Question 1208311
<pre>
How many intergers between 31 and 131 are divisible by 7 but not divisible by 6?

We start with {{{matrix(1,5, 7(INT(31/7)), "=", 7(4), "=", 28)}}}
Since 28 is SMALLER than 31, we ADD 7 to 28 to get 28 + 7 = 35, the SMALLEST INTEGER
between 31 and 131, that is DIVISIBLE by/is a MULTIPLE of 7.

We then continue with {{{matrix(1,5, 7(INT(131/7)), "=", 7(18), "=", 126)}}}
Since 126 is SMALLER than 131, we get 126 as the LARGEST INTEGER between 31 and 131, that is
DIVISIBLE by/is a MULTIPLE of 7.

So, ALL INTEGERS between 31 and 131, that are DIVISIBLE by/are MULTIPLES of 7, begin at 35 and end at 126.

So, the <font color = red><font size = 4><b>TOTAL number of INTEGERS, between 31 and 131, that are DIVISIBLE by/are
MULTIPLES of 7</font></font></b>, is {{{matrix(1,5, (126 - 35 + 7)/7, "=", 98/7, "=", highlight(highlight(14)))}}}


INTEGERS between 31 and 131, that are DIVISIBLE by both 7 and 6, start at 7(6) = 42.

We then continue with {{{matrix(1,5, 42(INT(131/42)), "=", 42(3), "=", 126)}}}
Since 126 is SMALLER than 131, we get 126 as the LARGEST INTEGER between 31 and 131, that is
DIVISIBLE by/is a MULTIPLE of 42.

So, the <font color = red><font size = 4><b>TOTAL number of INTEGERS between 31 and 131, that are DIVISIBLE by/are
MULTIPLES of 7 and 6, or 42</font></font></b>, is {{{matrix(1,5, (126 - 42 + 42)/42, "=", 126/42, "=", highlight(highlight(3)))}}}

<font color = green><font size = 4><b>TOTAL number of INTEGERS between 31 and 131, that are DIVISIBLE by/are MULTIPLES 
of 7, but are NOT DIVISIBLE by/are NOT MULTIPLES of 6 (or 42)</font></font></b> = <font color = blue><font size = 4><b>14 - 3 = </font></font></b><font color = green><font size = 4><b>11</font></font></b></pre>