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## OG 2020: Question No. 370

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)?

- 3X < 2Y
- X < Y – 3

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Source | OG 2020 |

Type | Data Sufficiency |

Topic | Algebra/Number Properties |

Sub-Topic | Inequalities/Basics |

Difficulty | Hard |

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### Solution

__Steps 1 & 2: Understand Question and Draw Inferences__

__Steps 1 & 2: Understand Question and Draw Inferences__

In this question, we are given

- 2.00X and 3.00Y are two numbers in decimal dorm with thousandths digits X and Y.

We need to determine

- Whether 3(2.00X) > 2(3.00Y) or not.

We can simplify the given expression as

- 3(2.00X) > 2(3.00Y)

Or, 3(2 + 0.00X) > 2(3 + 0.00Y)

Or, 6 + 3X/1000 > 6 + 2Y/1000

Or, 3X > 2Y

Hence, we need to determine whether 3X is greater than 2Y or not.

With this understanding, let us now analyse the individual statements.

__Step 3: Analyse Statement 1__

__Step 3: Analyse Statement 1__

As per the information given in statement 1, 3X < 2Y.

- From this statement, we can definitely conclude that 3X is not greater than 2Y.

Hence, statement 1 is sufficient to answer the question.

__Step 4: Analyse Statement 2__

__Step 4: Analyse Statement 2__

As per the information given in statement 2, X < Y – 3.

Or, X + 3 < Y.

Now, if 3X > 2Y, then

- Y < (3/2) X

Or, X + 3 < Y < (3/2) X

Or, X + 3 < (3/2) X

Or, 2X + 6 < 3X

Or, X > 6

Now, if X > 6, then from the relation X < Y – 3, we can say Y > 9.

- However, Y cannot be greater than 9, as Y is a digit.
- Therefore, we can say 3X is not greater than 2Y.

Hence, statement 2 is sufficient to answer the question.

__Step 5: Combine Both Statements Together (If Needed)__

__Step 5: Combine Both Statements Together (If Needed)__

Since we can determine the answer from either of the statements individually, this step is not required.

Hence, the correct answer choice is option D.