EIVs Question Bank - Q3 AB>CD

[iil-london]

If ab > cd and a, b, c and d are all greater than zero, which of the following CANNOT be true?

What would be an alternative way to answer this question ?

Thanks

[StaceyKoprince]

Please post the complete text of the question, including answers. I can't figure out what is and isn't true if I can't see the answers I'm supposed to be evaluating... :)

[Guest]

Apologies Stacy ... here's the question in FULL:

If ab > cd and a, b, c and d are all greater than zero, which of the following CANNOT be true?

(A) c > d
(B) d > a
(C) b/c < d/a
(D) a/c > d/b
(E) (cd)^2 < (ab)^2

The solution in the Question bank suggests going through each answer choice and plugging-in numbers.
But I am keen to find out if there is another approach to tackle this type of question ?

Thanks in advance.

[rfernandez]

If ab > cd and a, b, c and d are all greater than zero, which of the following CANNOT be true?

(A) c > d
(B) d > a
(C) b/c < d/a
(D) a/c > d/b
(E) (cd)^2 < (ab)^2

You can reason your way through this one without plugging in numbers:

A - Given ab > cd, on the right side of the inequality, one of three things can be happening: c > d, c = d, or c < d.
B - Similar to A, but about the left side.
C - If you divide both sides by c and by a, you get b/c > d/a. The inequality sign is facing the other way. C is not possible.
D - Here, divide both sides by c and by b and you get a/c > d/b.
E - Square both sides of the inequailty ab > cd and you wind up with the expression in answer choice E.

Rey

[steven.jacob.kooker]

If ab > cd and a, b, c and d are all greater than zero, which of the following CANNOT be true?

(A) c > d
(B) d > a
(C) b/c < d/a
(D) a/c > d/b
(E) (cd)^2 < (ab)^2

You can reason your way through this one without plugging in numbers:

A - Given ab > cd, on the right side of the inequality, one of three things can be happening: c > d, c = d, or c < d.
B - Similar to A, but about the left side.
C - If you divide both sides by c and by a, you get b/c > d/a. The inequality sign is facing the other way. C is not possible.
D - Here, divide both sides by c and by b and you get a/c > d/b.
E - Square both sides of the inequailty ab > cd and you wind up with the expression in answer choice E.

Rey

I understand that normally if you're dividing/multiplying by an unknown in inequalities it is possible for the sign to reverse direction? How can you rule out that not being the case here? Does that not apply because both sides are entirely variables?

[RonPurewal]

I understand that normally if you're dividing/multiplying by an unknown in inequalities it is possible for the sign to reverse direction?

Depends on what you're dividing by.

If you're dividing the two sides by something that is positive, then the inequality goes the same way. If you're dividing by something that is negative, it switches.

[RonPurewal]

How can you rule out that not being the case here? Does that not apply because both sides are entirely inequalities?

For the first question, see above.

I don't understand the second thing here.
An inequality has two sides. The two sides, together with the "<" or ">" sign between them, are AN inequality.
So...
* It makes no sense to talk about whether the two individual sides are inequalities.
* "Entirely inequalities" doesn't make a lot of sense, either. A statement either is or isn't an inequality; there's no gray area.

[steven.jacob.kooker]

How can you rule out that not being the case here? Does that not apply because both sides are entirely inequalities?

For the first question, see above.

I don't understand the second thing here.
An inequality has two sides. The two sides, together with the "<" or ">" sign between them, are AN inequality.
So...
* It makes no sense to talk about whether the two individual sides are inequalities.
* "Entirely inequalities" doesn't make a lot of sense, either. A statement either is or isn't an inequality; there's no gray area.

I'm sorry, I meant both sides of the inequality are "entirely variables." My question was in regard to how do you find the solution if you can't tell whether or not the sign changes when you multiply by variables in order to remove the denominators. Basically, how do you know on (C) that the sign doesn't reverse directions when you multiply out by the denominators? I believe I understand the concept now, though, thanks!

[georgepa]

My question was in regard to how do you find the solution if you can't tell whether or not the sign changes when you multiply by variables in order to remove the denominators. Basically, how do you know on (C) that the sign doesn't reverse directions when you multiply out by the denominators? I believe I understand the concept now, though, thanks!

Take a look at the question.

...a, b, c and d are all greater than zero.... They are all +ve numbers

[tim]

Thanks. Let us know if there are any further questions about this one.