OG 12th Problem Solving 141-160

Question 141 – “A club collected exactly $599….”
OG Explanation is fine.
Khan Academy Question 141 – 7:05

Question 142 – ‘”If y is the small positive integer…”
OG Explanation is fine.

Question 143 – “If [x] is the greatest integer…”
OG Explanation is fine.

Question 144 – “If 4-x/ ….”
OG Explanation is fine.
Khan Academy Question 144 – 0:40

Question 145 – “The trapezoid shown in the figure above….”
OG Explanation is fine.
Khan Academy Question 145, 1:55

Question 146 – “In a certain sequence, the term…”
OG Explanation is fine .

Question 147 – “In the figure above, V represents…”
OG Explanation is fine but you should know that triangle VPR, with P being the point 5 feet below V, is a 30-60-90.
Khan Academy Link Question 147 – 7:05

Question 148 – If x, y, and k are positive numbers….”
OG Explanation is too time consuming; I don’t know anyone who could do it by the OG Method in 2 minutes. I think the easiest way to do this is to recognize that this is really a weighted average problem. The way I did this was to think outside the problem and consider the extremes. The problem states that x < y. But what if x = y? we get:



Question 149 – “During a trip France…”
OG Explanation is fine. Alternatively we could pick numbers. Let’s pick a distance and a good choice would be a multiple of 60 and 40. Let’s pick 240 miles. If x = 50% of the distance or 120 miles, she spends 3 hours going 40 miles an hour and 2 hours going 60 miles. Her average speed is (3(40) + 2(60))/5 = (120+120)/5 = 240/5 = 48 miles per hour.

Choice A: (180-50)/2 = 130/2 = 65 INCORRECT
Choice B: (50+60)/4 = 110/4 does not equal 48 INCORRECT
Choice C: (300-50)/5 = 50 INCORRECT
Choice D: 600/65 is less than 10 INCORRECT
Choice E : 12,000/250 = 48 mph CORRECT

Question 150 – “If x = -1…”
OG Explanation is fine.
Khan Academy Question 150 – Begins at 1:55

Question 151 – “A toy store regularly …”
OG Explanation is fine.
Khan Academy Question 151 – 2:40



Question 152 – “The shaded portion of the rectangular…”
OG Explanation is fine.
Khan Academy Question 152 – Begins at 4:50

Question 153 – “Jack is now 14 years older than…”
OG Explanation is fine.  7.40, Q153 Khan

Question 154 – “An empty pool…”
OG Explanation is fine.
Khan Academy Link #154 – Begins at 0:00

Question 155 – “A positive number x….”
OG Explanation is fine.
Khan Academy Link Question 155 begins at 1:45

Question 156 – “A tank contains 10,000 gallons of a solution…”
OG Explanation is fine.
Khan Academy Question 156 – 3:30


Question 157 – “For any positive integer n…”
OG Explanation is too technical. Personally, I don’t like sigma notation (the greek “E”). To sum up the even integers 100 + 102 + 104 + … + 296 + 298 + 300: First figure out how many terms there are. The sequence is really the same as 2(50 + 51 + … + 149 +150). From 50 to 150, there are 101 terms (remember you have to subtract and add 1). So we have 101 terms and because this is an evenly spaced set, we can multiply the average of the set by the number of terms to compute the sum. (The average of an evenly spaced set is the average of the first and last terms).
(200)(101) = 20,200

If you forget that you can multiply the average, you could also use this method…
100 + 102 + … + 300 = (100 + 300) + (102 + 298) + ….
Each set of () adds up to 400 and because we have 101 terms, we have 50.5 of these sets (i.e. 200 at the end gets left out as there are 101 terms).
400(50.5) = 20,200

If you had trouble on this problem, you should review evenly spaced sets.

Question 158 – “A committee is composed of w women and m…..”
OG Explanation is fine.
Khan Academy Link 158 – Begins at 6:20

Question 159 – “How many prime numbers….”
OG Explanation is fine.

Question 160 – “The figure above…”
OG Explanation is fine.
Khan Academy Question 160, Begins at  9.20


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