An Important Sequence & a CR link

Here's a type of Sequences question I wasn't aware of, till now.

Repeating Patterns

Many times, repeating patterns will yield a remainder question.

The first term of a sequence is  -2 and the second term is 2. Each subsequent odd term is found by adding 2 to the previous term, and each subsequent even terms is found by multiplying the previous term by -1. What is the sum of the first 669 terms?

Clearly, we are not looking to enter all 669 terms and see what the last one is. But, we can do a few and check out the pattern.
n = 1, = -2
n = 2, = 2
n = 3, = 4
n = 4, = -4
n = 5, = -2
n = 6, = 2
Since we can see that the pattern will repeat every 4 terms, we can solve for the remainder after dividing 669/4. Since 4 goes into 668 evenly, we know that the value will be equivalent to that of the first term, which = -2.

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Also discovered a whole host of useful GMAT CR articles on BTG. Read the first two (in chronological order) and found them pretty useful. Even assumptions are of two types: sufficient and necessary! And the question type (by a subtle change in wording) can change the answer! Damn. Those 2 are definite re-read material.

Day 21 - 25

Day 21
Did questions from PR Math Bin 4 that I got wrong, and then later reviewed the stuff I didn't get with a Math whiz of a friend. :-)

Day 22
Went through BTG's Math FC's and kept aside the ones that require review.


Day 23
So, to improve on my not so great CR accuracy on GMATPrep1, I went back to PR CR section and tried reading it again. Didn't work. Got bored. So I picked up Verbal Bin 1 and solved all CR questions in it. I got all right, obviously. Cos it was Verbal Bin 1. Anyway...

Day 24
This Friday i.e. 27th December, 2009. Went through a couple of questions on GMATHacks. Thus, the barrage of new CPs on the blog.

Day 25
Did a few more questions from the same source.

I know...I'm not doing enough. But I am now.

Day 17 - 20

Day 17
IMS BRM (basic reference material) - P&C, Probability (some of it)

Day 18
IMS BRM - P&C, Probability
IMS WB (workbook) - P&C, Probability
GMATPrep1 error log - made

Day 19
IMS BRM - Time, Speed & Distance (TSD)
IMS WB - TSD
GMATPrep1 error log - analysed

GMATPrep1	PS	DS	CR	SC	RC
Percentage Correct	65%	24%	45%	71%	77%
Average Timing	2.14	1.54	1.96	1.08	1.84
Avg timing for correct qs	2.40	2.28	2.04	1.05	1.87
Avg timing for wrong qs	1.65	1.31	1.89	1.15	1.74
	0.75	0.97	0.15	-0.10	0.13

Day 20
PR Math Bin 4 (timed - 3 mins/qs)

PR MathBin4	PS	DS
Percentage Correct	67%	70%
Average Timing	2.59	2.28
Avg timing for correct qs	2.71	2.19
Avg timing for wrong qs	2.35	2.48
	0.37	-0.29

An easy calculation trick

From GMATHacks.com explanation to a Question of the Day.

= 16/125
To simplify that fraction, recognize that 125 is 1/8 of 1,000, so:
= (16/125)*(8/8)
= 128/1000
= 0.128.

CP #7

From GMATHacks again.

Commensalism is any relationship between two living things in which one benefits and the other is neither helped nor harmed. Oxpecker birds are commensal species that flock with the large mammals of the African Savannah. They feed on ticks, fleas, and flies that are attracted to the mammals' fur. Which of the following, if true, can most reasonably be inferred from the statements above?
(A)	Oxpecker birds are neither helped nor harmed by the large mammals of the African Savannah.
(B)	Ticks, fleas, and flies are commensal species in their relationship with both oxpecker birds and the large mammals of the African Savannah.
(C)	No species exist in a commensal relationship with oxpecker birds except for large mammals of the African Savannah.
(D)	In commensal relationships, the smaller of the species in the relationship usually benefits while the larger is neither helped nor harmed.
(E)	Preying on small creatures drawn to the fur of the large mammals of the African Savannah does not significantly affect those mammals.

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Answer: E

This is an inference question. The passage suggests that, since oxpecker birds are commensal species with large mammals, they benefit from the creatures that are attracted to the mammals' fur, but the mammals themselves are neither helped nor harmed by the relationship. Consider each choice, looking for a reasonable inference:

(A) This choice gets the commensal relationship exactly backwards.
(B) This is clearly wrong. If oxpecker birds feed on ticks, fleas, and flies, clearly the ticks, fleas, and flies are neither benefiting nor neutral in their relationship with the oxpecker birds.
(C) This choice is too extreme. The passage only describes this relationship; it doesn't tell us that it is exclusive.
(D) This is also too extreme. It may be true in some instances, but the three sentences of the passage don't provide enough evidence to reasonably deduce this.
(E) This is correct. It merely restates the definition of commensalism in terms of the role of the mammals in their relationship with oxpecker birds.

