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

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GMAT Club Legend
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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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Question Stats:

85% (00:22) correct 14% (04:02) wrong based on 7 sessions
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) \(108\)
[Reveal] Spoiler: OA

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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.
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4704
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 90

Kudos [?]: 1600 [0], given: 373

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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] 12 Aug 2018, 04:57
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