BTGModeratorVI wrote: ↑Sat May 16, 2020 7:25 am
If p and q are integers, such that p < 0 < q, and s is a nonnegative integer, which of the following must be true?
A. p^2 < q^2
B. p + q = 0
C. sp < sq
D. sp ≠ sq
E. p/q < s
Answer:
E
Source: Princeton Review
Approach #1
If p < 0 < q, then p is
NEGATIVE and q is
POSITIVE
So, p/q =
NEGATIVE/
POSITIVE, which means p/q is
NEGATIVE
If s is a non-negative integer, then we can be certain that p/q < s
Answer: E
Approach #2
The question asks, "Which of the following
must be true?"
So, if we can find a counterexample that shows an answer choice can be false, then we can eliminate that answer choice.
A. p² < q²
If p = -2 and q = 1, we get: (-2)² < 1²
Simplify to get: 4 < 1, which is not true.
Eliminate A
B. p + q = 0
If p = -2 and q = 1, we get: (-2) + 1 = 0, which is not true.
Eliminate B
C. sp < sq
p = -2, q = 1, and s = 0, we get: (0)(-2) < (0)(1)
Simplify to get: 0 < 0, which is not true.
Eliminate C
D. sp ≠ sq
p = -2, q = 1, and s = 0, we get: (0)(-2) ≠ (0)(1)
Simplify to get: 0 ≠ 0, which is not true.
Eliminate D
By the process of elimination, the correct answer must be E
Cheers,
Brent
