PQID = DS13841.01 | 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
| Source | OG 2020 |
| PQID | DS13841.01 |
| Type | Data Sufficiency |
| Topic | Algebra |
| Sub-topic | Inequalities |
| Difficulty | Medium |
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 form 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. —-(I)
Now, is 3X > 2Y implies
- IS Y < (3/2) X?
Using (I), this can be said as
Is X + 3 < Y < (3/2) X?
Is X + 3 < (3/2) X?
Is 2X + 6 < 3X?
Is X > 6?
Now, if X > 6, then from (I), we can say Y > 9.
- However, Y cannot be greater than 9, as Y is a single digit.
- Therefore, we can say X is not greater than 6, and hence 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.
Takeaways:
- 0.00X can be represented as X/1000.
- If x represents a digit in any number, say 23x4, then the only possible values for x are 0, 1, 2, …, 9.
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