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# If k is the smallest positive integer such that 2,940k

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Intern
Joined: 16 Feb 2013
Posts: 6
If k is the smallest positive integer such that 2,940k  [#permalink]

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04 May 2013, 09:17
4
00:00

Difficulty:

35% (medium)

Question Stats:

66% (01:26) correct 34% (01:54) wrong based on 170 sessions

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If k is the smallest positive integer such that 2,940k is the square of an integer, then k must be

A. 3
B. 5
C. 6
D. 15
E. 21
Intern
Joined: 23 Apr 2013
Posts: 21
Re: If k is the smallest positive integer such that 2,940k  [#permalink]

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04 May 2013, 09:52
1
streamingline wrote:
If k is the smallest positive integer such that 2,940k is the square of an integer, then k must be

A)3
B)5
C)6
D)15
E)21

Spoiler: :: OA
15

$$2940 = 2^2 * 3 * 5 * 7^2$$

So the smallest positive integer to be multiplied to make it a perfect square is 3 * 5 = 15

Correct Option is D
Intern
Joined: 16 Feb 2013
Posts: 6
Re: If k is the smallest positive integer such that 2,940k  [#permalink]

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04 May 2013, 18:35
Thanks, didn't realise K was multiplied by 2940
Manager
Joined: 03 Aug 2015
Posts: 53
Concentration: Strategy, Technology
Schools: ISB '18, SPJ GMBA '17
GMAT 1: 680 Q48 V35
Re: If k is the smallest positive integer such that 2,940k  [#permalink]

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11 Jan 2016, 07:23
streamingline wrote:
If k is the smallest positive integer such that 2,940k is the square of an integer, then k must be

A. 3
B. 5
C. 6
D. 15
E. 21

Hi,

Pls clarify whether K is a unit digit of the given No. or it is in multiplication?
Math Expert
Joined: 02 Sep 2009
Posts: 50613
Re: If k is the smallest positive integer such that 2,940k  [#permalink]

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11 Jan 2016, 07:24
ArunpriyanJ wrote:
streamingline wrote:
If k is the smallest positive integer such that 2,940k is the square of an integer, then k must be

A. 3
B. 5
C. 6
D. 15
E. 21

Hi,

Pls clarify whether K is a unit digit of the given No. or it is in multiplication?

It's a multiplication sign.
_________________
Senior SC Moderator
Joined: 22 May 2016
Posts: 2095
If k is the smallest positive integer such that 2,940k  [#permalink]

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06 Jul 2018, 09:04
1
streamingline wrote:
If k is the smallest positive integer such that 2,940k is the square of an integer, then k must be

A. 3
B. 5
C. 6
D. 15
E. 21

• Perfect square rule: A perfect square always has an even number of powers of prime factors.
That rule is often easier to remember this way:
all prime factors must come in pairs. Couplets.

There are no single "copies" of a prime factor in a perfect square.
If there is only one "copy" of a prime factor, or an odd number of copies, then the integer is not a perfect square.

• $$2,940 * k$$ is a perfect square

Prime factorize: $$2,940= 2 * 2 *3*5*7*7$$
This situation will not make a perfect square.
The 3s and the 5s are not in pairs. We need one more copy of each.
(We have $$3^1$$ and $$5^1$$, but exponents on prime factors must be even.)

$$k$$ is the number that provides the extra $$3$$ and the extra $$5$$
$$k = 3*5 = 15$$

$$2,940 * (3*5) = 44,100$$, which is $$210^2$$
If k is the smallest positive integer such that 2,940k &nbs [#permalink] 06 Jul 2018, 09:04
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