<p>If the statement above is true, which of the following statements must also be true?</p>
<p>A. If x > 3, then y = 4.
B. If x ≠ 4, then y ≠ 3.
C. If y > 3, then x = 4.
D. If y < 3, then x ≠ 4.
E. If y < 3, then x = 4.</p>
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<p>According to them, the answer is D. Can anyone explain? I reasoned that none of the* must * be true when I took the test, and randomly guessed (I don't see why if y < 3, then x CANNOT be equal to 4). </p>
<p>It's on the PSAT practice booklet you get when you register for a test (#18, section 2). This is the only math question I missed when taking it. My final scaled score was a 214 ): If I had gotten that question right, then I would have gotten an 80 in math instead of the 75 (wow, harsh curve) and "qualified" for national merit if it was a real test, so this is really bugging me. </p>
<p>Well, assume that D doesn’t have to be true, which would mean that for y < 3, x could equal 4. If x did equal 4, then y would have to be > 3, because of the original statement. Since y cannot be both < and > 3, D must be false.</p>
<p>OK, let me try to explain it (I took the PSAT practice too and got an 80 on Math): </p>
<p>"If x = 4, then y > 3.</p>
<p>If the statement above is true, which of the following statements must also be true?</p>
<p>A. If x > 3, then y = 4.
B. If x ≠ 4, then y ≠ 3.
C. If y > 3, then x = 4.
D. If y < 3, then x ≠ 4.
E. If y < 3, then x = 4."</p>
<p>Option A doesn’t necessarily have to be true, and neither do C, E, and B. Given the information, when y is smaller than 3, x simply cannot be 4, so choice (D) is correct. At x = 4, the y-values can start from 3.0000001 and go up, but they all MUST be greater than 3. Now when they’re SMALLER than 3, their x-value CANNOT be 4, because otherwise that would mean they would HAVE to be greater than 3.</p>
<p>This is a pretty tricky problem but it is a lot easier if you have studied logic. Last year in geometry we had a chapter about logic and some of the rules - this problem is a classic rule. If a statement is true, then its CONTRAPOSITIVE is also always a true. A contrapositive is the reverse of the statement plus nots. Here is an example. Pretend the SAT gives you the statement IF a=5 THEN b<3. All you can say is true is that if b is NOT less than 3 than a CANNOT =5. Look up contrapositive and logic on the internet if still confused, but these problems rarely show up on the PSAT/SAT.</p>
<p>Try to think this way: Consider a function that has a value of > 3 at x=4. If you pick another point from this function with value of <3, then this point cannot be x=4.</p>