In a certain store, the price of five pens is equal to the price of a

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 independent equations ensures a solution.

In a certain store, the price of five pens is equal to the price of a notebook. What is the cost of a ruler in this store?

(1) The cost of four pens and two notebooks is 10 dollars more than the cost of six rulers.
(2) The cost of seven notebooks is 25 dollars more than the cost of 15 rulers.

Transforming the original condition and the question, we obtain the below 2by2 table that are common in GMAT math test.



There are 6 variables (a,b,c,x,y,z), 1 equation (5x=y). We need 5 more equations to match the number of variables and equations. Since there is 1 each in 1) and 2), E has high probability of being the answer. Using both 1) & 2) together, 4x+2y=10+6z, 7y=25+1z, but the value of z is still unknown. Therefore the answer is E.

Normally for cases where we need 3 more equations, such as original conditions with 3 variables, or 4 variables and 1 equation, or 5 variables and 2 equations, we have 1 equation each in both 1) and 2). Therefore E has a high chance of being the answer (especially about 90% of 2by2 questions where there are more than 3 variables), which is why we attempt to solve the question using 1) and 2) together. Here, there is 80% chance that E is the answer, while C has 15% chance. These two are the key questions. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer according to DS definition, we solve the question assuming E would be our answer hence using ) and 2) together. (It saves us time). Obviously there may be cases where the answer is A, B, C or D.

oh yeah..this one is a real punisher for those who believe that 2 equations with 2 unknowns can be solved if given certain information...

we are told -> 5p=1n

1. 4p+2n=6r+10 or (14p-10)/6 = r
we can't find..since we have 2 variables...

2. 7n=15r+25
7n=35p
35p=15r+25
divide by 5
7p=3r+5
again not sufficient..

1+2
7p=3r+5
14p = 6r+10
now..combine with equation from first statement:
6r+10-10/6 = r
this is true for all values of r
10 just simply cancels
and we are left with 6r/6=r
clearly insufficient. C is out, and the only answer is

E

We don't know whether each of the pen has the same price, nor do we know whether each of the notebook has the same price. Even we assume the equal price for each item, state 1 and 2 are basically the same equation. Therefore, E is our answer.