Question 1179033
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The algebraic solutions from the other tutors are fine.<br>
But this problem is easily solved using a technique that is occasionally useful in comparing fractions.<br>
In most problems where fractions are being compared, it is easiest to get a common denominator.  But in a few kinds of problems, like this one, a solution is obtained more easily by making the numerators the same.<br>
So in this problem convert the 1/4 and 1/3 into equivalent fractions with numerator 2, as in the fraction 2/p.  Then you have<br>
{{{2/8 < 2/p < 2/6}}}<br>
From there the solution is trivial....<br>
ANSWER: p=7<br>