**Question 61** – “At a certain picnic, each of the guests…”

OG Explanation is fine. To combine both statements, suppose there are n guests. Then 0.6n(2 scoops) + 0.4n(1 scoop) = 120 scoops. That is, 1.2n + 0.4n = 120 1.6n = 120.

Khan Academy #55 – Begins at 0:00

**Question 62** – “For a convention, a hotel charges a daily room…”

OG Explanation is fine.

**Question 63** – “Stores L and M each sell a certain product at a different…”

OG Explanation is okay but there is any easier way to combine both statements. IF L’s discounts is $5 and that represents 10% off, then L’s regular price is $50 with the discounted price being $45. If M’s discount is $6 and represents 15% off, then M’s regular price is $40 with the discounted price being $34. Both statements TOGETHER are sufficient.

**Question 64 **– “If d denotes a decimal…”

OG Explanation is fine

Khan Academy (OG 11th) Question 58 – Begins at 9:20

**Question 65** – “How many integers are there between, but…”

OG Explanation is fine.

**Question 66** – “If n and t are positive integers…”

OG Explanation is fine.

**Question 67 **– “In a survey of 200 college graduates…”

OG Explanation is okay. Using the percents in the problem, 60 students received loans and 80 students received scholarships.

Statement 1: 25% of the 200 students, or 50 students, received scholarships. This means 50 received scholarships only, 30 received both, and 60-30 = 30 received loans only. Therefore, 50 + 30 + 30 or 110 received at least a scholarship or a loan. Since we are given that there are 200 students, we can calculate by subtraction the number of students that received neither the loan nor the scholarship and then find the percent. SUFFICIENT

Statement 2: 50% of those who have taken loans also received scholarship tells us that 30 students received both. Same information at Statement 1. SUFFICIENT.

The correct answer is D.

**Question 68 **– “Three machines K M and P….”

OG Explanation is fine.

**Question 69 **– “Of the four numbers represented on the number…”

OG Explanation is fine.

**Question 70** – “Mary persuaded n friends to donate $500….”

OG Explanation is fine.

**Question 71 **– “Carlotta can drive from her home to her office…”

OG Explanation is fine

Khan Academy (OG 11th) Question 63 – Begins at 0:00

**Question 72** – “Is x > y….”

OG Explanation is fine.

Khan Academy (OG 11th) Question 64 – Begins at 1:50

**Question 73 –** “If m is an integer, is m odd…”

OG Explanation is fine.

Khan Academy (OG 11th) Question 65 – Begins at 3:45

**Question 74 –** “What is the area of the triangular region…”

OG Explanation is fine.

Khan Academy (OG 11th) Question 66 – Begins at 6:45

**Question 75 –** “In the xy-plane…”

OG Explanation is fine.

**Question 76** – “If m p and t….”

OG Explanation is fine.

**Question 77** – “Each week a certain salesman…”

OG Explanation is fine.

**Question 78 **– “A total of $60,000 was invested…”

OG Explanation is fine.

**Question 79 **– “Leo can buy a certain computer for p1….”

OG Explanation is okay. Intuitively, you might realize that the first statement tells us that the tax rate is higher in State A. Statement 2 tells us that total tax paid in State A is greater than the total tax paid in State B. Still we do not which computer is overall more expensive. Consider this example:

Statement 1

Let p1 = $1,000 and t1 = 20%, total cost is $1200

Let p2 = $500 and t2 = 10%, total cost is $550 Computer 2 is cheaper

But if p2 = $3000 and t2 = 1% total cost is $3030. Computer 1 is cheaper

INSUFFICIENT

Statement 2

Using the same numbers and prices for p1, t1, p2, and t2

Let p1(t1) = 1000 x 20 = 20,000

Let p2(t2) = 500 x 10 = 5,000 p1(t1) > p2(t2)

Let p2(t2) = 3,000 x 1 = 3,000 p1(t1) > p2(t2)

INSUFFICIENT

Since the tax rates for computer 1 are higher than computer 2 for both examples in statement 2, both statements together are insufficient. The answer is E.

**Question 80 – “If r>0….”**

OG Explanation is okay.