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)
c > b d > a b/c > d/a a/c > d/b (cd)2 < (ab)
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If ab > cd and a, b, c and d are all greater than zero, w
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Brent@GMATPrepNow
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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
Brent Hanneson - Creator of GMATPrepNow.com
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ahmedshafea
- Junior | Next Rank: 30 Posts
- Posts: 19
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.
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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Jeff@TargetTestPrep
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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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