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# Given y = 1422960 * x . Which of the following is the value of X so th

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Intern
Joined: 10 Nov 2017
Posts: 13
Given y = 1422960 * x . Which of the following is the value of X so th  [#permalink]

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23 Oct 2018, 07:35
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Given y = 1422960 * x . Which of the following is the value of X so that y is a perfect square?

A.11
B.13
C.15
D.17
E.19
Math Expert
Joined: 02 Aug 2009
Posts: 7757
Given y = 1422960 * x . Which of the following is the value of X so th  [#permalink]

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23 Oct 2018, 08:25
3
3
Arun1994 wrote:
Given y = 1422960 * x . Which of the following is the value of X so that y is a perfect square?

A.11
B.13
C.15
D.17
E.19

Hi...

No calculations or prime factorization required...

1422960 has one 0,
so only one 5 in 1422960 as for two 5s, last two digits should be 00, 25, 50 or 75
So for y to be a square, there has to be a 5 in x to get two 5s in y..
Only C is a multiple of 5

C
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Given y = 1422960 * x . Which of the following is the value of X so th  [#permalink]

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23 Oct 2018, 08:08
Arun1994 wrote:
Given y = 1422960 * x . Which of the following is the value of X so that y is a perfect square?

A.11
B.13
C.15
D.17
E.19

METHOD: Prime factorize the number and make the exponent of each distinct prime factor an even number for it to be a perfect square

$$y = 1422960 * x = 4*355740*x = 4*35574*10*x = 4*2*17787*2*5*x = 4*2*7*2541*2*5*x$$
i.e. $$y = 4*2*7*2541*2*5*x = 4*2*7*7*363*2*5*x = 4*2*7*7*3*121*2*5*x = 2^4*3*5*7^2*11^2*x$$

i.e. To make all exponents even numbers we need $$3*5$$

i.e. $$x = 15$$

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Senior Manager
Joined: 09 Jun 2014
Posts: 269
Location: India
Concentration: General Management, Operations
Schools: Tuck '19
Given y = 1422960 * x . Which of the following is the value of X so th  [#permalink]

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23 Oct 2018, 08:18
1
Arun1994 wrote:
Given y = 1422960 * x . Which of the following is the value of X so that y is a perfect square?

A.11
B.13
C.15
D.17
E.19

Perfect square :A number made by squaring a whole number (say 16 is a perfect square of 4)

So,here is my approach to the beautiful question you posted

NOTE:Perfect square means even multiples of factors.

Lets factorize 1422960

1422960= 2*2*2*2*5*11*11*3*7*7
= (4^2)*(11^2)*(7^2)*5*3

so we have four 2's ,two 11's and two 7's and odd number of 5 and 11

So for y to be a perfect square we would require one more 3 and 5 .(This would make

So x becomes 5*3 that is 15 and thats our answer .

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Senior Manager
Joined: 09 Jun 2014
Posts: 269
Location: India
Concentration: General Management, Operations
Schools: Tuck '19
Re: Given y = 1422960 * x . Which of the following is the value of X so th  [#permalink]

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23 Oct 2018, 08:28
chetan2u wrote:
Arun1994 wrote:
Given y = 1422960 * x . Which of the following is the value of X so that y is a perfect square?

A.11
B.13
C.15
D.17
E.19

Hi...

No calculations or prime factorization required...

1422960 has one 0, so only one 5 in 1422960 as for two 5s, last two digits should be 00, 25, 50 or 75
So for y to be a square, there has to be a 5 in x to get two 5s in y..
Only C is a multiple of 5

C

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Joined: 29 May 2017
Posts: 128
Location: Pakistan
Concentration: Social Entrepreneurship, Sustainability
Re: Given y = 1422960 * x . Which of the following is the value of X so th  [#permalink]

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12 Nov 2018, 06:47
chetan2u wrote:
Arun1994 wrote:
Given y = 1422960 * x . Which of the following is the value of X so that y is a perfect square?

A.11
B.13
C.15
D.17
E.19

Hi...

No calculations or prime factorization required...

1422960 has one 0,
so only one 5 in 1422960 as for two 5s, last two digits should be 00, 25, 50 or 75
So for y to be a square, there has to be a 5 in x to get two 5s in y..
Only C is a multiple of 5

C

can you please explain why we need 00, 25, 50 or 75?
Senior Manager
Joined: 09 Jun 2014
Posts: 269
Location: India
Concentration: General Management, Operations
Schools: Tuck '19
Re: Given y = 1422960 * x . Which of the following is the value of X so th  [#permalink]

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12 Nov 2018, 07:11
Mansoor50 wrote:
chetan2u wrote:
Arun1994 wrote:
Given y = 1422960 * x . Which of the following is the value of X so that y is a perfect square?

A.11
B.13
C.15
D.17
E.19

Hi...

No calculations or prime factorization required...

1422960 has one 0,
so only one 5 in 1422960 as for two 5s, last two digits should be 00, 25, 50 or 75
So for y to be a square, there has to be a 5 in x to get two 5s in y..
Only C is a multiple of 5

C

can you please explain why we need 00, 25, 50 or 75?

One Five means there is an ODD number of 5 and for perfect squre we would requite another 5.

can you please explain why we need 00, 25, 50 or 75?

The bold basically means there will be even number of 5's and so this alternative approach of looking for one 5 in the option will not work.

Press Kudos if it helps!!
Re: Given y = 1422960 * x . Which of the following is the value of X so th   [#permalink] 12 Nov 2018, 07:11
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