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# If u is a multiple of prime number v, is u a multiple of v^2?

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Intern
Joined: 14 Jan 2015
Posts: 1
If u is a multiple of prime number v, is u a multiple of v^2?  [#permalink]

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Updated on: 16 Jan 2015, 01:31
5
00:00

Difficulty:

45% (medium)

Question Stats:

67% (01:24) correct 33% (01:26) wrong based on 147 sessions

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If u is a multiple of prime number v, is u a multiple of v^2?

(1) v < 6
(2) u = 42

Originally posted by RoberJr on 16 Jan 2015, 00:50.
Last edited by Bunuel on 16 Jan 2015, 01:31, edited 1 time in total.
Edited the question.
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Joined: 02 Sep 2009
Posts: 52278
Re: If u is a multiple of prime number v, is u a multiple of v^2?  [#permalink]

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16 Jan 2015, 01:38
If u is a multiple of prime number v, is u a multiple of v^2?

(1) v < 6 --> v can be 2, 3 or 5. We know nothing about u. Not sufficient.

(2) u = 42 --> u = 42 = 2*3*7. Since u is NOT a multiple of any prime in power of 2, then u cannot be a multiple of v^2. Sufficient.

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Re: If u is a multiple of prime number v, is u a multiple of v^2?  [#permalink]

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16 Jan 2015, 12:58
1
Hi RoberJr,

This DS question is a test of your ability to notice restrictions and consider possibilities.

We're told that V is a PRIME NUMBER and that U is a MULTIPLE of V. We're asked if U is a multiple of V^2. This is a YES/NO question.

Fact 1: V < 6

Since we were told that V is PRIME, and now we know that V is less than 6...

V can ONLY be 2, 3, or 5

IF....
V = 2
U = 4
The answer to the question is YES

V = 2
U = 6
The answer to the question is NO
Fact 1 is INSUFFICIENT

Fact 2: U = 42

Since U is a MULTIPLE of V, V can only be a handful of different numbers: 1, 42, 2, 21, 3, 14, 6, or 7

We ALSO know that V has to be PRIME. From that larger list, we can narrow the options down....

V can ONLY be 2, 3 or 7.

IF...
V = 2
V^2 = 4
U = 42
The answer to the question is NO

IF....
V = 3
V^2 = 9
U = 42
The answer to the question is NO

IF....
V = 7
V^2 = 49
U = 42
The answer to the question is NO.
Fact 2 is SUFFICIENT.

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Re: If u is a multiple of prime number v, is u a multiple of v^2?  [#permalink]

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17 Jun 2016, 14:39
RoberJr wrote:
If u is a multiple of prime number v, is u a multiple of v^2?

(1) v < 6
(2) u = 42

Question asks if a number has square of another prime number as its factor.

(1) v < 6

v can be 2, 3 or 5. We don't have any information about u. Not sufficient.

(2) u = 42
u= 42

factorize 42= 2*3*7. We see that no prime number is multiplied twice in the expression. Sufficient.

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Re: If u is a multiple of prime number v, is u a multiple of v^2? &nbs [#permalink] 17 Jun 2016, 14:39
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