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

Question

Data Insights (DI) Butler 2023-24       Click here for Details ]

At a certain high school, the 12 students in the senior class had to take end-of-the-year exams in four subjects. Here are the 12 students and their exam grades.

Student    English    History    Math    Science     Brendon  100  95  85  79    Cecelia  74  76  96  95    Claire  78  81  97  91    Dan  89  88  83  85    Greg  94  87  86  83    Heather  100  92  80  80    Jeff  96  91  88  82    Joel  75  75  98  93    John  95  93  84  87    Kat  73  81  94  92    Rebecca  70  80  93  95    Zach  72  84  99  95     ( Sort ↕  the table by clicking on the headers)

For each of the following statements, select "Yes" if the statement is true based solely on the information reported for these students and their grades. Otherwise, select "No."

chetan2u · Accepted Answer

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.

sood1596 · Answer

IMO answer is Yes, No and No

mayankdgmat · Answer

Yes, No, No

Statement 1: The grades on the science exam are negatively correlated with the grades on the English exam.

If we sort either of the science or english table. we can see when english score are reducing from 100 to 70 whereas science scores are increasing.
Hence negative correlations

Stmt 2: No more than three students scored more than 80 on each of the four exams.

When we sort english table in descending order, we have to check upto Dan and we can find 4 entries where score in all subject is greater than 80.

Stmt 3: If the "tech score" is the average of Math & Science exam scores, then the median "tech score" is above 90.

We need to find 6th and 7th term mean in a sequence of ascending tech score

VerbalFaker · Answer

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!

imRaj · Answer

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

chetan2u · Answer

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.

Gemmie · Answer

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

vic231 · Answer

chetan2u   Bunuel   Sajjad1994

I just want to confirm whether my approach to solving 2nd part is correct or not?

First, I note down all the students who scored above 80 in English -> Dan, Greg, John, Jeff, Brendon, Heather
All the above scored 80 in History as well.
In Maths, Heather scored 80 and got removed from above list.
In Science, Brendon scored 79 and got removed from list.

Final list: Dan, Greg, John, Jeff
Since they are 4 students and thus answer is  False

The 2nd approach which I was thinking was to just check whether we have more than 4 students scoring above 80 in all of the exams.

Which approach is the right one? and why?

cheshire · Answer

Either works but since it can be any 4 students that receive over an 80 on each test, you can just scan the list for scores higher than 80 which I think is faster.

RRINSEAD2025 · Answer

Hey guys, English isn't my native language and I don't know if thats the issue here, but I genuinely don't understand what the third question is asking. I'm reading it but it's not registering. I don't understand what the question is asking.

Could you explain it a bit more clearly?

Thank you

Could you explain it a bit more clearly?

Thank you

cheshire · Answer

The question is asking you to find if the median score of the students "tech scores" (the arithmetic mean of a students science and math score) is over 90. If you don't care about time and just want to solve the problem, you would average the math and science score of all students then order them from least to greatest. As we have an even number of scores we have to find the mean of the middle two scores: 85.5 and 93. This equals 89.25 which is less than 90 so the answer is NO.

adipisci · Answer

I have the same question.

Also, in a couple of similar questions, I answered in favor of a correlation and found the answer to be wrong.

Can someone please suggest what should be the correct answer in these cases where there is a general trend but 1 or 2 deviations?

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

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Student	English	History	Math	Science
Brendon	100	95	85	79
Cecelia	74	76	96	95
Claire	78	81	97	91
Dan	89	88	83	85
Greg	94	87	86	83
Heather	100	92	80	80
Jeff	96	91	88	82
Joel	75	75	98	93
John	95	93	84	87
Kat	73	81	94	92
Rebecca	70	80	93	95
Zach	72	84	99	95

Yes	No
		The grades on the science exam are negatively correlated with the grades on the English exam.
		No more than three students scored more than 80 on each of the four exams.
		If the "tech score" is the average of Math & Science exam scores, then the median "tech score" is above 90.

GMAT Graphs and Tables (G&T) Questions

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