Need help on 2 Math questions:)

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1

<p>hey there! okk could ya'll solve the following questions -:</p>

<ol>
<li>In the integer 3,589 the digits are all different and increase from left to right. How many integers are there between 4000 and 5000 that have different digits which increase from left to right?</li>
</ol>

<p>[ i COULD do this question but that would take like 10 - 15 mins as i would count each number. I was curious if there could be a shorter approach to this question which could solve this question in 1-2 minutes??]</p>

<ol>
<li>For all x, let the function f be defined by f(x) = a(x - h)^2 + k {where a, h and k are constants.} If a and k are positive, which of the following CANNOT be true :</li>
</ol>

<p>(a) f(10) = 1
(b) f(0) = -5
(c) f(0) = 5
(d) f(1) = -h
(e) f(-1) = h</p>

<p>[i have ABSOLUTELY NO IDEA about how to solve these type of questions...i usually get around 760 - 780 on math and get this particular typo of question wrong...is there some set way or formula to solve these kinda q?]</p>

2

<ol>
<li><p>I used brute force counting. I did not take 10-15 minutes.
4567, 4568, 4569
4578, 4579
4589
4678, 4679
4689
4789
Answer: 10</p></li>
<li><p>Since a is positive, a(x-h)^2 is greater than equal to zero (the square of any real number >= 0).</p></li>
</ol>

<p>k is also positive, so the sum of a(x-h)^2 + k = f(x) must be positive.</p>

<p>Choice b) has a negative value. (Cannot be possible!)
We do not know whether h is positive or negative. So the other choices are possibilities.</p>

3

<p>Listing by brute force is probably the safest bet…but for an inspired solution, see post #2 in this old thread:</p>

<p><a href=“http://talk.collegeconfidential.com/sat-preparation/462998-need-help-tough-real-sat-math-question.html[/url]”>http://talk.collegeconfidential.com/sat-preparation/462998-need-help-tough-real-sat-math-question.html&lt;/a&gt;&lt;/p&gt;