Each question is followed by two statements I and II Mark the answer 1 If the question can be answer...........

Math and Mental Ability Data Sufficiency

Each question is followed by two statements, I and II. Mark the answer:

1.If the question can be answered by using one of the statements alone, but cannot be answered using the other statement alone.

2.If the question can be answered by using either statement alone.

3. If the question can be answered by using both statements together, but cannot be answered using either statement alone.

4. If the question cannot be answered even by using both statements together.

LCM of 2 numbers is 630. What is the absolute difference between them?

I. HCF is 9.

II.The sum of the 2 numbers is 153.

Let’s break it down, step by step:

- We’re told the LCM of two numbers is 630. We need to find their absolute difference.

- Statement I: HCF is 9.

- With just HCF and LCM, you know the product of the two numbers: HCF × LCM = product of numbers.

- So, 9 × 630 = 5670. You want two numbers that multiply to 5670, both divisible by 9.

- But there could be several pairs that fit, and their differences will vary. Without another condition, this isn’t enough.

- Statement II: The sum is 153.

- Now you’re looking for two numbers adding to 153 and with an LCM of 630.

- Again, multiple pairs could work, and you can't pin down the exact difference with just this data.

- Both statements together:

- Now you know: their LCM (630), their HCF (9), and their sum (153).

- Since ab = HCF × LCM, and a + b = 153, you can set up simultaneous equations and solve for unique numbers.

- Only with both pieces can you find the absolute difference.

Let’s check the options:

- Option 1: If one statement alone works—not true.

- Option 3: If both together are needed—this fits

- Option 4: If even both aren’t enough—not the case.

So, the right answer is option:3, 3.

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