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For all real numbers a and b, the operation ⊕ is defined by

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For all real numbers a and b, the operation ⊕ is defined by [#permalink] New post 26 Mar 2018, 16:06
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83% (00:25) correct 16% (00:00) wrong based on 6 sessions
For all real numbers a and b, the operation ⊕ is defined by a ⊕ b = 2a – b. What is the absolute value of the difference between (3 ⊕ 1) ⊕ 2 and 6 ⊕ 3?

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[Reveal] Spoiler: OA
1

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Re: For all real numbers a and b, the operation ⊕ is defined by [#permalink] New post 02 Apr 2018, 19:31
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This is what I call a fake function problem. It looks as though it's a topic you've never studied, so it's tempting to skip it, but resist the urge. Nobody else has studied it either. They've simply created a symbol which represents a set of instructions. All you need to do is follow the instructions.

In this case, ⊕ means "double the number to the left and then subtract the number on the right." Let's do that with (3 ⊕ 1) ⊕ 2 and 6 ⊕ 3. Firstly, they often nest these fake functions inside of parenthesis. But all you need to do is perform the function inside the parenthesis first, then apply the result to the outside function.

So, 3 ⊕ 1 comes first. Just double 3 and subtract 1, giving us 5. Now since (3 ⊕ 1) = 5, we can plug in 5 in the place of the inside function, giving us 5 ⊕ 2. Repeating the process, let's double 5 and subtract 2, giving us 8.

Now we'll do 6 ⊕ 3: double 6 and subtract 3, giving us 9.

Finally, they want the absolute difference of these two values, or |8 - 9|, which equals 1.
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GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4749
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 93

Kudos [?]: 1652 [0], given: 396

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Re: For all real numbers a and b, the operation ⊕ is defined by [#permalink] New post 04 Apr 2018, 16:05
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Explanation

To follow the order of operations, first evaluate the expression in parentheses: 3 ⊕ 1 = 2(3) – 1 = 5, so now the first equation can be written as 5 ⊕ 2 = 2(5) – 2 = 8.

Next, rewrite the second equation so that you have 6 ⊕ 3 = 2(6) – 3 = 9. Finally,|8-9|=|-1|=1, so the answer is 1.
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Re: For all real numbers a and b, the operation ⊕ is defined by   [#permalink] 04 Apr 2018, 16:05
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