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 10-08-2012, 01:58 PM #1 New Member   Join Date: Feb 2012 Posts: 7 Help with PSAT math problems? How do I solve these problems? 1. How many positive integers less than 1,000 do not have 7 as any digit? (A) 700 (B) 728 (C) 736 (D) 770 (E) 819 2. 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? (A) None (B) One (C) Two (D) Four (E) More than four Reply
 10-08-2012, 02:15 PM #2 Senior Member   Join Date: Mar 2012 Location: Cambridge, MA Posts: 1,913 1. 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. 2. 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. Reply
 10-08-2012, 02:52 PM #3 Senior Member   Join Date: Nov 2009 Posts: 2,238 There's a likely typo in rspence's solution for (1) 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. Reply
 10-08-2012, 09:18 PM #4 New Member   Join Date: Feb 2012 Posts: 7 Thanks guys!! Reply
 10-09-2012, 12:33 AM #5 Senior Member   Join Date: Mar 2012 Location: Cambridge, MA Posts: 1,913 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. Yes, it should be 9 instead of 7. Reply

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