<li>A cube is assembled out of 64 smaller blue cubes of equal size and then all its faces are painted black. How many of the smaller cubes now have exactly two black faces?
A. 16
B. 18
C. 24
D. 32
E. 36</li>
</ol>
<p>The answer is C. 24</p>
<p>So I got the answer, but only after i drew a cube and counted out the cubes which took awhile. Does anyone know of a quicker way? </p>
<li>Joe is 6 years younger than Anna and 4 years older than Ricardo. What is the ratio of Anna’s age to Ricardo’s age?
A. 1:10
B. 4:6
C. 6:4
D. 10:1
E. Can’t be determined from info given</li>
</ol>
<p>Answer is E…can anyone explain? </p>
<li>If wx is a multiply of 10 and xy is an odd number, which of the following numbers must be even?</li>
</ol>
<p>I. w
II. x+y
III. wy</p>
<p>A. None
B. I only
C. II only
D. I and II only
E. I, II, and III</p>
<p>Answer is A
But doesn’t x and y both have to be odd in order to multiply and have an odd number…which would mean that x+y must then be even? </p>
<p>On the first one it has to be a 4x4x4 cube. Everything in the middle is obviously out. All corners are out since they would have 3 sides. All exposed center pieces are out since they only have one. That leaves 2 cubes on each edge of the cube. 2 x 12= 24.</p>
<p>Number two. Since you don't know actual ages, only relative to each other, you can't figure out a comparison. The older they get the closer the ratio of ages is. Without knowing at least one you can't figure it out.</p>
<p>I can't help on number three. I agree with you. I would have picked E. Since x and y would both need to be odd then w would have to be even to make the product an even number. Therefore w times any number would be even so all three would have to be true. At least that's the only way I can see it.</p>
<p>I don't know what's going on with #3. If all the numbers are taken to be integers, then the correct answer is E.</p>
<p>If the numbers don't have to be integers, then this is a dirty, rotten, trick question that doesn't belong on the SAT or any other test. In fact, it ends up being a question about the even-ness of non-integers, which barely makes sense. Does the question "Is pi even?" have any answer at all?</p>
<p>Yeah, #3's answer SHOULD BE E, and it should be given that we're talking about integers:</p>
<p>xy is odd, so x and y must both be odd. This means that w must be an even number, otherwise, wy couldn't be a multiple of 10. Two odds added make an even, so x+y is also even. And of course, wy is even since w is even.</p>
<p>Sly Si:</p>
<p>Pi is not even since it is not a multiple of 2 with another integer. That's how we define 'even'. It is not odd either, since it is not representable in the form 2k+1, where k is an integer. Clearly, all non-integers are neither odd nor even.</p>
<p>So yeah, it could work with non-integers. If the answer really is A, then this is really a dirty trick.</p>
<ol>
<li>Something I found out when I was bored...
3 sides painted-always 8
2 sides painted-12x-24 in which x is the number of cubes per side
1 side painted- 6*(x-2)^2
0 sides painted- (x-2)^3</li>
</ol>
<p>Caution: This only works for a cube. Im sure there is a way to do rectangles.</p>
<ol>
<li><p>What everyone else said.</p></li>
<li><p>Yeah I think its E.</p></li>
</ol>
<p>phuriku: That's technically correct, and that's what I was thinking, too. My point was that if they ask "Is X even", you can generally assume that X is an integer, since no one cares about the even-ness of nonintegers. I would feel differently if the question ended "Which of the following numbers must be an even integer".</p>
<p>sorry to burst all you guys' bubbles but the anwser is a. wx is taken to be a multiple ten where w is an integer and x is an integer but they aren't multiplied. It's taken as an actual number. So is xy. Its like w would = for instance 3, and x would = 0 so that 30 is a multiple of 10. Therefore x is automatically 0 and y is odd and w could be even or odd so none have to technically be even. I can see you reasoning that the variables would multiply with each other. It's a very poorly written problem and it shouldn't count because it can be interpreted in two different ways.</p>
<p>sorry to burst YOUR bubble bhsjr, but as written, the variables can only be thought of as multiplying one another. The SAT would clarify using capitalization or explanation if it meant for the letters to mean digits of a 2-digit number, not integers.</p>
thanks</p>