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# If w and z are positive is w/z < 1 ?

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Manager
Joined: 09 Jun 2010
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If w and z are positive is w/z < 1 ? [#permalink]

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26 Jul 2010, 00:58
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77% (00:38) correct 23% (00:19) wrong based on 157 sessions

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If w and z are positive is w/z < 1 ?

(1) w < 2
(2) z < 4
[Reveal] Spoiler: OA

Kudos [?]: 26 [0], given: 17

Math Expert
Joined: 02 Sep 2009
Posts: 41892

Kudos [?]: 129047 [1], given: 12187

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26 Jul 2010, 01:27
1
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Expert's post
xmagedo wrote:
If w and Z are positive is W/Z<1 ?

1 w<2
2 Z<4

As given that $$z$$ is positive we can safely multiply inequality $$\frac{w}{z}<1$$ by it and we'll get $$w<z$$. So the question becomes: is $$w<z$$?

(1) $$w<2$$. No info about $$z$$, not sufficient.
(2) $$z<4$$. No info about $$w$$, not sufficient.

(1)+(2) Still not sufficient, as $$w$$ from the range $$0<w<2$$ may or may not be more less than $$z$$ from the range $$0<z<4$$.

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Re: If w and z are positive is w/z < 1 ? [#permalink]

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28 Aug 2013, 17:52
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Hi Bunuel,
I agree with the answer. However, I noticed a typo in your explanation. "As given that z is positive we can safely multiply inequality by it and we'll get w>z. So the question becomes: is w>z?" When you multiply W/Z<1 by Z , you will get W<Z. Isn't that correct?

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Math Expert
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Re: If w and z are positive is w/z < 1 ? [#permalink]

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05 Feb 2017, 04:24
1
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Expert's post
anairamitch1804 wrote:
Bunuel wrote:
xmagedo wrote:
If w and Z are positive is W/Z<1 ?

1 w<2
2 Z<4

As given that $$z$$ is positive we can safely multiply inequality $$\frac{w}{z}<1$$ by it and we'll get $$w<z$$. So the question becomes: is $$w<z$$?

(1) $$w<2$$. No info about $$z$$, not sufficient.
(2) $$z<4$$. No info about $$w$$, not sufficient.

(1)+(2) Still not sufficient, as $$w$$ from the range $$0<w<2$$ may or may not be more less than $$z$$ from the range $$0<z<4$$.

Hello Bunuel,

If statement 1 would be "w<z" instead of "w<2" then also answer would be E?

In this case the answer would be A because the question asks exactly whether w < z.
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26 Jul 2010, 14:51
1) w<2 (not suufficient,we dont have Z value)
2) Z<4 (not sufficient, we dont have W value)

By considering 2 statements together
Is W/Z<1
If consider different values for W,Z
W/Z<1 = 1/2 =0.5 makes the statement true
W/Z<1= 1.99/1=1.99 makes the statement false

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Intern
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Re: If w and Z are positive is W/Z<1 ? 1 w<2 2 Z<4 [#permalink]

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24 Aug 2013, 21:46
OA is A ..
Can anyone tell why it is A?

Even I arrived at E.

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Math Expert
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Re: If w and Z are positive is W/Z<1 ? 1 w<2 2 Z<4 [#permalink]

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25 Aug 2013, 07:45
SUNGMAT710 wrote:
If w and Z are positive is W/Z<1 ?

1 w<2
2 Z<4

OA is A ..
Can anyone tell why it is A?

Even I arrived at E.

The correct answer is E, not A. Consider w=1 and z=2 for an YES answer and w=1 and z=1/2 for a NO answer.
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Re: If w and z are positive is w/z < 1 ? [#permalink]

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29 Aug 2013, 02:02
rumehta wrote:
Hi Bunuel,
I agree with the answer. However, I noticed a typo in your explanation. "As given that z is positive we can safely multiply inequality by it and we'll get w>z. So the question becomes: is w>z?" When you multiply W/Z<1 by Z , you will get W<Z. Isn't that correct?

Typo edited. Thank you.
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Re: If w and z are positive is w/z < 1 ? [#permalink]

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17 Jan 2014, 05:44
xmagedo wrote:
If w and z are positive is w/z < 1 ?

(1) w < 2
(2) z < 4

Lets combine straight away:

w = 1 and z = 3 and w/z is less than 1

w = 1 and z = 0.5 and w/z is greater than 1

Hence E
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Re: If w and z are positive is w/z < 1 ? [#permalink]

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04 Feb 2017, 23:16
Bunuel wrote:
xmagedo wrote:
If w and Z are positive is W/Z<1 ?

1 w<2
2 Z<4

As given that $$z$$ is positive we can safely multiply inequality $$\frac{w}{z}<1$$ by it and we'll get $$w<z$$. So the question becomes: is $$w<z$$?

(1) $$w<2$$. No info about $$z$$, not sufficient.
(2) $$z<4$$. No info about $$w$$, not sufficient.

(1)+(2) Still not sufficient, as $$w$$ from the range $$0<w<2$$ may or may not be more less than $$z$$ from the range $$0<z<4$$.

Hello Bunuel,

If statement 1 would be "w<z" instead of "w<2" then also answer would be E?
_________________

Thanks & Regards,
Anaira Mitch

Kudos [?]: 180 [0], given: 855

Re: If w and z are positive is w/z < 1 ?   [#permalink] 04 Feb 2017, 23:16
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