Question:
The number of 3 digit numbers, that are divisible by either 3 or 4 but not divisible by 48, is
The number of 3 digit numbers, that are divisible by either 3 or 4 but not divisible by 48, is
Updated On: Mar 20, 2025
- 507
- 432
- 472
- 400
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The Correct Option is B
Solution and Explanation
(A)Total 3-digit numbers:
\[
900 = 999 - 100 + 1.
\]
(B)Numbers divisible by 3:
\[
\frac{900}{3} = 300.
\]
(C)Numbers divisible by 4:
\[
\frac{900}{4} = 225.
\]
(D)Numbers divisible by both 3 and 4 (i.e., divisible by 12):
\[
\frac{900}{12} = 75.
\]
(E)Numbers divisible by either 3 or 4:
\[
300 + 225 - 75 = 450.
\]
(F) Numbers divisible by 48:
\[
\frac{900}{48} = 18.
\]
(G) Numbers divisible by either 3 or 4 but not 48:
\[
450 - 18 = 432.
\]
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Concepts Used:
Permutations and Combinations
Permutation:
Permutation is the method or the act of arranging members of a set into an order or a sequence.
- In the process of rearranging the numbers, subsets of sets are created to determine all possible arrangement sequences of a single data point.
- A permutation is used in many events of daily life. It is used for a list of data where the data order matters.
Combination:
Combination is the method of forming subsets by selecting data from a larger set in a way that the selection order does not matter.
- Combination refers to the combination of about n things taken k at a time without any repetition.
- The combination is used for a group of data where the order of data does not matter.