<ol>
<li>If x and y are two different integers and the
product 35xy is the square of an integer, which
of the following could be equal to xy ?
(A) 5
(B) 70
(C) 105
(D) 140
(E) 350
and
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</ol>
<p>Can someone explain me how to solve these problems,help pls…</p>
<p>This one is easy enough to do quickly on your calculator by plugging in the answers without the necessity of knowing the mathematical way. For each answer calculate
35 x (answer choice) and then see if the square root of the result is an integer. It’s only an integer for D.</p>
<p>If you MUST understand a more rigorous way, the prime factorisation of the square of an integer must have an even number of each prime factor.
35xy = 5 x 7 x (prime factorisation of x) x (prime factorisation of y)
So, the prime factorisation of XY must have a 5, a 7, and an even number of each prime factor in its remaining prime factorisation
5 = 5 No
70 = 2 x 5 x 7 An odd number (1) of 2’s. No.
105 = 3 x 5 x 7 An odd number (1) of 3’s No.
140 = 2 x 2 x 5 x 7 Meets our criteria!
350 = 2 x 5 x 5 x 7 An odd number (1) of 2’s. No</p>
<p>Heck, don’t worry about the theory. Plug in the answers!</p>
<p>ty , can some1 help with 2nd problem
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<p>Hint: look at plugging negative numbers on the scaled ribbon.</p>
<p>In addition, please note that plugging the numbers should be not at random. </p>
<p>Since the marks are equally spaced, one can set the distance between each mark at 1. With this information, you can set up an easy equation (x + 2 = x + y) that shows that y = 2. From there, one can plug the numbers or set another easy equation that shows that x = -6.</p>