I am a 2-digit number over 50. When you put me in groups of 7, two are left over. The sum of my digits is 11. What number am I?

It is between 60 and 70, I bet

Let's solve the problem step by step:

Step 1: Start by listing the possible 2-digit numbers over 50 that have their digits add up to 11.
These numbers are: 56, 65, 74, 83, 92 (since we are looking for a 2-digit number, we ignore 11).

Step 2: Check if any of these numbers, when divided by 7, leave a remainder of 2.
Let's test each of the numbers:

56 ÷ 7 = 8 remainder 0
65 ÷ 7 = 9 remainder 2
74 ÷ 7 = 10 remainder 4
83 ÷ 7 = 11 remainder 6
92 ÷ 7 = 13 remainder 1

Step 3: The number that we're looking for should be the one that, when divided by 7, leaves a remainder of 2. So, the number is 65.

Therefore, the number you are is 65.

To find the answer to this question, let's break it down step by step.

We are looking for a 2-digit number over 50, so let's start by listing down all the possible 2-digit numbers greater than 50:
51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, ...

Now, let's focus on the second clue. When you put the number in groups of 7, two are left over. This means that when you divide the number by 7, there will be a remainder of 2.

Next, we are given that the sum of the digits of the number is 11. This means that the sum of the tens digit and the units digit should equal 11.

Now, let's go through each of the possible numbers from our list and apply these conditions to find the correct number.

Starting with 51:
51 divided by 7 gives a remainder of 2. (Matches the second clue)
The sum of its digits (5 + 1) equals 6. (Doesn't match the third clue)

Moving to the next number, 52:
52 divided by 7 gives a remainder of 3. (Doesn't match the second clue)

We continue this process until we find the correct number that satisfies all the given conditions.

After going through the list, we find that the number that satisfies all the conditions is 57. Let's check:
57 divided by 7 gives a remainder of 2 (matches the second clue).
The sum of its digits (5 + 7) equals 12 (matches the third clue).

Therefore, the answer is 57. You are a 2-digit number over 50.