If 7ab8 is a 4-digit number that is divisible by 12 and a=b+1, then wh

Question

If 7ab8 is a 4-digit number that is divisible by 12 and a=b+1, then what can be the value of a+b?
(A) 3
(B) 5
(C) 9
(D) 12
(E) 17

gurmukh · Answer

Value of b can be 0,4 and 8 there fore value of a can be 1, 5 and 9 respectively.
Out of this only possible sum of a and b is 4+5 = 9.
Divisiblity of 4, last two digits should be divisible by 4
Divisiblity of 3, sum of the digits should be divisible by 3.
Option C is the answer

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ArunSharma12 · Answer

7ab8 is divisible by 12.
b8 is divisible by 4. so b can be

a + b = 3K (multiple of 3), as 7ab8 is divisible by 3
this means correct option must be a multiple of 3. ie option A,C and D can be the correct option.

Given: a =b +1. a,b are consecutive integers and the sum should be odd. option D cancels out.
a+b = 3 (a,b)=(2,1); but b can not be 1 as 18 is not divisible by 4.
a+b = 9 (a,b)=(5,4); this is the correct pair for (a,b)
Ans: C

preetamsaha · Answer

If 7ab8 is a 4-digit number that is divisible by 12 and a=b+1, then what can be the value of a+b?
divisible by 12 => divisible by 3 ,4. 
so, sum of the digits divisible by 3 .
since, 7+8=15 (divisible by 3 ) 
a+b must be divisible by 3 . 
let , a+b =3 and a=b+1 
so, b= 1 ( b8 i.e. 18 not divisible by 4 , rejected ) 
let , a+b =6 and a=b+1 
so, b= fraction (rejected ) 
let , a+b =9 and a=b+1 
so, b= 4 (48 divisible by 4 ,accepted )

a+b =9 
 correct answer C

MagnusSamIBA · Answer

Given that 7ab8 must be divisible by 12, we know it must be divisible by both 3 and 4.

For divisibility by 4, the last two digits, "b8", must be divisible by 4. Therefore, b can only be 0, 4, or 8.

For divisibility by 3, the sum of the digits 7 + a + b + 8 must be divisible by 3. Since 7 + 8 = 15 is divisible by 3, the sum a + b must also be divisible by 3.

Since a = b + 1, we now check values for b:

b must make "b8" divisible by 4,

a + b must be divisible by 3.

When b = 4, a becomes 5 (since a = b + 1). This satisfies both conditions: 48 is divisible by 4, and 5 + 4 = 9 is divisible by 3.

Thus, a + b = 9.

Answer: C (9)

If 7ab8 is a 4-digit number that is divisible by 12 and a=b+1, then wh

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If 7ab8 is a 4-digit number that is divisible by 12 and a=b+1, then wh

Prep Toolkit

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