Free Practice Question
PS · Problem Solving
705-805
Combinations
How many integers between 0 and 1570 have a prime tens digit and a prime units digit?
Answer Choices
Correct answer marked belowA
295
252
Correct
C
236
D
96
E
76
See the full step-by-step explanation
You can see the correct answer above. Sign in for free to unlock the complete worked solution.
Track your performance and improve
Get detailed analytics, unlock full explanations, and move up difficulty tiers as you practice.
Explanation
Preview
Official Explanation
Official
There are 4 single digit prime numbers: 2, 3, 5 and 7.
Hence, last two digits (tens and units) can take different values: 22, 23, ..., 77.
So, in each hundred there are 16 such numbers.
In 16 hundreds there will be such numbers, but 4 out of them will be more than 1570, namely: 1572, 1573, 1575 and 1577.…
Hence, last two digits (tens and units) can take different values: 22, 23, ..., 77.
So, in each hundred there are 16 such numbers.
In 16 hundreds there will be such numbers, but 4 out of them will be more than 1570, namely: 1572, 1573, 1575 and 1577.…
Read the full explanation
Sign in for free to see the complete step-by-step solution to this question.
Comments
Sign in to join the discussion
No comments yet
Be the first to share your thoughts and help others understand it better.
Sign in to commentWhat this question tests
What it tests
Whether you can count arrangements and selections correctly — permutations vs. combinations.
Common trap
Overcounting: treating a selection as ordered when order does not matter, or forgetting to divide by duplicates.
Details
Difficulty
705-805
Type
PS
Category