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sharmar
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M09 #23 19 Nov 2008, 10:17
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The price of a mobile phone of model A increased by 15% from last year while the price of a mobile phone of model B decreased by 25% from last year. Is the current price of a mobile phone of model A bigger than that of a mobile phone of model B?

1. Last year the price of a mobile phone of model B was 10 percent bigger than that of a mobile phone of model A
2. Last year model A cost $10 more than model B

(C) 2008 GMAT Club - [t]m09#23[/t]

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
* Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
* BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
* EACH statement ALONE is sufficient
* Statements (1) and (2) TOGETHER are NOT sufficient

S1 allows to express current prices of both models in terms of one variable and compare them. For example, if \(A\) is the last year's price of model A and \(B\) is the last year's price of model B, then:
\(\begin{eqnarray*} B_{current} &=& 0.75B = 1.1A*0.75\\ A_{current} &=& 1.15A\\ \end{eqnarray*}\)

Therefore, the current price of B is less than the current price of A. The question of course assumes that neither phone is given out for free.

S2 is obviously sufficient. If model A was more expensive than model B and model A gained in price while model B depreciated, then model A is still more expensive than model B.
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Don't S1 and S2 run counter to each other?? How can the cost of A last year be $10 more than B (S2) but the price of model B last year be 10% more than A (S1)???

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M09 #23 26 Nov 2008, 15:11
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sharmar
Quote:
The price of a mobile phone of model A increased by 15% from last year while the price of a mobile phone of model B decreased by 25% from last year. Is the current price of a mobile phone of model A bigger than that of a mobile phone of model B?

1. Last year the price of a mobile phone of model B was 10 percent bigger than that of a mobile phone of model A
2. Last year model A cost $10 more than model B

(C) 2008 GMAT Club - [t]m09#23[/t]

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
* Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
* BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
* EACH statement ALONE is sufficient
* Statements (1) and (2) TOGETHER are NOT sufficient

S1 allows to express current prices of both models in terms of one variable and compare them. For example, if \(A\) is the last year's price of model A and \(B\) is the last year's price of model B, then:
\(\begin{eqnarray*} B_{current} &=& 0.75B = 1.1A*0.75\\ A_{current} &=& 1.15A\\ \end{eqnarray*}\)

Therefore, the current price of B is less than the current price of A. The question of course assumes that neither phone is given out for free.

S2 is obviously sufficient. If model A was more expensive than model B and model A gained in price while model B depreciated, then model A is still more expensive than model B.

Don't S1 and S2 run counter to each other?? How can the cost of A last year be $10 more than B (S2) but the price of model B last year be 10% more than A (S1)???
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Thats true. Statement 1 and 2 both cannot go togather.
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M09 #23 24 Apr 2009, 22:48
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If the price of a mobile phone of model \(A\) increased by 15% from last year and the price of a mobile phone of model \(B\) decreased by 25% from last year, is the current price of a mobile phone of model \(A\) greater than that of a mobile phone of model \(B\) ?

1. Last year, the price of a mobile phone of model B was 10 percent greater than that of a mobile phone of model A
2. Last year, model A cost $10 more than model B


is it A?

OE never talks about condition no (2)

and OA given is D
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M09 #23 25 Apr 2009, 00:56
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should be D.
1) difference is in terms of percentage so whatever is the absolute figure the relation will be the same for price of A and B >> Suff

2) difference is in terms of absolute value. But the lesser absolute value(B) is decreasing and the higher absolute value(A) is increasing. So A will always be greater than B. ( Note, if A is less than B and if A is increasing and B is decreasing then this condition will be insufficient, I have explained it below ).

Actual problem:

eg. price of A is 11 => after 15% increase it is something greater than 11.
price of B is 1 => after 25% decrease it is something less than 1.
A > B

eg. price of A is 110 => after 15% increase it is something greater than 110.
price of B is 100 => after 25% decrease it is something less than 75.
A > B.

Sufficient.
So, D.

