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<p>In the figure above,ticks marks are equally spaced on the number line. What is the value of x?</p>
<p>1)4
2)6
3)16
4)18
5)22</p>
<p>I choosed 22 because if we minus 10 from 42 it would take us to 2,but the answer is 18. I don't understand why though ??!
Is there fast ways to solve these kind of problems without having to visualize it or brute forcing numbers?</p>
<p>A four-digit integer. WXYZ,in which W,X,Y, and Z each represent a different digit,is formed according to the following rules.</p>
<p>1) W = W + Y + Z
2) W = Y + 1
3) Z = W - 5;</p>
<p>What is the four digit integer?
I tried to solve it using playing with values,but and then using system of equation to solve,but didn't succeed..</p>
<p>3,4,6,7,10,12</p>
<p>The number n is to be added to the list above. If n is an integer,which of the following could be the median of the new list of seven numbers?</p>
<p>I - 6
II - 6.5
III - 7</p>
<p>1)I
2)II
3)III
4)I and III only
5)I,II,and III</p>
<p>In first problem, your figure does not indicate where x is located. </p>
<p>One strategy to solve the problem is to pretend you are at 2. Then count how many steps you must take to reach 42 (5 steps). In taking those five steps, you’ve increased by 40. So each step causes an increase of (40/5) or 8. Therefore, the tick marks are 2, 10, 18, 26, 34, and 42.</p>
<p>In the second problem, could you double check if you’ve typed the problem correctly?<br>
Statement 1) implies that Y+Z = 0; since Y and Z are integers of a number, Y and Z are both 0
Statement 2) implies that W = 1
Statement 3) implies that Z = -4 , but this contradicts our previous conclusion about Z. I don’t think the problem is typed correctly.</p>
<p>For the third problem, I would try two different numbers for n, one smaller than the existing numbers, and one larger than the existing numbers.
If n = 2, then the median for 2, 3, 4, 6, 7, 10, 12 is 6. So I. is possible.
If n = 13, then the median for 3, 4, 6, 7, 10, 12, 13 is 7. So III. is possible
6.5 cannot be the median no matter which integer you choose for n, since all numbers in the set are integers.</p>
<p>^Thanks for explanation of 1 and 3.</p>
<p>For 2 yes I have typed it correctly its from the blue book by the way.</p>
<p>how did you imply that Y + Z = 0; and W = 1 and Z = -4 ?</p>
<p>I got this with playing with it.</p>
<p>W = Y + 1 ->> Y = W - 1; then W > Y with 1 integer.
Z = W - 5; W > Y with 5 integer;</p>
<p>Z < W according to this information,but I still didn’t conclude how to solve it and get all four integers.
Because he didn’t represent some integers in order to limit the problem down.</p>
<p>If W = W + Y + Z, then subtract W from both sides of the equation.</p>
<p>0 = Y + Z ; Y and Z have to be 0 or positive integers if they represent digits in a number. So Y and Z have to be 0.</p>
<p>If W = Y + 1, then W = 0 + 1 = 1</p>
<p>Again, I think something is wrong with the statement of the problem. Why is there no equation with X in the problem?</p>
<p>Really try google for questions like this. It’s easier than searching the forums. This one has been hashed out pretty thoroughly (as has just about every even-mildly-challenging problem from the blue book)…I’ve said it before: it’s like having a free tutor available round the clock. Anyway, here’s a link to one of the threads:</p>
<p><a href=“http://talk.collegeconfidential.com/sat-preparation/879606-help-math-problems-these-types-drive-me-nuts.html[/url]”>http://talk.collegeconfidential.com/sat-preparation/879606-help-math-problems-these-types-drive-me-nuts.html</a></p>
<p>The mistake is in rule number 1. It should read
X = W + Y + Z</p>
<p>So the whole problem is
A four-digit integer. WXYZ,in which W,X,Y, and Z each represent a different digit,is formed according to the following rules.</p>
<p>1) X = W + Y + Z
2) W = Y + 1
3) Z = W - 5;</p>
<p>What is the four digit integer?</p>
<p>You can solve it by substitution or you can just play around and see what works. I think the second approach is best, especially if you start with rule 3. </p>
<p>Since Z = W - 5, the value of W must be 5, 6, 7, 8 or 9.
If W equals 9, Y equals 8. That makes X a two-digit integer. The maximum value of X is 9 - since X is a digit - so W can’t be 9.
For the same reason, W can’t be 8, 7, or 6 (try them all out and you’ll see). So W is 5, which makes Y equal to 4, Z equal to 0, and X equal to 9. The answer is 5940.</p>
<p>@Knowthestuff I see where you derived Y + Z = 0 from that makes perfect logic,but as I see with pckeller post the guy who posted the solution pretty much makes sense.</p>
<p>Thanks alot PrestigePrep I also saw the explanation on pckeller link,but your explanation is different its good to have many intuition on a problem.</p>
