Test: Number Play - 2 - Class 6 MCQ

To determine which of the given numbers is a supercell in the grid [45,78,92,31,60] we first need to define what a "supercell" is in this context.

Typically, a supercell might refer to a cell in a grid or array that meets certain criteria, such as being greater than the average of its surrounding numbers. However, without a specific definition provided, we can't definitively categorize any of the numbers as a supercell.

If we assume a supercell is defined as being greater than the average of the other numbers in the grid, we can calculate the average and then check which number(s) exceed it.

Let's calculate the average of the numbers in the grid:

1. Calculate the sum of the numbers:

   45+78+92+31+60=306

2. Calculate the average:
    

3. Average
   

4. Now we can compare each number to this average:

5. 45: Not greater than 61.2
6. 78: Greater than 61.2
7. 92: Greater than 61.2
8. 31: Not greater than 61.2
9. 60: Not greater than 61.2

10. Based on this assumption, the numbers that could be considered "supercells" are 78 and 92.

     

     

The smallest 4-digit number is 1000, but when reversed, it remains the same. 1001, when reversed, becomes 1001, which is the same, but 1001 is smaller than other options when comparing original and reversed numbers.

A palindromic number reads the same forward and backward. Among the given options, only 12321 is palindromic.

Structure of a 5-digit palindrome:

A 5-digit palindrome has the form abcba‾\overline{abcba}abcba, where:

• The first digit is a,
• The second digit is b,
• The third digit is c,
• The fourth digit is b,
• The fifth digit is a.

Conditions:

1. The third digit ccc is twice the second digit bbb, i.e., c=2b.
2. The fourth digit bbb is twice the third digit ccc, i.e., b=2c.

Solving:

From the second condition, b=2c. Using this in the first condition c=2b, substitute b=2c into c=2b:

c=2(2c)=4c..

This gives a contradiction, as the only possible solution to c=4c is c=0.

If c=0, then b=2c=0. So, the palindrome becomes a0c0a‾=a000a.

Now, aaa is a non-zero digit (since it's a 5-digit number), and the only palindrome fitting this structure would be 10001.

Final Answer:

The number is 10001