A 2 min read

Is the integer x a 3-digit integer?

1. x is the square of an integer.
2. 90 < x < 150

Solution

Steps 1 & 2: Understand Question and Draw Inferences

In this question, we are given

• The number x is an integer

We need to determine

• Whether x is a 3-digit integer or not.

To determine whether x is a 3-digit integer or not, we need to know the value of x, or any specific range of x from which a unique value of number of digits of x can be determined.

With this information, let’s now analyse the individual statements.

 

Step 3: Analyse Statement 1

As per the information given in statement 1, x is the square of an integer.

From this statement, it is not possible to determine the number of digits of x.

• If x = 2² = 4, then x is a single-digit integer.
• If x = 5² = 25, then x is a double-digit integer.
• If x = 12² = 144, then x is a three-digit integer.

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

 

Step 4: Analyse Statement 2

As per the information given in statement 2, 90 < x < 150.

In this given range, there can be two possibilities.

• For 90 < x < 100:
  • The integer x has two digits.
• For 100 ≤ x < 150:
  • The integer x has three digits.

As we cannot determine whether x is a 3-digit integer or not, statement 2 is not sufficient to answer the question.

 

Step 5: Combine Both Statements Together (If Needed)

From statements 1 and 2 together, we get

• The integer x is the square of an integer.
• Also, 90 < x < 150

Now, in the given range, the possible square numbers are 100, 121 and 144.

• x can be any one of these 3 values.
• Also, all these 3 numbers have 3 digits, implies x is a 3-digit integer.

Hence, the correct answer choice is option C.