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# M21-26

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 01:51
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Difficulty:

25% (medium)

Question Stats:

74% (01:11) correct 26% (01:22) wrong based on 85 sessions

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If the salt concentration in Northern Lake increased by 20% from 1900 to 2000 while that in Southern Lake decreased by 10%, is in 2000, the salt concentration in Northern Lake higher than that in Southern Lake?

(1) In 1900 the salt concentration in Southern Lake was 10% higher than that in Northern Lake

(2) In 1900 the salt concentration in Southern Lake was 4%

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16 Sep 2014, 01:51
Official Solution:

If the salt concentration in Northern Lake increased by 20% from 1900 to 2000 while that in Southern Lake decreased by 10%, is in 2000, the salt concentration in Northern Lake higher than that in Southern Lake?

Statement (1) by itself is sufficient. Denote $$x$$ as the salt concentration in Northern Lake in 1900. Then the salt concentration in Southern Lake in 1900 is $$1.1x$$. By 2000, the concentration of salt in Northern Lake became $$1.2x$$ while that in Southern Lake became $$1.1*x*0.9 = 0.99x \lt 1.2x$$.

Statement (2) by itself is insufficient. S2 says nothing about the concentration in Northern Lake in 1900.

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29 Oct 2014, 23:34
Bunuel wrote:
Official Solution:

Statement (1) by itself is sufficient. Denote $$x$$ as the salt concentration in Northern Lake in 1900. Then the salt concentration in Southern Lake in 1900 is $$1.1x$$. By 2000, the concentration of salt in Northern Lake became $$1.2x$$ while that in Southern Lake became $$1.1*x*0.9 = 0.99x \lt 1.2x$$.

Statement (2) by itself is insufficient. S2 says nothing about the concentration in Northern Lake in 1900.

Hi Bunuel,
Pardon my ignorance, I cannot comprehend how Concentration of southern lake is 1.1x in 1900.
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30 Oct 2014, 02:03
mpenmetc wrote:
Bunuel wrote:
Official Solution:
If the salt concentration in Northern Lake increased by 20% from 1900 to 2000 while that in Southern Lake decreased by 10%, is the current salt concentration in Northern Lake higher than that in Southern Lake?

(1) In 1900 the salt concentration in Southern Lake was 10% higher than that in Northern Lake

(2) In 1900 the salt concentration in Southern Lake was 4%

Statement (1) by itself is sufficient. Denote $$x$$ as the salt concentration in Northern Lake in 1900. Then the salt concentration in Southern Lake in 1900 is $$1.1x$$. By 2000, the concentration of salt in Northern Lake became $$1.2x$$ while that in Southern Lake became $$1.1*x*0.9 = 0.99x \lt 1.2x$$.

Statement (2) by itself is insufficient. S2 says nothing about the concentration in Northern Lake in 1900.

Hi Bunuel,
Pardon my ignorance, I cannot comprehend how Concentration of southern lake is 1.1x in 1900.

In 1900 the salt concentration in Southern Lake was 10% higher than that in Northern Lake, so if x is concentration in Northern Lake in 1900, then concentration in Northern Lake in 1900, would be 1.1x.
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21 Nov 2014, 03:50
1
mpenmetc wrote:
Hi Bunuel,
Pardon my ignorance, I cannot comprehend how Concentration of southern lake is 1.1x in 1900.

Even I had the same doubt. Hope my explanation helps! We don't know what was the level of salt concentration in each lake at 1990. Let us assume them as Y and X respectively. This implies the following:

Year SL NL
1990 y 1x
2000 .9y 1.2x

(1) y = 1.1x
Now by subsituting, y = 1.1x in the above table, we will get the following:
SL in 1990 1.1x
SL in 2000 .99x

Now, we are asked if current salt concentration in NL > SL
Salt concentration at SL and NL at 2000 are 0.99x (calculated above) and 1.2x (given in the Q). This is sufficient as we know SL < NL.
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21 Nov 2014, 04:16
joseph0alexander wrote:
mpenmetc wrote:
Hi Bunuel,
Pardon my ignorance, I cannot comprehend how Concentration of southern lake is 1.1x in 1900.

Even I had the same doubt. Hope my explanation helps! We don't know what was the level of salt concentration in each lake at 1990. Let us assume them as Y and X respectively. This implies the following:

Year SL NL
1990 y 1x
2000 .9y 1.2x

(1) y = 1.1x
Now by subsituting, y = 1.1x in the above table, we will get the following:
SL in 1990 1.1x
SL in 2000 .99x

Now, we are asked if current salt concentration in NL > SL
Salt concentration at SL and NL at 2000 are 0.99x (calculated above) and 1.2x (given in the Q). This is sufficient as we know SL < NL.

Thanks a lot for the reply. Last time i was trying to derive 1.1x from main question rather than statement 1. Its all clear now.
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21 Nov 2014, 04:31
I couldn't crack while doing the test. I'm realizing the importance of writing down EVERYTHING on my pad more and more now. Glad I could help.

