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

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.

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