Overlapping Sets In An Interesting GMAT, GRE Quant Problem

There are 750 male and female participants in a meeting. Half of the female participants and one-quarter of the male participants are Democrats. One-third of all the participants are Democrats. How many of the Democrats are female?

(A) 75
(B) 100
(C) 125
(D) 175
(E) 225

Relative Range Distance Rate Time GMAT, GRE Problem

The distance between Mercury and Earth changes due to the orbits of the planets. When Mercury is at its closest point to Earth, it is 48 million miles away. When Mercury is at its furthest point from Earth, it is 138 million miles away. For a science project, Ruby calculates the maximum and minimum amount of time it would take to travel from Earth to Mercury in a spacecraft traveling 55 miles per hour. Approximately what are the times, in days?

(A) 3,636 and 10,454
(B) 14,545 and 41,818
(C) 36,364 and 104,545
(D) 87,272 and 250,909
(E) 872,727 and 2,509,091

GMAT, GRE Remainder Question with Variable Choices

A refresher on remainders follows the solution. 

When integer b is divided by 13, the remainder is 6. Which of the following cannot be an integer?

A) 13b/52
B) b/26
C) b/17
D) b/12
E) b/6



"When b is divided by 13, if the remainder is 6"
Let's take that to mean the following:
b/13 = q remainder 6
q will be an integer since it's essentially the answer to the equation.

Rearrange, remembering that remainders stay the same number when you multiply by the divisor (which is 13 in this case)
b = 13q + 6

Plug in the answers so we can see which works best.

A) 13b/12

Will 13(13q + 6)/12 equal an integer if we plus in for q? 

Let's say q = 6. 

If q = 6, then 13q + 6 = 84, which is is divisible by 12; hence 13(84)/12 is an integer.

B) b/26

Could (13q + 6)/26 result in an integer for an integer value of q? 

First off, 26 is exactly 2 times 13. So, for any integer value of q, 13q will either be divisible by 26 if q is even or produce a remainder of 13 if q is odd. 

Adding 6 to 13q, the expression will either produce a remainder of 6 or 19, but will never produce a remainder of zero. So, (13q + 6)/26 = b/26 can never equal an integer.

B.

GMAT GRE Probability Problem

Set A: {1, 3, 4, 6, 9, 12, 15}

If three numbers are randomly selected from set A without replacement, what is the probability that the sum of the three numbers is divisible by 3?

A. 3/14
B. 2/7
C. 9/14
D. 5/7
E. 11/14