Help with PSAT math problems?

Test Preparation
1

<p>How do I solve these problems?</p>

<ol>
<li>How many positive integers less than 1,000 do not have 7 as any digit?</li>
</ol>

<p>(A) 700
(B) 728
(C) 736
(D) 770
(E) 819</p>

<ol>
<li>Points A, B, and X do not all lie on the same line. Point X is 5 units from A and 3 units from B. How many other points in the sma eplane as A, B, and X are also 5 units from A and 3 units from B?</li>
</ol>

<p>(A) None
(B) One
(C) Two
(D) Four
(E) More than four</p>

2

<ol>
<li><p>Consider the numbers 000 - 999. We want to find the # of integers in this set that do not contain 7’s. There are 7 choices for the first digit, 7 for the second, 7 for the third (two-digit numbers are represented by a leading 0). 7^3 = 729. However this includes 000, so we subtract 1, leaving 728, B.</p></li>
<li><p>Draw triangle ABX, with AX = 5, BX = 3. If you draw a circle of radius 5 centered at A, and a radius of circle 3 centered at B, you will see that the two circles intersect at X, as well as one other point (obtained by reflecting X across AB). Hence the answer is B. This assumes that A and B are already determined.</p></li>
</ol>

3

<p>There’s a likely typo in rspence’s solution for (1)</p>

<p>The corrected version is:

  1. Consider the numbers 000 - 999. We want to find the # of integers in this set that do not contain 7’s. There are 9 choices (0,1,2,3,4,5,6,8,9) for the first digit, 9 for the second, 9 for the third (two-digit numbers are represented by a leading 0). 9^3 = 729. However this includes 000, so we subtract 1, leaving 728, B.</p>
4

<p>Thanks guys!!</p>

5

<p>Wow, I feel like an idiot lol. Makes me remind of King Arthur’s confusion of “1, 2, 5!” in Monty Python & the Holy Grail.</p>

<p>Yes, it should be 9 instead of 7.</p>