Math SAT help

Test Preparation SAT Preparation
1

<p>Please help and explain if you can.</p>

<ol>
<li>in a recipe for sugar cookies the ratio of flour to sugar is 3:2. If the recipe is doubled in order to make twice the number of cookies, the ratio of flour to sugar will be...</li>
</ol>

<p>A. 3:1 B 2:1 C 3:2 D 1:1 E 3:4</p>

<ol>
<li>The rectangle in a diagram of the fencing surrounding an animal pen 20 m by 5 m. If an additional 4 square meters is to be enclosed by moving just one side of the pen, while retaining its regular shaped what is the LEAST possible number of meters of additional fencing needed?</li>
</ol>

<p>A 2.0 B 1.6 C 1.0 D 0.8 E 0.4</p>

<ol>
<li>If m and k are positive integers and 5m+4k=26, what is the value of m?</li>
</ol>

<p>A. 2 B 3 C 4 D 5 E 6</p>

<ol>
<li>If r and a are even positive integers and 20<rs<25, what is the number of possible values of product rs?</li>
</ol>

<p>(Isnt it 2 since you can have either 22 or 24?)</p>

<ol>
<li>Charles and David live the same walking distance, d kilometers from school. It took Charles and David 20 minutes and 15 minutes, respectively, to walk directly from home to school without stopping.</li>
</ol>

<p>P= the average number of kilometers per hour at which Charles walked
Q= the average number of kilometers per hour at which David walked</p>

<p>What is Q-P in terms of d?
A. 4d B 3d C. d D. 1/3d E. 1/4d</p>

2

<p>In number 4 I assume you mean s, and not a. 22 is not the product of 2 even positive integers. It can only be written as 22x1 or 2x11.</p>

3

<p>Oh yes I meant s. so its just 24 then?</p>

4

<p>1.should be the same ratio because youre just making the same thing just twice as much. The ingredient ratios don’t change.</p>

<ol>
<li>5m+4k=26
You know that in order to get a six, you’ll need to multiply the 4 to get a 6 in the single digits. 4x4=16 which leaves 5m=10
M=2</li>
</ol>

5

<p>In number 5, Q = 3d and P = 4d but I don’t understand what the question means by Q-P</p>

6

<p>I would have assumed to subtract 3d-4d but that gives a negative number, could you possibly explain how you got 3d and 4d?</p>

7

<ol>
<li>in a recipe for sugar cookies the ratio of flour to sugar is 3:2. If the recipe is doubled in order to make twice the number of cookies, the ratio of flour to sugar will be…</li>
</ol>

<p>A. 3:1 B 2:1 C 3:2 D 1:1 E 3:4</p>

<p>C 3:2</p>

<p>You have for example 3 grams of flour and 2 grams of sugar (because of the ratio), you then double it.</p>

<p>You now 6 grams of flour and 4 grams of sugar. What is the ratio now? 6:4 which is also 3:2.</p>

8

<ol>
<li>Charles and David live the same walking distance, d kilometers from school. It took Charles and David 20 minutes and 15 minutes, respectively, to walk directly from home to school without stopping.</li>
</ol>

<p>P= the average number of kilometers per hour at which Charles walked
Q= the average number of kilometers per hour at which David walked</p>

<p>What is Q-P in terms of d?
A. 4d B 3d C. d D. 1/3d E. 1/4d</p>

<p>If d=20. </p>

<p>P=1km per hour.
Q=4/3km per hour. Naturally David must walk proportionally faster than Charles.</p>

<p>20 minutes/ 15 minutes = x km per hour/1 km per hour. x= 4/3</p>

<p>Q-P = 1/3</p>

9

<ol>
<li>If m and k are positive integers and 5m+4k=26, what is the value of m?</li>
</ol>

<p>A. 2 B 3 C 4 D 5 E 6
fgdgfdsjkgl;fa</p>

10

<p>/* 1. in a recipe for sugar cookies the ratio of flour to sugar is 3:2. If the recipe is doubled in order to make twice the number of cookies, the ratio of flour to sugar will be…</p>

<p>A. 3:1 B 2:1 C 3:2 D 1:1 E 3:4 */</p>

<p>You can use a ratio box for this:</p>

<p>F : S : Total
3 : 2 : 5</p>

<p>If you make your constant 1 (for 1 batch of cookies), you’ll keep that 3:2 ratio.</p>

<p>But, if you want to double the cookies, you’ll need to make your constant 2 (or double the “total” amount of goop to get 10:</p>

<p>F: S: total
3: 2: 5 <— same ratio</p>

<h2>2: 2: 2 <— Constant</h2>

<p>6: 4: 10 <— total with doubled…</p>

<p>So Flour to Sugar is 6:4 → 3:2 (C)</p>

<hr>

<p>/* 2. The rectangle in a diagram of the fencing surrounding an animal pen 20 m by 5 m. If an additional 4 square meters is to be enclosed by moving just one side of the pen, while retaining its regular shaped what is the LEAST possible number of meters of additional fencing needed?</p>

<p>A 2.0 B 1.6 C 1.0 D 0.8 E 0.4 */</p>

<p>So, you have a rectangle that is 20m X 5m == 100 Sq.M.</p>

<p>You want to add 4 sq.m. to only 1 side (so you ultimately want 104 sq.M.)</p>

<p>You can add it to one of the sides, so you’ll either do </p>

<p>20m X ?m == 104 sq.m, OR</p>

<p>?m X 5m == 104 sq.m.</p>

<p>When you try both of them with your calculator, you’ll get:</p>

<p>20m x (5.2)m == 104 sq.m. AND
(20.8)m x 5m == 104 sq.m.</p>

<p>Thus, you have either an extra .2 or an extra .8. BUT remember, you are adding .2 or .8 to 1 side.</p>

