Question

If $9\#3=6$ ; $15\#3=9$ ; $60\#4=32$ ; then what is the value of $27\#3=$ ?
A. $24$
B. $15$
C. $13$
D. $33$

Answer 1

Hint: In this question we have been given values of three expressions and the values of fourth expression is asked. Firstly we have to find the common pattern among the first three expressions by analyzing it. Then using the same pattern we will find the value of the fourth expression.

Complete step-by-step answer:
It is given that:
$9\#3=6$
$15\#3=9$
$60\#4=32$
So as we can see that the above can’t be obtained just by multiplying the two numbers but we can see that the first number is completely divisible by the second number but again the expression will not be satisfied.
So we will use two operations in one expression for satisfying it.
We can see that one adding both the number and dividing the sum by $2$we can satisfy the expression as follows:
$9\#3=6$
$\Rightarrow \left( 9+3 \right)\div 2=6$
Next we can see,
$15\#3=9$
$\Rightarrow \left( 15+3 \right)\div 2=9$
Further for third expression we can see,
$60\#4=32$
$\Rightarrow \left( 60+4 \right)\div 2=32$
So it can be concluded that all the expressions have one common pattern which is the sum of both digits divided by $2$.
So we can find the value of $27\#3$ as follows:
$27\#3=\left( 27+3 \right)\div 2$
$\Rightarrow 27\#3=\dfrac{30}{2}$
On dividing the above value we get,
$27\#3=15$
Hence correct option is (B)
So, the correct answer is “Option B”.

Note: This type of question can be tricky at times as it’s difficult to find out the pattern among them. So the one thing we can do is to see what all operations it can use for satisfying each expression. One thing is to be noted that one of the right side values is a multiple of left side values so it should be completely divided by one of the values on the left. We can cross check our answer as follows: As we got the answer as we can see that is divided by completely.