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# D and F represent two distinct digits. If the number 457D89F is divisi

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Math Expert
Joined: 02 Sep 2009
Posts: 61537
D and F represent two distinct digits. If the number 457D89F is divisi  [#permalink]

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01 Nov 2019, 03:49
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12
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Difficulty:

75% (hard)

Question Stats:

55% (02:10) correct 45% (02:29) wrong based on 219 sessions

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D and F represent two distinct digits. If the number 457D89F is divisible by 36, what is the value of (D+F)?

A. 3
B. 6
C. 9
D. 10
E. 12

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Posts: 8254
Re: D and F represent two distinct digits. If the number 457D89F is divisi  [#permalink]

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01 Nov 2019, 07:37
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1
Bunuel wrote:
D and F represent two distinct digits. If the number 457D89F is divisible by 36, what is the value of (D+F)?

A. 3
B. 6
C. 9
D. 10
E. 12

Are You Up For the Challenge: 700 Level Questions

$$36=4*9$$

Divisibility rule of 9
The digits add up to a multiple of 9..
So, 4+5+7+D+8+9+F=33+D+F
The immediate multiple above 33 is 36, so D+F=3, or D+F=3+9=12

To check between the two check for --
Divisibility rule of 4
The last two digits should be divisible by 4, so 9F should be divisible by 4...
F can be 2 or 6 as 92 and 96 are divisible by 4

Now D+F=3...F can be 2, so D=1...Possible
D+F=12...F can be 6, so D is 6, but D and F are DISTINCT...NOT Possible

A
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Re: D and F represent two distinct digits. If the number 457D89F is divisi  [#permalink]

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01 Nov 2019, 04:18
3
D and F represent two distinct digits. If the number 457D89F is divisible by 36, what is the value of (D+F)?

36= 9*4 therefore when we add up the digits the number should be divisible by 9

A. 3----33+3=36
B. 6---- 33+6=39
C. 9---33+9=42
D. 10---33+10=43
E. 12---33+12=45

therefore options A and E are divisible by 9

between options A and E 457D89F---must also be divisible by 4

F can take the values- 2, 6

3= 1+2, 3+0--- therefore D=1 and F=2
12= 9+3, 8+4,7+5------ none of these sums contain 2 or 6

option A is the correct option!!
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Re: D and F represent two distinct digits. If the number 457D89F is divisi  [#permalink]

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Updated on: 02 Nov 2019, 01:28
Bunuel wrote:
D and F represent two distinct digits. If the number 457D89F is divisible by 36, what is the value of (D+F)?

A. 3
B. 6
C. 9
D. 10
E. 12

factor of 36 ; 2^2*3^2
so the no has to be even and divisible by 9
457D89F
we can hae 4571892 ; D+F ; 1+2 ; 3
IMO A

Originally posted by Archit3110 on 01 Nov 2019, 03:56.
Last edited by Archit3110 on 02 Nov 2019, 01:28, edited 1 time in total.
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Re: D and F represent two distinct digits. If the number 457D89F is divisi  [#permalink]

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01 Nov 2019, 04:25
Between A and E....since the number has to be divisible by 9 also. E is a contender . Hoewever, per the restrictions of question and considering the fact that last two digits have to be divisible by 4 as well, possible combinations are

90 that means F is 0 and D is 12 but D shd be single digit. Discard
92 Discard, same reasoning as above
96 . Discard as this makes D=F=6

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Re: D and F represent two distinct digits. If the number 457D89F is divisi  [#permalink]

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03 Nov 2019, 08:36
To be divisible by 36, it has to be divisible by 9 &4
to be divisible 4, last 2 digits should be divisible 4 which means it can be either 92 or 96. Hence F could be 2 or 6
to be divisible by 9, sum should be divisible 9 i.e 33+D+F should be divisible by 9
if F =2 D=1 F+D =3
if F=6 D=7 F+D =13 (Not an option )
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Re: D and F represent two distinct digits. If the number 457D89F is divisi  [#permalink]

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16 Nov 2019, 06:53
Bunuel wrote:
D and F represent two distinct digits. If the number 457D89F is divisible by 36, what is the value of (D+F)?

A. 3
B. 6
C. 9
D. 10
E. 12

Are You Up For the Challenge: 700 Level Questions

Since 457D89F is divisible by 9
(4+5+7+D+8+9+F) is divisible by 9
D + F + 6 is divisible by 9.
Only A 3 & E 12 satisfy the condition

Since 457D89F is divisible by 4
9F is divisible by 4
F is 2 or 6
If F = 2; D = 1; D+F=3 since D=10 is not possible
If F = 6; D = 6; Not possible since D & F are different digits.

D + F + 3

IMO A
Re: D and F represent two distinct digits. If the number 457D89F is divisi   [#permalink] 16 Nov 2019, 06:53
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