OG 2015, #41

Is 4^(x+y) = 8^(10)? 1.) x - y = 9 2.) y/x = 1/4 I've seen the solution for the above problem, but I'm confused why I could not solve for x and y using each statement separately? Once you get down to the point that you're solving: Does x + y = 15? At this point, why could I not use Statement 1 as fo...

Use of colon

The defense lawyer and witnesses portrayed the accused as a victim of circumstance, his life uprooted by the media pressure to punish someone in the case. A.) circumstance, his life B.) circumstance, and his life C.) circumstance, and his life being D.) circumstance; his life E.) circumstance: his l...

Divisibility yes/no question

Is integer x divisible by 24? 1.) x is divisible by 6. 2.) x is divisible by 4. I understand how to do this which "trying numbers". I would like to understand how to approach this using prime factors. For instance: 24 is equal to: 3*2*2*2. Statement (1) provides that x is divisible by 3*2 ...

Necessary Assumption

Any help/guidance on how to approach the following would be appreciated. In casual conversation, people experience little psychological discomfort in admitting that they have some particular character flaw if and only if they consider trivial the flaw to which they admit. Therefore, if in casual con...

Factors/Multiples problem

If 375y = x^2 and x and y are positive integers, then which of the following must be an integer?

I.) y/15

II.) y/30

III.) y^2/25

A.) I only
B.) III only
C.) I and II only
D.) I and III only
E.) I, II, and III only

Brent - thank you that really helps. As a quick follow-up, does that mean the concept of using and trying to sight Pythagorean triples is helpful only for when we have 2 known sides then? In other words, just having a right triangle and 1 side of a known Pythagorean triple is not enough to deduce th...

Can anyone help me understand how to use the "Double Set Matrix" or "Tic Tac Toe" method to solve the following similar problem? I think I'm running astray somewhere (see image below). If this problem doesn't lend itself to the method, is there a key way to identify why not? Than...

Probability and Permutation problem

Any help on how to best approach the following problem would be appreciated.

If a fair two-sided coin is flipped 6 times, what is the probability that tails is the result at least twice but at most 5 times?

A) 5/8
B) 3/4
C) 7/8
D) 57/64
E) 15/16