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How many numbers between 0 and 1670 have a prime tens digit

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ivycation2024

Joined: 15 Apr 2024

Last visit: 05 Feb 2026

Posts: 13

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07 Jul 2025, 03:04

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Could you explain why it's (3/4) * 16?

KarishmaB

Galiya

Dear all
help me please to solve the problem below:

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

We have 10 digits (0 - 9) and 4 of them are prime (2, 3, 5, 7). So (4/10)th of consecutive numbers will have prime digits in their unit's place.
Similarly, if we want prime digits in ten's place, again (4/10)th of 100 consecutive numbers will have prime digits in ten's place.

So in 100 consecutive numbers, (4/10)*(4/10) = 16/100 will have prime digits in both unit's and ten's places.

Number of numbers with both units and tens digit prime in the first 1600 = (16/100) * 1600 = 256
Number of numbers with both units and tens digit prime in leftover 70 numbers = (3/4) * 16 = 12

Required number of numbers = 256 + 12 = 268