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# For numbers p, q, and r, (p × q × r) < 0 and Magoosh; Lele,

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For numbers p, q, and r, (p × q × r) < 0 and Magoosh; Lele, [#permalink]  02 Dec 2018, 09:59
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Question Stats:

66% (00:37) correct 33% (00:47) wrong based on 33 sessions
For numbers $$p$$, $$q$$, and $$r$$, $$(p * q * r) < 0$$ and $$\frac{(p * q)^2}{r} < 0$$

 Quantity A Quantity B $$p * q$$ $$0$$

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given
[Reveal] Spoiler: OA

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Re: For numbers p, q, and r, (p × q × r) < 0 and Magoosh; Lele, [#permalink]  02 Dec 2018, 20:36
We have (p*q)^2 / r < 0. Since anything in power of 2 or any even is positive then as this expression is negative we can construe that r must be negative.

We have p*q*r <0 so either one or 3 of them are negative.
We know that r is negative. Two approaches are possible either r is negative and p&q are positive, then (p*q) is positive and The answer is A. Or the two of p&q are negative then (p*q) is again positive and bigger than 0, So, the answer is A.
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Re: For numbers p, q, and r, (p × q × r) < 0 and Magoosh; Lele, [#permalink]  03 Dec 2018, 02:19
Expert's post
Carcass wrote:
For numbers $$p$$, $$q$$, and $$r$$, $$(p * q * r) < 0$$ and $$\frac{(p * q)^2}{r} < 0$$

 Quantity A Quantity B $$p * q$$ $$0$$

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given

$$\frac{(p * q)^2}{r} < 0$$..
since $$(p*q)^2$$ is positive, r<0...

Now $$p*q*r<0.....(p*q)*r<0$$..
As we know r<0, $$p*q>0.....A>B$$

A
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Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

Re: For numbers p, q, and r, (p × q × r) < 0 and Magoosh; Lele,   [#permalink] 03 Dec 2018, 02:19
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