<p>t^2 - k^2 < 6
t + k < 4</p>
<p>If t and k are positive integers in the inequalities above and t > k, what is the value of t?</p>
<p>1)1
2)2
3)3
4)4
5)5</p>
<p>How to solve such question without brute forcing ? the number to do it a fast algebrical way?</p>
<p>t^2 - k^2 < 6
t + k < 4</p>
<p>If t and k are positive integers in the inequalities above and t > k, what is the value of t?</p>
<p>A)1
B)2
C)3
D)4
E)5</p>
<p>Let’s start with choice (C) as our first guess. If t=3, then there is no possible value for k, because t+k<4. So we see that we can eliminate (C), (D), and (E).</p>
<p>Let’s try (B) next. If t=2, then k must be 1. In this case t^2-k^2=4-1=3 which is less than 6. So (B) is the answer.</p>
<p>Note that the following 3 conditions immediately lead to unique values for t and k:</p>
<p>(1) t, k are positive integers.
(2) t > k
(3) t + k < 4</p>
<p>The only numbers satisfying these three conditions are t=2 and k=1.</p>
<p>If you’re still confused, here is the detailed reasoning:</p>
<p>Since k is a positive integer, k must be at least 1. Since t > k, t must be at least 2. If we try to increase t, then condition (3) will be violated.</p>
<p>^Yes,Thanks I understand your logic makes perfect sense.</p>