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Re: y - the smallest +ve integer [#permalink]
08 Mar 2011, 06:27
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142.) If y is the smallest positive integer such that 3150 multiplied by y is the square of an integer, then y must be
a) 2 b) 5 c) 6 d) 7 e) 14
upon factoring 3150 i got following prime factors 3,3,5,5 nd 2
3,150=2*3^2*5^2*7, now 3,150*y to be a perfect square y must complete the odd powers of 2 and 7 to even number (perfect square has even powers of its primes), so the least value of y is 2*7=14. In this case 3,150y=(2*3^2*5^2*7)*(2*7)=(2*3*5*7)^2=perfect square.
Re: If y is the smallest positive integer such that 3150 [#permalink]
23 Mar 2012, 20:27
Create a prime factor tree for 3,150 and see what numbers do not have a pair. 3150 = 5x5x3x3x7x2.... the 7 and 2 do not have a second pair to make it a perfect square of a number. so y must be 7*2 = 14 _________________
Re: If y is the smallest positive integer such that 3,150 multip [#permalink]
15 Aug 2014, 13:24
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