<p>19.</p>
<p>(x-a)^5 = (x-a) * k^4</p>
<p>In the equation above, x and k are positive integers and 0 < a < x. Which of the following must be equal to x?</p>
<p>a) k
b) k - a
c) k / a
d) a^4
e) k^4 + a</p>
<p>Help much appreciated.</p>
<p>~Thanks</p>
<p>(x-a)^5 = (x-a) * k^4</p>
<p>In the equation above, x and k are positive integers and 0 < a < x. Which of the following must be equal to x?</p>
<p>a) k
b) k - a
c) k / a
d) a^4
e) k^4 + a</p>
<p>divide both sides by (x-a)</p>
<p>(x-a)^4 = k^4</p>
<p>take forth root of both sides
x-a = k (we can exclude the +/- uncertainty normally created by an even power because we know that (x-a) will equate to a positive number and we know that k is a positive number too.</p>
<p>isolate x</p>
<p>x = k + a</p>
<p>which is not an answer choice so I either messed up or the answer choices are wrong. The former is very probable :D.</p>
<p>this is from the PSAT 10.15.2005 section 2 #19.</p>
<p>^^intellec7's answer is improbably correct :D. choice c) is k+a.</p>
<p>my apologies, it is supposed to be k + 4. Thanks intellec</p>
<p>How about this one:</p>
<ol>
<li>At a party, there was one pizza for every 3 people, one salad for every 6 people, and one cake for every 8 people. If the total number of pizzas, salads, and cakes was n, then in terms of n, how many people were at the party?</li>
</ol>
<p>a) 8n/5
b) 3n/2
c) 7n/4
d) 2n
e) 9n/4</p>
<p>Once again, from the 10.15.2005 PSAT, Section 2, #18</p>
<p>Is the answer A by any chance?</p>
<p>yea, answer is A. But how is it done?</p>
<p>Lets say if there were 12 pizzas then it would be 36 people.
3x = total people. (x is the number of pizzas)</p>
<p>now continue from here.. it should be easy.</p>