Question

If 100 = 4, 1000= 8 then 10000= ?
16
14
32
10

Answer 1

Given:

100 = 4, 1000= 8

To find:

10000= ?

Solution:

The given sequence is 100 = 4, 1000= 8.

Now, we need to find the number for 10000=?

• When we multiply 100 by 10, we get 1000

         => 100 x 10 = 1000

• When we multiply 1000 by 10, we get 10000

        => 1000 x 10 = 10,000

• Now, when we multiply the number 4 by 2, we get 8.

        => 4 x 2 = 8

• In the same way, multiply the number 8 by 2, we get 16.

        => 8 x 2 = 16.

So, 10000 = 16.

ALTERNATE WAY:

100 = 4, 1000= 8 then 10000=?

100 = 4

=> 10² = 2²

1000= 8

=> 10³ = 2³

10000 = ?

=> $10^{4} = 2^{4}$

Hence, If 100 = 4, 1000= 8 then 10000= 16

Answer 2

Answer :- 16 .

Logic :- Convert binary form into decimal form .

Explanation :-

• Converting into Decimal form starting from right = D1 * 2⁰ + D2 * 2¹ + D3 * 2² + D4 * 2³ + D5 * 2⁴ _______ .

100 = 4

→ 0 * 2⁰ + 0 * 2¹ + 1 * 2²

→ 0 + 0 + 4

→ 4

similarly,

1000 = 8

→ 0 * 2⁰ + 0 * 2¹ + 0 * 2² + 1 * 2³

→ 0 + 0 + 0 + 8

→ 8

then , converting next binary form into decimal form we get,

10000 = ?

→ 0 * 2⁰ + 0 * 2¹ + 0 * 2² + 0 * 2³ + 1 * 2⁴

→ 0 + 0 + 0 + 0 + 16

→ 16 (Ans.)

More examples :-

→ 1110 = 0 * 2⁰ + 1 * 2¹ + 1 * 2² + 1 * 2³ = 0 + 2 + 4 + 8 = 14 .

→ 1111 = 1 * 2⁰ + 1 * 2¹ + 1 * 2² + 1 * 2³ = 1 + 2 + 4 + 8 = 15 .

Points to remember :- Given question is a logical question of reasoning from chapter Matrix . Always remember that in matrix we can't make series like use of different numbers in given terms .

Example :-

→ 100 * 10 = 1000 => 1000 * 10 = 10000

and,

→ 4 * 2 = 8 => Then next will be , 8 * 2 = 16 .

as we can see that, In first we multiplied with 10 and in next we multiplied with 2 .

In matrix we must add, subtract, multiply or divide with same numbers .

Hence, correct answer with suitable logic of binary and decimals numbers will be 16 .

Learn more :-

423:24::534:60::752:70::245:?

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Use inductive reasoning to determine the next two terms in the sequence:

A , 6 , D , 16 , H , 46 , M , 136

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