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# Is the positive integer n a multiple of 20?

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Manager
Joined: 18 Feb 2019
Posts: 163
Location: India
GMAT 1: 490 Q47 V13
GPA: 3.6
Is the positive integer n a multiple of 20?  [#permalink]

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18 Feb 2019, 11:01
1
2
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Difficulty:

35% (medium)

Question Stats:

67% (01:29) correct 33% (01:34) wrong based on 24 sessions

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Is the positive integer n a multiple of 20?

(1) n^3 is a multiple of 60.
(2) 10 is a factor of square root on n.
Manager
Status: Manager
Joined: 27 Oct 2018
Posts: 207
Location: Malaysia
GPA: 3.67
WE: Pharmaceuticals (Health Care)
Re: Is the positive integer n a multiple of 20?  [#permalink]

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18 Feb 2019, 13:38
Question: does $$n = 2^2*5^1*k?$$

Statement 1:
$$n^3 = 60m$$
$$n^3 = 2^2*5^1*3^1*m$$
since n is a positive integer, $$n = 2^1*5^1*3^1*q$$ , so n is for sure a multiple of 30.
We don't know whether q is an even number, so insufficient.

Statement 2:
$$\sqrt{n} = 10p$$
$$n = 100p^2$$ , so n is divisible by 20 regardless of the value of p --> sufficient

B
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Manager
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Location: India
GMAT Date: 03-15-2015
WE: Education (Education)
Re: Is the positive integer n a multiple of 20?  [#permalink]

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18 Feb 2019, 22:09
Statement 1 :
$$n^3=1000$$
n=10
Or
$$n^3=4000 , n=20$$
Not sufficient
Statement 2 :
$$\sqrt{n}=10k$$
$$n=100k^2$$
Sufficient
B
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Re: Is the positive integer n a multiple of 20?  [#permalink]

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18 Feb 2019, 22:24

Solution

Given:
• The number n is a positive integer

To find:
• Whether n is a multiple of 20 or not

Approach and Working:
If we express 20 in terms of its prime factors, we get 20 = 2^2 x 5^1
• Therefore, if n is a multiple of 20, then n must have 2^2 and 5 as its factors.

Analysing Statement 1
As per the information given in statement 1, n^3 is a multiple of 60.
• Or, n^3 = 2^2 x 3 x 5 x k, where k is a positive integer
• From this, we can say that k must have at least 2, 3^2 and 5^2.
• However, we cannot say whether n is a multiple of 20 or not.

Hence, statement 1 is not sufficient to answer the question.

Analysing Statement 2
As per the information given in statement 2, 10 is a factor of square root of n.
• Therefore, we can say that 100 should be a factor of n.
• As 100 is a multiple of 20, we can say that n is also a multiple of 20.

Hence, statement 2 is sufficient to answer the question.

Hence, the correct answer is option B.

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Re: Is the positive integer n a multiple of 20?   [#permalink] 18 Feb 2019, 22:24
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