Question

question 9 of 10
which of the following is most likely the next step in the series?
a.
b.
c.
d.

Explanation:

Step1: Analyze the pattern of dots

First figure: Let's count the dots. The first has 3 dots (arranged as 2 on top, 1 below? Wait, looking at the figures: first is 3 dots (maybe 2 in top row, 1 in bottom left), second is 5 dots (3 in top, 2 in bottom left), third is 7 dots (4 in top, 3 in bottom left). Wait, wait, let's count again. First figure: 3 dots (like a small triangle? Wait, first image: two dots on top, one below left. So total 3. Second: three dots on top, two below left. Total 5. Third: four dots on top, three below left. Total 7. So the pattern is: number of dots in top row: 2, 3, 4... and bottom left row: 1, 2, 3... So total dots: 3, 5, 7... which is an arithmetic sequence with common difference 2. So next total dots should be 9. Now let's check the options:

Option A: Let's count. Top row: 3, bottom left: 2. Total 5? No. Wait, maybe my initial count is wrong. Wait, first figure: let's look at the actual dots. First: • •
•
So that's 3 dots. Second: • • •

• •

So 5 dots. Third: • • • •

• • •

So 7 dots. So the pattern is top row has n+1 dots, bottom left row has n dots, where n starts at 1 (first figure: n=1, top=2, bottom=1; n=2, top=3, bottom=2; n=3, top=4, bottom=3). So next, n=4: top row 5 dots, bottom left row 4 dots? Wait no, wait the third figure: top row 4, bottom 3. So next (fourth) should be top row 5, bottom row 4? Wait no, let's check the options. Option C: top row 5, bottom row 4? Wait option C: • • • • •

• • • •

So top 5, bottom 4: total 9. Let's check other options:

Option A: top 3, bottom 2: total 5. No. Option B: top 4, bottom 4: total 8. No. Option D: top 6, bottom 3: total 9? Wait no, D's top row: 6? Wait D: • • • • • •

• • •

Top 6, bottom 3: total 9. But our pattern was top row increasing by 1, bottom row increasing by 1. So first: top 2, bottom 1 (3); second: top 3, bottom 2 (5); third: top 4, bottom 3 (7); so next: top 5, bottom 4 (9). So option C has top 5, bottom 4. Let's check option C: the figure for C is • • • • • (top row 5) and • • • • (bottom row 4). Yes, that's 5+4=9. So that's the next in the sequence.

Step2: Verify with the pattern

The sequence of total dots: 3, 5, 7, so next is 9. Now check each option:

• A: Let's count. Top row: 3, bottom row: 2. Total 5. Not 9.
• B: Top row: 4, bottom row: 4. Total 8. Not 9.
• C: Top row: 5, bottom row: 4. Total 9. Correct.
• D: Top row: 6, bottom row: 3. Total 9? Wait 6+3=9, but the pattern is top and bottom increasing by 1 each time. So top should be 5, bottom 4. So D's top is 6, bottom 3: that's not following the top and bottom both increasing by 1. So C is correct.

Answer:

C. • • • • •

• • • • (Option C)