GATE 2024 EC GA Q.8: solution and answer

GATE 2024 · ECGA Q.8 · 2 marks · MCQ

The bar chart shows the data for the percentage of population falling into different categories based on Body Mass Index (BMI) in 2003 and 2023.

[Bar chart]

Based on the data provided, which one of the following options is INCORRECT?

(A)
The ratio of the percentage of population falling into overweight category to the percentage of population falling into normal category has increased in 20 years.
(B)
The ratio of the percentage of population falling into underweight category to the percentage of population falling into normal category has decreased in 20 years.
(C)
The ratio of the percentage of population falling into obese category to the percentage of population falling into normal category has decreased in 20 years.
(D)
The percentage of population falling into normal category has decreased in 20 years.

Answer and solution

ANSWER

(C) is the INCORRECT statement. The obese-to-normal ratio rose from 15/50 = 0.30 in 2003 to 25/30 ≈ 0.83 in 2023, so it increased and did not decrease.

Official answer: CSource: Official answer key, GATE 2024 EC (IISc Bengaluru)

Read the chart. Every bar ends exactly on a 5% gridline. 2003 (blue): Underweight $10%$ , Normal $50%$ , Overweight $25%$ , Obese $15%$ . 2023 (orange): Underweight $5%$ , Normal $30%$ , Overweight $40%$ , Obese $25%$ . As a check, each year adds up to $100%$ : $10 + 50 + 25 + 15 = 100$ and $5 + 30 + 40 + 25 = 100$ .
(A) Overweight to Normal: $\frac{25}{50} = 0.50$ in 2003 and $\frac{40}{30} \approx 1.33$ in 2023. The ratio went up, so (A) is correct.
(B) Underweight to Normal: $\frac{10}{50} = 0.20$ in 2003 and $\frac{5}{30} \approx 0.17$ in 2023. The ratio went down, so (B) is correct.
(C) Obese to Normal: $\frac{15}{50} = 0.30$ in 2003 and $\frac{25}{30} \approx 0.83$ in 2023. The ratio went up, but (C) says it decreased, so (C) is INCORRECT.
Quick check without dividing: if the numerator rises and the denominator falls, the ratio must rise. Obese went up ( $15 \to 25$ ) while Normal went down ( $50 \to 30$ ), so the ratio cannot have decreased.
(D) Normal went from $50%$ to $30%$ , a decrease, so (D) is correct.
Only (C) is false, and the question asks for the INCORRECT statement. Answer: (C).

KEY IDEA

Read each bar off the 5% gridlines, then look at which way each ratio moves. When a ratio's numerator rises and its denominator falls, the ratio has to rise. Normal fell from 50% to 30% while Obese rose from 15% to 25%, so Obese/Normal went up. That makes (C) false without any division.

WATCH OUT FOR

One slip is swapping the legend colours (orange is 2023, blue is 2003). If you read the years the wrong way round, (A), (B) and (D) all become false and (C) becomes true, so you get three 'incorrect' options where the question allows one. That mismatch is itself a warning that the chart was misread. Another slip is forgetting the question asks for the INCORRECT statement and choosing one of the three true ones.

From the GATE 2024 EC paper. Every question of this paper · Download the full paper · All 9 Data interpretation questions, with notes

GATE 2024 EC GA Q.8: solution and answer

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