Question 4/20: Set 5 - Try Out - General Reasoning (SNBT)

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The following table shows motorcycle sales data (in millions) from three different factories.

Year	Factory X	Factory Y	Factory Z
2013	$2.5$	$4.0$	$0.4$
2014	$2.3$	$4.6$	$0.2$
2015	$1.9$	$5.0$	$0.1$
2016	$1.3$	$5.2$	$0.05$

The table above represents the motorcycle sales chart (in millions) from factories X, Y, and Z from 2013—2016.

The statement that is least consistent with the table is...

The increase in motorcycle sales at factory Y forms a second-level arithmetic sequence

The increase in motorcycle sales at Factory Z forms a geometric sequence pattern

One of the highest percentage decreases in motorcycle sales occurred at factory Z in 2015-2016

Motorcycle sales at factory Y are more than double the total sales of factory X and Z

The highest percentage decrease in motorcycle sales at factory X occurred in 2014-2015

Explanation

We need to analyze each statement to find the one that is least consistent (false) based on the table data.

Analysis of Factory Y Sales Increase

The increase in motorcycle sales at factory Y forms a second-level arithmetic sequence.

Factory Y sales data: $4.0, 4.6, 5.0, 5.2$ .

Let's calculate the difference (increase) between years:

4.6 - 4.0 = 0.6

5.0 - 4.6 = 0.4

5.2 - 5.0 = 0.2

The first-level difference sequence is $0.6, 0.4, 0.2$ . Next, let's calculate the second-level difference:

0.4 - 0.6 = -0.2

0.2 - 0.4 = -0.2

Since the second-level difference is constant ( $-0.2$ ), it is true that Factory Y's sales data forms a second-level arithmetic sequence.

(Statement Consistent)

Analysis of Factory Z Sales Pattern

The increase in motorcycle sales at Factory Z forms a geometric sequence pattern.

Factory Z sales data: $0.4, 0.2, 0.1, 0.05$ .

Let's check the ratio:

\frac{0.2}{0.4} = \frac{1}{2}

\frac{0.1}{0.2} = \frac{1}{2}

\frac{0.05}{0.1} = \frac{1}{2}

Since the ratio is constant ( $\frac{1}{2}$ ), it is true that the data forms a geometric sequence.

(Statement Consistent)

Analysis of Factory Z Sales Decrease

One of the highest percentage decreases in motorcycle sales occurred at factory Z in 2015-2016.

Factory Z Decrease (2015-2016):

\frac{0.1 - 0.05}{0.1} \times 100\% = 50\%

Other high decreases (e.g., Factory X 2015-2016):

\frac{1.9 - 1.3}{1.9} \times 100\% \approx 31.6\%

Since $50\% > 31.6\%$ , Factory Z's decrease of 50% is indeed one of the highest (the highest in this comparison).

(Statement Consistent)

Comparison of Factory Y Sales with X and Z

Motorcycle sales at factory Y are more than double the total sales of factory X and Z.

Let's calculate the total sales for each factory:

\text{Total Y} = 4.0 + 4.6 + 5.0 + 5.2 = 18.8 \text{ million}

\text{Total X} = 2.5 + 2.3 + 1.9 + 1.3 = 8.0 \text{ million}

\text{Total Z} = 0.4 + 0.2 + 0.1 + 0.05 = 0.75 \text{ million}

Sum of X + Z and its double:

\text{X} + \text{Z} = 8.0 + 0.75 = 8.75 \text{ million}

2 \times (\text{X} + \text{Z}) = 2 \times 8.75 = 17.5 \text{ million}

Since $18.8 > 17.5$ , this statement is correct.

(Statement Consistent)

Analysis of Factory X Sales Decrease

The highest percentage decrease in motorcycle sales at factory X occurred in 2014-2015.

Let's calculate Factory X's percentage decrease for each year:

2013-2014: \frac{2.5 - 2.3}{2.5} \times 100\% = \frac{0.2}{2.5} \times 100\% = 8\%

2014-2015: \frac{2.3 - 1.9}{2.3} \times 100\% = \frac{0.4}{2.3} \times 100\% \approx 17.4\%

2015-2016: \frac{1.9 - 1.3}{1.9} \times 100\% = \frac{0.6}{1.9} \times 100\% \approx 31.6\%

From the calculations above, the highest percentage decrease occurred in 2015-2016 (approx. $31.6\%$ ), not 2014-2015.

(Statement NOT Consistent)

Therefore, the statement that is least consistent with the table is that the highest percentage decrease in motorcycle sales at factory X occurred in 2014-2015.

Command Palette

Number 4

Explanation

Analysis of Factory Y Sales Increase

Analysis of Factory Z Sales Pattern

Analysis of Factory Z Sales Decrease

Comparison of Factory Y Sales with X and Z

Analysis of Factory X Sales Decrease