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Obligatory disclaimer of a follow up post: I'm not recommending that anyone buy Bitcoin! (In fact if it were me I'd be selling, but don't take investment advice from me, for goodness sake!) It just seemed like a neat way to frame an idea I thought might be helpful.

by Matt@VeritasPrep

Thu Dec 07, 2017 4:20 pm
Forum: Helpful Resources
Topic: When to STOP studying for the GMAT
Replies: 3
Views: 3587

ok sure

Great post, Ceilidh! One thing I'd add: progress on the GMAT isn't linear! It's much harder to get from 650 to 700 than it is to get from 500 to 650. I tell students this a lot, but there's a perfect illustration in the news this week - Bitcoin! Everyone's heard about the unfathomable price spike of...

by Matt@VeritasPrep

Thu Dec 07, 2017 4:16 pm
Forum: Helpful Resources
Topic: When to STOP studying for the GMAT
Replies: 3
Views: 3587

No prob!

by Matt@VeritasPrep

Thu Dec 07, 2017 3:57 pm
Forum: GMAT Math
Topic: help
Replies: 12
Views: 9630

subjected to this again

Fun follow up conceptual question: the harmonic mean of 20 and 30 just happens to be 24. Is this a shortcut to solve this problem, or just a coincidence? Explain your answer. :)

*Jeopardy music*

by Matt@VeritasPrep

Thu Dec 07, 2017 3:56 pm
Forum: GMAT Math
Topic: time speed distance question
Replies: 3
Views: 3888

I see you've already done this, but it might be a good idea to copy the entire thread to the Helpful Resources subforum: it'll have less of a chance of getting swept off the main page! (Though I suppose it could keep being resurrected :))

by Matt@VeritasPrep

Thu Dec 07, 2017 3:53 pm
Forum: GMAT Math
Topic: Master List of Quant/GMAT Math Resources
Replies: 9
Views: 5550

This isn't really answerable because it isn't clear if we're replacing the marbles between draws. (It *sounds* like we aren't, but it isn't clear.) If we ARE replacing the marbles, then it's just ((# of yellow marbles) / (# of marbles))³ If we AREN'T replacing the marbles, then it's (# of yellow / ...

by Matt@VeritasPrep

Tue Dec 05, 2017 6:36 pm
Forum: Problem Solving
Topic: There are three blue marbles, three red marbles ....
Replies: 3
Views: 1069

A little easier:

x² - 8xy + 16y² = 0

(x - 4y)² = 0

x = 4y

by Matt@VeritasPrep

Tue Dec 05, 2017 6:30 pm
Forum: Problem Solving
Topic: If x >= 0 and x=root(8xy-16y^2), then, in terms of y, x=?
Replies: 3
Views: 1033

wv

I've got a quick way!

x² + 5|x| + 6 = 0

(|x| + 2) * (|x| + 3) = 0

(|x| + 2) = 0 or (|x| + 3) = 0

|x| = -2 or |x| = -3

But no absolute values are negative, so there are no real solutions to this equation.

by Matt@VeritasPrep

Tue Dec 05, 2017 6:27 pm
Forum: Problem Solving
Topic: If x is an integer, how many possible values
Replies: 3
Views: 2339

Piggybacking on David's answer, 154 * 18/4 => 154 * 4.5, so the answer has to be more than 150 * 4, or more than 600. From there it's a cinch!

by Matt@VeritasPrep

Tue Dec 05, 2017 6:19 pm
Forum: Problem Solving
Topic: Elana was working to code protocols for computer...
Replies: 4
Views: 1158

We could also invoke the Lazy Testwriter Principle: the answers are probably friendly and/or small numbers, so try those. Let's start with x-y+z=-1 This looks like -1 - 0 + 0, so let's say x = -1, y = 0, and z = 0. If we plug those into our other two equations: -x + y + z => -(-1) + 0 + 0 => 1 and x...

by Matt@VeritasPrep

Tue Dec 05, 2017 6:14 pm
Forum: Problem Solving
Topic: If x-y+z=-1, -x+y+z=1, and x+y-z=-1, then x+y+z=?
Replies: 4
Views: 1133

Yet another way: If our solutions are -6 and 3, then we can say (-6)² -6 * b + c = 0 and 3² + 3b + c = 0 so: 36 - 6b + c = 0 and 9 + 3b + c = 0 Now just solve the two equations! Let's multiply the bottom one by 2: 18 + 6b + 2c = 0 then add it to the top one: 54 + 3c = 0 54 = -3c -18 = c Now plug c...

by Matt@VeritasPrep

Tue Dec 05, 2017 6:02 pm
Forum: Problem Solving
Topic: If -6 and 3 are the solutions of the...
Replies: 4
Views: 1177

Another way:

Remember that the roots of (x + r) * (x + s) = 0 are x = -r and x = -s.

We're told that -r = -6 and -s = 3, so r = 6 and s = -3. Plugging those in, we have

(x + 6) * (x + -3) = 0

and foiling

x*x + 6x - 3x - 18 = 0

or

x*x + 3x - 18 = 0

so b = 3, c = -18, and b + c = -15.

by Matt@VeritasPrep

Tue Dec 05, 2017 5:43 pm
Forum: Problem Solving
Topic: If -6 and 3 are the solutions of the...
Replies: 4
Views: 1177

s = 100 * 101 * ... * 199 * 200

t = 100 * 101 * ... * 199 * 200 * 201

t = s * 201

t/201 = s

so:

1/t + 1/s is the same as

1/t + 1/(t/201) is the same as

1/t + 201/t is the same as

202/t


Also, for those flashcarding this:

Given two legs of a triangle, the area of the triangle has the range: 0 < area ≤ (given side * other given side) / 2

by Matt@VeritasPrep

Tue Dec 05, 2017 5:24 pm
Forum: Problem Solving
Topic: One side of a triangle has lenght 8 and a second side...
Replies: 3
Views: 1078

Let's avoid trig, since the GMAT doesn't expect us to know it. Visualizing the triangle, we can make the area about as small as we'd like by simply extending the third side as far as it can go: https://s8.postimg.org/stqfnzyqp/Screen_Shot_2017-12-05_at_5.18.22_PM.png As our base approaches 8 + 5, ou...

by Matt@VeritasPrep

Tue Dec 05, 2017 5:23 pm
Forum: Problem Solving
Topic: One side of a triangle has lenght 8 and a second side...
Replies: 3
Views: 1078