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If x, y, and z are all positive and 0.04x = 5y = 2z, then which of the

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Math Expert
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V
Joined: 02 Sep 2009
Posts: 53066
If x, y, and z are all positive and 0.04x = 5y = 2z, then which of the  [#permalink]

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New post 15 Jan 2019, 00:11
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

81% (00:51) correct 19% (01:23) wrong based on 54 sessions

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Re: If x, y, and z are all positive and 0.04x = 5y = 2z, then which of the  [#permalink]

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New post 15 Jan 2019, 01:48
Bunuel wrote:
If x, y, and z are all positive and 0.04x = 5y = 2z, then which of the following is true?

A. x < y < z
B. x < z < y
C. y < x < z
D. y < z < x
E. z < y < x


With multiple "=" signs, put "= k"

0.04x = 5y = 2z = k

x = k/0.04 = 100k/4 = 25k

y = k/5

z = k/2

So y < z < x

Answer (D)
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Re: If x, y, and z are all positive and 0.04x = 5y = 2z, then which of the  [#permalink]

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New post 15 Jan 2019, 05:21

Solution


Given:
    • x, y and z are positive
    • 0.04x = 5y = 2z

To find:
    • Which of the given options is true?

Approach and Working:
5y = 2z
    • Implies, z = 2.5y
    • Thus, z > y

0.04x = 2z
    • Implies, x =50z
    • Thus, x > z

Therefore, x > z > y

Hence, the correct answer is Option D

Answer: D

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Re: If x, y, and z are all positive and 0.04x = 5y = 2z, then which of the  [#permalink]

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New post 15 Jan 2019, 05:36
Bunuel wrote:
If x, y, and z are all positive and 0.04x = 5y = 2z, then which of the following is true?

A. x < y < z
B. x < z < y
C. y < x < z
D. y < z < x
E. z < y < x


Best way of doing such questions is to convert the terms in single variable
0.04x = 0.008x = 0.02x
y = 0.008x
z = 0.02 x

Answer is D. y < z < x
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Re: If x, y, and z are all positive and 0.04x = 5y = 2z, then which of the  [#permalink]

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New post 15 Jan 2019, 08:21
Bunuel wrote:
If x, y, and z are all positive and 0.04x = 5y = 2z, then which of the following is true?

A. x < y < z
B. x < z < y
C. y < x < z
D. y < z < x
E. z < y < x


\(0.04x = 5y = 2z\)

Or, \(4x = 500y = 200z = 1000\) \((Say)\)

So, \(x = 250\) ; \(y = 2\) & \(z = 5\)

So, \(y < z < x\), Thus Answer must be (D)
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Re: If x, y, and z are all positive and 0.04x = 5y = 2z, then which of the  [#permalink]

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New post 17 Jan 2019, 17:59
Bunuel wrote:
If x, y, and z are all positive and 0.04x = 5y = 2z, then which of the following is true?

A. x < y < z
B. x < z < y
C. y < x < z
D. y < z < x
E. z < y < x


Let’s use positive real numbers for x, y, and z.

If we let x = 1000, then 0.04x = 40.

Thus:

5y = 40

y = 8

Finally:

2z = 40

z = 20

So we see that y < z < x.

Answer: D.
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Re: If x, y, and z are all positive and 0.04x = 5y = 2z, then which of the   [#permalink] 17 Jan 2019, 17:59
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