CP #25

MGMAT CAT#2


The greatest common factor of 16 and the positive integer n is 4, and the greatest common factor of n and 45 is 3. Which of the following could be the greatest common factor of n and 210?

		3
		14
		30
		42
		70

Solution

The greatest common factor (GCF) of two integers is the largest integer that divides both of them evenly (i.e. leaving no remainder).

One way to approach the problem is to consider what the GCFs stated in the question stem tell us about n:

The greatest common factor of n and 16 is 4. In other words, n and 16 both are evenly divisible by 4 (i.e., they have the prime factors 2 × 2), but have absolutely no other factors in common. Since 16 = 2 × 2 × 2 × 2, n must have exactly two prime factors of 2--no more, no less.

The greatest common factor of n and 45 is 3. In other words, n and 45 both are evenly divisible by 3, but have absolutely no other factors in common. Since 45 = 3 × 3 × 5, n must have exactly one prime factor of 3--no more, no less.  Also, n cannot have 5 as a prime factor.

So, n must include the prime factors 2, 2, and 3. Furthermore, n is not divisible by 8, 9, or 5.

The number 210 has the following prime factorization: 210 = 2 x 3 x 5 x 7. Thus n and 210 are both divisible by 2 and 3, and both might be divisible by 7, but it is not the case that both numbers are divisible by 4 or by 5:

(A) 3: missing a 2
(B) 14: missing a 3
(C) 30: n cannot be divisible by 5
(D) 42: Correct. n and 210 are both divisible by 2 and 3, and n could be divisible by 7.
(E) 70: n cannot be divisible by 5 and must be divisible by 3.

The correct answer is D.

OG12 quant almost done

40 more questions from OG12 done. 19/20 right in PS (avg time: 1:56) and 18/20 right in DS (avg time: 2:16).

I feel more focus was in order while doing DS questions, but there are probably more concepts I need to understand in greater depth in order to get my questions right at a quicker pace.

GMAT Love!

Back to OG12 Quant

Wohkay! Seems like I've been out of touch with OG type Math questions for too long.
Did 20 PS and 20 DS questions (timed) today.
Got 4 wrong in PS and...wait for it...9 wrong in DS! Eeeks!
Gotta review and get back to official questions! Good thing I have only the medium-difficult questions remaining... :)

GMAT love to the rest of you! Hope you're studying hard for the next 72 hours...to be able to party tomorrow night without guilt! :)

The beginning of reality.

Started OG12 this morning - 14 PS and 10 CR questions. Got 2 CR questions wrong. And I'm going to get excited every time I get a Verbal question wrong from now on, esp CR. Because if I get an OG question wrong, it will help me learn where I'm going wrong! :)


Also done with Speed Math chapter 9, still going through chapter 10.

Spent some time in office doing questions from BTG's articles. Was fun! :) I need to get back in the groove now, still hoping to get done with GMAT by mid-November. Wish me luck guys, I neeeed it!

Happy Gmatting!

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.

 -------------------------------------------------------------------

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!

CP #3

Another good question. They haven't posted the answer yet.

MGMAT Challenge Problem of the Week

10/26/09

Machines A, B, and C

Machines A, B, and C can either load nails into a bin or unload nails from that bin. Each machine works at a constant rate that is the same for loading and for unloading, although the individual machines may have different rates. Working together to load at their respective constant rates, machines A and B can load the bin in 6 minutes. Likewise, working together to load at their respective constant rates, machines B and C can load the bin in 9 minutes. How long will it take machine A to load the bin if machine C is simultaneously unloading the bin?

(A)	12 minutes
(B)	15 minutes
(C)	18 minutes
(D)	36 minutes
(E)	54 minutes

I think the answer is C. I don't think my method is long, but I do think I took a little extra time to think up of the process (again, cos I doubted my concept clarity a little, and so didn't quickly start to solve it the way I was thinking...tried applying formula first, but what good is that if I don't know the concept extremely well?). I'll wait till tomm for them to give the right answer, as well as their explanation. Then I'll compare my answer with theirs. 

Edit: The OA is C.