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If the operation @ is defined (OG16)

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by boomgoesthegmat » Thu May 19, 2016 3:46 pm
If the operation @ is defined by x @ y = sqrt(xy) for all positive numbers x and y, then (5 @ 45) @ 60 =

A) 30
B) 60
C) 90
D) 30sqrt(15)
E) 60sqrt(15)

OA: A
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by Brent@GMATPrepNow » Thu May 19, 2016 4:04 pm
boomgoesthegmat wrote:If the operation @ is defined by x @ y = √(xy) for all positive numbers x and y, then (5 @ 45) @ 60 =

A) 30
B) 60
C) 90
D) 30√15
E) 60√15

OA: A
I call these "Strange Operator" questions.
We want to evaluate: (5 @ 45) @ 60

Start with (5 @ 45)
(5 @ 45) = √[(5)(45)]
= √225
= 15


So, (5 @ 45) @ 60 = 15 @ 60
From here, 15 @ 60 = √[(15)(60)]
= √900
= 30

Answer: A

RELATED RESOURCE (video)
- Strange operators: https://www.gmatprepnow.com/module/gmat ... /video/976
- Additional practice: https://www.gmatprepnow.com/module/gmat ... /video/977

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Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Jeff@TargetTestPrep » Sun Jun 24, 2018 5:04 pm
boomgoesthegmat wrote:If the operation @ is defined by x @ y = sqrt(xy) for all positive numbers x and y, then (5 @ 45) @ 60 =

A) 30
B) 60
C) 90
D) 30sqrt(15)
E) 60sqrt(15)
We are given that the operation @ is defined by x@y = √(xy) for all positive numbers.

We are next given that (5@45)@60. Following PEMDAS rules, we want to begin with the operation inside the parentheses. According to the operation, x will be replaced with 5, and y will be replaced with 45. Thus, we have:

5@45 = √(5 *45) = √225 = 15

We have determined that (5@45) = 15, so we substitute 15 for (5@45) to obtain 15@60.

According to the operation, x will now be replaced with 15 and y will now be replaced with 60. Thus we have:

15@60 = √(15*60) = √900 = 30

Answer: A

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