Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 24 Aug 2016, 09:45

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If the operation @ is defined by x@y=(xy)^1/2 for all

Author Message
TAGS:

### Hide Tags

Manager
Joined: 02 Dec 2012
Posts: 178
Followers: 4

Kudos [?]: 1870 [1] , given: 0

If the operation @ is defined by x@y=(xy)^1/2 for all [#permalink]

### Show Tags

17 Dec 2012, 07:43
1
KUDOS
3
This post was
BOOKMARKED
00:00

Difficulty:

5% (low)

Question Stats:

88% (01:51) correct 12% (01:18) wrong based on 697 sessions

### HideShow timer Statistics

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) $$30\sqrt{15}$$
(E) $$60\sqrt{15}$$
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 34420
Followers: 6248

Kudos [?]: 79387 [2] , given: 10016

Re: If the operation @ is defined by x@y=(xy)^1/2 for all [#permalink]

### Show Tags

17 Dec 2012, 07:46
2
KUDOS
Expert's post
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) $$30\sqrt{15}$$
(E) $$60\sqrt{15}$$

$$(5@45)@60 =(\sqrt{5*45})@60=(\sqrt{225})@60=15@60=\sqrt{15*60}=30$$.

_________________
Moderator
Joined: 01 Sep 2010
Posts: 2994
Followers: 714

Kudos [?]: 5729 [2] , given: 969

Re: If the operation @ is defined by x@y=(xy)^1/2 for all [#permalink]

### Show Tags

17 Dec 2012, 07:50
2
KUDOS
I'm writing the answer but Bunuel is too fast to reply, a machine
_________________
Director
Status: 1,750 Q's attempted and counting
Affiliations: University of Florida
Joined: 09 Jul 2013
Posts: 513
Location: United States (FL)
Schools: UFL (A)
GMAT 1: 600 Q45 V29
GMAT 2: 590 Q35 V35
GMAT 3: 570 Q42 V28
GMAT 4: 610 Q44 V30
GPA: 3.45
WE: Accounting (Accounting)
Followers: 25

Kudos [?]: 665 [0], given: 630

Re: If the operation @ is defined by x@y=(xy)^1/2 for all [#permalink]

### Show Tags

24 Oct 2013, 20:11
1
This post was
BOOKMARKED
I tried to keep the numbers as manageable as possible and use numbers that I knew the perfect squares of.

$$(5@45)@60$$= $$\sqrt{5*(5*9)}$$ $$=5*3=15$$

$$15@60=$$ $$\sqrt{(3*5)*(3*4*5)}$$ $$= 3*5*2= 30$$
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 11036
Followers: 509

Kudos [?]: 133 [0], given: 0

Re: If the operation @ is defined by x@y=(xy)^1/2 for all [#permalink]

### Show Tags

01 Nov 2014, 05:13
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Manager
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 228
Location: United States (CA)
Followers: 5

Kudos [?]: 35 [0], given: 0

Re: If the operation is defined by xy=(xy)^1/2 for all [#permalink]

### Show Tags

21 Jun 2016, 10:29
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) $$30\sqrt{15}$$
(E) $$60\sqrt{15}$$

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

_________________

Jeffrey Miller
Scott Woodbury-Stewart
Founder and CEO

Re: If the operation is defined by xy=(xy)^1/2 for all   [#permalink] 21 Jun 2016, 10:29
Similar topics Replies Last post
Similar
Topics:
1 The operation & is defined for all integers a and b by the 3 24 Oct 2013, 10:47
14 The operation ⊗ is defined for all nonzero numbers a and b 5 18 Dec 2010, 08:46
44 If the operation @ is defined for all integers a and b 26 18 Sep 2010, 20:16
2 If the operation is defined for all positive integers x and 6 03 Nov 2009, 07:10
3 If the operation (*) is defined for all integers a and b by 6 01 Oct 2007, 16:04
Display posts from previous: Sort by