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The expression x$y is defined as , where y ≠ 0. What is the

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sandy
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The expression x$y is defined as , where y ≠ 0. What is the [#permalink] New post   27 Jul 2018, 07:02
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The expression x$y is defined as \(\frac{x^2}{y}\), where y ≠ 0. What is the value of 9$(6$2)?

(A) \(\frac{1}{2}\)
(B) \(\frac{9}{4}\)
(C) \(\frac{9}{2}\)
(D) \(18\)
(E) \(108\)
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C
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Re: The expression x$y is defined as , where y ≠ 0. What is the [#permalink] New post   28 Jul 2018, 02:27
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sandy wrote:
The expression x$y is defined as \(\frac{x^2}{y}\), where y ≠ 0. What is the value of 9$(6$2)?

(A) \(\frac{1}{2}\)
(B) \(\frac{9}{4}\)
(C) \(\frac{9}{2}\)
(D) \(18\)
(E) \(108\)



Phase 1:

6$2 = \(\frac{6^2}{2}\)

= 18

Phase 2:

9$18 = \(\frac{9^2}{18}\)

= 81 / 18

= 9/2
The best answer is C.
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sandy
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Re: The expression x$y is defined as , where y ≠ 0. What is the [#permalink] New post   12 Aug 2018, 04:57
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Explanation

This problem defines a function for the made-up symbol $. The order of operation rules (PEMDAS) stay the same even when the problem uses made-up symbols.

First, calculate the value of the expression in parentheses, \(6\$2\). Plug x = 6 and y = 2 into the function: \(\frac{6^2}{2}=\frac{36}{2}=18\).

Replace \(6\$2\) with 18 in the original expression to give 9$18. Again, plug x = 9 and y = 18 into the function:

\(9\$18=\frac{9^2}{18}=\frac{81}{18}=\frac{9}{2}\).
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Re: The expression x$y is defined as , where y 0. What is the [#permalink] New post   24 Aug 2022, 09:41
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Given that x$y = \(\frac{x^2}{y}\) and we need to find the value of 9$(6$2)

Lets start by finding the value of 6$2

To find 6$2 we need to compare what is before and after $ in 6$2 and x$y

=> We need to substitute x with 6 and y with 2 in x$y = \(\frac{x^2}{y}\) to get the value of 6$2

=> 6$2 = \(\frac{6^2}{2}\) = \(\frac{36}{2}\) = 18

=> 9$(6$2) = 9$18 = \(\frac{9^2}{18}\) = \(\frac{81}{18}\) = \(\frac{9}{2}\)

So, Answer will be C
Hope it helps!

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Re: The expression x$y is defined as , where y 0. What is the [#permalink]
24 Aug 2022, 09:41
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