<p>I was doing so well studying for the SAT until I stumbled upon this question: I want to scream, I can't seem to solve it.</p>
<p>BB, Test 1, Section 7
16) A four-digit integer, WXYZ, in which W, X, Y, and Z each represent a different digit, is formed according to the following rules.
1. X = W + Y + Z
2. W = Y + 1
3. Z = W - 5
What is the four-digit integer?</p>
<p>its not so bad actually, hope this explanation helps:
write everything in terms of Y.
So W = Y+1,
X = (Y+1) + Y + (Y+1) - 5 = 3Y - 3
Y = Y
Z = (Y+1)-5 = Y-4
Now this means that Y >=4 because otherwise Z would be negative. But if Y is 5 then X would become a 2 digit number. Hence Y has to be 4. So plug in 4 for Y to get the following: 5940</p>
<p>Is that right? I dont have the blue book</p>
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<p>My method:
X is the greatest of the 4 digits; W+Y+Z =/=10+. 9 is the greatest digit that X can be (otherwise it’d be 2 digits).<br>
Z is the smallest digit, with Z+5 = W and Z+4 = Y. As you can see, Z must be zero because Z+5 (W) and Z+4 (Y) + Z = 9. If Z were any higher, X would be 2 digits.</p>
<p>Makes perfect sense, thank you. Basically Z can’t be negative, so the minimum value for W is 5. The minimum for Y would be 4, in order to make W 5. That’s 9, the only possibility for X that is under 10. So then Z must be 0.</p>
<p>I feel a lot better now.</p>