Funny Function

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zagcollins: Master | Next Rank: 500 Posts; Posts: 167; Joined: Wed Jun 11, 2008 10:58 pmFollowed by: 1 member; Thanked: 2 times

by zagcollins » Mon Jul 21, 2008 7:41 am

For all positive integers m and v, the expression m Θ v represents the remainder when m is divided by v. What is the value of ((98Θ33)Θ17) - (98Θ(33Θ17))?

A.-10
B.-2
C.8
D.13
E.17

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Source: Beat The GMAT — Problem Solving | Mon Jul 21, 2008 7:41 am

Canman: Senior | Next Rank: 100 Posts; Posts: 58; Joined: Fri Jul 11, 2008 5:00 am; Thanked: 4 times

by Canman » Mon Jul 21, 2008 9:30 am

Easiest to attack this by starting from the inside parantheses and working your way out.

(98*33)*17 - (98*(33*17)

98/33 = 2 32/33 as a mixed fraction, so remainder is 32. Continue to use this logic

32*17 = 1 15/17, remainder is 15

so..

15 - (98*(33*17)

other side...

33/17 = 1 16/17
98/16 = 6 2/16

put it all together...

15 - 2 = 13

Ans D

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sudhir3127: Legendary Member; Posts: 829; Joined: Mon Jul 07, 2008 10:09 pmFollowed by: 3 members; Location: INDIA; Thanked: 84 times

by sudhir3127 » Mon Jul 21, 2008 9:36 am

My answer is 13 as well

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reachac: Legendary Member; Posts: 572; Joined: Fri Feb 22, 2008 9:25 am; Thanked: 21 times

by reachac » Mon Jul 21, 2008 9:45 am

IMO D

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zagcollins: Master | Next Rank: 500 Posts; Posts: 167; Joined: Wed Jun 11, 2008 10:58 pmFollowed by: 1 member; Thanked: 2 times

by zagcollins » Mon Jul 21, 2008 10:07 am

good explanation canman....tried the same logic but wasnt sure....thanks!

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Mon Jan 08, 2018 4:55 pm

zagcollins wrote:For all positive integers m and v, the expression m Î˜ v represents the remainder when m is divided by v. What is the value of ((98Î˜33)Î˜17) - (98Î˜(33Î˜17))?

A.-10
B.-2
C.8
D.13
E.17

Let's start with the first set of parentheses before the minus sign:

98/33 = 2 remainder 32

Next we have:

32 Î˜ 17

32/17 = 1 remainder 15

So, (( 98 Î˜ 33 ) Î˜ 17 ) = 15.

Let's move to the second set of parentheses after the minus sign:

33/17 = 1 remainder 16

Next we have:

98 Î˜ 16 = 6 remainder 2

Thus, ( 98 Î˜ (33 Î˜ 17)) = 2.

So, (( 98 Î˜ 33 ) Î˜ 17 ) - ( 98 Î˜ (33 Î˜ 17)) = 15 - 2 = 13

Answer: D

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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