If ab > cd and a, b, c and d are all greater than zero, which of the following CANNOT be true?
c > b d > a b/c > d/a a/c > d/b (cd)2 < (ab)
If ab > cd and a, b, c and d are all greater than zero, w
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- vinay1983
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Please repost the question in proper format for the benefit of everybody.
You can, for example never foretell what any one man will do, but you can say with precision what an average number will be up to!
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Here's the original question
a) c > b
This can be true (if a=8, b=1, c=3, d=2), so we'll eliminate A
b) d > a
This can be true (if a=1, b=8, c=3, d=2), so we'll eliminate B
c) b/c < d/a
If we multiply both sides by c and by a, we get ab < cd, BUT we're told that ab > cd
So, it can never be true that b/c < d/a, which means C must be the correct answer.
Nevertheless, let's check the remaining answer choices for "fun".
Aside: since a and c are both positive, it's perfectly acceptable to multiply both sides of the inequality by a and c. Had we not been certain that a and c are positive, it would not be acceptable to multiply both sides by a and c.
d) a/c > d/b
If we multiply both sides by c and by b, we get ab > cd.
This confirms the given information (that ab > cd)
Since the statement that a/c > d/b must be true, we'll eliminate D
e)(cd)² < (ab)²
This can be true (if a=1, b=8, c=3, d=2), so we'll eliminate E
Aside: We can also use a helpful rule to show why E it always true. The rule that says, If 0 < x < y, then 0 < x² < y²
Since ab > 0 and cd > 0, and since 0 < cd < ab, then it must be true that 0 < (cd)² < (ab)²
Answer = C
Cheers,
Brent
For this question, we can either ELIMINATE any answer choice that CAN be true, or we can look for a statement that can NEVER be true.If ab > cd and a,b,c and d are all greater than zero, which of the following cannot be true?
a) c > b
b) d > a
c) b/c < d/a
d) a/c > d/b
e)(cd)² < (ab)²
a) c > b
This can be true (if a=8, b=1, c=3, d=2), so we'll eliminate A
b) d > a
This can be true (if a=1, b=8, c=3, d=2), so we'll eliminate B
c) b/c < d/a
If we multiply both sides by c and by a, we get ab < cd, BUT we're told that ab > cd
So, it can never be true that b/c < d/a, which means C must be the correct answer.
Nevertheless, let's check the remaining answer choices for "fun".
Aside: since a and c are both positive, it's perfectly acceptable to multiply both sides of the inequality by a and c. Had we not been certain that a and c are positive, it would not be acceptable to multiply both sides by a and c.
d) a/c > d/b
If we multiply both sides by c and by b, we get ab > cd.
This confirms the given information (that ab > cd)
Since the statement that a/c > d/b must be true, we'll eliminate D
e)(cd)² < (ab)²
This can be true (if a=1, b=8, c=3, d=2), so we'll eliminate E
Aside: We can also use a helpful rule to show why E it always true. The rule that says, If 0 < x < y, then 0 < x² < y²
Since ab > 0 and cd > 0, and since 0 < cd < ab, then it must be true that 0 < (cd)² < (ab)²
Answer = C
Cheers,
Brent
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It's probably easiest to try smart numbers here, with the goal of MAKING EACH ANSWER TRUE. If you're unable to do this after a little effort, there's a good chance that you've found the answer.
For instance, trying A, we could say a = 10, b = 1, c = 3, d = 1/2. Then ab > cd, as given, but c > b. Working that way down the line, as Brent did, we'll ultimately arrive at the right answer.
For instance, trying A, we could say a = 10, b = 1, c = 3, d = 1/2. Then ab > cd, as given, but c > b. Working that way down the line, as Brent did, we'll ultimately arrive at the right answer.
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We could also use algebra to prove that C is impossible.
d/a > b/c
Since a and c are both positive, we can crossmultiply without changing the sign:
cd > ab
But this contradicts what we were told in the stem! We know ab > cd.
Since C leads to an impossible inequality, it must be false, and we're done.
d/a > b/c
Since a and c are both positive, we can crossmultiply without changing the sign:
cd > ab
But this contradicts what we were told in the stem! We know ab > cd.
Since C leads to an impossible inequality, it must be false, and we're done.
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We can divide the given inequality by ac since we know that all of our variables are greater than zero:varun289 wrote:If ab > cd and a, b, c and d are all greater than zero, which of the following CANNOT be true?
A. c > b
B. d > a
C. b/c < d/a
D. a/c > d/b
E. (cd)^2 < (ab)^2
ab/(ac) > cd/(ac)
b/c > d/a
Since b/c will always be greater than d/a, b/c < d/a can NEVER be true.
Answer: C
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