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Source: — Data Sufficiency |
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by imskpwr » Tue Jul 17, 2012 7:37 am
If p < q and p < r, is pqr < p?

pqr - p < 0

p(qr-1) < 0

so, either P < 0 and qr-1 > 0
or p > 0 and qr-1 < 0


(1) pq < 0

either P < 0 and q > 0
or P > 0 and q < 0

Insufficient

(2) pr < 0

either P < 0 and r > 0
or P > 0 and r < 0

Insufficient

Combining (1) and (2), we get
P < 0 and r > 0 and q > 0
Here, q * r can be 0.4 and so pqr may not be > p
OR
P > 0 and r < 0 and q < 0
Here also, q * r can be 1.6( that is q = r = -0.4) and so pqr may not be > p

hence answer is D ie together also these conditions are not sufficient.
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by Anurag@Gurome » Tue Jul 17, 2012 9:28 am
niketdoshi123 wrote:If p < q and p < r, is pqr < p?

(1) pq < 0
(2) pr < 0
Algebraic Approach:
If pqr < p, then (pqr - p) < 0 ---> p(qr - 1) < 0
Hence, for pqr to be less than p, any of he following must be satisfied
  • 1. p > 0 and qr < 1
    2. p < 0 and qr > 1
Statement 1: p and q are of opposite sign.
As p < q, p must be negative and q must be positive.
But we don't know about r.

Not sufficient

Statement 2: p and r are of opposite sign.
As p < r, p must be negative and r must be positive.
But we don't know about q.

Not sufficient

1 & 2 Together: p is negative, q and r are positive.
But qr may or may not be greater than 1.

Not sufficient

The correct answer is E.
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by Anurag@Gurome » Tue Jul 17, 2012 9:33 am
Picking Numbers:
One look at the statements and the given conditions should be enough to identify that p must be negative but q and r must be positive. So we will pick numbers accordingly.

Now consider the following cases,
  • 1. p = -1, r = q = 1 ---> pqr < p ---> YES
    2. p = -1, r = q = 1/2 ---> pqr > p ---> NO
Both of the above examples satisfies both the statements.

The correct answer is E.
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