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# Y and Z are both positive numbers less than 1. Is Y > Z ?

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Math Expert
Joined: 02 Sep 2009
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Y and Z are both positive numbers less than 1. Is Y > Z ?  [#permalink]

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03 Jun 2018, 11:12
00:00

Difficulty:

75% (hard)

Question Stats:

55% (02:36) correct 45% (02:17) wrong based on 108 sessions

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Y and Z are both positive numbers less than 1. Is Y > Z ?

(1) The hundredths digit of Y is greater than the tenths digit of Z and less than the hundredths digit of Z.
(2) The thousandths digit of Y is greater than the hundredths digit of Y and less than the tenths digit of Y.

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Re: Y and Z are both positive numbers less than 1. Is Y > Z ?  [#permalink]

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03 Jun 2018, 11:19
Is the OA E?
Statement 1: Doesnt say any thing about the tenths digit of Y
Statement 2: Doesnt say anything abbout Z

Combining both, no enough info about the tenths digit of Y.
E
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Re: Y and Z are both positive numbers less than 1. Is Y > Z ?  [#permalink]

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03 Jun 2018, 11:30
2
Bunuel wrote:
Y and Z are both positive numbers less than 1. Is Y > Z ?

(1) The hundredths digit of Y is greater than the tenths digit of Z and less than the hundredths digit of Z.
(2) The thousandths digit of Y is greater than the hundredths digit of Y and less than the tenths digit of Y.

Ans: C
IMO

Stem: Y and Z are both positive numbers less then 1. so Y= . abc and Z= . pqr Imagine.
Now to know if Y>Z we need to know the relation between a and p, b and q, c and r.. and so on.
Reason: If a>p then Y>Z; if a<p then Y<Z: both of these cases will give us the ans but if a=p then we need to know the relation between b and q for finding the lesser and higher values. and so on unless we get the ans.

Now from statement 1: it is given that b>p and b<q from this we do not know the relation between a and p without it we can not know if Y>Z or not.
you can try by putting values put a =1 once and a=9 second time while given p=3 and rest with your choice.. (Not Suff)

State: 2 only gives us info about its own digit's relation. c>b and c<a: but it doesn't talk about anything of Z. (Not Suffi.)

Together from two we know that c>b and a>c so a>b always OR a is the highest among a,b,and c.
from statement one we know that b>p always.
This tells us that a>p always and we know if a>p always Y>Z always..

Hence together both statements are sufficient to ans: (C)
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Y and Z are both positive numbers less than 1. Is Y > Z ?  [#permalink]

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06 Jun 2018, 00:03
IMO, Ans C

Q stem states that both numbers are positive fractions. So, unit digits are 0.

St.1+2 confirm that tenth digit of Y is greater than that of Z. Hence, Sufficient.
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Re: Y and Z are both positive numbers less than 1. Is Y > Z ?  [#permalink]

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06 Jun 2018, 03:29
Bunuel wrote:
Y and Z are both positive numbers less than 1. Is Y > Z ?

(1) The hundredths digit of Y is greater than the tenths digit of Z and less than the hundredths digit of Z.
(2) The thousandths digit of Y is greater than the hundredths digit of Y and less than the tenths digit of Y.

Let, Y= 0.abc and Z= 0.pqr

ST-1:

b>p and b<q
egs. of Y and Z:
Y=0.135 and Z=0.21 ==> Y>Z
Y=0.035 and Z=0.21 ==> Y<Z
Not Suff.

ST-2

a>b>c

Not suff

ST-1 + ST-2

a>c>b>p

hence, a>p ie., tenth digit of Y is greater than tenth digit of Z.

Hence, Y>Z. distinct answer. Hence, ST 1 + ST 2 is suff.

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Re: Y and Z are both positive numbers less than 1. Is Y > Z ?  [#permalink]

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04 Sep 2018, 00:47
Bunuel wrote:
Y and Z are both positive numbers less than 1. Is Y > Z ?

(1) The hundredths digit of Y is greater than the tenths digit of Z and less than the hundredths digit of Z.
(2) The thousandths digit of Y is greater than the hundredths digit of Y and less than the tenths digit of Y.

Solution:

Let the tenths, hundredths and thoousandths digits of Y and Z be: Ty, Hy, Thy and Tz, Hz , Thz respectively.
we want to know if Ty>Tz. As the units digit is 0 in both Y and Z numbers.

From 1:
Hy>Tz and Hy< Hz, with this info we cannot find the relation between Ty and Tz. NOT SUFF

From 2:
Thy>Hy and Thy<Ty, with this info we cannot find the relation between Ty and Tz, NOT SUFF

1+2:
from 1: Tz<Hy<Hz
from 2: Hy<THy<Ty

Tz < Hy and Ty > Hy. Therefore, Ty>Tz. SUFF

Re: Y and Z are both positive numbers less than 1. Is Y > Z ?   [#permalink] 04 Sep 2018, 00:47
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