Data Sufficiency

rijul007 wrote:

pemdas wrote:@Ron, I am still under impression that there is at least one assumption involved with this question if we select answer B (not C). The question states: S is a set of (ALL-implied) integers such that to contain a and -a (two different numbers, if a=!0 and one number if a=0), b (the third different number) and ab (the fourth different number). We know that at least four different numbers can be in the set S -> a,-a,b,ab.

Now, Ron, don't we make an assumption by selecting answer B, that there are two numbers which are the same -a=b. Otherwise how we effect the condition 2) and allow for ab=-4 such as 2*(-2)=-4?

We've agreed from beginning that there can be four different numbers: a,-a,b,ab.

You are doing the same mistake again. You are considering a and b as particular elements of the set.

Kindly re-read the prev posts


Heres another ex to make it clearer
You must have heard of the saying
All work and no play makes jack a dull boy.
Here jack is not a particular guy.
Jack represents all those who work all day and dont play.

Similarly in this ques., a and b are no particular elements. They can be any elements of the set.

Another eg.,
Lets say we have an arithematic progression
2,4,6,8,10,....

If a(n) is the nth term of the AP
And we are given a condition
a(n) = a(n-1) +2

Here, does a(n) represent a particular element of the AP?
No, its a general term that represents any term.

In this ques lets say we do have two particular nos a and b
Then the set would turn out to be
S = {a,b,-a,-b,ab,-ab,ab^2,ba^2,....}
It would have infinite no of elements
except for a case {1,-1}, which has just two elements

I hope am able to clarify your doubt.

pemdas wrote:@rijul007 by following your logic, we can state since Question stem provides a set S contains integers, and asks whether -4 is in the set S, we don't need any statements AT ALL!

rijul007 wrote:

pemdas wrote:@rijul007 by following your logic, we can state since Question stem provides a set S contains integers, and asks whether -4 is in the set S, we don't need any statements AT ALL!

Yes, set S contains integer, but does that mean it contains ALL the integers?

pemdas wrote:you mean that in st(2) and opting ans. B

rijul007 wrote:

pemdas wrote:@rijul007 by following your logic, we can state since Question stem provides a set S contains integers, and asks whether -4 is in the set S, we don't need any statements AT ALL!

Yes, set S contains integer, but does that mean it contains ALL the integers?

(2) 2 is in S.

Condition 1:
2 and -2 both are in set S

Condition 2:
2*(-2) = -4 is also in S

Sufficient

pemdas wrote:it would be interesting to know the source of original question.
@karthikpandian19, please update us per source of this question.

@Ron, I am still under impression that there is at least one assumption involved with this question if we select answer B (not C). The question states: S is a set of (ALL-implied) integers such that to contain a and -a (two different numbers, if a=!0 and one number if a=0), b (the third different number) and ab (the fourth different number). We know that at least four different numbers can be in the set S -> a,-a,b,ab.

Now, Ron, don't we make an assumption by selecting answer B, that there are two numbers which are the same -a=b. Otherwise how we effect the condition 2) and allow for ab=-4 such as 2*(-2)=-4?

We've agreed from beginning that there can be four different numbers: a,-a,b,ab. How it comes that we consider two of no-s -a=b set in certain relation (value) if they can be in any relation (value)?

again, in your formula example, Pi*r^2, I agree r can be any radius BUT it must be always within the range of lengths made by connecting points equidistant from a center with the center.

I am still questioning answer B

lunarpower wrote:by the way, here's another GMAT PREP problem:

If there are more than two numbers in a certain list, is each of the numbers in the list equal to 0?
(1) The product of any two numbers in the list is equal to 0.
(2) The sum of any two numbers in the list is equal to 0.

this problem can absolutely be re-written as follows:

In the sequence a(sub 1), a(sub 2), a(sub 3), ... [these are subscripts], ..., aN, is each element of the sequence equal to 0?
(1) For any integers u and v, where 1 < u < N and 1 < v < N, the product of a(sub u) and a(sub v) is 0.
(2) For any integers u and v, where 1 < u < N and 1 < v < N, the sum of a(sub u) and a(sub v) is 0.

do you see the connection?