<p>1 . If xy=2, yz=5, xz=10 and x>0 then xyz =</p>
<p>A.5
B.10
C.17
D.50
E.100</p>
<li>A four digit integer , WXYZ, in which W, X, Y, Z each represent a different digit, is formed according to the following rule:
<li>X= W+Y+Z</li>
<li>W= Y+1</li>
<li>Z= W-5</li>
</ol></li>
</ol>
<p>What is the four digit</p>
<li>90n+23p=4523</li>
</ol>
<p>If n and p are positive integers in the equation above, what is one possible value of n + p ?</p>
<p>can't you help "your friend" ?</p>
<p>the first answer is 10
got it by guessing numbers</p>
<p>and number 3 should be able to be solved with guessing too : p</p>
<p>Ok, so first off, I think the answers are B. 10, 5940, and 51. For the first one, if you just multiply (xy)(yz)(xz) you obtain the answer for (x^2)(y^2)(z^2) = (2)(5)(10) = 100, but (x^2)(y^2)(z^2) is really equal to (xyz)^2 so then you take the square root of 100 to get an answer of 10.
Next for the second question, I used a trial and error method. I assumed that W, X, Y, and Z must between 0 - 9 because those are all single digits. Now you know that W is 5 greater than Z and since W also 1 greater than Y, Y must be 5 greater than Z as well. But if you just look at that, W and Y, based on the amount they must be greater than Z is already 9 and since I assumed that all those numbers must be between 0-9, I realized that Z=0 so that X, the sum of X Y and Z must be between 0 -9 so therefore I concluded that W = 5, X = 9, Y = 4, and Z = 0.
Finally, for the last question, I immediately noticed that the last 2 digits on the total sum was equal to the 2 digits in 23, so I figured that p must be 1. Then I subtracted 23 from 4523 to get that 90n = 4500 and so i divided and found that n = 50. Now 50 + 1 = 51 so therefore n + p = 51 for one possible solution</p>
<p>The second one is just a system of equations.</p>
<p>x = w + y + z
w = y + 1 ; y = w - 1
z = w - 5</p>
<p>Just replace y and z in terms of w.
x = w + (w - 1) + (w - 5)
x = 3w - 6</p>
<p>Since z = w - 5 w must by 5 or greater. If w was 6 or greater, then x must be a 2 digit number, so you know w must equal 5.</p>
<p>Since we established that w = 5, just plug w into each equation and you have your answer.</p>