p < q and p < r .... Is pqr < p ?
1. pq < 0
Thus, p and q must be of opposite signs. However since p < q , this means p must be the negative one.
=> p < 0 and q > 0
We also have p < r ... however this doesn't tell us whether r is positive or negative.
If r > 0 => pqr < 0
If r < 0 => pqr > 0
INSUFFICIENT
2. pr < 0
This is exactly analogous to the previous statement, except here we are confused about the sign of q.
INSUFFICIENT
Both 1 and 2:
pq < 0 and pr < 0 tells us that : p < 0 , q > 0 and r > 0
This means that pqr is going to be < 0
However we know nothing about the relative absolute values of the quantities pqr and p, which would be necessary to identify which is the greater negative quantity.
For example: If p = -1 and q = r = 0.5 => pqr = -0.25 which is > p
But, If p = -1 and q = r = 2 => pqr = -4 which is < p
INSUFFICIENT
Pick E
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Source: Beat The GMAT — Data Sufficiency |
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albatross86
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Abhay is back!!!albatross86 wrote:p < q and p < r .... Is pqr < p ?
1. pq < 0
Thus, p and q must be of opposite signs. However since p < q , this means p must be the negative one.
=> p < 0 and q > 0
We also have p < r ... however this doesn't tell us whether r is positive or negative.
If r > 0 => pqr < 0
If r < 0 => pqr > 0
INSUFFICIENT
2. pr < 0
This is exactly analogous to the previous statement, except here we are confused about the sign of q.
INSUFFICIENT
Both 1 and 2:
pq < 0 and pr < 0 tells us that : p < 0 , q > 0 and r > 0
This means that pqr is going to be < 0
However we know nothing about the relative absolute values of the quantities pqr and p, which would be necessary to identify which is the greater negative quantity.
For example: If p = -1 and q = r = 0.5 => pqr = -0.25 which is > p
But, If p = -1 and q = r = 2 => pqr = -4 which is < p
INSUFFICIENT
Pick E
As usual gr8 explanation......
--Anand--
By the same token:
(1) if pq < 0, from stem and (1) we know that p<0
so, question can be rephrased from pqr < p to
qr > 1?....(since p < 0 )
Insufficient since we don't know sign of q.
(2) pr < 0
Also, implies p<0, and original question changes from
"pqr < p" to "qr > 1?" sign reverses since p<0.
Insufficient for same reason as in (1).
(1) and (2): p<0, q>0, and r>0:
" qr > 1?"
we don't know whether q and r are either integers or fractions
Insufficient.
OA is E as proved earlier.
(1) if pq < 0, from stem and (1) we know that p<0
so, question can be rephrased from pqr < p to
qr > 1?....(since p < 0 )
Insufficient since we don't know sign of q.
(2) pr < 0
Also, implies p<0, and original question changes from
"pqr < p" to "qr > 1?" sign reverses since p<0.
Insufficient for same reason as in (1).
(1) and (2): p<0, q>0, and r>0:
" qr > 1?"
we don't know whether q and r are either integers or fractions
Insufficient.
OA is E as proved earlier.
(1) p<0, q>0 we don't know r so INSUFFICIENT
(2) p<0, r>0 we don't know q so INSUFFICIENT
COMBO: p<0, q,r>0 but we don't q and r greater than 1 so INSUFFICIENT
answer is E
(2) p<0, r>0 we don't know q so INSUFFICIENT
COMBO: p<0, q,r>0 but we don't q and r greater than 1 so INSUFFICIENT
answer is E
