At a certain high school, the 12 students in the senior class had to

If we sort the English marks in decreasing order. The general trend of science marks is increasing. However, there are a couple places where the Science marks have decreased compared to prior value (e.g. when English marks go from 95 to 94, Science marks go from 87 to 83. Also when English marks go from 74 to 73, similar thing is happening). Does this not mean that the English marks are not negatively correlated with Science marks? Or do we have to see the general trend? Please enlighten me if I am missing on something. Thanks in advance!

Different terms used in GMAT DI section
Correlation would mean the general trend.
Directly proportional and inversely proportional would mean no deviation in relationship.
Increase in one vs increase/decrease in other would again mean no deviation in relationship.

­Hey chetan2u, is there a way to solve the 3rd part of the Q logically in mind.Like i sorted the data in ascending order.But could not figure out without doing calculation whether the median will be less than or greater than 90. thanks in advance

­
Yeah surely there. But you require to scan the data without error.

When you observe the data, exactly half have the marks in both subjects in 90s, so the average too will be in 90s. The other half do not have any of the two scores in 90s, so the average will be less than 90.

Thus, the answer boils down to the two middle values, one of which will be highest in 80s, and other lowest in 90s.
Here the scanning data minutely is important.

Sort any in ascending/desceding order, say ascending order. 
Median will be average of 6th and 7th mean.

7th: The lower half will give you the lowest, 93+95 and 94+92 are the lowest, and 94+92 is the lowest with average in middle as 93.
6th: Next, look at the upper half. For the median to be above 90, you have to have the 6th to be greater than 87(as 7th is 93). Possible ways 87+88 or 88+88 or 89+89 or 86+89 or 88+89. None gives you these combinations.
Rather if you look for the largest sum, just add the units digit where 8 is the tens digit. 4+7 is the largest. Thus, 84+87 will give average of 85.5

Answer: The median will be (85.5+93)/2, <90

Reading the solution may have taken time, but the answer can be found in a much shorter time.
 

1. ­The grades on the science exam are negatively correlated with the grades on the English exam. => Yes

Sort by Science or Exam, we can see one goes up and the other goes down

2. No more than three students scored more than 80 on each of the four exams. => No

Sort by one of the subjects, for example, English, there are at least 4 scoring more han 80 on each exam

• Jeff
• John
• Greg
• Dan

3. If the "tech score" is the average of Math & Science exam scores, then the median "tech score" is above 90. => No

Sort by Math, the 6th and 7th are 88 and 93
Sort by Science, the 6th and 7th are 87 and 91

the 4 middle of tech scores are 87 88 91 and 93
=> Median is the avg of 88 and 91 => 89.5 < 90