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Challenge #3: Percentages

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by aneesh.kg » Sun Feb 10, 2013 11:21 am
The population of a city, which was X in January, increases by a certain amount in February of the same year and becomes Y. Then Y increases by a certain amount in March of the same year and becomes Z. Is the percentage change from X to Y greater than that from Y to Z?
(1) Y - X = Z - Y
(2) X = 150, Z = 300

OA: Later
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Source: — Data Sufficiency |
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by hemant_rajput » Mon Feb 11, 2013 7:54 am
aneesh.kg wrote:The population of a city, which was X in January, increases by a certain amount in February of the same year and becomes Y. Then Y increases by a certain amount in March of the same year and becomes Z. Is the percentage change from X to Y greater than that from Y to Z?
(1) Y - X = Z - Y
(2) X = 150, Z = 300

OA: Later
Source: Self-designed
solution is A
1.
we know difference in population for 2 months is equal. Lets take some arbitrary values, say 100,120,140 for Jan, Feb and Mar resp.

so percentage change from jan to feb is 20% but from feb to mar is 16.67 %.
so sufficient.

2. now we know the population in Jan and Mar but we don't know the population in Feb. It can as low as 151 or as high as 299.

so insufficient.
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by Sam_hellboy » Tue Feb 12, 2013 12:23 am
IMO A
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by vishalbpr » Tue Feb 12, 2013 3:45 am
Answer should be C...

1. Y-X = Z - Y

So percentage changes would be
(Y-X)/X and (Z - Y)/Y. Though we are aware Y-X = Z-Y but we do not know the X and Y, so it is not possible to get the result.

2. X = 150 and Z = 300, Again Y is not mentioned, so not possible to find the ratio...

After consider both the statements X = 150, Y =225 and Z = 300, now it is possible to find the exact percentage.

Hope I am correct.
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by hemant_rajput » Tue Feb 12, 2013 4:23 am
vishalbpr wrote:Answer should be C...

1. Y-X = Z - Y

So percentage changes would be
(Y-X)/X and (Z - Y)/Y. Though we are aware Y-X = Z-Y but we do not know the X and Y, so it is not possible to get the result.

2. X = 150 and Z = 300, Again Y is not mentioned, so not possible to find the ratio...

After consider both the statements X = 150, Y =225 and Z = 300, now it is possible to find the exact percentage.

Hope I am correct.

you don't need to know the value of x, y and z. for any value of x, y and z, with accordance to statement 1, percentage change of population from x to y will always be greater than change of population from y to z.

Hence 1 is sufficient.
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by vishalbpr » Tue Feb 12, 2013 4:40 am
hemant_rajput wrote:
vishalbpr wrote:Answer should be C...

1. Y-X = Z - Y

So percentage changes would be
(Y-X)/X and (Z - Y)/Y. Though we are aware Y-X = Z-Y but we do not know the X and Y, so it is not possible to get the result.

2. X = 150 and Z = 300, Again Y is not mentioned, so not possible to find the ratio...

After consider both the statements X = 150, Y =225 and Z = 300, now it is possible to find the exact percentage.

Hope I am correct.

you don't need to know the value of x, y and z. for any value of x, y and z, with accordance to statement 1, percentage change of population from x to y will always be greater than change of population from y to z.

Hence 1 is sufficient.
I think you are right... X < Y, so percentage change will be higher in X to Y transition than Y to Z transition...

Thanks for correcting me
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by hemant_rajput » Tue Feb 12, 2013 7:42 am
vishalbpr wrote:
hemant_rajput wrote:
vishalbpr wrote:Answer should be C...

1. Y-X = Z - Y

So percentage changes would be
(Y-X)/X and (Z - Y)/Y. Though we are aware Y-X = Z-Y but we do not know the X and Y, so it is not possible to get the result.

2. X = 150 and Z = 300, Again Y is not mentioned, so not possible to find the ratio...

After consider both the statements X = 150, Y =225 and Z = 300, now it is possible to find the exact percentage.

Hope I am correct.

you don't need to know the value of x, y and z. for any value of x, y and z, with accordance to statement 1, percentage change of population from x to y will always be greater than change of population from y to z.

Hence 1 is sufficient.
I think you are right... X < Y, so percentage change will be higher in X to Y transition than Y to Z transition...

Thanks for correcting me
No problem; sometime in hurry we skip things which is conspicuous to us. I think, In the end that's, which make all the differences.


cheers,
Hemant
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by AJP » Tue Mar 12, 2013 7:17 am
Y-X=Z-Y
Y-150=300-Y
Y=225
Percentage increase from January to February is 75*100/150 = 50 o/o
percentage increase from February to March is 75*100/225 = 33.33 o/o
So increase o/o from January to February is more than from February to March.

i think my answer is correct
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by Brent@GMATPrepNow » Tue Mar 12, 2013 7:45 am
aneesh.kg wrote:The population of a city, which was X in January, increases by a certain amount in February of the same year and becomes Y. Then Y increases by a certain amount in March of the same year and becomes Z. Is the percentage change from X to Y greater than that from Y to Z?
(1) Y - X = Z - Y
(2) X = 150, Z = 300
Target question: Is the percentage change from X to Y greater than that from Y to Z?

Given: X < Y < Z

Required formula: % increase = 100(new - original)/original

Statement 1: Y - X = Z - Y
Let I = Y - X = Z - Y
So, the % increase from X to Y = 100(Y-X)/X = 100I/X
The % increase from Y to Z = 100(Z-Y)/Y = 100I/Y

IMPORTANT: since X < Y, we know that 100I/X > 100I/Y
In other words, the percentage change from X to Y is greater than that from Y to Z.
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: X = 150, Z = 300
There are several cases that meet this condition. Here are two:
Case a: X=150, Y=299, Z=300, in which case the percentage change from X to Y is greater than that from Y to Z?
Case b: X=150, Y=151, Z=300, in which case the percentage change from X to Y is not greater than that from Y to Z?
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

Cheers,
Brent
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by nikhilgmat31 » Thu Sep 03, 2015 5:18 am
answer is A. -- Major point to identify in question is that changes In both months is different.

But if it is given that values increased by same amount then statement 2 is also sufficient.

150 -> 225
225 -> 300
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by Max@Math Revolution » Fri Sep 04, 2015 3:04 am
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and equations ensures a solution.


The population of a city, which was X in January, increases by a certain amount in February of the same year and becomes Y. Then Y increases by a certain amount in March of the same year and becomes Z. Is the percentage change from X to Y greater than that from Y to Z?
(1) Y - X = Z - Y
(2) X = 150, Z = 300

Transforming the original condition and the question, we have percentage change =(After-Before)*100/Before.

Since the question is essentially (Y-X)*100/X>(Z-Y)*100/Y, in case of (1) substituting Y-X=Z-Y and multiplying 100 to both sides gives us 1/X>1/Y?, in other words if Y>X?. Since the population increases by a certain amount, the answer is yes and therefore it is sufficient.
The answer is A.

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