M09 #23

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.

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.

The statements must be changed! They are confusing and take precious time during the test! They cannot contradict each other!

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.