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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)? – OG 2020 Question #370 with Solution

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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)?

  1. 3X < 2Y
  2. 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

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

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

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)

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.

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