If 2.00X and 3.00Y are 2 numbers in decimal form with thousandths digits X and Y

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

3(2.00X) > 2(3.00Y)

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

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

3X > 2Y

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

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.

Statement 2: X < Y - 3.

X + 3 < Y.

Now, if 3X > 2Y, then

Y < (3/2) X

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

X + 3 <  (3/2) X

2X + 6 < 3X

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.

The correct option is D.