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

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A number x is 32% of a number y. If y is 20% of z, what is z [#permalink] New post 18 Jul 2018, 17:08
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52% (00:55) correct 47% (01:39) wrong based on 19 sessions
A number x is 32% of a number y. If y is 20% of z, what is z in terms of x?

A. \(0.064x\)

B. \(0.64x\)

C. \(6.4x\)

D. \(\frac{x}{0.064}\)

E. \(\frac{x}{0.64}\)

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[Reveal] Spoiler: OA

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Re: A number x is 32% of a number y. If y is 20% of z, what is z [#permalink] New post 18 Jul 2018, 19:47
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Carcass wrote:
A number x is 32% of a number y. If y is 20% of z, what is z in terms of x?

A. \(0.064x\)

B. \(0.64x\)

C. \(6.4x\)

D. \(\frac{x}{0.064}\)

E. \(\frac{x}{0.64}\)

Kudos for R.A.E


Here x =32% of y = 0.32y

and \(y = 0.2z\)

or \(0.32y = 0.32 * 0.2z\)

or \(x = 0.064z\)

or \(z = \frac{x}{0.064}\)
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Re: A number x is 32% of a number y. If y is 20% of z, what is z [#permalink] New post 19 Jul 2018, 12:27
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Carcass wrote:
A number x is 32% of a number y. If y is 20% of z, what is z in terms of x?

A. \(0.064x\)

B. \(0.64x\)

C. \(6.4x\)

D. \(\frac{x}{0.064}\)

E. \(\frac{x}{0.64}\)

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Given

y = 0.2 z

x = 0.32 (0.2z) = 0.064z

So,

x = 0.064z

z = x / 0.064

The best answer is D.
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Re: A number x is 32% of a number y. If y is 20% of z, what is z [#permalink] New post 22 Jul 2018, 17:31
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Carcass wrote:
A number x is 32% of a number y. If y is 20% of z, what is z in terms of x?

A. \(0.064x\)

B. \(0.64x\)

C. \(6.4x\)

D. \(\frac{x}{0.064}\)

E. \(\frac{x}{0.64}\)

Kudos for R.A.E


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
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Re: A number x is 32% of a number y. If y is 20% of z, what is z   [#permalink] 22 Jul 2018, 17:31
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