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I know it's not a difficult question, but I've made the same sort of mistake on earlier questions too. I had used POE to come down to A & E. But, by then I had lost track of the question I guess, and chose A. A Veritas Prep GMAT Tip of the Week talks about such mistakes.

CP #6

From GMATHacks.com

Bipedal dinosaurs' standing posture differs from virtually every visual depiction of them created before the 1970s, when scientists reevaluated their assumptions about tripod-style balance.
(A)	Bipedal dinosaurs' standing posture differs from
(B)	Bipedal dinosaurs stood in a posture that differs from
(C)	Bipedal dinosaurs exhibited standing postures that differ from those of
(D)	The standing posture of bipedal dinosaurs differs from
(E)	The characteristics of bipedal dinosaurs' standing posture differ from those of

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Answer: C

The words "differ from" signal that there is a comparison. In this case, the comparison is between the actual posture of dinosaurs and the posture as depicted by certain images. As written, the sentence is incorrect: it compares the actual standing posture with "every visual depiction." We can't compare a posture with a picture as those are unlike things.

Choice (B) makes the same mistake, comparing a posture with pictures. (C) makes a proper comparison between "standing postures" and "those of." The word "those" takes the place of "standing postures," so we're comparing the actual standing postures with the standing postures as depicted. (D) makes the same mistake as (A) and (B). (E) is complicated but is yet another comparison error. It compares characteristics of standing posture with "those" (characteristics) of visual depictions. Those are different things, so (C) must be correct.

CP #5

Question #2 from Kaplan Problem Solving challenge.

The “connection” between any two positive integers a and b is the ratio of the smallest common multiple of a and b to the product of a and b.  For instance, the smallest common multiple of 8 and 12 is 24, and the product of 8 and 12 is 96, so the connection between 8 and 12 is 

The positive integer y is less than 20 and the connection between y and 6 is equal to . How many possible values of y are there?

	7
	8
	9
	10
	11

Answer Explantion:

If the connection between y and 6 is , then the least common multiple of y and 6 must equal the product 6y. The least common multiple of two numbers equals the product of the two numbers only when there are no common factors (other than 1). Since y is a positive integer less than 20, check all the integers from 1 to 19 to see which ones have no factors greater than 1 in common with 6:  1, 5, 7, 11, 13, 17, and 19. So there are 7 possible values for y.

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In my own words (which I can actually understand!),

for the ratio to be 1:1, the LCM should be =6y (so that it cancels out with the product).

For this to be possible, y should NOT be a multiple of 6, and should not include 2,3 or any multiples of 2,3. The only numbers that are not multiples of 2,3 and 6 are 1,5,7,11,13,17,19, a total of 7 numbers!

Why I got it wrong:
I actually randomly guessed on this one cos I knew it would take me more thinking to get the right answer, and so I tried applying the pacing advice I read on a MGMAT forum today.

CP #4

This is a Kaplan Problem Solving Challenge question. It's a 25 minute quiz with 16 questions. I finished it just in time, but I got 2/16 wrong. Here's the first one:


In the diagram above, the line y = 4 is the perpendicular bisector of segment JK (not shown).  What is the distance from the origin to point K ?

	4
	8

Answer Explantion:

Don't try to keep all the information in your head - add to the diagram so you can refer to it as you solve. Horizontal line y = 4 is the perpendicular bisector of JK, so JK must be vertical and parallel to the y-axis. Draw in segment JK, dropping straight down from point J through the x-axis. Before you can find the distance from the origin to point K, you need to know its coordinates. K is directly below J so both points are the same distance from the y-axis and their x-coordinates must be the same. So the x-coordinate of K is 6. Since the line y = 4 bisects JK, the vertical distance from J to the line must be the same as the vertical distance from the line to K. Vertical distance is the difference between the y-coordinates, so the vertical distance from J to line y = 4 is 10 - 4, or 6. Therefore the difference between the y-coordinates of line y = 4 and point K is also 6, so the y-coordinate of K = 4 - 6, making -2 the y-coordinate of point K. So the coordinates of point K are (6, -2). You will notice that K, the origin O, and the point where JK crosses the x-axis is a right triangle, with its hypotenuse being the distance from the origin to point K. Use the Pythagorean theorem to find the length of the hypotenuse. Hypotenuse² = (length of leg lying on the x-axis)² + (length of the leg parallel to the y-axis)² = 6² + 2² = 40. So the distance from the origin to K =  = .

What I did wrong

1. Didn't remember distance formula

2. Made a mistake in considering K (6,0) since I didn't realise that my K to line y=4 was only 4 points away, not 6.

Wow, this is a first! Didn't remember the formula, AND made a silly mistake!