If \(2.00X\) and \(3.00Y\) are \(2\) numbers in decimal form with thousandths digits \(X\) and \(Y,\) is \(3(2.00X) > 2(3.00Y) ?\)

(1) \(3X < 2Y\)

(2) \(X < Y - 3\)

Answer: D

Source: Official Guide

## If \(2.00X\) and \(3.00Y\) are \(2\) numbers in decimal form with thousandths digits \(X\) and \(Y,\) is

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## Global Stats

**Given: 2.00X and 3.00Y are 2 numbers in decimal form with thousandths digits X and Y**

**Target question:**

**Is 3(2.00X) > 2(3.00Y)?**

This is a good candidate for rephrasing the target question.

Since X is the thousandths digit, we can write: 2.00X = 2 + X/1000

Since Y is the thousandths digit, we can write: 3.00Y = 3 + Y/1000

So, the target question becomes: Is 3(2 + X/1000) > 2(3 + Y/1000)?

Expand both sides: Is 6 + 3X/1000 > 6 + 2Y/1000)?

Subtract 6 from both sides: Is 3X/1000 > 2Y/1000)?

Multiply both sides by 1000 to get: Is 3X > 2Y ?

**REPHRASED target question:**

**Is 3X > 2Y?**

*Aside: the video below has tips on rephrasing the target question*

**Statement 1:3X < 2Y**

PERFECT!!

The answer to the REPHRASED target question is NO, 3X is NOT greater than 2Y

Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

**Statement 2: X < Y − 3**

Add 3 to both sides to get: X + 3 < Y

This one is TRICKY!!

The solution relies on the fact that X and Y are DIGITS (0, 1, 2, 3, 4, 5, 6, 7, 8 or 9)

Let's examine all possible DIGIT solutions to the inequality X + 3 < Y

case a: X = 0, and Y = 4,5,6,7,8 or 9. In all possible cases,

**3X < 2Y**

case b: X = 1, and Y = 5,6,7,8 or 9. In all possible cases,

**3X < 2Y**

case c: X = 2, and Y = 6,7,8 or 9. In all possible cases,

**3X < 2Y**

case d: X = 3, and Y = 7,8 or 9. In all possible cases,

**3X < 2Y**

case e: X = 4, and Y = 8 or 9. In all possible cases,

**3X < 2Y**

case f: X = 5, and Y = 9. In all possible cases,

**3X < 2Y**

Now that we've examine all possible values of X and Y, we can see that the answer to the REPHRASED target question is always the same: NO, 3X is NOT greater than 2Y

Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,

Brent