GATE ECE 2018 | GA | Question: 3

Question

If the number $715\blacksquare423$ is divisible by $3(\blacksquare$  denotes the missing digit in the thousandths place$),$ then the smallest whole number in the place of $\blacksquare$ is _________.

• A. $0$
• B. $2$
• C. $5$
• D. $6$

Comments

Simply use options and virtual calculator.

Answer 1

Divisibility rule of 3: 

A number is divisible by 3 if sum of its digits is divisible by 3.

Let the digit in thousands place be $x$.

$7+1+5+x+4+2+3= 22+x$

Smallest possible value of $x$ so that the sum is divisible by $3$ is $2$ ($24\mod 3=0$)

Hence option (B) is correct answer

Comments

wow. this is faster than using virtual calc. Thanks!

Answer 2

We know that the Divisibility Rule of 3 says that if the sum of the digits are a multiple of 3 or can be divided by 3 then the digit itself can be divided by 3

Now, we're assuming the missing number to be x

So, Sum = 7 + 1 + 5 + x + 4 + 2 + 3 = 22 + x

Now, we'll be verifying all the options

Option A) 0 , then  Sum = 22 -----> Discarded as 22 cannot be divided by 3

Option B) 2 , then  Sum = 24 -----> Accepted as 24 is a multiple of  3

Option C) 5 , then  Sum = 27 -----> Accepted as 27 is a multiple of 3

Option D) 6 , then  Sum = 28 -----> Discarded as 28 cannot be divided by 3

Now the question tells us that in the place of x we can only accept the smallest whole number

So, the feasible answer would be 2 i.e option B)

Answer 3

Sum the known digits and lets take unknown as x 

7 + 1 + 5 + x + 4 + 2 + 3 = 22 + x 

if we take x = 2 then total sum is 7 + 1 + 5 + 2 + 4 + 2 + 3 = 24 which is divisible by 3 (24 mod 3 = 0)

and if x = 5 then total sum is 7 + 1 + 5 + 5 + 2 + 4 + 2 + 3 = 27 it is also divisible by 3 ( 27 mod 3 =0 )

In question smallest possible value of x asked

so correct answer for x is 2 which is OPTION : B

Answer 4

We are given the number $715\square423$ and asked to find the smallest digit $\square$ such that the number is divisible by 3.

Now check options

If $\square=0$, then $7150423$ is not divisible by 3.

If $\square=2$, then $7152423$ is divisible by 3.

If $\square=5$, then $7155423$ is divisible by 3.

If $\square=6$, then $7156423$ is not divisible by 3.

Both 2 and 5 make the number divisible by 3. Since the question asks for the smallest such digit, the answer is $2$

 

Answer 5

Answer is B (2)