1. Question 2.
How many three-digit numbers which are divisible by 7 can be formed using the first three prime numbers (without repetition)?
Pick ONE option
A) 1
B) 2
C) 4
D) 6
Answers
Solution:
First three prime numbers are 2, 3 and 5
We need to form as many three digit numbers we can form from above given three prime numbers.
Number of ways to form three-digit number from three numbers = 3! = 6 ways
There will be 6 three-digit numbers which are as follows :-
235
253
325
523
352
532
Now, we need to check how many numbers are divisible by 7
Divisibility of 7 => We have to double the last digit of the number given and then subtract it from the remaining number. If is it divisible by 7 then whole number will be divisible by 7.
235
Divisibility of 7 =>
Double last digit 5 i.e. 10
Subtract from remaining number = 23 - 10 = 13
13 is not divisible by 7 that means whole number will not be divisible by 7.
253
Divisibility of 7 =>
Double last digit 3 i.e. 6
Subtract from remaining number = 25 - 6 = 19
19 is not divisible by 7 that means whole number will not be divisible by 7.
325
Divisibility of 7 =>
Double last digit 5 i.e. 10
Subtract from remaining number = 32 - 10 = 13
22 is not divisible by 7 that means whole number will not be divisible by 7.
523
Divisibility of 7 =>
Double last digit 3 i.e. 6
Subtract from remaining number = 52 - 6 = 46
46 is not divisible by 7 that means whole number will not be divisible by 7.
352
Divisibility of 7 =>
Double last digit 2 i.e. 4
Subtract from remaining number = 35 - 4 = 31
31 is not divisible by 7 that means whole number will not be divisible by 7.
532
Divisibility of 7 =>
Double last digit 2 i.e. 4
Subtract from remaining number = 53 - 4 = 49
49 is divisible by 7 that means whole number will be divisible by 7.
Only A) 1 i.e. 532 out of all three-digit numbers will be divisible by 7.
Given : three-digit numbers formed using the first three prime numbers (without repetition)
To find : how many numbers which are divisible by 7
Solution:
First three prime numbers are 2 , 3 & 5
6 numbers can be formed using these 3 digits with out repetition
235
253
325
352
523
532
235 = 7 * 33 + 4
253 = 7 * 36 + 1
325 = 7 * 46 + 3
352 = 7 * 50 + 2
523 = 7 *74 + 5
532 = 7 * 76
532 is the only three-digit number which is divisible by 7 can be formed using the first three prime numbers(without repetition)
only 1 three-digit number which is divisible by 7 can be formed using the first three prime numbers (without repetition)
Option A is correct
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