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.

Abdulla wrote:Is pq = 1?


(1) pqp = p

(2) qpq = q



OA is E

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.

Let's go back to your break down of each step:

(1) p(pq - 1) = 0

great so far!

p = 0 or pq = 1

also great!

p = 0, pq = 1 - you get pq =1

not so great!

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.

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.

?????

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.

?????

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.

You are correct that if p = 2, pq = 1. But what if p = 0? Then:

pqp = p

0*q*0 = 0

Clearly, here, pq = 0. So, from statement one, pq can equal 1; but it can also equal 0. Therefore, the first statement is not sufficient. You can apply similar reasoning to statement two, and to the combination of the two statements.

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:

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.

Let's go back to your break down of each step:

(1) p(pq - 1) = 0

great so far!

p = 0 or pq = 1

also great!

p = 0, pq = 1 - you get pq =1

not so great!

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.

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:

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.

Let's go back to your break down of each step:

(1) p(pq - 1) = 0

great so far!

p = 0 or pq = 1

also great!

p = 0, pq = 1 - you get pq =1

not so great!

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?"

and a statement yields:

x = 1 or x =2,

then the statement is not sufficient because when x = 1, the answer to the question (is x =2?) is "no" and when x = 2, the answer to the question is "yes". Because we can get both a "yes" and a "no" answer, the statement is not sufficient.

In yes/no DS questions, we need either a definite "yes" or a definite "no" to have sufficiency.