<p>The average (arithmetic mean) of 4 different integers is 75. If the largest integer is 90, what is the least possible value of the smallest integer?</p>
<p>A)1
B)19
C)29
D)30
E)33</p>
<p>The correct answer is E. Can someone explain it, please? I'm sort of panicking because I'm taking the SAT soon and I can't even answer this question!!</p>
<p>90 + 3x / 4 = 75 </p>
<p>90 + 3x =300 </p>
<p>300 in this problem 900 will come only through adding 90 + 89 + 88 + 33 = 300</p>
<p>so the answer is ( E )</p>
<p>Indeed. If the mean of four integers is 75, then their sum is 300. (The mean comes from dividing the sum by the number of integers; to get the sum back, multiply the mean by the number of integers. 4 * 75 = 300.)</p>
<p>Since 90 is the greatest of the integers, and we want to find the smallest possible value for one of the integers, make two of them as large as possible. Since the other integers are less than 90, and since all the integers are unique, choose 89 and 88. 90 + 89 + 88 = 267. It takes 33 more to make 300.</p>
<p>Oh, thank you…I get it now :)</p>
<p>How do you know if the question is asking for unique integers? When I did the problem I got 90, 90, 90, 30 (Anser D: 30)</p>