<ol>
<li><p>Widowed in 1859, novelist Margaret Oliphant succeeded (to provide) for (her own) and her brother’s children with the (profits from) her books, which numbered (well over) 100 volumes.</p></li>
<li><p>In the triangle ABC, if angle a> angle b >angle c, which of the following must be true?</p></li>
</ol>
<p>I. 60< a< 180
II.45< b< 90
III. 0< c< 60</p>
<p>A. I only
B. II only
C. I and III only
D. II and III only
E. I, II, and III</p>
<ol>
<li><p>If the average (arithmetic mean) of q, r,s, and t, is 10, what is the average of s-r, 3r+t, 10-r, and 6+q? </p></li>
<li><p>if x^10 = 5555 and x^9/y = 5, what is the value of xy?</p></li>
</ol>
<p>Yes … A for 33. The usage is “to succeed in <something>”, and “to succeed to a position”, as for example succeed to the throne. So the corrected sentence is:</something></p>
<p>Widowed in 1859, novelist Margaret Oliphant succeeded in providing for her own and her brother’s children with the profits from her books, which numbered well over 100 volumes.</p>
<ol>
<li>In the triangle ABC, if angle a> angle b >angle c, which of the following must be true?</li>
</ol>
<p>I. 60< a< 180
II.45< b< 90
III. 0< c< 60</p>
<p>We know that a+b+c=180. So c must be less than 60, for if it were equal or greater than 60, then b will be greater than 60 (b>c), and a will be greater than 60 (a>b). The sum a+b+c will than be greater than 180.</p>
<p>We also know that b and a are less than 180, and that a is greater than 60, for if a were equal or less than 60 than both b and c will be less than 60. The sum a+b+c will than be less than 180.</p>
<p>We can only conclude that b is less than 180.</p>
<ol>
<li>q + r + s +t has to equal 40 (their average is 10 when added together and divided by 4 and thus total is 4 X 10.</li>
</ol>
<p>Let the average of s - r + 3r + t + 10 - r + 6 + q = 4Y (that is the total of the 4 sets of numbers where Y is the average). Now just do the math: s + r + t + q + 16 = 4Y, and thus s+r+t+q = both 40 and 4y -16; 40= 4y-16; y=6 which is the average of the second set of numbers</p>
<p>Drusba: Close but the answer to 37. is 14. You’re math was right up until the end when you said 40=4y-16. y=14.</p>
<p>Fogcity: I confirm your answer to 28., which is C in short explanation.</p>
<ol>
<li>Since x^9/y = 5, y = x^9/5. Substitute x^9/5 into xy for y, and you have x^10/5. Substitute 5555 for x^10 and you have 5555/5, which is 1111.</li>
</ol>