Lets see the corollary, that is if it is given that B is 10 more than A.
eg. price of A is 1 => after 15% increase it is 1.15.
price of B is 11 => after 25% decrease it is 8.25
A < B.

eg. price of A is 100 => after 15% increase it is 115.
price of B is 110 => after 25% decrease it is 82.5.
A > B.
So, in this case this condition will be insufficient.

nitya34
If the price of a mobile phone of model \(A\) increased by 15% from last year and the price of a mobile phone of model \(B\) decreased by 25% from last year, is the current price of a mobile phone of model \(A\) greater than that of a mobile phone of model \(B\) ?

1. Last year, the price of a mobile phone of model B was 10 percent greater than that of a mobile phone of model A
2. Last year, model A cost $10 more than model B


is it A?

OE never talks about condition no (2)

and OA given is D
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M09 #23 10 Jun 2009, 01:11
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But you're picking a case that works.

What if A = 1
and B = 11

Then new A = 1.15
new B = 8.25

The OA is wrong.

Economist
should be D.
1) difference is in terms of percentage so whatever is the absolute figure the relation will be the same for price of A and B >> Suff

2) difference is in terms of absolute value. But the lesser absolute value(B) is decreasing and the higher absolute value(A) is increasing. So A will always be greater than B. ( Note, if A is less than B and if A is increasing and B is decreasing then this condition will be insufficient, I have explained it below ).

Actual problem:

eg. price of A is 11 => after 15% increase it is something greater than 11.
price of B is 1 => after 25% decrease it is something less than 1.
A > B

eg. price of A is 110 => after 15% increase it is something greater than 110.
price of B is 100 => after 25% decrease it is something less than 75.
A > B.

Sufficient.
So, D.

Lets see the corollary, that is if it is given that B is 10 more than A.
eg. price of A is 1 => after 15% increase it is 1.15.
price of B is 11 => after 25% decrease it is 8.25
A < B.

eg. price of A is 100 => after 15% increase it is 115.
price of B is 110 => after 25% decrease it is 82.5.
A > B.
So, in this case this condition will be insufficient.

nitya34
If the price of a mobile phone of model \(A\) increased by 15% from last year and the price of a mobile phone of model \(B\) decreased by 25% from last year, is the current price of a mobile phone of model \(A\) greater than that of a mobile phone of model \(B\) ?

1. Last year, the price of a mobile phone of model B was 10 percent greater than that of a mobile phone of model A
2. Last year, model A cost $10 more than model B


is it A?

OE never talks about condition no (2)

and OA given is D
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M09 #23 10 Feb 2010, 00:49
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The statements must be changed! They are confusing and take precious time during the test! They cannot contradict each other!
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M09 #23 10 Feb 2010, 01:15
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The price of a mobile phone of model A increased by 15% from last year while the price of a mobile phone of model B decreased by 25% from last year. Is the current price of a mobile phone of model A bigger than that of a mobile phone of model B?

1. Last year the price of a mobile phone of model B was 10 percent bigger than that of a mobile phone of model A
2. Last year model A cost $10 more than model B

(C) 2008 GMAT Club - m09#23

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
* Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
* BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
* EACH statement ALONE is sufficient
* Statements (1) and (2) TOGETHER are NOT sufficient


Here's an explanation,

Let Price Cell Phone A last year be X , and that of Model B be Y
According to Information given in the question

Model A's current price = X + 15/100X , Model B's current price = Y - 25/100Y

Now lets work with the statements given.

1) Last year the price of a mobile phone of model B was 10 percent bigger than that of a mobile phone of model A

Y = 10/100X , so we have a relationship between Y and X , Substitute this value of Y in Model B's current price

Model B's current price = 10/100X - (25/100*10/100)X, which is clearly lesser than Model A's current price X + 15/100X - hence sufficient.

2)Last year model A cost $10 more than model B

X = Y + 10 or Y = X - 10 , again substitute this value in Model B's current Price and we can compare the two to tell if X's current price is greater or less than B's current price.

No point getting bogged down in calculations.

Hence answer - D, each statement alone is sufficient.

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