**Question 32 – “Is the value..”**

OG Explanation is fine.

**Question 33 – “Last year, if Elena…”**

OG Explanation is fine.

**Question 34 – “If p, q, x, y, and….”**

OG Explanation is fine. Statement 1 tells us nothing about y and z. y could be less than p or greater than q which would affect the median.

**Question 35 – “If w + z….” **

OG Explanation is fine but a little intuition on statement 2 would go a long way. If w and z are consecutive odd integers, this means they are close to each other and that 2w is close to 28. So w is around 14. Looking near 14, the numbers 13 and 15 work. Thus wz = 13(15) or equivalently, 15(13). Statement 2 is sufficient.

The answer is B.

**Question 36 – “Elena receives…”**

OG Explanation is fine.

**Question 37 – “What is the…”**

OG Explanation is fine.

**Question 38 – “Machine X….”**

OG Explanation is fine.

**Question 39 – “Can positive integer p be….”**

This OG Explanation is beating around the bush. If positive integer p can be expressed as the product of two integers, each of which is greater than 1, then p cannot be prime. Why? A prime number has only two factors: itself and 1. Thus, a prime number cannot be expressed as the product of two integers that are both greater than 1. So we can rephrase the question, is positive integer p composite (i.e. not prime)?

Statement 1: p can be 32, 33, 34, 35, or 36. All of these numbers are not prime. SUFFICIENT.

Statement 2: If p is odd, p can be prime or not prime. INSUFFICIENT.

Thus, the answer is A.

Question 40 – “Is x<…”

OG Explanation is fine. Alternatively, we could pick numbers. Let z=3.

Statement 1: y>3 Nothing about x, so INSUFFICIENT

Statement 2: x>3 Nothing about y, so INSUFFICIENT

Combining both statements, y=5 and x=4 in which case x<y or y=4 and x=5 in which x>y. So both statements together are not sufficient. The answer is E.