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E.. 44100...
by brute force, but didnt take that long.. once i multiplied the given choices by 3150 it was pretty easy to identify if they were square of any integers or not..
_________________

Success is my only option, failure is not -- Eminem

If y is the smallest positive integer such that 3,150 multiplied by y is the square of an integer, then y must be

A. 2

B. 5

C. 6

D. 7

E. 14

Matt, if i were in the test process and saw this question, I would immediately solve as gamjatang did. However, upon your request, i try to look for some quick reasoning: that is to multiple/ divide 3150 by 2

NOTE: Any number(contains at least two digits) having 0 as unit digit have only one 2 as a factor. Why? coz after dividing it by 2, the unit digit is 5 ---> it's odd and thus can't be further divided by 2. So we need an answer choice which is a multiple of 2 to evenize the factor 2 of 3150 ----> B and D out. The blue part is not so important ...it gonna be useful incase most of the answer choices are odd.

Now multiple 3150 by 2 ---> 6300 = 63*10^2= 7*3^3*10^2 ---> we need one more 7 ---> it must be 14 ( = 2*7)

Laxieqv,
You said - ny number(contains at least two digits) having 0 as unit digit have only one 2 as a factor. Why? coz after dividing it by 2, the unit digit is 5 ---> it's odd and thus can't be further divided by 2.

Let's take 100, - divide by 2 -> you will get 50. and 100=10*10=2*2*5*5

laxieqv wrote:

desiguy wrote:

If y is the smallest positive integer such that 3,150 multiplied by y is the square of an integer, then y must be

A. 2

B. 5

C. 6

D. 7

E. 14

Matt, if i were in the test process and saw this question, I would immediately solve as gamjatang did. However, upon your request, i try to look for some quick reasoning: that is to multiple/ divide 3150 by 2

NOTE: Any number(contains at least two digits) having 0 as unit digit have only one 2 as a factor. Why? coz after dividing it by 2, the unit digit is 5 ---> it's odd and thus can't be further divided by 2. So we need an answer choice which is a multiple of 2 to evenize the factor 2 of 3150 ----> B and D out. The blue part is not so important ...it gonna be useful incase most of the answer choices are odd.

Now multiple 3150 by 2 ---> 6300 = 63*10^2= 7*3^3*10^2 ---> we need one more 7 ---> it must be 14 ( = 2*7)

Laxieqv, You said - ny number(contains at least two digits) having 0 as unit digit have only one 2 as a factor. Why? coz after dividing it by 2, the unit digit is 5 ---> it's odd and thus can't be further divided by 2.

Let's take 100, - divide by 2 -> you will get 50. and 100=10*10=2*2*5*5

laxieqv wrote:

desiguy wrote:

If y is the smallest positive integer such that 3,150 multiplied by y is the square of an integer, then y must be

A. 2

B. 5

C. 6

D. 7

E. 14

Matt, if i were in the test process and saw this question, I would immediately solve as gamjatang did. However, upon your request, i try to look for some quick reasoning: that is to multiple/ divide 3150 by 2

NOTE: Any number(contains at least two digits) having 0 as unit digit have only one 2 as a factor. Why? coz after dividing it by 2, the unit digit is 5 ---> it's odd and thus can't be further divided by 2. So we need an answer choice which is a multiple of 2 to evenize the factor 2 of 3150 ----> B and D out. The blue part is not so important ...it gonna be useful incase most of the answer choices are odd.

Now multiple 3150 by 2 ---> 6300 = 63*10^2= 7*3^3*10^2 ---> we need one more 7 ---> it must be 14 ( = 2*7)

ah, sorry, i meant there's only 0 as the unit digit and the tens digit is odd ...as in here, 3150 ..thank you for reminding me.

coz : for example : a5*2 ...2*5 = 10 , this 1 is add to a*2 ...a*2 is always even ---> 2*a+1 is odd ...so those numbers with odd tens digit and 0 as unit digit are fine.