<p>Since you have 2 sides on this rectangle, you’ll need to double it, and end up with either .4 or 1.6.</p>

<p>.4 is smaller, so I think the answer is (E. .4)</p>

<hr>

<p>/*3. If m and k are positive integers and 5m+4k=26, what is the value of m?</p>

<p>A. 2 B 3 C 4 D 5 E 6 */</p>

<p>This seems to be taking advantage of positive integers (ie. whole numbers > 0). I would plug in the answers (backsolve) to see which results in two positive integers.</p>

<p>A 5(2) + 4k == 26 → 4k == 16 → k == 4
B 5(3) + 4k == 26 → 4k == 11 → k == 11/4
C 5(4) + 4k == 26 → 4k == 6 → k == 6/4
D 5(5) + 4k == 26 → 4k == 1 → k == 1/5
E 5(6) + 4k == 26 → 4k == -4 → k == -1</p>

<p>It seems that (A) is the only one that results in an integer for variable k, so you should keep it.</p>

<hr>

<p>/* 4. If r and a are even positive integers and 20<rs<25, what is the number of possible values of product rs?</p>

<p>(Isnt it 2 since you can have either 22 or 24?) */</p>

<p>I’m going to assume rs == ra, because you have 3 variable in this question, which is aconfusing. So, re-writing as RA… RA… RA</p>

<p>ra == 2 even, positive integers.</p>

<p>BOTH have to be even and positive. So, 22 is not going to work, since it’s 2 * 11 (not both even)</p>

<p>2 even result in even… so you are right that you have 22 or 24, but only 24 will be a result of 2 even integers (6 * 4).</p>

<hr>

<p>/*5. Charles and David live the same walking distance, d kilometers from school. It took Charles and David 20 minutes and 15 minutes, respectively, to walk directly from home to school without stopping.</p>

<p>P= the average number of kilometers per hour at which Charles walked
Q= the average number of kilometers per hour at which David walked</p>

<p>What is Q-P in terms of d?
A. 4d B 3d C. d D. 1/3d E. 1/4d */</p>

<p>This is about Distance, Rate, and Time. You want to realize that D = R*T.</p>

<p>This is an EXCELLENT place to plug in. I want to create the distance, d. Elsewise you will have problems.</p>

<p>I want d to be evenly divisible by 20m and 15m. That is 1/3 of an hour and 1/4 of an hour. Because distance/rate/time is often in hours, I will turn 20m and 15m into 1/3 and 1/4. It might help me understand what’s what.</p>

<p>Since there are 3s and 4s, I will make my total distance to school: 12 miles.</p>

<p>Charles → Distance (12) == Rate(?) * Time(1/3) == Rate(36 Miles / Hour)… obviously, since he did 12 miles in 20 minutes, he’ll do 36 miles in 60 minutes… 1 hour</p>

<p>David → Distance (12) == Rate(?) * Time(1/4) == Rate(48 miles / Hour) … obviously, since he did 12 miles in 15 minutes, he’ll do 48 miles in 60 minutes… 1 hour</p>

<p>p == 36 | q == 48</p>

<p>Q - P == 48 - 36 == 12</p>

<p>D == 12</p>

<p>D.</p>

<p>====
If I made a mistake, please correct me. It’s pretty easy to mis-read SAT questions.</p>

<p>Cheers,
Craig</p>

11

<p>

</p>

<p>Note a bad idea to plug a number here, but the simpler ones work better. In this case, why not simply use a distance of 1. That means that the rates by Charles and David are simply … 3 and 4 kph. Following that the Q-P is obviously 1, which happens to be d. </p>

<p>Then one needs to be sure to pick the right answer (and it is not CHOICE D) </p>

<p>

</p>

<p>See above! </p>

<p>

</p>

<p>True, and especially true when one is WASTING time working through synthetic questions written by wannabe test writers. Again, and again, resist the urge to work through non-ETS questions as the problems are usually poorly written with erroneous and misleading answers. In the same vein, do NOT rely on suggested answers in sites such as yahoo. Stick to released tests that come with the CORRECT answers, and toss the rest in the garbage bin.</p>

12

<h1>5 (re: Xiggi)</h1>

<p>You are right! Meant C (lowercase d alone!) Read the question correctly… misread the answer choices… all in all, weak efforts. :)</p>

<p>But, you are right about the cruddy questions. Students should only REALLY use blue book+ questions. The other folks’ questions (mine included) should only be looked at when explaining a concept before a very long foray into the blue book.</p>

<p>Craig</p>

13

<p>And isn’t n°1 A because you only double the cookies not the flour?</p>

14

<p>^^</p>

<p>The baker probably wants all the cookies to taste the same :)</p>

15

<p>@craiggonzales,
for number 2, it specifically says that you must only move one side of the pen, not both of them. Plus it doesn’t make sense to divide by 2 anyway (confused by your logic there because the result does not equal 104)</p>

<p>Thus the answer is D. 0.8</p>

16

<p>@theshins,</p>

<p>You are right, though I think it’s a weirdly worded question. In my brain, I read the “move one side of the pen” to literally be 1 side, instead of just the length or just the width, which would result in a trapezoid instead of a rectangle, I think.</p>

<p>CG</p>