Math question?

Test Preparation SAT Preparation
1

<p>Okay, so I've been going through Magoosh SAT online prep and I came across this question yesterday. I haven't understood how to do it. I've tried equations and logic and literally everything!
Anyways, here it is:</p>

<p>On a certain multiple-choice test, 9 points are awarded for each correct answer, and 7 points are deducted for each incorrect or unanswered question. Sally received a total score of 0 points on the test. If the test has fewer than 30 questions, how many questions are on the test?</p>

<p>A.Cannot be determined
B.16
C.19
D.21
E.24</p>

<p>Some help would be appreciated! The answer is B.</p>

2

<p>I’m not surer If this is the right way to do it, But this is how I figured it out, obviously,
9c-7w=0,
taking the Lcm of 9 and 7 It’s 63. Using Logic, The person would have had to get either 9 right and 7 wrong or vice versa for the equation to hold true. Thus, it’s nothing but 9+7= 16.</p>

3

<p>9c - 7w = 0 → 9c = 7w</p>

<p>Since 9 and 7 are relatively prime, c must be divisible by 7 and w must be divisible by 9. The only solution is to let c = 7 and w = 9 (any other solution would imply c+w > 30). 7+9 = 16, B.</p>

4

<p>I tried to solve this question, and it was difficult. Precisely, it was time consuming. In the question you are given the range of the number of questions in the test which is A<30, and you are required to find the exact number of questions. </p>

<p>Total questions are less than 30 which means X, total correct questions plus Y, total incorrect answers is equal to 16, 19, 21, or 24</p>

<p>You know that for every correct question you get 9 points, so 9X while for every wrong question you lose 7 points, so 7Y. This is the equation you’ll make to get the total score of the test: 9X -7y</p>

<p>Therefore, since the total score is 0, you get the equation 9x-7y=0
You’ll have to try getting the answers of x and y from the simultaneous equations:</p>

<p>• X+Y= (16, 19, 21, or 24) and
• 9X-7Y=0</p>

<p>With four trials, you will get to know that 16 could be the only answer because you will get integers (non decimal) that are X=7 and Y=8.</p>

<p>Note that there might be an easier ways of solving this question, for I often tend to solve in difficult, obscure methods.</p>

5

<p>^Eek. Too long of a solution for an SAT problem.</p>

6

<p>Thanks guys!! Actually, this problem was there in Magoosh’s 10 hardest SAT questions, which you can see if you want:
[10</a> Most Difficult SAT Questions | Magoosh SAT Blog](<a href=“http://magoosh.com/sat/2011/10-most-difficult-sat-questions/]10”>http://magoosh.com/sat/2011/10-most-difficult-sat-questions/)
Anyways, thanks for your help! I’m pretty sure I’ve got it :)</p>