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

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Math Expert
Joined: 02 Sep 2009
Posts: 64175
If ▢ and △ represent digits, is the 5-digit number 14,2▢△ is divisible  [#permalink]

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23 May 2020, 07:47
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35% (medium)

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71% (01:25) correct 29% (01:10) wrong based on 34 sessions

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If $$\square$$ and $$\triangle$$ represent digits, is the 5-digit number $$14,2\square \triangle$$ is divisible by 25.

(1) $$\square + \triangle = 12$$
(2) The 5-digit number $$14,2\square \triangle$$ is divisible by 5.

DS20434

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Re: If ▢ and △ represent digits, is the 5-digit number 14,2▢△ is divisible  [#permalink]

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23 May 2020, 08:42
1
Sir statement 2 is making five digit no. Kindly confirm whether its a square on unit place or triangle

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Posts: 64175
Re: If ▢ and △ represent digits, is the 5-digit number 14,2▢△ is divisible  [#permalink]

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23 May 2020, 09:03
1
yashikaaggarwal wrote:
Sir statement 2 is making five digit no. Kindly confirm whether its a square on unit place or triangle

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Edited. It's: (2) The 5-digit number $$14,2\square \triangle$$ is divisible by 5.
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Re: If ▢ and △ represent digits, is the 5-digit number 14,2▢△ is divisible  [#permalink]

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23 May 2020, 09:20
1
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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If ▢ and △ represent digits, is the 5-digit number 14,2▢△ is divisible  [#permalink]

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23 May 2020, 09:44
2
Bunuel wrote:
If $$\square$$ and $$\triangle$$ represent digits, is the 5-digit number $$14,2\square \triangle$$ is divisible by 25.

(1) $$\square + \triangle = 12$$
(2) The 5-digit number $$14,2\square \triangle$$ is divisible by 5.

DS20434

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
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Re: If ▢ and △ represent digits, is the 5-digit number 14,2▢△ is divisible  [#permalink]

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23 May 2020, 12:54
If □◻ and △△ represent digits, is the 5-digit number 14,2□△ is 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
Re: If ▢ and △ represent digits, is the 5-digit number 14,2▢△ is divisible   [#permalink] 23 May 2020, 12:54

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

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