Question

If 215y2 is a multiple of 3 and 11, where y is a single digit number, then find the value of y​

Answer 1

Answer:

1

Step-by-step explanation:

Since the number 21y5 is a multiple of 9.

So, the sum of its digits 2+1+y+5=8+y is a multiple of 9.

∴(8+y) is either 0 or 9 or 18 or ...

Since y is a digit, so (8+y) must be equal to 9.

i.e., 8+y=9

⇒y=9−8=1

Answer 2

Final Answer:

The correct value of the single-digit number y​ in the number 215y2 which is a multiple of 3 and 11, is 8.

Given:

The number 215y2 is a multiple of 3 and 11, where y is a single-digit number.

To Find:

The value of the single-digit number y​ in the number 215y2 that is a multiple of 3 and 11.

Explanation:

Note the following vital points.

• The number which is a multiple of 3 must be divisible by 3.
• The number which is a multiple of 11 must be divisible by 11.
• The number which is divisible by 3, has the sum of its constituent digits divisible by 3.
• The number which is divisible by 11, has the difference between the sum of its constituent digits in the odd places and the sum of its constituent digits in the even places, is divisible by 11.

Step 1 of 3

Since, the number 215y2 is to be divisible by 3, write the following equation, where p is any natural number.

$2+1+5+y+2=3p\\10+y=3p$

Step 2 of 3

Since, the number 215y2 is to be divisible by  11, write the following equation, where p is any natural number.

$(2+5+2)-(1+y)=11p\\9-1-y=11p\\8-y=11p$

Step 3 of 3

By inspection, the only single-digit number satisfying the above two formed equations is 8, which is also confirmed by the following observations.

• $21582\div3=7194$
• $21582\div11=1962$

Therefore, the required value of the single-digit number y​ in the number 215y2 which is a multiple of 3 and 11, is 8.

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