A simple problem, and a harder one (Both Math)

Test Preparation SAT Preparation
1

<p>Really Simple Algebra/Arithmetic Problem</p>

<p>A marketing company expects 6% of people to return surveys sent to them in the mail. Of the surveys they actually get back, 1/3 are unreadable. If the company wants to receive 200 readable surveys, how many must they mail out?</p>

<p>If 1/3 of the incoming surveys are unreadable, then for the company to have 200 good ones, they must have received 300. So 300 is 6% of some number. You find what number by multiplying 300 by 100 and then dividing by 6. The answer is 5000.</p>

<p>This makes sense to me, but why doesn't the following method work?</p>

<p>.06x(1/3)=200
.02x=200
200/.02=10000.</p>

<p>Those Annoying Letter Problems</p>

<p>In the correctly worked multiplication problem below, each letter represents a distinct digit from 0 through 9. What digit must D represent?</p>

<p>ADA
A
BABA</p>

<p>The problem is ADA*A=BABA if you didn't get my diagram.</p>

<p>I hate these questions with a passion! Does anybody have a quick, or at least, systematic way to solve all kinds of these problems?</p>

<p>Thanks for reading (and hopefully responding) to my post!</p>

2

<p>1) (2/3)(6/100)X = 200
0.04X = 200
X = 5000</p>

<p>you took1/3 but it should be 2/3 because 2/3 are readable.</p>

3

<p>Oops! Nice catch, I must be tired...</p>

<p>any techniques to share for solving the letter problem?</p>

4

<p>ADA
X A</p>

<hr>

<p>BABA</p>

<p>(100A + 10D + A)(A) = 1000B + 100A + 10B + A
(101A + 10D)(A) = 1010B + 101A
101A^2 + 10DA = 1010B + 101A
101A^2 + 10DA - 101A = 1010B
101A^2 + A(10D - 101) = 1010B
Since RHS is multiple of 101, and first term of LHS is multiple of 101 too, the second term must also be a multiple of 101, for which D will have to be 0.
Hence, D = 0</p>

5

<p>In fact since A x A ends with A A can only be 1,5,6
And by observation we get</p>

<p>505 X 5 = 2525</p>

6

<p>The first way you showed, will that work with any multiplication problem like this? And can you give an example of doing this problem with addition (is division and subtraction similiar?).</p>

<p>And why is it that if the RHS and the LHS are both multiples of something, so is the second? is that just a rule? I've never heard of it.</p>

<p>Thanks so much for your prompt responses!</p>

7

<p>no that is because 101 is prime.</p>

8

<p>well, if you ever have ANY math question, just PM me the question or thread.</p>

9

<p>101 is prime, so all terms have to be multiples of 101.</p>

10

<p>Well, I was just wondering if there was a consistent way to do the letter-type problems, or if it's just basically logic and reasoning.</p>

11

<p>some can be solved by intuition directly, else the questions that they give will be such that once u solve this way, you can get the answer by simple logic after a certain point.</p>

12

<p>ETS does try hard to make this as much as a "aptitude" test as possible. Not every question will have a "consistent" method, or an equation, to solve. Logic is a big piece of the puzzle on the SAT.</p>

<p>For the second question, you can just just pick any b-a-b-a number and divided by a. Bam , you get your answer, 5 seconds.</p>

13

<p>"For the second question, you can just just pick any b-a-b-a number and divided by a. Bam , you get your answer, 5 seconds."</p>

<p>Wrong</p>

<p>5959/9 = 662.1111
6767/7=966.7142
3434/4=858.5</p>

<p>Doing that only works for 5 different baba numbers.</p>

14

<p>oh i guess i got lucky then. Nevermind.</p>

15

<p>yup, it has to be written properly first, what's the big deal just writing the number as proper sum of the digits with their place values...
anyway this thread's done :)</p>