If symbol denotes one arithmetic operation what is the value

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galinaphillips: Junior | Next Rank: 30 Posts; Posts: 28; Joined: Sat May 26, 2007 10:12 am; Thanked: 1 times

by galinaphillips » Sat Jun 02, 2007 4:47 pm

This question is from the MBA.com practice test 2.

If # denotes one of the four arithmetic operations addition, subtraction, multiplication and division, what is the value of 1 # 2?
(1) n # 0 = n for all integers n
(2) n # n = 0 for all integers n

Statement (2) ALONE is sufficient, but statement (1) along in not sufficient.

This is the right answer, but I'm not sure why. Could someone help me with the logic of this?

Thanks!

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Source: Beat The GMAT — Data Sufficiency | Sat Jun 02, 2007 4:47 pm

zozo123: Senior | Next Rank: 100 Posts; Posts: 56; Joined: Tue Feb 13, 2007 6:19 am

by zozo123 » Sun Jun 03, 2007 7:18 am

If # denotes one of the four arithmetic operations addition, subtraction, multiplication and division, what is the value of 1 # 2?

(1) n # 0 = n for all integers n

=> n # 0 = n can be : n - 0 = n OR n + 0 = n then # can be + or -

(2) n # n = 0 for all integers n

=> n - n = 0 : ok
=> n + n = 0 :nok
=> n * n = 0 :nok
=> n / n = 0 :nok

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galinaphillips: Junior | Next Rank: 30 Posts; Posts: 28; Joined: Sat May 26, 2007 10:12 am; Thanked: 1 times

Thanks

by galinaphillips » Sun Jun 03, 2007 6:47 pm

Thanks!!!

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mendiratta: Junior | Next Rank: 30 Posts; Posts: 26; Joined: Tue May 08, 2007 8:22 pm; Thanked: 1 times

by mendiratta » Sun Jun 03, 2007 8:10 pm

zozo123 wrote:If # denotes one of the four arithmetic operations addition, subtraction, multiplication and division, what is the value of 1 # 2?

(1) n # 0 = n for all integers n

=> n # 0 = n can be : n - 0 = n OR n + 0 = n then # can be + or -

(2) n # n = 0 for all integers n

=> n - n = 0 : ok
=> n + n = 0 :nok
=> n * n = 0 :nok
=> n / n = 0 :nok

In 2) - what if n = 0 (because it says for all integers n)?
=> n - n = 0 : ok
=> n + n = 0 :ok
=> n * n = 0 :ok
=> n / n = 0 :nok

so we can't tell what is the function "#".

is there anything wrong in above explanation because I think answer should be E.

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jayhawk2001: Community Manager; Posts: 789; Joined: Sun Jan 28, 2007 3:51 pmFollowed by: 1 member; Location: Silicon valley, California; Thanked: 30 times

by jayhawk2001 » Sun Jun 03, 2007 8:25 pm

mendiratta wrote:
In 2) - what if n = 0 (because it says for all integers n)?
=> n - n = 0 : ok
=> n + n = 0 :ok
=> n * n = 0 :ok
=> n / n = 0 :nok

so we can't tell what is the function "#".

is there anything wrong in above explanation because I think answer should be E.

(2) says n#n = 0, for all integers n. By virtue of being a statement
that is true, the condition HAS to be true for all integers n. This means, for
any value of n, n#n should be = 0. So, if the condition is satisfied
for n=0 and not satisfied for n=1, the above statement doesn't
hold true.

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