Question

Which number(s) must be subtracted from $3173$ to make it divisible by $8?$

• A. $29$
• B. $50$
• C. $805$
• D. $1610$

Answer 1

Answer: (A), (C)

$805$

When we divide last three digits of $3173$ by 8, we get 5 as remainder.

That means, if we subtract 5 from the number i.e. $3173-5=3168$, then the resulted number i.e. $3168$ would be divisible by 8.

Now, if we subtract 8 or mutiples of 8 from $3168$, resulted difference would also be divisible by 8.

Hence, if we subtract $(5+8n,\text{where}n\text{is an integer})$ from 3173, the resulted difference would definately be divisible by 8.

Option(a):
$\because 29=5+8\times 3$
Hence, $(3173-29)$ is divisible by 8.

Option(b):
$\because 50\ne 5+8\times 5$
Hence, $(3173-50)$ is not divisible by 8.

Option(c):
$\because 805=5+8\times 100$
Hence, $(3173-805)$ is divisible by 8.

Option(d):
$\because 1610\ne 5+8\times 200$
Hence, $3173-1610$ is not divisible by 8.