A Question on multiple graph charts with varied weights

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You must have come across multiple Line graph charts, but seldom you see multiple graph charts with varied weights.Here is one for you fresh from the oven. Try it out. Over the next week, we will be posting a few more questions.

'Dereck and Sons sells pigments in 4 regions. The data presented in the graph shows sales in 2 regions & average sales for all 4 regions over the period of 12 months in the year 2011.

Based on the given information select the options that most accurately complete the following statements.

1. The worst performance in terms of combined sales for other regions that Dereck and Sons operated in was in the month[s] of _______.'

A. March B. June & July C. July & August D. June, July & August E. November

2. Combined sales of other 2 regions for the month of June'11 is $ __________M.

A. 1975 B. 2350 C. 2550 D. 4700

Hello friends,

The answers for Q1 is November, & for Q2 is $2550 M.

Let us understand the time management aspect of GMAT IR. You need to attempt 12 questions in 30 minutes. This means on an average 2.5 minute per dataset!

As far as second part of the question is concerned, it is quite obvious that one will have to calculate the numerical value of sales for other 2 regions with the application of formula- '4 times average minus sum of region 1 and region 2'. However, when it comes to first part of the question, there are 5 months to consider for probable answers- March, June, July, August, & November.

It is not advisable to calculate the values of other 2 regions' sales for all 5 months. We can simply observe the graph, & eliminate few months as probable answer.

Let's understand our objective. We have to minimize 4*Average sales - Region 1 sales - Region 2 sales. This leads to a conclusion that an ideal worst performing month would be the one whose Average sales are lowest & Region 1 & 2 sales are the highest among all option months.

Well, there is no ideal month present in the graph, whose Average sales are lowest & Region 1 & 2 sales are the highest as well.

Because Lowest Average sales month - March;
Highest Region 1 sales month - November;
Highest Region 2 sales month- November.

The shortlisted options would be March, & November only. We can discard other 3 months, as they do not qualify. Pl. see the analysis.

June & July months are disqualified because their region 2 sales are the lowest among all months. It will not help minimize regions 3 & 4 sales. Similarly, August month is also disqualified because its region 1 & 2 sales are at mediocre level. Again, it will not help minimize regions 3 & 4 sales. So we discard these months.

Now can we zero in on March or November without calculating numerical values of regions 3 & 4 sales?

Let's look at our findings again for March & November months.
While November month has 2 positive factors - Highest Region 1 & 2 sales, March month has only one positive factor - Lowest Average sales.
So can we discard March vis-a-vis November now?

Well not really! And the reason is that the weight of Average sales is 4 times that of region 1 or 2 sales in the formula.

So there are 2 approaches to conclude March or November as an answer.

Approach 1:- Observe the graph again & look for 4 times the gain on account of Average sales for the month of March Vs. the gain on account of Region 1 & 2 sales for the month of November.

March:- Gain of 1/2 scale over November. So 4 times gain would be '4*1/2 scale = 2 scale'.
November:- Gain of 3 scale over March for region 1, & gain of 1/2 scale over March for region 2. So collectively total gain of 3.5 scale over March.

So it is obvious that Total gain of November over March is more, hence November month is the answer.

Approach 2:- You better calculate the sales values for March & November. Here it is.

Region 3 & 4 sales for November = 4*1500 - 2000-1950 = $2050 M
Region 3 & 4 sales for November = 4*1450 - 1700-1900 = $2200 M. .

So clearly the answer is November month.

Should you wish to see interactive audio-visual solution to this question, pl. visit e-GMAT free trial.

Regards!

Shalabh Jain