Question:medium

The sum of the numbers from 1 to 100, which are not divisible by 3 and 5.

Show Hint

Find the sum 1 to 100, then take away the sum of multiples of 3 and the sum of multiples of 5.
Updated On: Jul 13, 2026
  • 2946
  • 2732
  • 2632
  • 2317
Show Solution

The Correct Option is D

Solution and Explanation

Step 1: Use the natural number sum formula for the whole range.
The sum of the first $n$ natural numbers is $\frac{n(n+1)}{2}$. For the numbers 1 to 100:
\[ 1+2+\cdots+100 = \frac{100\times101}{2} = 5050 \]

Step 2: Add up the multiples of 3 by factoring out the 3.
The multiples of 3 from 3 to 99 are $3\times1, 3\times2,\ldots,3\times33$, so their sum is 3 times the sum of the first 33 natural numbers:
\[ 3(1+2+\cdots+33) = 3\times\frac{33\times34}{2} = 3\times561 = 1683 \]

Step 3: Add up the multiples of 5 by factoring out the 5.
The multiples of 5 from 5 to 100 are $5\times1,\ldots,5\times20$, so their sum is 5 times the sum of the first 20 natural numbers:
\[ 5(1+2+\cdots+20) = 5\times\frac{20\times21}{2} = 5\times210 = 1050 \]

Step 4: Remove both sets from the full sum.
Take the numbers that are multiples of 3 and the numbers that are multiples of 5 out of the total 5050:
\[ 5050 - 1683 - 1050 = 2317 \]
This 2317 is the sum of every number between 1 and 100 that is not divisible by 3 and not divisible by 5.

Final Answer:
The required sum is 2317.
\[ \boxed{2317} \]
Was this answer helpful?
0

Top Questions on Number System

Questions Asked in XAT exam

Read the scenario and answer the question:
The upper hinge of a dataset is the median of all the values to the right of the median of the dataset in an ascending arrangement, while the lower hinge of the dataset is the median of all the values to the left of the median of the dataset in the same arrangement.
For example, consider the dataset 4, 3, 2, 6, 4, 2, 7. When arranged in the ascending order, it becomes 2, 2, 3, 4, 4, 6, 7. The median is 4 (the bold value), and hence the upper hinge is the median of 4, 6, 7, i.e., 6. Similarly, the lower hinge is 2. 
A student has surveyed thirteen of her teachers, and recorded their work experience (in integer years). Two of the values recorded by the student got smudged, and she cannot recall those values. All she remembers is that those two values were unequal, so let us write them as A and B, where A < B. The remaining eleven values, as recorded, are: 5, 6, 7, 8, 12, 16, 19, 21, 21, 27, 29. Moreover, the student also remembers the following summary measures, calculated based on all the thirteen values: 
Minimum: 2
Lower Hinge: 6.5 
Median: 12 
Upper Hinge: 21 
Maximum: 29
View Solution
Read the following scenario and answer the questions that follow.
A T20 cricket match consists of two teams playing twenty overs each, numbered 1 to 20. The runs scored in any over is a non-negative integer. The run rate at the end of any over is the average runs scored up to and including that over, i.e., the run rate at the end of the kth over is the average number of runs scored in overs numbered \(1, 2, …, k,\) where \(1 \leq k \leq 20, k\) a positive integer.
The following table indicates the run rate of a team at the end of some of the overs during a T20 cricket match (correct up to 2 decimal places), where \(1 \leq N – 2 < N + 6 \leq 20\), N a positive integer. It is also known that the team did not score less than 6 runs and more than 15 runs in any over.
Over NumberRun Rate
N-28.00
N7.43
N+28.11
N+48.45
N+68.08
View Solution