­The table shows the sales forecast from January to June of last year

Can the linear constant also lead to negative coorelation between the Actual VS Predicted sold products?

 
­No, this wording and context implies a positive correlation, where Actual = (Some Constant) * (Predicted) 

 
­Hey chetan2u and GMATCoachBen, I marked the option E. why can't we take negative correlation between actual and forecast in St2. If  one plots forecast on x-axis and then actual units on y-axis and then visualise the linear graph, one cannot say whether the march actual units will decrease or increase compared to actual units in april. Thanks in advance 
 

We are told projections and actuals had a constant linear relationship.

Even if it is negative, April projections being larger would always be larger.

Say, actual=x*projected
March: 8=x*16, so x is 0.5
Thus in April actual = 0.5*20 =10 >8.

How about Actual + Forecast = 28 ?

Is this a constant linear relationship ?

KarishmaB can you please help

­I'm having the same question as well. Can anyone else chime in?

Flatrun3 and Ayushi0002

Linear relationship means a straight line relationship. It depends on slope of line and could be
Positive: Both increase with each other
Negative: one increases and other decreases

In Algebra, it is represented by y=mx+b

Posted from my mobile device

Exactly chetan2u - there is mentioned that the relationship is linear - +ve or -ve, we aren’t sure so how can we say on the predicted basis that the no of products sold in march were actually less than April. if we aren’t aware of what kind of linear relationship .

­Further explanation of this upon request:

A "linear relationship" is a line. When I say x and y have a linear relation, it represents a line on the xy axis. i.e. y = mx + c

I do not understand what is meant by a "constant linear relationship". I would just take it as a line i.e. a linear relationship.
I would not think that it means y = mx. As I mentioned before, if there is some particular curriculum in which a constant linear relationship means "y = mx" then I do not know. But a google search did not give any such information. So I doubt many people would equate "constant linear relationship" to y = Constant * x and hence the question would not pass the GMAT filter. 

We know that y = constant * x is direct variation and I would look for that term to arrive at the conclusion that I have to use that relation here. 

Hence, in this question, as given, this is what I imagine is also possible: 

Hence it is possible that the actual number of units sold in April is less than the number sold in March even using the data from both statements. 

Hence my answer here would be (E).
 ­

i think this is what linear relationship between the forecast and actual means.
­

­No,

Number of Products sold can never be negative.

­exactly this is what I feel and thereforeI marked option E. Can anyone please let me know if I am wrong.

Hey Karishma,
Can we say that y=kx ; and use direct and inverse variation ( similar to what we use in ratios) to solve for the actual value for April or since the question does not mention direct variation, would it be wiser to stick to the possibility of there exisitng an intercept value and hence do not pursue this unless direct variation ( positive or negative) is mentioned? ­KarishmaB­

 
I don't know what you mean by k = yx. There is certainly not an inverse variation between actual and predicted values.
But the answer expects us to consider constant, linear relationship as y = kx. 

­As I mentioned above, "constant, linear relationship" does not mean that to me at all and I don't think that a live question of GMAT would use this. 
But do keep in mind that if you do come across this term on the GMAT, they perhaps mean y = kx if nothing else makes sense. 

S2)
Looking at some of the posts let me clarify some fundamentals:

A linear relation is y=mx+c

y=mx is a proportional relationship (this is also linear)

y=2x is positive sloped increasing linear function
y=-2x is a negative sloped decreasing linear function
y=0 is 0 sloped linear function


A linear relationship can have a positive or a negative slope .

Hence this question has some piece of information missing. Although we can assume forecast should somehow be positively correlated to actuals but this is crossing the scope of the problem.

Hence if slope is positive , ans is yes
If slope is negative , ans is no
If slope is 0, ans is no

Looks like a poor quality question from GMAC

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­chetan2u Bunuel If the relation is negative, then won't the equation be actual = - (k)*projected
The slope of the curve has to be negative for negative correlation and not 0.5, isn't?

I marked E . Can you help me in understanding what I am missing

GMATCoachBen Can you please post the official solution?