OG 12th Problem Solving 161-180

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+25) as 6+32 or 38, and 5 + 24 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: a2 + b2 + c2 = d2, you can plug in chug.   102 + 102 + 52 = d2 = 100 + 100 + 25 = 225.   If d2 = 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


One Response to OG 12th Problem Solving 161-180

  1. Maude says:

    Spot on with this write-up, I really feel this amazing site needs a lot more attention. I’ll probably be back again to see more,
    thanks for the information!

Leave a Reply

Your email address will not be published. Required fields are marked *

*

You may use these HTML tags and attributes: <a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <strike> <strong>