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gmatblood: Master | Next Rank: 500 Posts; Posts: 489; Joined: Tue Jul 05, 2011 11:10 am; Thanked: 28 times; Followed by:5 members

x and y

by gmatblood » Mon Oct 31, 2011 1:23 am

Is x @ y = y @ x, for all real values of x and y?

Stmt 1: x @ y = 1/x + 1/y
Stmt 2: x @ y = x - y

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Source: Beat The GMAT — Data Sufficiency | Mon Oct 31, 2011 1:23 am

shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 am; Thanked: 230 times; Followed by:21 members

by shankar.ashwin » Mon Oct 31, 2011 1:35 am

Edited: '0' is a real number as well

(1) x @ y = 1/x + 1/y
y @ x = 1/y + 1/x
Addition will give you the same value, except for x or y =0, when the equation becomes indeterminable. Sufficient

(2) x @ y = x - y
y @ x = y - x

x-y = y-x, only when x=y.

A IMO

Last edited by shankar.ashwin on Mon Oct 31, 2011 5:34 am, edited 2 times in total.

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pemdas: Legendary Member; Posts: 1084; Joined: Fri Apr 15, 2011 2:33 pm; Thanked: 158 times; Followed by:21 members

by pemdas » Mon Oct 31, 2011 1:36 am

the click here is @, it must be @ in all cases

st(1) x@y=(x+y)/xy, we quickly note this statement cannot be solved if x and/or y=0 and 0 is real value Sufficient to answer No
st(2) x@y=x-y, here we have no undefined solution areas so we can conclude Sufficient to answer Yes

d

gmatblood wrote:Is x @ y = y @ x, for all real values of x and y?

Stmt 1: x @ y = 1/x + 1/y
Stmt 2: x @ y = x - y

Success doesn't come overnight!

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vaibhavgupta: Master | Next Rank: 500 Posts; Posts: 416; Joined: Tue Aug 30, 2011 2:18 pm; Location: Delhi, India; Thanked: 13 times; Followed by:9 members

by vaibhavgupta » Mon Oct 31, 2011 5:32 am

gmatblood wrote:Is x @ y = y @ x, for all real values of x and y?

Stmt 1: x @ y = 1/x + 1/y
Stmt 2: x @ y = x - y

IMO D

Whts OA?

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saketk: Legendary Member; Posts: 608; Joined: Sun Jun 19, 2011 11:16 am; Thanked: 37 times; Followed by:8 members

by saketk » Tue Nov 01, 2011 2:29 am

gmatblood wrote:Is x @ y = y @ x, for all real values of x and y?

Stmt 1: x @ y = 1/x + 1/y
Stmt 2: x @ y = x - y

stmt 1: @ can be any mathematical expression here.

let's take few numbers here.
X=1 and Y=1

so, we have 1@1 = 2

from stmt 2: if I take same values then

1@1 = 0

--

If I combine the 2 statements then -- then I get

1@1 =2 and 1@1 = 0

two contradicting statements?

or am I missing something?

what's the source of this question?