<p>Hi I feel kinda silly for asking this, especially since my SAT prep book has this listed under difficulty level "E". The explanation in the back makes absolutely no sense to me so I'm hoping someone on this site can help. The question is as follows:</p>
<p>"If p+1 is a multiple of 3, what is the greatest multiple of 3 that is less than p+1."</p>
<p>If you can explain to me how you got your answer, it'd be of great help.
Thanks :)</p>
<p>Is it p-2? You didn’t provide answer choices.</p>
<p>If p+1 is a multiple of 3, that means the following are multiples of 3 as well:
p+1, p+4, p+7, p+10, p+13, etc.</p>
<p>As you can notice, each term is 3 more than the preceding term. This is because if you add 3 to a multiple of 3, the sum will also be a multiple of 3. So if you were to work backwards in this pattern, because it asks for the greatest number that is LESS than p+1, it would be p+1-3 or p-2.</p>
<p>Another approach is substituting a number for p. Let’s make p=5. Therefore, p+1=6, and 6 is a multiple of 3, so p=5 satisfies the initial condition. The greatest multiple of 3 less than 6 is 3. If p=5, how do you arrive to 3? Subtract 2! Therefore you get p-2. Hope I was more clear than the book.</p>
<p>Thank you! Your explanation was a lot clearer than my book’s explanation but I’m confused as to why the answer is “p-2” if the question asks for a multiple. It’s a not a MC question so if this were to hypothetically pop up on the real test, I can’t bubble in “p-2”. Is there an actual numerical number?</p>
<p>Well the question gives you no way to determine p so we are forced to leave the answer as p-2. There’s no way this can be an actual grid-in question because you can’t enter variables in the grids. This leads me to believe that this is simply a practice question or example of a specific concept from your book. If this question were to appear on an actual test, it would be mulltiple choice.</p>
<p>p+1 is a multiple of 3. This means we can add or subtract any multiple of 3 and still get a multiple of 3. The greatest multiple of 3 less than p+1 occurs when you simply subtract 3 from p+1, which is just (p+1) - 3 = p-2.</p>
<p>When you are confused on a question like this simply plug in a number. For example, let p+1 be 6, so that p is 5. Then the “answer” is 3. Now plug 5 in fpr p in each answer choice, and cross out any choices that DO NOT give 5. </p>
<p>Even if you don’t need it for this problem, thiis is an important SAT strategy - if you don’t learn it well you will be at a serious disadvantage.</p>
<p>Multiples of a number are just multiplied by consecutive rational numbers.
Eg. for multiples of 3 we have 3<em>1 , 3</em>2, 3*3 , etc
If p+1 is a multiple of 3, let’s assume 3 is multiplied by some integer x.
p +1 =3x
x = p+1/3
The next multiple below it will be multiplied by x-1
Take 1 from the left hand side of the equation above.
x-1 = (p+1)/3 -1
=(p-2)/3
the multiple we are looking for becomes 3(x-1) = 3 * (p-2)/3 = p-2
I hope I solved your problem</p>