What is the difference between the number of male participants and the number…

2024

What is the difference between the number of male participants and the number of female participants in the event E2 from all the six countries together?

Answer: C. 1732ConceptWhen a group of N members is split between two categories in the ratio m : f, one share (one "part") equals N/(m + f). The two categories differ by (m…

  1. A.

    1724

  2. B.

    1728

  3. C.

    1732

  4. D.

    1734

Show answer & explanation

Correct answer: C

Concept

When a group of N members is split between two categories in the ratio m : f, one share (one "part") equals N/(m + f). The two categories differ by (m − f) such parts, so the gap between them is N × (m − f)/(m + f). Counts taken from separate groups simply add up, so the overall gap for an event is the sum of the group-wise gaps — the ratios themselves must never be added.

Application

Read only the E2 columns of the table and apply gap = N × (m − f)/(m + f) to each country:

Country

E2 participants (N)

M : F

Gap = N × (m − f)/(m + f)

India

500

17 : 8

500 × 9/25 = 180

US

1440

7 : 5

1440 × 2/12 = 240

China

1160

13 : 7

1160 × 6/20 = 348

Russia

1320

7 : 4

1320 × 3/11 = 360

England

840

9 : 5

840 × 4/14 = 240

Germany

728

3 : 1

728 × 2/4 = 364

Working each row out in full:

  1. India: one part = 500/25 = 20, so males = 17 × 20 = 340 and females = 8 × 20 = 160; gap = 180.

  2. US: one part = 1440/12 = 120, so males = 7 × 120 = 840 and females = 5 × 120 = 600; gap = 240.

  3. China: one part = 1160/20 = 58, so males = 13 × 58 = 754 and females = 7 × 58 = 406; gap = 348.

  4. Russia: one part = 1320/11 = 120, so males = 7 × 120 = 840 and females = 4 × 120 = 480; gap = 360.

  5. England: one part = 840/14 = 60, so males = 9 × 60 = 540 and females = 5 × 60 = 300; gap = 240.

  6. Germany: one part = 728/4 = 182, so males = 3 × 182 = 546 and females = 1 × 182 = 182; gap = 364.

  7. Total gap = 180 + 240 + 348 + 360 + 240 + 364 = 1732.

Cross-check

Add the six E2 headcounts: 500 + 1440 + 1160 + 1320 + 840 + 728 = 5988. Since males + females = 5988 and males − females = 1732, males = (5988 + 1732)/2 = 3860 and females = (5988 − 1732)/2 = 2128. The country-wise male counts add to 340 + 840 + 754 + 840 + 540 + 546 = 3860 and the female counts to 160 + 600 + 406 + 480 + 300 + 182 = 2128, which matches.

So across all six countries the male participants in E2 exceed the female participants by 1732.

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