SAT Question of the day Nov 11 2012
In the figure above, which quadrants contain pairs that satisfy the condition ?
B. and only
C. and only
D. and only
E. , , , and
Ha… finally a question for those who remember their Trig !
and so many ways to solve – such fun!
Well, not really, everyone can answer this one. What are we asked? Where in the Cartesian plain the value of the X coordinate (horizontal location) divided by the value of the Y coordinate (the vertical coordinate) can equal 1?
Well X divided by Y = 1 whenever X and Y have the same value.
Now, if they are both positive it is clear that we are in the I quadrant. so I is true (bye bye answers D).
Before you mark A and move on ask yourself is there anywhere else their values might be equal?
Yes, actually when we are in quadrant III both X and Y are negatives and can have the same values (negative over negative is positive). That means III is also true (fair well to answer B). What happens in quadrants II and IV? well either the X is negative and the Y is positive (II) or the X is positive and the Y is negative (IV) – that means that even if they have the same absolute value the answer will be NEGATIVE 1 . We are left with answer C.
For Trig people – x/y = Tan(alpha) and Tan is positive in Quad I and III – easy work for you.
Yet another strategy. As you may be aware by now, following my recommended strategies, it is a good practice to read the answers as part of the reading of the question. Quad I appears in 4 out of the 5 answers – there is a good chance the statement is correct there. That means that we should start and check if the statement can be correct in Quad II – two advantages – saves time and hoop over answer A – because the question is not “find a Quad where the statement is correct” it is rather “find ALL the Quad where the statement is correct”and if you are on the last part of the growling 3+ hour test you might overlook it.
The SAT website reported 60% success by >100,000 people – which mean it is a mid-level question.