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The number by which $− 2 3 − 3$ should be divided so that the quotient is $49 − 2$ is:

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− 2 3

− 4 3

− 5 3

− 9 3

answer is A.

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Detailed Solution

Given a number

− 2 3 − 3

.
Let the number = x.
According to the question,

− 2 3 − 3 ÷ x = 49 − 2

Now, using property of exponents

a b − n = b a n

− 3 2 3 ÷ x = 942

⇒ − 3 2 3 × 1 x = 942

Simplifying,

3 × 3 × 3 − 2 × − 2 × − 2 × 1 x = 9 × 9 4 × 4

⇒ − 27 8 × 1 x = 9 × 9 4 × 2 × 2

⇒ − 27 8 × 1 x = 9 × 9 8 × 2

⇒ 1 x = 9 × 9 8 × 2 ÷ − 27 8

⇒ 1 x = 9 × 9 8 × 2 × 8 − 27

⇒ 1 x = 3 − 2

⇒ 3 x = − 2

⇒ x = − 2 3

The value of

x = − 2 3

.
Hence, option 1 is correct.

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