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If each of # and $ can be replaced by +, -, or *. How many values are

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If each of # and $ can be replaced by +, -, or *. How many values are  [#permalink]

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New post 22 Jul 2019, 00:58
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

42% (01:51) correct 58% (01:45) wrong based on 19 sessions

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Location: India
Re: If each of # and $ can be replaced by +, -, or *. How many values are  [#permalink]

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New post 22 Jul 2019, 01:06
Bunuel wrote:
If each of # and $ can be replaced by +, -, or *. How many values are there for the expression 2#2$2 ?

A. 2
B. 3
C. 4
D. 6
E. 8


Given: Each of # and $ can be replaced by +, -, or *.
Asked: How many values are there for the expression 2#2$2 ?


There are 3 options for # and 3 options for $ => Total 3*3 = 9 options

2+2+2 = 6
2+2-2 = 2
2+2*2 = 6
2-2+2 = 2
2-2-2 = -2
2-2*2 = -2
2*2+2 = 6
2*2-2 = 2
2*2*2 = 8

Unique values for the expression 2#2$2 = {6,2,-2,8} = 4 values

IMO C
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Re: If each of # and $ can be replaced by +, -, or *. How many values are  [#permalink]

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New post 22 Jul 2019, 02:17
We have to choose 2 out of the 3 signs. Since repetition is allowed we will get 3*3 ways.
Use PEMDAS/BODMAS for this .It looks like this :
2+2+2=6
2-2-2=-2
2*2*2=8
2+2*2=6
2*2+2=6
2+2-2=2
2-2+2=2
2*2-2=2
2-2*2=-2

We have 4 distinct values .Answer is C
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Re: If each of # and $ can be replaced by +, -, or *. How many values are   [#permalink] 22 Jul 2019, 02:17
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