**Question 161 – “The positive integer n is divisible by 25….”**

OG Explanation is fine.

Khan Academy #161, Starts at 0:00

**Question 162 – “A fruit salad mixture…”**

OG Explanation is fine.

Khan Question 163 – Begins at 0:00

**Question 163 – “This year Henry will save…”**

OG Explanation is okay. Alternatively, we could pick numbers. Suppose his salary is $100 and he saves $20. He spends $80 and next year needs $40. He saving $20 and needs $40 next year so for each dollar, he needs 1 more dollar on top of that. So r = 1 and our answer should be 1/5 since 20/100 = 1/5.

Answer A: 1/(1+2) = 1/3 INCORRECT

Answer B: 1/(2(1) + 2) = 1/4 INCORRECT

Answer C: 1/(3(1)+2) = 1/5 CORRECT

Answer D: 1/(1+3) = 1/4 INCORRECT

Answer E: 1/(2(1)+3) = 1/5 CORRECT

However, when we plugged in we got two correct answer choices. In our case we used r as 1. However we need to vary r. So picking different numbers:

Suppose his salary is $100

He spends $90

He saves $10, or 1/10th of his salary

He needs $45 next year

He needs and extra $35 or $3.50 per dollar put in.

r = 2.5

Having eliminated A,B, and D:

Choice C: 1/(3(3.5)+2) = 1/(12.5) = INCORRECT

Choice E: 1/(2(3.5)+2) = 1/(7+3) =1/10 CORRECT

Answer choice is E.

This is a tough question, but in retrospect, $100 may have not been the best choice to start out with – a number divisible by 3 might be better.

**Question 164 – “If m^-1 = -1/3…”**

OG Explanation is fine.

**Question 165 – “Lois had x dollars…”**

OG Explanation is fine. Alternatively, you could pick numbers. Suppose x=2 and the total, y, = $12. Then Lois has $7 and Jim has $5.

Answer A: (12-2)/2 = $5 CORRECT

Answer B: 12 – 2/2 = $11 INCORRECT

Answer C: (12/2) – 2 = $4 INCORRECT

Answer D: 2(12)-2 = $22 INCORRECT

Answer E: $12 – 2(2) = $8 INCORRECT

The Answer is A.

Khan Academy Question 164, 2.20

**Question 166 – “During a certain season….”**

OG Explanation is fine.

Khan Academy Question 165, 3.30

** Question 167 – “Of 30 applicants for a job…”**

OG Explanation is fine. Alternatively, there are 30 total people. If 3 people do not have 4 years experience and do not have a degree, then 27 people have a degree, 4 years experience, or both.

# of people who at least one = # of people with degree + # of people with experience – # of people with both.

27 = 18 + 14 – both

Both = 5

(For math majors: A union B = A + B – A intersect B, the problem is asking for A intersect B)

The answer is A.

Khan Academy Question 166, 6.05

**Question 168 – “If 1 + 1/x…”**

OG Explanation is fine.

Khan Academy Question 167 – 0.00

**Question 169 – “Last year for every 100 million vehicles…”**

OG Explanation is fine.

Khan Academy 168 – Begins at 0:55

**Question 170 – “Thirty percent of the members of a swim…”**

Khan Academy Question 169, 2.55

**Question 171 – “What is the difference between the sixth and the fifth…”**

OG Explanation is fine but I would evaluate (6+2^{5}) as 6+32 or 38, and 5 + 2^{4} as 5+16 or 21. 38-21=17. There is no need to do all the distribution in the OG Explanation.

**Question 172 – “If (x-1)^2 = 400, which….”**

OG Explanation is fine.

Khan Academy 171 – Begins 7:25.

**Question 173 – “Which of the following….”**

OG Explanation is okay. Alternatively, you could rearrange the inequality to: x2 ≤ 1. From here, x can take a value from -1 to 1.

Khan Academy Question 172 – 8.50

**Question 174 – “The probability is ½ that a certain coin…”**

OG Explanation is fine.

Khan Academy #173 – Begins at 0:00

**Question 175 – “Of the final grades received by the students…”**

OG Explanation is fine.

Khan Academy Question 174, Begins at 1.50

**Question 176 – “As x increases from 165 to 166…”**

Khan Academy Question 175, Begins at 3:30

**Question 177**

“A rectangular box is 10 inches wide….”

OG Explanation is fine. Alternatively, if you know the super-Pythagorean theorem: a^{2} + b^{2} + c^{2} = d^{2}, you can plug in chug. 10^{2} + 10^{2} + 5^{2} = d^{2 }= 100 + 100 + 25 = 225. If d^{2} = 225, d is the square root or 15.

Khan Question 176 – Begins at 6.35

**Question 178 – “The table above shows the number…”**

OG Explanation is fine

Khan 179, Begins at 4.20

**Question 179 – “The ratio of two quantities is 3 to 4….”**

OG Explanation is fine.

Khan 181 – Begins at 1.05

**Question 180 – “If the average (arithmetic mean) of x and y is 60……….”**

OG Explanation is fine.

Khan Academy Question 182, Begins at 3:00

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