ruposh6240 wrote:
How many numbers between 0 and 1670 have a prime tens digit and a prime units digit?
A. 268
B. 272
C. 202
D. 112
E. 262
You can do it in many ways, two ways are
I.
A) take first thousand numbers that is 0 to 999First digit can only be 0
second digit can be any of 10 digits 0-9
third and fourth digit can be any of the 4 prime digit - 2,3,5,7
so total 1*10*4*4=160
B) take next 600 numbers that is 1000 to 1599First digit can only be 1
second digit can be any of 6 digits 0-5
third and fourth digit can be any of the 4 prime digit - 2,3,5,7
so total 1*6*4*4=96
C) take next 70 numbers that is 1600 to 1670First digit can only be 1
second digit can be only 6
third digit can be only 2, 3 or 5
and fourth digit can be any of the 4 prime digit - 2,3,5,7
so total 1*1*3*4=12
TOTAL = 160+96+12=268II.
let us see how many such digits are there in 100s as these numbers will get repeated in each 100..
so both digits can be any of 4 prime numbers - 2,3,5,7 thus 4*4=16
now there are 17 hundreds till 1700, so \(17*16=272\)
but
we are also counting 1672, 1673, 1675 and 1677 so subtract 4, thus 272-4=268
A