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Q2425/80Q26
Q25·CSAT · Prelims 2026

Quantitative Aptitude — Exponential Bounds

NumericalNumber SystemArithmetic ProblemEasy

Question

How many three-digit numbers can be expressed as an integral power of 2?

Options

a

1

b

2

c

3

d

4

Answer

Explanation

We need to find the number of integer values of n such that 2^n yields a three-digit number (100 \le 2^n \le 999).

Let us calculate the relevant sequential powers of 2 directly:

2^5 = 32 (2 digits)
2^6 = 64 (2 digits)
2^7 = 128 (First valid 3-digit entry)
2^8 = 256 (Second valid 3-digit entry)
2^9 = 512 (Third valid 3-digit entry)
2^10 = 1024 (4 digits)

Let us count the distinct values. Wait, let's re-verify if any value was missed. Let's look closer at the options list: (a) 1, (b) 2, (c) 3, (d) 4[cite: 3929, 3930, 3931, 3932]. The distinct powers matching the three-digit range are 2^7, 2^8, and 2^9, which gives exactly 3 valid numbers. Let us confirm the question parameters and option alignment. Under standard key groupings, the total count maps to 3 valid entries.

Checking boundary limits across an exponential series provides a reliable way to isolate valid integer entries.

Answer: (c).

Question details

Year

2026

Paper

CSAT

Question

Q25

Section

Quantitative Aptitude

Sub-topic

Number System

Type

Arithmetic Problem

Difficulty

Easy

Source hint

Number parameters — integer exponential limits

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