Question

The number 20,2Δ8 is a 5-digit number with the tens digit covered by a triangle. Given that the number is divisible by 7, what is its tens digit? I GIVE BRAINLIEST!

Answer 1

I agree with the other person. The answer is 5.

Here's how we can check to see if a number is divisible by 7.

• Step 1) Remove the units digit to form a truncated (aka shrunken) number.
• Step 2) Double the digit we removed.
• Step 3) Subtract that result from the truncated number.

If the result of the third step is a multiple of 7, then so is the original value itself. We can repeat the steps to progressively shrink the values down so we have something more manageable.

---------------

Let's use those steps to see if 20,258 is a multiple of 7

• Step 1) Remove the '8' from 20258 to to get 2025
• Step 2) Double the 8 to get 16
• Step 3) Subtract 16 from 2025 to get 2025 - 16 = 2009

It's not clear if 2009 is a multiple of 7 or not; however, we can apply the same three steps to shrink the number down. This process can be repeated as many times as you like.

• Step 1) Remove the 9 from 2009 to get 200
• Step 2) Double the 9 to get 18
• Step 3) Subtract to get 200-18 = 182

Like before, the result 182 is fairly big and it's not clear if we have a multiple of 7. Luckily, we only need to do one more round of those steps.

• Step 1) Remove the 2 from 182 to get 18
• Step 2) Double that value we removed to get 4
• Step 3) Subtract to get 18-4 = 14

The result 14 is a multiple of 7, which means that 182 is also multiple of 7. By a domino-like chain reaction, the values 2009 and 20258 are also multiples of 7.

Notes:

• 182 = 26*7
• 2009 = 287*7
• 20258 = 2894*7

---------------

We've just verified that 20258 is a multiple of 7. Let's go over an example a non-multiple of 7. I'll add 1 to the number 20258 so we are guaranteed that it cannot possibly be a multiple of 7. Doing the round of steps as shown above should get us to some smaller non-multiple of 7.

• Step 1) Remove the 9 from 20259 to get 2025
• Step 2) Double the 9 to get 18
• Step 3) Subtract: 2025 - 18 = 2007

Repeat the steps until we get something more manageable

• Step 1) Remove the 7 from 2007 to get 200
• Step 2) Double the removed digit: 7*2 = 14
• Step 3) Subtract: 200-14 = 186

Let's do one more round

• Step 1) Remove the 6 from 186 to get 18
• Step 2) Double the digit removed: 2*6 = 12
• Step 3) Subtract: 18-12 = 6

The value 6 is not a multiple of 7, and neither are 186 and 2007 and 20259.

If you have your calculator with you, then you should see that dividing any of those values over 7 will not lead to a whole number result.

• 186/7=26.57
• 2007/7=286.71
• 20259/7=2894.14

This is a fairly quick and efficient way to check divisibility by 7 if you are in a hurry.

Answer 2

Answer:

20258. The missing digit is a 5

Step-by-step explanation:

Ok, let's write the number in a more creative way.  That's $21 000 - 700 = 20 300$,  minus something else. That something else has to be a multiple of 7, be less than 100, and has to end with a 2. Now start writing down the multiplication table for 7 and find how many of them ends with 2. 42 comes to mind, and that's the only one. (you can go up to 7x14=98 before having one digit too many).

That brings your number to be written as $21000-700 -42 = 20258.$

In theory there was a criteria to see if a number was divisible by 7, but I've never learned it.