Abdulla wrote:Is pq = 1?
(1) pqp = p
(2) qpq = q
OA is E
Let's go back to your break down of each step:mehravikas wrote:I am confused after checking the OA. I guess the answer should be D.
from 1 you get -
p (pq - 1) = 0
p = 0, pq = 1 - you get pq =1
from 2 -
p (pq - 1) = 0
q = 0, pq = 1 - you get pq =1
We also get p = 0 and q = 0 but we don't need individual values of p or q. in both the statements we get pq = 1, I think that should be sufficient.
not so great!p = 0, pq = 1 - you get pq =1
When picking numbers in DS, it is important to pick different kinds of numbers that satisfy the statement. You want to see if, through picking numbers, you can prove the statement is NOT sufficient. By picking only one number in statement one, you haven't proved that it is sufficient to answer the question. You've only proved that it could lead to pq = 1; not that it has to.gdrea3 wrote:I am totally confused as to why the answer isn't D. Seems to me like statements are saying the same thing. I used actual numbers and my answers proved that both statements were sufficient:
Statement 1: pqp=p
So if p=2, then 4p=2 and p=1/2 so p*q does equal one (2*1/2)=1, correct?
Statement 2: qpq=q
So if q=3 then 9p=3, p=1/3 so p*q (3*1/3)=1 sufficient.
?????
Stuart Kovinsky wrote:Let's go back to your break down of each step:mehravikas wrote:I am confused after checking the OA. I guess the answer should be D.
from 1 you get -
p (pq - 1) = 0
p = 0, pq = 1 - you get pq =1
from 2 -
p (pq - 1) = 0
q = 0, pq = 1 - you get pq =1
We also get p = 0 and q = 0 but we don't need individual values of p or q. in both the statements we get pq = 1, I think that should be sufficient.
(1) p(pq - 1) = 0
great so far!
p = 0 or pq = 1
also great!
not so great!p = 0, pq = 1 - you get pq =1
You just proved that EITHER p = 0 OR pq = 1
So, pq COULD be 1, but if p is 0 then pq = 0. Therefore, (1) is insufficient.
(2) same thing - you proved that either q=0 OR pq=1. Again, that's a possible NO answer and a possible YES answer, so insufficient.
Combining the statements:
we could certainly pick p=q=1 to get a "yes" answer to the question.
However, we could also pick p=q=0 to get a "no" answer to the question.
Therefore, even after combining we don't have enough info to solve: choose E.
If the question is "Is x = 2?"mehravikas wrote:Ok..Let's try another example. A very basic question -
Is x = 2?
1. x^2 - 3x + 2 = 0
From above we get x = 1 or x = 2.
In this case also we can't say that statement 1 is sufficient to answer the question? because we also get x = 1?
I do understand when question stem is asking "what is the value of x?" but if the question is specifically asking about a value as in the question above (x = 2?) and we do get that value from the statement, why is that statement not sufficient?
Please explain.
Stuart Kovinsky wrote:Let's go back to your break down of each step:mehravikas wrote:I am confused after checking the OA. I guess the answer should be D.
from 1 you get -
p (pq - 1) = 0
p = 0, pq = 1 - you get pq =1
from 2 -
p (pq - 1) = 0
q = 0, pq = 1 - you get pq =1
We also get p = 0 and q = 0 but we don't need individual values of p or q. in both the statements we get pq = 1, I think that should be sufficient.
(1) p(pq - 1) = 0
great so far!
p = 0 or pq = 1
also great!
not so great!p = 0, pq = 1 - you get pq =1
You just proved that EITHER p = 0 OR pq = 1
So, pq COULD be 1, but if p is 0 then pq = 0. Therefore, (1) is insufficient.
(2) same thing - you proved that either q=0 OR pq=1. Again, that's a possible NO answer and a possible YES answer, so insufficient.
Combining the statements:
we could certainly pick p=q=1 to get a "yes" answer to the question.
However, we could also pick p=q=0 to get a "no" answer to the question.
Therefore, even after combining we don't have enough info to solve: choose E.
