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

\(36=4*9\)

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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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

4+5+7+8+9+D+F= 33+D+F

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 ; divisibility rule of 4(last two digits must be divisible by 4-- 92,96 are both divisible)

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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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
Bunuel please check answer should be A..

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

A is the correct answer.

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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 )
Hence answer is A

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

Must be divisible by 9 and 4.

Divisible by 9, leaves options A and E.

Divisible by 4 leaves option A (only choice with E remains if D=F=6, but question stem says they are distinct)

IMO: A

If a number is divisible by 36 then it is divisible by 4 and 9 both.
Divisiblity of 4 last two digits of a number should be divisible by 4
Divisiblity of 9 sum of the
digits should be divisible by 9.
F can be 2 or 6
And sum the digits is 33 + D+ F
If D =2 then F = 1
Hence option A is the answer

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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

36's factorial 1,2,4,9,12,36.
457D89F would be divisible by 36 if the sum of the distinct number is divisible by the factorial 2,4,9,12
sum of the number without D and F is 33
if we added 3 it would 36 which is divisible by all the factors.

try it with others option. you will found incorrect.

The existing digits add up to 33 and theses digits add up to 6. For a number to be divisible by 36 the sum of the digits should be 9 since 3+6 adds up to 9 and is a multiple of 9. So given the existing digits adding up to 6 D+F should add upto 3. That brings down to A and E but then since D and F have to be distinct from other digits they have to be 1 and 2 adding up to 3. Hence A

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Could you do the same thing when considering 36 as 6 and 6?

Cellchat

No, we can not check divisibility of 36 by 6*6 because they are not relatively prime numbers

We need to break th enumber into parts that have no common factor with other parts other than 1

i.e. for divisibility of 24 we need to check with 8 and 3 and so on

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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Concept -
If a number is divisible by both co-primes then the number is also divisible by the product of co-primes and vice versa

36 is a product of 4 & 9 and they are co-prime numbers.

Using divisibility test of 4 - last two digits should be divisible by 4
92 & 96 are divisible by 4
F has two values 2 and 6

Using divisibility test of 9 -
Sum of the number should be divisible by 9
4+5+7+8+9+D+F = 33 +D +F
For two values of F
Sum is 33 + 2 = 35 &
33+6 =39
Now
35 + 1 = 36 divisible by 9
39 + 6 = 45 divisible by 9

Two sets of D & F are -
(2,1) & (6,6)

But the question states that the two numbers are distinct hence answer is 2+1=3!

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457D89F/36 , Remainder = 0, D+F = ?

Divisible by 36 => divisible by both 4 and 9

1) Divisibility of 4 => 9F must be divisible by 4
Since F is digit (0-9), F can have only 2 values i.e. 2 and 6, so that 9F will be divisible by 4.
2) Divisibility by 9 => sum of all the digits must be divisible by 9.
=> 4+5+7+D+8+9+F = 33+D+F must be divisible by 9.
Now, Since we know F can be 2 and 6 only,
(35+D)/9 and (39+D)/9 should give remainder as 0
Since D is a digit, check for the values for which (35+D)/9 and (39+D)/9 gives remainder as 0
You will see (35+D)/9 will yield a remainder as 0 for D = 1 and (39+D)/9 will yield a remainder as 0 for D = 6.
=> (D,F) can be (1,2) and (6,6)
But, D and F are distinct digits (as per question stem)
=> (D,F) = (1,2)
=> D+F = 3 (A)

Multiple of 3 and 2 only if sum is divisible by 3 and last digit 2

both is satisfied id D=1; F=2

THerefore IMO A

To be divisible by 36, a number must be divisible both by 4 and 9. A number is divisible by 4 if its last two digits are divisible by 4 and divisible by 9 if the sum of its digits is divisible by 9. In order for the number 457D89F to be divisible by 4, the last two digits must be 92 or 96. The sum of its digits other that D and F is 33, so the sum of its all digits must be 36 or 45 in order for the number be divisible by 9. If it is 45, then last digit must be 6. However, if the last digit F is 6, then D also must be 6. But since we are given that these digits are distinct, the sum of the digits cannot equal to 45. So the sum of the digits of the digits of the number must be 36. In this case the last digit of the number must be 2 and digit D must be 1. D+F=1+2=3 A)

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

if the Number is divisible by 36 means the number is divisible by 2,3,4,9
if number is divisible by 4 means 9F is divisble by 4 means F-2,6
if number is divisible by 3 then sum of digit is divisible by 3 =4+5+7+D+8+9+F= 17+16+D+F=33+D+F for this D+F is 3,12
if F= 2 then D is 1 only
if F=6 then D is 6 only.
But the question said the digit are distinct so D+F=3

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