Quick ACT math problem

Test Preparation ACT Preparation
1

<p>From McGraw’s 8th practice test.</p>

<p>For every positive 2-digit number, a, with units digit x and tens digit y, let b be the 2-digit number formed by reversing the digits of a. Which of the following expressions is equivalent to a-b?</p>

<p>a) 0
b) 9x-y
c) 9y-x
d) 9(x-y)
e) 9(y-x)</p>

<p>The example I used was 97 - 79. In 97, a, x is clearly 7 and y is clearly 9.
97 - 79 = 18. Therefore I picked e, which suited my example.
However, it turns out that the correct answer is (d). I guess it works for some cases.</p>

<p>Answer explanation:
You are given that a is a number with units digit x and tens digit y. Therefore, x is equivalent to 10 times y, and a = xy = 10x+y. You are given that b is formed by reversing the digits of a. Therefore, b = yx = 10y+x. Set up and equation and solve for a-b as follows:
a - b = (10x+y)-(10y+x)
= 10x + y - 10y - x
= 9x - 9y
=9(x-y)</p>

<p>The part I don’t understand is “Therefore, x is equivalent to 10 times y”, and why my example is wrong.
Thanks a lot!</p>

2

<p>McGraw Hills is the worst book ever. I’ve noticed at least 5 mistakes in the 3 tests that I’ve taken from them. </p>

<p>I think you’re right, but I hate questions like these.</p>

<p>The units digit is the right most digit, and the tens digit is the first digit in the two digit number. Therefore, a=yx and not xy. 1=yx=10y+x. 10y+x works because y is the tens digit number. So lets say our number is 97. 9 is the tens digit, so 10(9)+7=97. </p>

<p>I think your answer is right and the book is wrong, sine they appear to have mixed up the units and tens digits.</p>

3

<p>Very often, I found error on these books too. I guess the one who edits the Math section did not get 800 in Math himself. LOL.</p>

4

<p>you mean 36 ;)</p>

<p>beware of this book though! I have found mistakes in the science and english sections that seriously messed with my understanding of the concepts…</p>

5

<p>I like the fact that you get so much practice from it though</p>