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# If the product of the digits of a two-digit number x is 6, what is the

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Math Expert
Joined: 02 Sep 2009
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If the product of the digits of a two-digit number x is 6, what is the [#permalink]

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13 Apr 2016, 13:09
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If the product of the digits of a two-digit number x is 6, what is the value of x?

(1) x has only one unique prime factor.
(2) $$\sqrt{x}$$ is an integer.
[Reveal] Spoiler: OA

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Joined: 14 Sep 2015
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Re: If the product of the digits of a two-digit number x is 6, what is the [#permalink]

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13 Apr 2016, 14:28
The 2 digits that can yield a product of 6 include: 16, 32, 23 and 61.

First Statement:Both 32 and 16 can produce the unique prime factor 2 only. Insufficient.

Second Statement: sqrt(x) being a positive integer. Only 16 fits this to give 4. Sufficient.

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Last edited by fizzywah on 14 Apr 2016, 22:52, edited 1 time in total.
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Re: If the product of the digits of a two-digit number x is 6, what is the [#permalink]

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14 Apr 2016, 00:09
Bunuel wrote:
If the product of the digits of a two-digit number x is 6, what is the value of x?

(1) x has only one unique prime factor.
(2) $$\sqrt{x}$$ is an integer.

Assume the number to be x = ab
Given: a*b = 6
This means x = 16 or x = 32 or x = 23 or x = 61

Statement 1: x has only one unique prime factor
In all the cases, there is only one prime factor and the product of the digits = 6
Hence there can be more than one value of x.
Insufficient

Statement 2: $$\sqrt{x}$$ is an integer
Out of x = 16 or x = 32 or x = 23 or x = 61,
$$\sqrt{x}$$ is an integer only for x = 16
Hence we have only one value of x.
Sufficient

Option B
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Re: If the product of the digits of a two-digit number x is 6, what is the [#permalink]

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14 Apr 2016, 16:02
If the product of the digits of a two-digit number x is 6, what is the value of x?

(1) x has only one unique prime factor.
(2) $$\sqrt{x}$$ is an integer.

Let X = AB.
Given AxB = 6. This means AB can be 16, 23,32,61.

Statement 1: X has only 1 unique prime factor.

So X can be - 16, 23, 32 and 61. Not sufficient.

Statement 2: $$\sqrt{x}$$ is an integer.

The only perfect square in the numbers identified is 16. Hence sufficient.

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Re: If the product of the digits of a two-digit number x is 6, what is the [#permalink]

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16 Nov 2017, 01:16
Because x * y = 6, therefore, x can be 1/2/3/6 as all are factors of 6.
Statement 1 - X can be 3 or 2. Not sufficient.
Statement 2 - X has to be 1 since x^1/2 = integer. Only possible with 1. Sufficient
Hence B
Re: If the product of the digits of a two-digit number x is 6, what is the   [#permalink] 16 Nov 2017, 01:16
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