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Difficulty: Sub 505 Level,   Functions and Custom Characters,   Remainders,                           
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Re: For all positive integers m and v, the expression m Θ v represents the [#permalink]
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nycgirl212 wrote:
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 (( 98 Θ 33 ) Θ 17 ) - ( 98 Θ (33 Θ 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 Θ 17

32/17 = 1 remainder 15

So, (( 98 Θ 33 ) Θ 17 ) = 15.

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

33/17 = 1 remainder 16

Next we have:

98 Θ 16 = 6 remainder 2

Thus, ( 98 Θ (33 Θ 17)) = 2.

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

Answer: D
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Re: For all positive integers m and v, the expression m Θ v represents the [#permalink]
( 98 Θ 33 ) Θ 17 ) =15
98 Θ (33 Θ 17) =2
so answer should be 13
Answer D
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Re: For all positive integers m and v, the expression m Θ v represents the [#permalink]
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Gilb17 wrote:
Hi guys, I am working through the OG 2019 for Quant and I jumped into this question (Q83). I did exactly the same work as in previous answer and got to he answer of 13. However the OG answer is not 13, it is -2.

Is this a known typo or are we all missing something?


Hey Gilb17

We are not missing out on anything.

The answer is indeed 13 and not -2.

It can be a typo :).
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Re: For all positive integers m and v, the expression m Θ v represents the [#permalink]
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 (( 98 Θ 33 ) Θ 17 ) - ( 98 Θ (33 Θ 17)) ?

A) -10
B) -2
C) 8
D) 13--> correct
E) 17

Details:
(( 98 Θ 33 ) Θ 17 ) - ( 98 Θ (33 Θ 17))
= (( 98 % 33 ) % 17 ) - ( 98 % (33 % 17))
= 32%17 - 98%16; as 98 = 33*2 +32 and 33=17+16
= 15 - 2; as 32=17+15 and 98 = 16*6 +2
=13
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For all positive integers m and v, the expression m v represents the [#permalink]
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Top Contributor
Given that m Θ v = the remainder when m is divided by v and we need to find the value of (( 98 Θ 33 ) Θ 17 ) - ( 98 Θ (33 Θ 17)))

Lets start by finding the value of 98 Θ 33

Now, according to the definition of the function 98 Θ 33 = the remainder when 98 is divided by 33 = 32 (as 98 = 33*2 + 32)
( Watch this video to learn about the Basics of Remainders)

=> (( 98 Θ 33 ) Θ 17 ) - ( 98 Θ (33 Θ 17))) = ((32 Θ 17 ) - ( 98 Θ (33 Θ 17)))
Similarly, 32 Θ 17 = the remainder when 32 is divided by 17 = 15
33 Θ 17 = the remainder when 33 is divided by 17 = 16

=> ((32 Θ 17 ) - ( 98 Θ (33 Θ 17))) = ( 15 - ( 98 Θ 16)) = 15 - 2 ( as 98 when divided by 16 gives 2 remainder) = 13

So, Answer will be D
Hope it helps!

Watch the following video to learn the Basics of Functions and Custom Characters

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Re: For all positive integers m and v, the expression m v represents the [#permalink]
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Re: For all positive integers m and v, the expression m v represents the [#permalink]
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