e-GMAT Integrated Reasoning Articles

Hello all,

Here are few approaches that we think would be applicable to this particular question. Please pick best approach as per you, and why you think so.

Approach 1 - Computational Approach

Current Mean = Sum of all 13 data/13 = 185/13=14.23;
New Mean = (Sum of all 13 data + 5+19)/15 = 209/15= 13.53;
Mean decreases instead of increasing. Answer is NO.

Approach 2 - Smart Computational Approach

To get the value of current mean, we need to sum all 13 datasets, an approach that is time consuming.
Let’s make some observations. Observe Lawn Tennis column when arranged in ascending order.



There are 9 data points- 4, 6, 8…..20 as highlighted in red color. These data points form a series with equal interval. So their sum is equal to middle-most value*9= 12*9= 108.
Now, Current Mean = Sum of all 13 data points/13 = (Sum of all 9 data points + 18+19+20+20)/13 = (108+77)/13=185/13=14.23;
New Mean = (Sum of all 13 data points + 5+19)/15 = 209/15= 13.53;
Mean decreases rather than increasing. Answer is NO.

Approach 3 - Logical computational approach

Calculation of current mean is done in same manner as is done in approach 2.

We find that current mean is 14.23, which is greater than the mean (12) of Manish and Imran [(5+19)/2=12].
What will be the new mean of after inclusion of Manish and Imran?

Mean fundamental

Mean of a dataset cannot be less than the least value (Here it is ‘12’) and more than the highest value (Here it is ’14.23’). It will lie in between (do not read- Mid value). This implies that the new mean after inclusion of Manish and Imran will be less than 14.23.
So mean decreases rather than increases.

Approach 4 - Logical approach

Mean of 2 new values added= (5+19)/2=12
Current Mean of 13 data points is not known.

We need to deduce whether the new mean increases ?

New mean > Current mean, only and only if current mean < 12 (Mean of the 2 new values). Because if current mean > 12, the lower value 12 will pull the current mean towards it, and in that scenario, new mean will be less than the current mean

So we need to find whether the current mean < 12 or not?

Say current mean = x.

To answer the question, we need to know if the current mean increases by at least 2 points or not when the two data points are included?

So Is New mean > x+2?

We can form a mathematical equation as below



There are 13 data points & 2 new inclusions - so total 15 data points for new mean

Upon solving, we get x ≤ -3. This means to get an increment of 2 over the current mean, current mean has to be at the max. -3.
Well, -3 is an absurd value since the mean of given data set cannot be this value.

Mean fundamental

Mean of a dataset cannot less than the least value (Here it is ‘4’- Karren’s score), and more than highest value (Here it is ‘20’- Stacey’s score). So the answer is NO.

Approach 5 - Inference approach

Inference through New mean

For new mean to absorb an increment of minimum 2 points over the current mean, the current mean has to be much less than 12, because after an increment of 2 or more points, new mean MUST be less than 12.

Let’s observe what could be the probable value of current mean?



Let’s look at the Lawn tennis column. From Karren till Joe, there are total 8 data points. Their mean would be equal to median, because they have an equal interval of 2 points successively.
Now, the median of these 8 data points is 11 [(10+12)/2]. So mean would also be equal to 11. Rest of the data points are much higher than 11, so current mean would be more than 11. We already concluded earlier that new mean MUST be less than 12. If current mean is more than 11, then after an increment of 2, it can never be less than 12. So the answer is NO.

Hope this helps build your fundamentals. Do attempt challenging MSR question posted today.

-Shalabh