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# What is the value of N? (1) N is the least integer such that

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Re: What is the value of N? (1) N is the least integer such that [#permalink]

Solution

We need to find the value of N.

Since we are not given much information, let us analyse both the statements one by one.

Statement-1N is the least integer such that (0.0036) * (0.00078) * (6370) * 10^N is an integer.

Let us write $$(0.0036) * (0.00078) * (6370) * 10^N$$ in simplified form.

•$$= (0.0036) * (0.00078) * (6370) * 10^N$$
• = $$(0.0036) * (0.00078) * (637) * 10^N*10$$
• = $$(0.0036) * (0.00078) * (637) * 10 ^{(N+1)}$$
• = $$(36* 10^{-4}) * (78*10^{-5}) *637* 10^{(N+1)}$$
• = $$(36) * (78 ) *637* 10^{(N+1-4-5)}$$
• = $$36*78* 637*10^{(N-8)}$$

The power of 10 cannot be negative. Hence, for the least value of N, N-8 should be equal to 0.
• $$N-8=0$$
• $$N=8$$

Therefore, Statement 1 alone is sufficient to answer the question.

Statement-2N is a factor of 64 and N has exactly 4 factors.

A number having $$4$$ factors can be written in the two forms.

• $$N= p1* p2$$, where $$p1, p2$$are prime numbers
• $$N= p^{3}$$, where $$p$$ is a prime number.

Since$$N$$ is a factor of $$64$$, therefore $$N$$ has only $$1$$prime factor, that is $$2$$.
Hence, $$N= 2^3=8$$

Therefore, Statement 2 alone is sufficient to answer the question.

Thus, we can find the answer by each of the statement alone.