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# Tip #38 to Get a Top SAT Math Score (page 2)

By McGraw-Hill Professional
Updated on Sep 10, 2011

### Medium

1. For negative integers m and n, if |m| + |n| = 8, what is the least possible value for mn ?
1. 8
2. 0
3. –4
4. –6
5. –16
|4 + x| = 8
|3 – y| = 5
2. If in the equations above x < 0 and y < 0, what is the value of xy ?
1. –32
2. –24
3. 6
4. 12
5. 24
3. If |1 + 2a| < 1, what is one possible value of a ?

### Hard

1. If m = |n|, then m could equal
1. 0
2. n
3. n
1. I only
2. III only
3. I and II
4. II and III
5. I, II, and III

1. C Great "Use the Answers" review! Try each answer choice in the equation. Choice C is correct, since |6 –18| = |–12| = 12 and |6 –(–6)| = |12| = 12.
2. D Again, "Use the Answers." Try each answer choice in the question.
1. |2 + 3| = 5 correct
2. |–2 + 3| ≠ 5 incorrect
3. |–8 + 3| = 5 correct
3. So I and III are correct, and choice D is the answer.

4. D Remember to underline the vocab term "negative integers" so you don't forget about it. We must consider the possible values for m and n:
5. |–7| + |–1| = 8, m =–7, n =–1

|–6| + |–2| = 8, m =–6, n =–2

|–5| + |–3| = 8, m =–5, n =–3

|–4| + |–4| = 8, m =–4, n =–4

|–3| + |–5| = 8, m =–3, n =–5

|–2| + |–6| = 8, m =–2, n =–6

|–1| + |–7| = 8, m =–1, n =–7

So try each possible pair of m and n to see which gives the least value for m – n. –7 – (–1) =–6 and is the least value.

6. E Since x < 0, x must equal –12 since |4 + (– 12)| = |–8| = 8. And in the equation |3 – y| = 5, y equals –2 since |3 –(–2)| = 5. So xy = (–12)(–2) = 24.
7. –1 < a < 0. Start by just trying some numbers and see if you can get one that works. Any positive numbers yield an answer that is too large, and 0 is still too big since |1 + 2(1)| = 1. So try –1. |1 + 2(–1)| = |–1| = 1, so that doesn't work. What if a =–0.52. That works, so –0.5 is an answer; in fact any number between 0 and –1 works.
8. E Let's look at each choice. Could m equal
1. 0 Definitely, 0 = |0|.
2. n Sure, n = |n| could work if n > 0.
3. – n Sure, – n = |n|, if n < 0. Nice!
9. So all three work.

Go to: Tip #39