Explanation:

Alright, here’s how we break it down:

Quantity I: 2, 3, 4, 15, 56, X

- Look at the pattern:

- 2×1+1=3

- 3×1+1=4

- 4×3+3=15

- 15×3+11=56

There’s an increase in multiplier and addends. Let’s try:

- Next multiplier is 4 (adding 1), next addend sequence is 1, 1, 3, 11… (difference doubles, so next is 21). So, 56×4+21 = 224+21 = 245

- So, X = 245

Quantity II: 3, 2, 7, 16, 71, Y

- Pattern is a bit tricky, but looking closer:

- 3×1-1=2

- 2×2+3=7

- 7×2+2=16

- 16×4+7=71

Next, 71×4+16 = 284+16 = 300

- So, Y = 300

Quantity III: 14, 16, 28, 64, 144, Z

- This looks like:

- 14×1+2=16

- 16×1+12=28

- 28×2+8=64

- 64×2+16=144

Next: 144×2+32=288+32=320

- So, Z = 320

Comparing:

X = 245

Y = 300

Z = 320

Relations:

- X < Y

- Y < Z

So, X < Y < Z

Here’s what that means for your options:

- Option 1: X > Y > Z — nope, not it.

- Option 2: X < Y > Z — definitely not it, Y is not greater than Z.

- Option 3: X < Y < Z — yes, that fits.

- Option 4: X = Y > Z — not true, values are all different.

- Option 5: X = Y < Z — also not it.

So, you picked Option 2. Based on this,

The correct answer is Option 3: X < Y < Z

Option 3 is the one that matches.

Let me know if you want to check the patterns for any of these sequences in more detail!