Monday
March 10, 2014

# Homework Help: Algebra

Posted by Anonymous on Tuesday, March 26, 2013 at 11:20pm.

a and b are digits such that \overline{120ab} is a multiple of 3, 5 and 7. What is the value of \overline{ab} ?

• Algebra - Ian, Friday, March 29, 2013 at 8:20pm

ab = 75
Archaic solution: only possibilities for ab are 01 through 99. Eliminate all of those not divisible by 5, which leaves: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55. 60, 65, 70, 75, 80, 85, 90, and 95. Eliminate those not divisible by 3 (divisibility rule for 3) , which leaves 15, 30, 45, 60, 75, and 90. Now eliminate those not divisible by 7, which leaves ab = 75. Divisibility rule for 7: double the last digit and subtract from the remaining digits. If the ramaining digits are divisible by 7, then the original number is divisible by 7. So, our number is 12075. 5 + 5 =10. Subtracting: 1207 - 10 = 1197. 1197mod7 has no remainder, thus our solution.

Related Questions

math - The bases of trapezoid ABCD are \overline{AB} and \overline{CD}. Let P be...
Maths - a and b are digits such that 120ab¯¯¯¯¯¯¯¯ is a multiple of 3, 5 and 7. ...
ALGEBRA - Find the requested probabilities.  P(\overline{A}) \ \text{if} \ P(A...
Algebra - Middle School - Use the digits in the year 2010 and the operations...
pre algebra - the digits 0,1,2,3,4,5,6,7,8,9 are repeated in such a way thatwhen...
holy heart - Using digits 2, 3, 5, 6, 7 and 9, how many 3-digit numbers can be ...
Math - The digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 are repeated in such a way that ...
math - 1)a number of two digits is such that the digits is 11 and the number is...
Arithmetic Operations - Find a set of 4 distinct positive integers a,b,c,d such ...
math - x has 3 digits. the tens digits is half the hundreds digits. the number ...

Search
Members