**Question 61 – “ If 2x(5n)=…” **

OG Explanation is fine.

**Question 62 – “In the equation…”**

OG Explanation is pretty good and it was nice of them to give three methods for Statement I – though I don’t know who would use method 3.

**Question 63 – “A Town T….”**

OG Explanation is good but long. You could set up a chart, but personally I feel this way is easier.

To start with, Town T has 20,000 residents. 60% or 12,000 are female. Also, 8,000 are male.

Statement 1: “The number of female residents who were born in Town T is twice the number of male residents who were not born in T.”

(Female Born, Female not born, Male Born, Male not born) = (2, 11998, 7999, 1) or (20, 11980, 7990, 10). These are two possibilities and yield different percentages. INSUFFICIENT.

Statement 2: “The number of female residents who were not born in Town T is twice the number of female residents who were born in Town T” This statement tells us that the ratio of [females residents who were not born in Town T] to [female residents who were born in Town T] is 2 to 1. Because, there are 12,000 females: statement 2 tells us there were 8,000 females not born in T and 4,000 females that were born in T. We know nothing the male residents of T so we cannot get a percentage for all the residents. INSUFFICIENT.

Thus, we have eliminated A, B, and D.

Combining both statements:

By statement 2, Female Born = 4,000. By statement 1, this is twice of the males not born. Therefore, the number of males not born is 2,000. There are 8,000 males. So we are left with:

Female Born: 4,000

Female Not-Born: 8,000

Male Born: 6,000

Male Not Born: 2,000

Based on the above information, we can find what percent of the residents were born in town T. The correct answer is C.

**Question 64: “If y is an….”**

OG Explanation is fine.

**Question 65: “In Triangle XYZ…”**

OG Explanation is fine.

**Question 66: “If the average…”**

OG Explanation is too complicated. It is easier just to draw out these consecutive integers.

Statement 1:

9, 11 range is 2; average is 10. (Note: there is only 1 set of 2 consecutive odd integers than can average 10).

7,9,11,13 range is 6, average is still 10 (i.e. we added 2 numbers that summed up to 20) ……

3,5,7,9,11,13,15,17 (range is 14, average 10).

3 is the least of the integers. SUFFICIENT

Statement 2:

Because this is a sequence of consecutive odd integers, the average of the first and the last numbers is equal to the average of the entire sequence.

For 17 and x to average out to 10, 17+x=2(10). Therefore x=3.

Drawing this out 3,5,7,9,11,13,15,17. SUFFICIENT

Each statement alone is sufficient. The answer is D.

** **

**Question 67 – “What was the ratio…”**

OG Explanation is fine.

**Question 68 – “Is xy <….”**

OG Explanation is fine.

**Question 69 – “If x, y, and….”**

OG Explanation is fine. Alternatively, you could pick numbers and look for counterexamples but that might be more difficult.

**Question 70 – “K is a set….”**

OG Explanation is fine.