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

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Math Expert
Joined: 02 Sep 2009
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A number x is 32% of a number y. If y is 20% of z, what is z in terms  [#permalink]

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19 Jul 2018, 01:40
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35% (medium)

Question Stats:

70% (01:44) correct 30% (01:41) wrong based on 82 sessions

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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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Re: A number x is 32% of a number y. If y is 20% of z, what is z in terms  [#permalink]

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19 Jul 2018, 01:48
1
x= 0.32y...........(1)
y= 0.2z............(2)

Put (2) in (1)

x= 0.32*0.2z
x= 0.064z

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 in terms  [#permalink]

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19 Jul 2018, 02:04
Bunuel wrote:
A number x is 32% of a number y. If y is 20% of z, what is z in terms of x?

Given,
x = 32% of y
= 0.32y

y = 20% of z
= 0.2z

0.32y = 0.32 * 0.2z
x = 0.064z
z = x / 0.064

Hence, D.
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A number x is 32% of a number y. If y is 20% of z, what is z in terms  [#permalink]

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19 Jul 2018, 02:21

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.

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Re: A number x is 32% of a number y. If y is 20% of z, what is z in terms  [#permalink]

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19 Jul 2018, 07:23
Bunuel 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. $$\frac{x}{0.64}$$

$$y = \frac{z}{5}$$

$$x = \frac{32}{100}*\frac{z}{5}$$

Or, $$x = 0.064z$$

Or, $$z = \frac{x}{0.064}$$ , Answer must be (D)
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Re: A number x is 32% of a number y. If y is 20% of z, what is z in terms  [#permalink]

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22 Jul 2018, 18:31
Bunuel 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. $$\frac{x}{0.64}$$

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

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Re: A number x is 32% of a number y. If y is 20% of z, what is z in terms  [#permalink]

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22 Jul 2018, 18:47
x=.32y
y=.2z

z=y/.2
z=(x/.32)/.2=x/.064
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Joined: 22 Oct 2017
Posts: 19
Re: A number x is 32% of a number y. If y is 20% of z, what is z in terms  [#permalink]

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28 Feb 2019, 01:50
ScottTargetTestPrep wrote:
Bunuel 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. $$\frac{x}{0.64}$$

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

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?
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Re: A number x is 32% of a number y. If y is 20% of z, what is z in terms  [#permalink]

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03 Mar 2019, 07:14
1
paolodeppa wrote:
ScottTargetTestPrep wrote:
Bunuel 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. $$\frac{x}{0.64}$$

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

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.
_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Re: A number x is 32% of a number y. If y is 20% of z, what is z in terms   [#permalink] 03 Mar 2019, 07:14
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