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Integer Property Questions

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by bluemets » Sun Dec 30, 2012 10:54 am
I'm finding that I'm having difficulty translating the questions into correct algebraic expressions. Anyone have specific advice to improve?

I.e PS 155

If y is the smallest positive integer such that 3,150 multiplied by y is the square of an integer, then y must be...
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by jkaustubh » Sun Dec 30, 2012 11:19 am
The value of y is 14

Factorize 3150 for 3150*y to be a perfect square, we need to have a 2 and a 7

hence the minimum possible value of y is 14
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by Param800 » Sun Dec 30, 2012 11:22 am
hello bluemets,

I usually solve these questions like this...

If I see any number in such questions and I think I can factor it, that's the first thing I do... so in this question 3150 = 5*7*9*5*2

Now..the question says what's the minimum number needed to make this a perfect square..
So we know if we multiply by 14 ( 2*7)... the above number will be a perfect square..
so.. 3150 *14 = 5*5*3*3*14*14 = ( 5*3*14)^(2)

You must be wondering why I didn't multiply by some other number like 4*14 ...this will also make it a perfect square..but the thing to be noted is that the question is asking for MINIMUM ( SMALLEST) positive integer.. so the answer will be 14.
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