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Question

Difficulty: MediumCombined and Mixed Diagrams

A technology company manufactured a total of 400400 units (where 11 unit = 1,0001,000 smartphones) across five different models (M1, M2, M3, M4, and M5) in 2026.

The percentage distribution of the total smartphones manufactured is as follows:
M1: 25%25\%
M2: 20%20\%
M3: 30%30\%
M4: 15%15\%
M5: 10%10\%

The following table shows the ratio of Domestic Sales to Exports for each model:

ModelDomestic Sales : Exports
M13 : 2
M21 : 3
M37 : 3
M41 : 2
M54 : 1

Based on the provided data, what is the positive difference between the number of M2 smartphones exported and the number of M4 smartphones sold domestically?

  1. 40,00040,000Answer
  2. B
    10,00010,000
  3. C
    20,00020,000
  4. D
    4040

Answer

40,00040,000
The correct answer is found by first determining the true total (400,000400,000), applying the percentages to find the production of M2 (80,00080,000) and M4 (60,00060,000), using the ratios to find M2 exports (80,000×34=60,00080,000 \times \frac{3}{4} = 60,000) and M4 domestic sales (60,000×13=20,00060,000 \times \frac{1}{3} = 20,000), and finally subtracting the two (60,000−20,000=40,00060,000 - 20,000 = 40,000).

Step-by-Step Solution

1
Calculate the total number of smartphones manufactured.
400×1,000=400,000400 \times 1,000 = 400,000 smartphones.
The unit multiplier must be applied to find the absolute base value before calculating model-specific quantities.
2
Calculate the total number of M2 and M4 smartphones manufactured.
M2 = 20%20\% of 400,000=80,000400,000 = 80,000. M4 = 15%15\% of 400,000=60,000400,000 = 60,000.
Applies the pie chart percentages to the total production.
3
Calculate the number of M2 smartphones exported.
Ratio is 1:31:3, so export fraction is 31+3=34\frac{3}{1+3} = \frac{3}{4}. M2 Exported = 80,000×34=60,00080,000 \times \frac{3}{4} = 60,000.
Extracts the correct part of the ratio corresponding to exports.
4
Calculate the number of M4 smartphones sold domestically.
Ratio is 1:21:2, so domestic fraction is 11+2=13\frac{1}{1+2} = \frac{1}{3}. M4 Domestic = 60,000×13=20,00060,000 \times \frac{1}{3} = 20,000.
Extracts the correct part of the ratio corresponding to domestic sales.
5
Find the positive difference between the two calculated values.
60,000−20,000=40,00060,000 - 20,000 = 40,000.
Answers the final question asked in the stem.

Key Concept

Combining percentage distribution data with ratio data to find absolute comparative values.
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Topics

Combined and Mixed Diagrams

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