Question

1. If X and Y are the two digits of the number 347XY such
that the number is completely divisible by 80, then what
is the value of X + Y?
यदि x तथा Y एक संख्या 347XY के दो अंक इस प्रकार हैं कि
संख्या 80 से पूर्णत: विभाजित हो जाती है, तो x +Y का मान क्या है?
(a) 2
(b) 4
(c) 6
(d) 8​

Answer 1

We have:-

• A number 347XY where X is the ten's digit and Y is the unit's digit.
• It is completely divisible by 80.

What to FinD:-

• Value of X + Y?

Solution:-

For solving these kind of questions, we generally make use of divisibility rules. But these rules is not available for all the larger numbers. Hence, divisibility of larger composite numbers is determined if it is divisible by the product of its coprime pair of factors.

• Coprime factors of 80 = 16,5

Then, Y can be 0/5 but 5 is not possible since it is to be made divisible by 80. Hence, Y = 0$.$

Now, our number is 347XY. For divisibility of 16, the last 4 digits of the number should be divisible by 16. By little hit Trial division, we can find that when X = 2, 4720 (last 4 digits) is divisible by 16.

Therefore:-

• For X = 2 and Y = 0, the number is divisible by 16.

• And the value of X + Y would be 2 + 0 = 2 (Option A)

Answer 2

Step-by-step explanation:

Given :

• If X and Y are the two digits of the number 347XY .

• the number is completely divisible by 80,

To Find :

• what is the value of X + Y?

Solution :

Since the number is divisible by 80 which is a multiple of 10, the last digit ‘Y’ is 0.

x = 2, 34720 is exactly divisible by 80.

According to the Question :

x + y

2 + 0 = 2

• Hence the x + y = 2