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

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DS Forum Moderator
Joined: 21 Aug 2013
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Location: India
What is the value of N? (1) N is the least integer such that  [#permalink]

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12 Mar 2018, 22:24
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Difficulty:

35% (medium)

Question Stats:

78% (01:43) correct 22% (01:43) wrong based on 69 sessions

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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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13 Mar 2018, 07:37
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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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13 Mar 2018, 08:05
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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

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

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25 Mar 2018, 07:11

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.

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Re: What is the value of N? (1) N is the least integer such that &nbs [#permalink] 25 Mar 2018, 07:11
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