only one possible answer, which is the number of  \"highlight%28highlight%28137%29%29\".   \r\n" );
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\n" ); document.write( "\n" ); document.write( "The solution method is a logical analysis in three steps.\r
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\n" ); document.write( "\n" ); document.write( "First,  we filter out many possible numbers based on simple divisibility properties.\r
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\n" ); document.write( "\n" ); document.write( "Then we analyze the remaining  4  cases and exclude three of them that do not work.\r
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\n" ); document.write( "\n" ); document.write( "Finally,  we check that the remaining number satisfies all the conditions.\r
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\n" ); document.write( "\n" ); document.write( "This way we find a  UNIQUE  solution to the problem.\r
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