Is my math wrong?

[ogwarf]

Hey guys,

I came a cross this problem which is quite silly, but I'd like someone to show me where/why my math is wrong.
I know that him holding/wearing the stuff can be seen differently.
I'm posting from my phone so I'll just paste it.
See attachment for the problem.
The issue is the trickiness of the last row.

My math:
x+x+x=30
3x=30
X=10

y+y+x=20
2y+10=20
2y=10
y=5

z+z+y=13
2z+5=13
2z=8
z=4

x/2+(x*y*z) * z/2=t
5+(10*5*4) *2=t
5+200*2=t
5+400=t
t=405

Much appreciated!

 

[tkhunny]

Why do you doubt?

How do you know that boots and ice cream add the same as numbers?

 

[Steven G]

Where does xyz come from?

 

[Dr.Peterson]

My first question would be what the numbers represent. If they are prices, or weights, or just about anything else I can think of, then it makes no sense to multiply them. Also, in the last line we have the man holding a pair of cones and wearing a pair of shoes; not knowing what the numbers mean, we can't be sure they should be added, multiplied, or what. The math can't be called wrong when the problem is unclear.

I think it's a trick question that is not meant to be taken seriously in the first place, perhaps just to cause arguments like so much on social media.

But if it makes sense at all, I'd call it x/2 + (x + y + z)*(z/2).

 

[pka]

\(\displaystyle \begin{align*}\text{Shoes }S&=10 \\\text{People }P&=5\\\text{Cones }C&=4 \\S+P\cdot C&=30\end{align*}\)

 

[Otis]

... I know that him holding/wearing [x and z] can be seen differently ...

x/2 + (x*y*z) * z/2 = t ...

Hi ogwarf. Yes, I interpreted the symbol of the boy holding cones and wearing the special shoes differently than you did. I added the cones' and shoes' values to the boy's value.

y + z + x

Hence, I got t = 43

You interpreted the boy with the cones and shoes as:

y * z * x

?

 

[Steven G]

I would add to get x+y+z

 

[Otis]

Another interpretation.

x = value of a shoe (left or right, same value)
y = value of a boy
z = value of a cone (filled with whatever)

Now, a pair of adjacent shoes represents implied multiplication: x^2

Same goes for a pair of cones: z^2

The boy with 2 shoes and 2 cones all superimposed: y*x^2*z^2

3x^2 = 30
2y + x^2 = 20
2*z^2 + y = 13

x = sqrt(10)
y = 5
z = 2

t = x + y * z^3 * x^2

t = 400 + sqrt(10)

Wait, I just thought of another interpretation ...

No, don't wait.

?

 

[Steven G]

Another interpretation.

x = value of a shoe (left or right, same value)
y = value of a boy
z = value of a cone (filled with whatever)

Now a pair of adjacent shoes represents implied multiplication: x^2

Same goes for a pair of cones: z^2

The boy with 2 shoes and 2 cones all superimposed: y*x^2*z^2

3x^2 = 30
2y + x^2 = 20
2*z^2 + y = 13

x = sqrt(10)
y = 5
z = 2

t = x + y * z^3 * x^2

t = 400 + sqrt(10)

Wait, I just thought of another interpretation ...

No, don't wait.

?

Nice, actually very nice. Good job! I ask that you get a raise. Do you want a two or three inch raise.

 

[pka]

Yes, I interpret the symbol of the boy holding cones and wearing shoes differently than you have:
y + z + x
I get t = 43
You interpreted the boy with cones and shoes as:

I fully realize that this is a RANT!
After reading this thread, must wonder if any of you have ever served as a editor for a testing company? The first rule is: Every question must have a commonly agreed upon meaning. There is no case where someone could say “I interpret the symbol of the boy holding cones and wearing shoes differently than you have”. The shoes don't even match.
This question is clearly about recognition of variables and order of operations.

 

[Otis]

... There is no case where someone could say “I interpret the symbol of the boy holding cones and wearing shoes differently than you have” ...

Of course, we're not working in a test-editing environment, and ogwarf did acknowledge that the question is quite silly, so others and I have been interpreting.

... The shoes don't even match ...

I'm not sure which shoes you're looking at.

We have two different representations of the boy -- one where he's wearing black shoes and he's empty-handed (2nd and 3rd equations) and one where he's wearing the red shoes and he's holding the cones (4th equation).

In post #5, you've assigned symbol P to represent both representations, so I'm wondering whether you've missed these differences or you've ignored them (as all serious test editors ought).

?

 

[lookagain]

The issue is the trickiness of the last row.

Having two symbols next to each should not mean multiplication, necessarily, especially
with a right shoe next to a left shoe. They are different symbols. I wonder if the usual
order of operations is meant to be used in the last line.

I'll make assumptions:

A pair of shoes is worth 2S.
One shoe is worth S.

A pair of cones is worth 2C.
One cone is worth C.

The person not holding anything, and not wearing the special shoes, is worth P.
However, in the last line, the person holding the pair of cones and wearing the pair
of special shoes is worth P + 2C + 2S.

I will assume the usual order of operations.

first line:

2S + 2S + 2S = 30 -->
6S = 30 -->
S = 5

second line:

P + P + 2S = 20 -->
2P + 2S = 20 -->
2P + 2(5) = 20 -->
2P + 10 = 20 -->
2P = 10 -->
P = 5

third line:

2C + 2C + P = 13 -->
4C + P = 13 -->
4C + 5 = 13 -->
4C = 8 -->
C = 2

fourth line:

S + (P + 2C + 2S)*C =
5 + (5 + 2*2 + 2*5)*2 =
5 + (5 + 4 + 10)*2 =
5 + (19)*2 =
5 + 38 =
43 . . . . . . . . . . . . . . . . . . Answer

 

[tkhunny]

Still haven't answered my second question.

 

[Otis]

... 43 ... Answer

Same as mine (Jomo's and Peterson's, too, I suspect).

So 43 is official; majority rules.