A number x is 32% of a number y. If y is 20% of z, what is z in terms

Solution

Given:

• x is 32% of y.
• y is 20% of z

To find:

• z in terms of x.

Approach and Working:

• x=0.32y----------------(1)
• y= 0.2 z------------------(2)

o Hence, by substituting the value of y in equation (1), we get:

 x =0.32*0.2 z
 x= 0.064z or z= \(\frac{x}{0.064}\)

Hence, the correct answer is option D.

Answer: D

\(y = \frac{z}{5}\)

\(x = \frac{32}{100}*\frac{z}{5}\)

Or, \(x = 0.064z\)

Or, \(z = \frac{x}{0.064}\) , Answer must be (D)

We can create the equations:

x = 0.32y

x = 32y/100

100x/32 = y

25x/8 = y

and

y = 0.2z

y = z/5

Substituting, we have:

25x/8 = z/5

125x/8 = z

We see that choices A, B, and C will not be correct. To see which choice between D and E is correct, let’s multiply 125x/8 by 8/8:

1000x/64 = x/(64/1000) = x/0.064

So z = x/0.064

Answer: D

x=.32y
y=.2z

z=y/.2
z=(x/.32)/.2=x/.064
Answer D

How did you make the intuition of multiplying by 8/8? It doesn't seem like a common sense intuition, so what's the thought process behind it?

We are multiplying 125x/8 by 8/8 in order to get an equivalent expression that resembles the ones in the answer choices. Scanning the answer choices, we only see answers in the form of x multiplied by decimal expressions where the last two digits are 64, or x divided by decimal expressions where the last two digits are 64. This tells us that we need a power of 10 and a 64, one of them in the numerator and the other one in the denominator. Therefore, by multiplying the expression 125z/8 by 8/8, not only we get a 1000 in the numerator, we also get a 64 in the denominator; both of which are necessary to produce a decimal where the last two digits are 64. Since we obtained the power of 10 in the numerator and the 64 in the denominator, the answer is in the form of x divided by the decimal we obtained but if it were the other way around, i.e. if 64 was in the numerator and the power of 10 was in the denominator, the answer would have been x multiplied by the decimal we obtained, in which case we would consider answer choices A, B or C.

Thanks…i was dividing 125/8 like an idiot and wondering why tf answer I’m getting is not even an option