If ▢ and △ represent digits, is the 5-digit number 14,2▢△ divisible

Answer is C

Statement 1 : [] + ∆ = 12
Now the ordered pair can be
(9,3)(8,4)(7,5)(6,6)(5,7)(4,8)(3,9) (not sufficient)

Statement 2:
14,2[]∆ is divisible by 5,
That means ∆ is 5,
But [] can be any integer from 1to 9 (not sufficient)

Statement 1&2:
[]+∆= 12 => ∆=5
=> [] = 12-5
[] = 7

Putting value of []&∆ in 14,2[]∆
We get 14,275 which is divisible by 25.

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Asked: If \(\square\) and \(\triangle\) represent digits, is the 5-digit number \(14,2\square \triangle\) is divisible by 25.
For a number to be divisible by 25, last 2 digits should be {00,25,50,75}

(1) \(\square + \triangle = 12\)
If \((\square, \triangle)\)= (8,4); NO
Bur if \((\square, \triangle)\)= (7,5); YES
NOT SUFFICIENT

(2) The 5-digit number \(14,2\square \triangle\) is divisible by 5.
\(\triangle \)= {0,5}
If \(\square = 1\); NO
But if\( (\square, \triangle)\) = {(0,0),(2,5),(5,0),(7,5)}; YES
NOT SUFFICIENT

(1) +(2)
(1) \(\square + \triangle = 12\)
(2) The 5-digit number \(14,2\square \triangle\) is divisible by 5.
\( \triangle\) = {0,5}
\((\square, \triangle) = (7,5)\); Since \((\triangle, \square) \neq (12,0)\)
SUFFICIENT

IMO C

If □◻ and △△ represent digits, is the 5-digit number 14,2□△ divisible by 25.

(1) □+△=12
(2) The 5-digit number 14,2□△ is divisible by 5.

For digit to be divisible by 25 it should end with 25 ,50 ,75, or 00.
(1) □+△=12
Possibilities of pairs (9,3) (8,4), (7,5) (6,6)
Pair 7,5 is divisible by 25 but other pairs are not.
Insufficient

(2) The 5-digit number 14,2□△ is divisible by 5.
possible answers △ can take 0 and 5, But □ can be 1-9 any values But not all divisible by 25 like pair (4,0) (4,5) and more
Insufficient

Combining 1 and 2 :
Only pair 7,5 can be answer: Adds to 12 and divisible by 5 and pair 7,5 will be divisible by 25.
Sufficient

IMO C

The number which is divisible by 25 that number has to be divisible by 5 also. In that case state A is sufficient to ans the question. i dont agree with the solution.

This is an official question and the correct answer is C. We are not given that the number is divisible by 25, the question asks whether the number is divisible by 25.

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