OG 12th Problem Solving 101-120

Question 100 – “T = (5/9)(K-32)…”
OG Explanation is fine.
Khan Academy Link OG 11th #102 – 4:15

Question 101 – “The water from one outlet…”
OG Explanation is fine.
Khan Academy Link OG 11th #103 – 5:55

Question 102 – “If a square mirror has a 20-inch…”
OG Explanation is fine.


Khan Academy Link OG 11th #105 – 10:45

Question 103 – “The present ratio of students…”
Khan Academy Link OG 11th #106 – 0:00

Question 104 – “What is the smallest integer n…”
OG Explanation is fine.
Khan Academy Link OG 11th #107 – 2:15

Question 105 – “Sixty percent of the members of a study….”
OG Explanation is good.

Question 106 – “When positive integer x is divided…”
OG Explanation is fine.

Question 107 – “If x is the product of the positive integers….”
OG Explanation is fine. You are basically prime factorizing 8!

Question 108 – “If t = 1/(2^9 x 5^3)…..”
OG Explanation is fine.

Question 109 – “A pharmaceutical company received $3 million…”
OG Explanation is fine. Alternatively, we could convert the royalties in the percents. $3 million over $20 million is 15%. $9 million on the next $108 million is 9/108 = 1/12. 1/12 is approx 8.3%.
A decrease from 15% is not quite half (otherwise the other royalty would be 7.5%) but the decrease is more than 33% (a third less than 15% is 10%). Only answer choice C works here.

Question 110 – “If p is the product of the integers….”
OG Explanation is fine.

Question 111 – “If candy bars that regularly sell for….”
OG Explanation is fine.
Khan Academy #110, Begins at 0:00

Question 112 – If s > 0….”

Khan Academy Link OG 11th #111 – Begins at 1:50

Question 113 – “The front of a 6-foot-by….”
OG Explanation is fine but I think it helps to draw it out. I like how Sal Khan does it.


Khan Academy Link OG 11th #112, 2:45

Question 114 – “If a = -0.3, which…”
OG Explanation is fine.
Khan Academy Link OG 11th #113, 6:00

Question 115 – “Mary’s income is 60%…”
OG Explanation is fine. Alternatively, say Tim’s income is 100, Mary’s is 160. Tim’s income is 40% less than Juan’s. 0.6 or (3/5)(Juan’s income) = Tim’s income. So you need to multiply by the reverse (5/3). (5/3)(100) = Juan’s income = 166.67
What percent of Juan’s income is Mary’s income, (we will represent it by x)
(x%)(166.67) = (160)
x% = 160/166.67
Dividing it out, x% is slightly less than 100%. It is not 80% as 80% of 166.67 = 166.67 – 16.667(2)

Khan Academy Link OG 11th #115 - Begins at 0:00

Question 116 – “Each dot in the table above…”
OG Explanation is fine. Alternatively, we can notice that for the 5th city (i.e. city E), there are 4 dots, the patter will continue to the 30th city and we will have 29 dots. So are task is to sum up 1 + 2 + …. + 29.
1 + 2 + 3 + … + 27 + 28 + 29 = (1+29) + (2+28) + …. = (30) + (30) + ….; notice we have 29 terms so we can only make 14 pairs. The last term is the median which is 15 (i.e. evenly spaced set, mean = median). Therefore, the answer is (30)(14) + 15 = 435.

Khan Academy Link OG 11th #116 –   1:45

Question 117 – “If n is positive….”
OG Explanation is fine. Alternatively, you could pick numbers and estimate but the direct algebra approach is probably better. Here’s how you might do that.
Let n=1.

The correct answer is E.

Question 118 – “The ratio of the length of to the width of a rectangular advertising….”
OG Explanation is fine.
Khan Academy Link OG 11th #118, 6:50

Question 119 – “Which of the following is equivalent to the pair…”
OG Explanation is fine.

Question 120 – “David has d books…”
OG Explanation is fine. Alternatively, we could pick numbers. Since David has 3 times Jeff’s books and half of Paula’s books, we should pick a number that is divisible by both 3 and 2. Let’s pick 12.

Suppose David has 12 books.   Jeff has 4 books.  Paula has 24 books.   The total number of books is 12 + 4 + 24 = 40  books or 40/12 = 10/3 the number  of books David has.   The answer is C.

Khan Academy Link OG 11th #120, begins at 0.00


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