<p>1.The number n is a 2-digit number. When n is divided by 10, the remainder is 9, and when n is divided by 9, the remainder is 8. What is the value of n?</p>
<p>The answer is 89.</p>
<p>How do you guys approach problems similar to the one above? i tried to think of a algebraic formula but none of them worked! Please help!</p>
<p>The graphs of the functions f and g are lines, as shown in the figure above. If f(x) = mx + b for some constants m and b, which of the following could define the function g ?</p>
<p>So n/10 has a remainder of 9. What can be divided by 10? 10, 20, 30, 40, 50, etc.</p>
<p>Therefore, anything that can be divided by 10 with a remainder of 9 can be: 19, 29, 39, 49, 59, 69, etc., anything 9 more than something that divides by 10 evenly.</p>
<p>Then, if you divide by 9, the remainder is 8. So look for any number ending in 9, which is 8 more than something that divides evenly by 9. This way, when you divide it by 9, 8 is the remainder, and if you divide it by 10, 9 is the remainder.</p>
<p>Your answer is 89, because 89/10 = 8 r9, and 89/9 = 9 r8</p>
<p>For the second one, keep in mind that m is f(x)'s slope and b is f(x)'s y-intercept. </p>
<p>f(x)'s slope (m) is positive, less that 1 and less than g(x)'s slope. Therefore, g(x)'s slope should be greater than m (that's why it says 1/m for g(x)'s slope, as m is less than 1) and it should be positive as well, as you can see from the diagram.</p>
<p>f(x)'s y-intercept (b) is positive and smaller number (in magnitude) than g(x)'s y-intercept. Therefore, g(x)'s y-intercept should be greater than m in magnitude (that's why it says b/m for g(x)'s y-intercept, as m is less than 1) and it should be negative instead of positive, as you can see from the diagram.</p>
<p>Can you elaborate on the first question? what if it was "if N divided by 11 has a remainder of 9"? Your method works fine but i was hoping there was a formula for those questions.</p>
<p>You could solve the first one like this if you wanted, but I don't know how efficient it would be.</p>
<p>N can be written in the form 10a+9 when 1<=a<=9
D: (19,29,39,49,59,69,79,89,99)</p>
<p>N can be written in the form 9b+8 when 1<=b<=10
D: (17,26,35,44,53,62,71,80,89,98)</p>
<p>Your answer is the intersection of the domains, in other words the value that is common to both sets. I can't think of another way to do it. If anyone knows how to solve for N given N%10=9 and N%9=8 then there is an easier way to do it, but I don't know how to solve equations involving modulus.</p>
<p>There's no formula, it's a logic question. You use the basic properties of a set of numbers (e.g. the ten's set). The question would be more difficult to answer if n was divided by 11.</p>
Going algebraically,
10a+9 = 9b+8
10a+1 = 9b
9b is a 2-digit number (it can't be 1-digit): it's a multple of 9 and ends with 1
9b = 81</p>
<h1>n = 9b+8 = 81+8 = 89</h1>
<p>
[quote=tennischick035]
If anyone knows how to solve for N given N%10=9 and N%9=8 then there is an easier way to do it, but I don't know how to solve equations involving modulus.
N mod 10 = 9
(9)N mod 90 = 81 <---------- A
N mod 9 = 8
(10)N mod 90 = 80 <--------- B
Subtract A from B:
N mod 90 = -1
N mod 90 = 89</p>
<h1>N = 89</h1>
<p>Q2.
This must be SAT II Math question
Graphs y=f(x) and y=g(x) appear symmetrical relative to the bisector of the first quadrant (y=x), therefore g(x) is the inverse of f(x).
Finding the inverse of y=mx+b:
x = my+b
x/m = y + b/m
y = x/m - b/m
g(x) = x/m - b/m</p>
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