You also try writing everything down on your pad, it might help! Best wishes!
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16 Feb 2015, 21:53
just wondering:

when we look at statement (1):
the salt concentration could be 1 but it could be also 0,11 in the one lake and 0,01 in the other lake. which would lead to 0,099 > 0,012 ...
so statement 1 should not be sufficient.

where I go wrong?
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Joined: 02 Sep 2009
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17 Feb 2015, 01:54
eddyki wrote:
just wondering:

when we look at statement (1):
the salt concentration could be 1 but it could be also 0,11 in the one lake and 0,01 in the other lake. which would lead to 0,099 > 0,012 ...
so statement 1 should not be sufficient.

where I go wrong?

Year ---- Northern Lake ---- Southern Lake
1900 -------- x -------------------- 1.1x
2000 ---- 1.2x -------------------- 0.9*1.1x = 0.99x
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17 Feb 2015, 11:42
Bunuel wrote:
eddyki wrote:
just wondering:

when we look at statement (1):
the salt concentration could be 1 but it could be also 0,11 in the one lake and 0,01 in the other lake. which would lead to 0,099 > 0,012 ...
so statement 1 should not be sufficient.

where I go wrong?

Year ---- Northern Lake ---- Southern Lake
1900 -------- x -------------------- 1.1x
2000 ---- 1.2x -------------------- 0.9*1.1x = 0.99x

whats wrong about picking numbers like

Year ---- Northern Lake ---- Southern Lake
1900 -------- 0,01 -------------------- 0,11
2000 ---- 1.2*0,01 = 0,012 -------------------- 0.9*0,11 = 0,099

We fulfill the 10% statement given by statement 1

ah ok! i got it: it was 10% higher, but not as an absolute % value
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23 Jul 2015, 05:32
QQ here is- Do we know what is the present year. I can't simply assume its 2000.
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01 Aug 2015, 21:45
Bunuel wrote:
Official Solution:

Statement (1) by itself is sufficient. Denote $$x$$ as the salt concentration in Northern Lake in 1900. Then the salt concentration in Southern Lake in 1900 is $$1.1x$$. By 2000, the concentration of salt in Northern Lake became $$1.2x$$ while that in Southern Lake became $$1.1*x*0.9 = 0.99x \lt 1.2x$$.

Statement (2) by itself is insufficient. S2 says nothing about the concentration in Northern Lake in 1900.

Hi Bunuel,
Aren't we assuming in this question that the salt concentration of Norther Lake in 1990 is not 0%
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19 Jul 2016, 23:35
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Top Contributor
@ Others and Bunuel,
I request some help here in understanding the wordings.
Instead of keyword "current" shouldn't we explicitly mention "year 2000" or mention that "there was no change in salt concentration."
I don't remember the question but there is an OG DS problem where options mentions about recent two years but question asks about past year.
Because of this confusion, I selected E here.
Math Expert
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20 Jul 2016, 01:11
JarvisR wrote:
@ Others and Bunuel,
I request some help here in understanding the wordings.
Instead of keyword "current" shouldn't we explicitly mention "year 2000" or mention that "there was no change in salt concentration."
I don't remember the question but there is an OG DS problem where options mentions about recent two years but question asks about past year.
Because of this confusion, I selected E here.

Edited as suggested. Hope it's OK now. Thank you.
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25 Sep 2016, 01:10
Let
Salt concentration in Northern Lake, in 1900 = N
Salt concentration in Southern Lake, in 1900 = S

Given:
1900 : 2000
N : 1.2N -- Concentration in Northern Lake
S : 0.9S -- Concentration in Southern Lake

Question is asking, In 2000, Whether the salt concentration in Northern Lake higher than that in Southern Lake
=> 1.2N > 0.9 S => Question is asking whether N > 0.75S ??

Statement 1 :
In 1900 the salt concentration in Southern Lake was 10% higher than that in Northern Lake

It means: S = 1.1N (10% higher ==> N + 10N/100)
==> N = 0.90S
We can say definitely say Yes N > 0.75s
Hence Sufficient.

Statement 2 :
In 1900 the salt concentration in Southern Lake was 4%

We are not given anything about Northern Lake , Hence not sufficient

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06 Jul 2018, 23:35
Bunuel wrote:
Official Solution:

If the salt concentration in Northern Lake increased by 20% from 1900 to 2000 while that in Southern Lake decreased by 10%, is in 2000, the salt concentration in Northern Lake higher than that in Southern Lake?

Statement (1) by itself is sufficient. Denote $$x$$ as the salt concentration in Northern Lake in 1900. Then the salt concentration in Southern Lake in 1900 is $$1.1x$$. By 2000, the concentration of salt in Northern Lake became $$1.2x$$ while that in Southern Lake became $$1.1*x*0.9 = 0.99x \lt 1.2x$$.

Statement (2) by itself is insufficient. S2 says nothing about the concentration in Northern Lake in 1900.

Hi you are assuming here that x has some value other than zero, but question stem does not say so. what if x is zero? that means there is no salt at all in northern lake them statement 1 is insufficient and in that case C will be the right answer. please clarify me if am wrong?
Re: M21-26 &nbs [#permalink] 06 Jul 2018, 23:35
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# M21-26

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