Daily Math Questions

Test Preparation SAT Preparation
1

<p>Hey guys, I'm prepping for the Dec SAT and I think a daily math questions would help me improve. Can anyone help me with these questions? If you nee help too, feel free to post.</p>

<ol>
<li>Kyle's lock combination consists of 3 two-digit numbers. The combination satisfies the three conditions below.</li>
</ol>

<p>-One number is odd
-One number is a multiple of 5
-One number is the day of the month of Kyle's birthday</p>

<p>If each number satisfies exactly one of the conditions, which of the following could be the combination of the lock?</p>

<p>A. 14-20-13
B. 14-25-13
C. 15-18-16
D. 20-15-20
E. 34-30-21</p>

<p>I'm confused because A, B, and D all fit the conditions...</p>

2

<p>I’m not agreeing with how the question is given to us; but I’ll give you the answer they’re looking for. </p>

<p>The only thing you missed was the word “one.” ONE number is odd. ONE number is a multiple of 5. And ONE number… you get it. </p>

<p>A. 14-20-13
B. 14-25-13 - Eliminate because it has 2 odd numbers.
C. 15-18-16 - Eliminate because 15 can’t satisfy two requirements.
D. 20-15-20 - Eliminate because it has two multiple of 5’s.
E. 34-30-21 - Eliminate because 21 and 30 work, but 34 doesn’t satisfy the birthday requirement. </p>

<p>A!</p>

3

<p>Omg I feel so stupid. Thank you so much!</p>

<p>Here’s another one I need help with:</p>

<p>Let x be defined as [x]=x^2-x for all values of x. If [a]=a-2, what is the value of a?</p>

<p>A. 1
B. 1/2
C. 3/2
D. 6/5
E. 3</p>

4

<p>This is not an SAT question, it’s just an SAT-level question I made up.</p>

<p>Q: If p and q are positive integers such that pq = 50, which of the following cannot equal (p^2)q?</p>

<p>A: 50
B: 100
C: 200
D: 250
E: 500</p>

5

<p>@maraudersmap, are you sure your question is correctly typed? Here’s what I did:</p>

<p>[a] = a^2 - a = a - 2</p>

<p>a^2 - 2a + 2 = 0</p>

<p>a = (2 ± sqrt(4 - 8))/2, i.e. two complex solutions.</p>

6

<p>I’m pretty sure the question is: Let x be defined as [x]=x^2-x for all values of x. If [a]=[a-2], what is the value of a?</p>

7

<p>The question is typed correctly, [ ] is one of those weird symbols</p>

8

<p>[a] = a-2 and [a] = [a-2] mean completely different things…</p>

9

<p>sorry, you guys are right. It’s [a-2]</p>

10

<p>Then it’s just</p>

<p>a^2 - a = (a-2)^2 - (a-2)</p>

<p>a^2 - a = a^2 - 5a + 6 (upon expanding, simplifying). a^2 cancels, leaving</p>

<p>-a = -5a + 6 → a = 3/2</p>

11

<p>Thank you very much! I’ll post when I have more questions, I’m currently not at home haha [:</p>

12

<p>rspence, is the answer to your question C. ?</p>

13

<p>^JackTC yep. All the other answer choices are in the form 50p, where p is a factor of 50.</p>

14

<p>Can you go over how you got that question exactly? The way I did it took too long</p>

15

<p>The solution involves thinking of (p^2)(q) as p(pq). Since pq = 50, this is equal to 50p. All the answer choices are multiples of 50, but note that p must be a factor of 50, so 50p must be (a factor of 50) times 50.</p>

<p>200 is 50*4, and 4 is not a factor of 50, so C is the answer.</p>

16

<p>That’s a good example, rspence. The SAT loves the give you an expression and then tell you what a part of the factored form of the expression equals. They particularly like to do this with the difference of two squares and the occasional square of a sum or difference. The moral is, " If it can be factored, factor it." Or more colloquially, “Take it apart so that you can see more clearly what it’s made of.” It’s a shame that schools tend to spend months teaching kids how to factor and little time explaining why you might want to do it.</p>

17

<p>Maybe I am too lazy…but when I see a question like this, I just try numbers. It took about twenty seconds to run through the pairs…1 and 50, 2 and 25, 5 and 10, 10 and 5 … At that point, I had ruled out all but c.</p>

<p>Rspence has the more clever solution, but when I am doing sat questions, I like to be “the dumbest kid who gets it right”. That’s not to suggest that you never need insight. I’m just saving brain power until I really need it :)</p>

<p>Btw, nice question – has that SAT feel.</p>

18

<p>Thanks guys.</p>

<p>Yeah, I’m pretty sure every SAT question that has a factorable expression should be factored. That seems to be the general trend in such questions. Also, SAT questions tend to have multiple solutions, one usually involves plugging in numbers at random (which is usually a long solution) and another that involves a little algebra. Finding the quickest solution saves a ton of time and then it’s much easier to score 800.</p>

19

<p>Can someone help me with this probability question?</p>

<p>The Acme Plumbing Company will send a team of 3 plumbers to work on a certain job. The company has 4 experienced plumbers and 4 trainees. If a team consists of 1 experienced plumber and 2 trainees, how many different such teams are possible?</p>

20

<ol>
<li><p>Start with the more restrictive case. Since you need to make combinations of two trainees, start with them. Call them A,B,C, and D. You can get 6 combinations of 2.</p>

<pre><code> AB, AC, AD
BC, BD remember BA is already included AB = BA
CD
</code></pre></li>
</ol>

<p>Now, pair each of the possible trainee combinations with each of the experienced plumbers.</p>

<pre><code> 6 Teams of trainees times 4 experienced plumbers = 24 possible tems
</code></pre>