newkid Posted May 19, 2005 Share Posted May 19, 2005 What is the smallest positive interger by which 126 can be multiplied so that the product is the square of an interger? (A) 4 (B) 7 © 9 (D) 14 (E) 126 Quote Link to comment Share on other sites More sharing options...
Paliwal800 Posted May 19, 2005 Share Posted May 19, 2005 Two methods to solve this one. 1st : 126 * x = x^2 = x * x Therefore, x = 126 Answer is E 2nd : If you are not good with forming equations. Use value-plug in , start with option C - 9 9^2 = 81 So we want a greater number. Plug in 14, 14^2 = 196 , so not possible. Has to be option E, Not neccessary to calculate. Cheers, Neel Quote Link to comment Share on other sites More sharing options...
arjmen Posted May 19, 2005 Share Posted May 19, 2005 Go with D Prime factorise 126 to get, 126 = 2*3*3*7 To make this a perfect square (say N), we need N = (2^2)*(7^2)*(3^2) Therfore the smallest positive interger that we need to multiply 126 with is 2*7 = 14 1 Quote Link to comment Share on other sites More sharing options...
Paliwal800 Posted May 19, 2005 Share Posted May 19, 2005 D is correct. Makes more sense of the question. Quote Link to comment Share on other sites More sharing options...
lamerde Posted July 19, 2005 Share Posted July 19, 2005 arjmen has the right answer. Brilliant Quote Link to comment Share on other sites More sharing options...
jacuzzi Posted July 20, 2005 Share Posted July 20, 2005 Armjen, Would you explain what you mean by "perfect square"? Thanks... Quote Link to comment Share on other sites More sharing options...
kon13 Posted July 20, 2005 Share Posted July 20, 2005 Arnjen, cheers mate, the answer is sipmle and correct! i never found such an easy way to deal with such a problem!! cheers again! Quote Link to comment Share on other sites More sharing options...
rayarya Posted July 29, 2005 Share Posted July 29, 2005 answer is D. what the problem asking of you is, for what y, y * 126 = x^2. remember y has to be smallest number possible. find the factors of 126. 126 = 18 * 7 ==> 2 * 3*3*7. here 3 is already in square fashion. we need one 2 and a 7 to make it 2*2 * 3*3 *7*7. therefore the number is 2*7 = 14. --C Quote Link to comment Share on other sites More sharing options...
letusMBA Posted July 30, 2005 Share Posted July 30, 2005 Hi Arjmen, You solve many problems with clear distinction. Could I know little bit on your math back ground ? Anand at the same time if you could suggest best study material to understand probability and number theory. Pl. advise someyhing too easy for you so that I could digest it. I could advise all aspirants to go to Arjmens profile and visit all the Qs Arjmen has answered. It would help a lot !! Thanks for your great participation ( It is more of tutoring!). Quote Link to comment Share on other sites More sharing options...
jsr_idhar Posted August 11, 2005 Share Posted August 11, 2005 Arjmen: Great work! Brute force multiplication led me to 14. Quote Link to comment Share on other sites More sharing options...
RamN Posted July 8, 2008 Share Posted July 8, 2008 nice approach arjmen ! Quote Link to comment Share on other sites More sharing options...
winna.7 Posted July 25, 2008 Share Posted July 25, 2008 factorize 126 .. u get 126=3*3*2*7 now to make this a sqaure , we know we need another 2 and another 7 there. so 2*7 = 14 is the answer. Quote Link to comment Share on other sites More sharing options...
gmatbuster Posted July 29, 2008 Share Posted July 29, 2008 126 = 7*9*2 complete the squares...by multiplying by 2 and 7 => 2*7 = 14 Quote Link to comment Share on other sites More sharing options...
gettomanish Posted August 6, 2008 Share Posted August 6, 2008 This is really one of the best possible way to reach to the solution. Guys pls share more such tricks.......... Quote Link to comment Share on other sites More sharing options...
winna.7 Posted August 19, 2008 Share Posted August 19, 2008 split 126 into its factors. u get 126= 2*7*3*3 .so to make it a square, u simply need another 2 and 7 , so answer= 2*7=14 .Ans D Quote Link to comment Share on other sites More sharing options...
krusta80 Posted August 19, 2008 Share Posted August 19, 2008 What is the smallest positive interger by which 126 can be multiplied so that the product is the square of an interger? (A) 4 (B) 7 © 9 (D) 14 (E) 126 Every square integer is made up of prime factors to even powers, so let's break down 126... 126 = 2*63 = 2*7*9 = 2^1 * 3^2 * 7^1 Now, we see clearly that 2 and 7 are to odd powers, so we need to multiply by 2^1 * 7^1 to make them even. 2*7 = 14 D it is Quote Link to comment Share on other sites More sharing options...
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