In the figure above, segments PR and QR are each parallel to one of

1) not sufficient: we will get the coordinates of point Q but not length
2) not sufficient: again we wont get the length

Combining both We get the lengths of both lines and from there we can find the ratio

1) not sufficient
2) not sufficient

Combining: You can either calculate the length of PQ or, as I did, calculated the slope of line PQ.

Since slope = 1, it means that angle RPQ and PQR must have 45 degrees. Thus, the length of QR to the length of PR must be 1.

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 the figure above, segments PR and QR are each parallel to one of the rectangular coordinate axes. Is the ratio of the length of QR to the length of PR equal to 1?

(1) c = 3 and d = 4.
(2) a = -2 and b = -1.

The question is actually asking whether QR=PR and whether the gradient of the line passing through P and Q is 1
There are 4 variables (a,b,c,d) but there are only 2 equations, so there is high chance (C) will be the answer.
Looking at the conditions together, slope=(-2-3)/(-1-4)=1, and this answers the question 'yes' and the answer becomes (C).

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, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. 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 using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.

We can determine the coordinates of R without much extra work

R(c,b)
The question is then is (d-b)/(c-a) = 1?

stat.1 - gives only one coordinate. IS
Stat.2 - gives only one coordinate. IS

Combined we have all the coordinates.

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