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

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

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New post 12 Mar 2018, 23:24
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Question Stats:

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What is the value of N ?

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

(2) N is a factor of 64 and N has exactly 4 factors.

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

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New post 13 Mar 2018, 08:37
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amanvermagmat wrote:
What is the value of N ?

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

(2) N is a factor of 64 and N has exactly 4 factors.

Posted from my mobile device



Statement I..
(0.0036)*(0.00078)*(6370)*10^n= \(36*10^{-4}*78*10^{-5}*637*10*10^n=36*78*637*10^{-4-5+1+n}\)
So n+1-4-5=0....n=8
Suff

Statement II..
64 has only one PRIME factor 2..
So 4 factors means 2^{3+1} so n =2^3=8
Suff

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

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New post 13 Mar 2018, 09:05
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1
What is the value of N ?

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

We need not solve this, it is a (constant No) * 10 ^N, hence least value of N can be found out.
Sufficient.

(2) N is a factor of 64 and N has exactly 4 factors.
Any number N has 4 factors if it is of from (prime)^3 or of the form (Prime1)*(Prime2)
since 64 is 2^6, it has only one prime factor (2)
N is 2^3

Sufficient


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

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New post 25 Mar 2018, 08:11

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

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Re: What is the value of N? (1) N is the least integer such that   [#permalink] 25 Mar 2018, 08:11
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