Combined and Mixed Diagrams

2 questions

A technology company manufactured a total of $400$ units (where $1$ unit = $1,000$ 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: $25\%$
M2: $20\%$
M3: $30\%$
M4: $15\%$
M5: $10\%$

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

Model	Domestic Sales : Exports
M1	3 : 2
M2	1 : 3
M3	7 : 3
M4	1 : 2
M5	4 : 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?

40,000

10,000

20,000

40

Show answer & explanation

Answer: $40,000$

Answer

40,000

The correct answer is found by first determining the true total (

400,000

), applying the percentages to find the production of M2 (

80,000

) and M4 (

60,000

), using the ratios to find M2 exports (

80,000 \times \frac{3}{4} = 60,000

) and M4 domestic sales (

60,000 \times \frac{1}{3} = 20,000

), and finally subtracting the two (

60,000 - 20,000 = 40,000

Step-by-Step Solution

Calculate the total number of smartphones manufactured.

400 \times 1,000 = 400,000

smartphones.

The unit multiplier must be applied to find the absolute base value before calculating model-specific quantities.

Calculate the total number of M2 and M4 smartphones manufactured.

M2 =

20\%

400,000 = 80,000

. M4 =

15\%

400,000 = 60,000

Applies the pie chart percentages to the total production.

Calculate the number of M2 smartphones exported.

Ratio is

1:3

, so export fraction is

\frac{3}{1+3} = \frac{3}{4}

. M2 Exported =

80,000 \times \frac{3}{4} = 60,000

Extracts the correct part of the ratio corresponding to exports.

Calculate the number of M4 smartphones sold domestically.

Ratio is

1:2

, so domestic fraction is

\frac{1}{1+2} = \frac{1}{3}

. M4 Domestic =

60,000 \times \frac{1}{3} = 20,000

Extracts the correct part of the ratio corresponding to domestic sales.

Find the positive difference between the two calculated values.

60,000 - 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.

Question 2Question →

A consumer electronics brand released its regional sales data for the last quarter. The bar chart data displays the total volume of units sold across four geographical regions, with values expressed in thousands. The accompanying table breaks down these regional totals into three specific product categories: Air Conditioners (AC), Refrigerators, and Washing Machines, represented as percentages of each region's total sales.

Total Sales by Region (in thousands):
- North: $15$
- South: $25$
- East: $12$
- West: $18$

Region	Air Conditioners	Refrigerators	Washing Machines
North	$40\%$	$35\%$	$25\%$
South	$30\%$	$50\%$	$20\%$
East	$25\%$	$45\%$	$30\%$
West	$35\%$	$40\%$	$25\%$

Based on the provided data, what is the total number of Refrigerators sold in the South and East regions combined?

18,500

17,900

17.9

10,500

Show answer & explanation

Answer: $17,900$

Answer

The total number of Refrigerators sold in the South and East regions combined is

17,900

The correct answer accurately incorporates the 'in thousands' scale multiplier to find the true base sales for the South (

25,000

) and East (

12,000

) regions. It then calculates the respective Refrigerator sales independently (

50\%

25,000 = 12,500

and

45\%

12,000 = 5,400

) before adding them to reach

17,900

Step-by-Step Solution

Calculate the absolute total sales for the South and East regions.

South:

25 \times 1,000 = 25,000

. East:

12 \times 1,000 = 12,000

The stem indicates that the regional totals are expressed in thousands, so the given figures must be multiplied by

1,000

to find the true base values.

Calculate the number of Refrigerators sold in the South region.

50\%

25,000 = 0.50 \times 25,000 = 12,500

The table specifies that Refrigerators make up

50\%

of the total sales in the South region.

Calculate the number of Refrigerators sold in the East region.

45\%

12,000 = 0.45 \times 12,000 = 5,400

The table specifies that Refrigerators make up

45\%

of the total sales in the East region.

Add the two values together.

12,500 + 5,400 = 17,900

The question asks for the combined total of Refrigerators sold in both the South and East regions.

Key Concept

Extracting and combining data accurately across mixed formats (absolute values with multipliers and percentage distributions).

Combined and Mixed Diagrams

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes