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A 2 min read

## PQID = DS10602.01 | OG 2020 Question No. 290

If S is a set of odd integers and 3 and –1 are in S, is –15 in S?

1. 5 is in S.
2. Whenever two numbers are in S, their product is in S.

## Solution

#### Steps 1 & 2: Understand Question and Draw Inferences

In this question, we are given that:

• S is a set of odd integers
• The numbers 3 and -1 are in S

We need to determine

• Whether the number -15 is in S or not.

As we do not have any other information about the elements present in S, let us now analyse the individual statements.

#### Step 3: Analyse Statement 1

As per the information given in statement 1, the number 5 is in the set S.

• However, from this statement we cannot say whether the number -15 is present in S or not.

Hence, statement 1 is not sufficient to answer the question.

#### Step 4: Analyse Statement 2

As per the information given in statement 2, whenever two numbers are present in S, their product is also present in S.

We already know that 3 and -1 are present in S.

• Therefore, we can say that (3 × -1) or -3 is also present in S.
• However, we can’t say whether -15 is present in S or not.
• Note that even with the rule in statement 2, we need a 5 in set S to be able to create -15.
• But we have no idea about the presence of 5.

Hence, statement 2 is not sufficient to answer the question.

#### Step 5: Combine Both Statements Together (If Needed)

From statements 1 and 2, we can say

• 3, -1, -3 and 5 are all present in set S.
• Also, for any two elements present in S, their product is also present in S.
• Therefore, we can say (-3 × 5) or -15 is also present in S.

As we can determine that -15 is present in S by combining both statements, the correct answer is option C.

### Takeaways:

1. Be careful with translations. – “Set S is a set of odd integers” does NOT mean that S has ALL the odd integers in the world. The article “a” in “a set” is important!
2. Be careful not to drag statement 1 when individually analyzing statement 2. This is a common mistake in DS. In this question, you would have marked B if you made that mistake!

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