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GATE 2020 EC GA Q.10: solution and answer

GATE 2020 · ECGA Q.10 · 2 marks · MCQ

The following figure shows the data of students enrolled in 5 years (2014 to 2018) for two schools P and Q. During this period, the ratio of the average number of the students enrolled in school P to the average of the difference of the number of students enrolled in schools P and Q is______.

GATE 2020 EC GA question 10: A clustered vertical bar chart.Tap to open full size
Figure from the GATE 2020 EC paper. It is part of the question.
Figure description

A clustered vertical bar chart. Horizontal axis titled "Year" with five categories: 2014, 2015, 2016, 2017, 2018. Vertical axis titled "Number of students (in thousands)", from 0 to 9 with gridlines at every integer. Legend in the upper left inside the plot area: "School P" (red/pink bar, hatched) and "School Q" (light blue bar, hatched). In each year the School P bar is on the left and the School Q bar on the right. Values (in thousands): 2014 — P = 3, Q = 4; 2015 — P = 5, Q = 7; 2016 — P = 5, Q = 8; 2017 — P = 6, Q = 7; 2018 — P = 4, Q = 5.

  1. (A)

    8 : 23

  2. (B)

    23 : 8

  3. (C)

    23 : 31

  4. (D)

    31 : 23

Answer and solution

ANSWER

The ratio is 23 : 8, option (B).

Official answer: BSource: Official answer key, GATE 2020 EC (IIT Delhi)

  1. Read the chart (in thousands). School P: . School Q: .

  2. Total for P: , so the average for P is thousand.

  3. Difference in each year, (Q is higher every year, so the size of the difference has no sign ambiguity): .

  4. Sum of the differences: , so the average difference is thousand. (Check: .)

  5. Both averages are taken over the same 5 years, so the cancels in the ratio:

  6. So the ratio is , which is option (B).

KEY IDEA

Both averages are taken over the same 5 years, so the ratio of the averages equals the ratio of the totals: . Since Q is higher than P every year, the sum of the yearly differences is simply .

WATCH OUT FOR

Using the average of School Q () in place of the average difference, which gives (option C), or turning the ratio upside down to get (option A). The question asks for P's average divided by the average difference, in that order.

From the GATE 2020 EC paper. Every question of this paper · Download the full paper · All 9 Data interpretation questions, with notes

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