OG 12th Problem Solving 181-200

Question 181 – “ If ½ of the air in a tank is removed….”
Alternatively, you can use the 1 minus approach.


Khan Academy Question 183 – Begins at 4.50

Question 182 – “If the two-digit integers M and N….”
OG Explanation is fine but I didn’t see that you had to test for a multiple of 11. Alternatively, you could try to find a counterexample for each.
44 = 13 + 31
99 = 44 + 55
121 = 65 +56
165 = 69 + 96
Khan Academy Question 184 – Begins at 6.40

Question 183 – “Car X and Car Y traveled….”
OG Explanation is fine. Alternatively (abstract approach), d = rt. If the rate increases by 50% it is the same as being multiplied by (3/2), if d is to say the same, t must be multiplied by (2/3). (2/3)(2 hours) = 4/3 hours or 1 and 1/3 hours.
Khan Academy Link 185 – Begins at 0.00

Question 184 – “If the average (arithmetic mean) of the four numbers K, 2K+3,…….”
OG Explanation is fine.
Khan Academy 186 – 1.25

Question 185 – “If p is an even integer….”
OG Explanation is fine. Alternatively, you could pick numbers.
Khan Academy 187 –  4.25

Question 186 – “Drum X is ½ full of oil and Drum Y…”
OG Explanation. Alternatively, you could pick numbers for the capacity. Because we have 2/3 and 1/2, a number with factors of 2 and 3 would be a good pick. Let’s pick 24 gallons for Drum Y and 12 gallons for Drum X.

Drum X is ½ full of oil. It is has 6 gallons. Y is 2/3 full and has 16 gallons. If all of X is poured into Y, Y will have 22 gallons.

Drum Y fraction to capacity: 22/24 = 11/12
Khan Academy Question 188 – 7:10

Question 187 – “If x > 0, x/50 ,,, “
OG Explanation is fine.
Khan Academy Question 189 –  9.25

Question 188 – “If the operation * is defined…”
OG Explanation is fine.
Khan Academy Question 190 – Begins at 0.00

Question 189 – “The inside dimensions of a rectangular wooden box….”
OG Explanation is fine.
Khan Academy Question 191 – Begins at 1:30

Question 190 – “What is the units digit of….”
OG Explanation is fine.
Khan Academy #194 – Begin at 9.30

Question 191 – “Pat will walk from Intersection X to Intersection Y….”
OG Explanation is okay. Alternatively, the number of way you could arrange UUURR is 5!/(2!3!) = 10 using the combinations formula.
Khan Academy Question 195 – Begins at 0.00

Question 192 – “The ratio by volume of soap to alcohol to water…”
OG Explanation is too complicated.
Starting S to A to W: 2 to 50 to 100
Soap to Alcohol Ratio Double While Soap to Water is Halved:

Starting with Soap to Alcohol:
Currently 2 to 50
We Need 4 to 50
Combined 4 to 50 to WATER

Soap to Water is Halved:
Currently 2 to 100
Needed 4 to 100
Combined 4 to 50 to 400

If we have 100 Alcohol, we can adjust the ratio to
8 to 100 to 800.
The answer is E.
Khan Academy #196 – Begins at 3.30

Question 193 – “If 75% of a class answered the first question…”
OG Explanation is fine. Alternatively, you could pick numbers (i.e. there are 100 students) instead of working in percents.
Khan 197, Begins at 6.50

Question 194 – “In the rectangular coordinate system above the line….”
OG Explanation is fine. Remember that slope of a perpendicular bisector is the negative reciprocal.
Khan Academy Question 199 – Begins at 1.15

Question 195 – “A store currently charges the same price….”
OG Explanation is fine. Alternatively, you could check the answer choices directly. Examples:

Khan Academy Question # 200, Begins at 5:00
In general, if the answer choices are in ascending or descending order, you should start in the middle (answer choice C) and move accordingly using algebraic reasoning.

Question 196 – “In the table above, what is the number of green marbles….”
OG Explanation is fine.
Khan Academy Question 205 – Begins at 0:00

Question 197 – “A point on the edge of a fan….”
OG Explanation is fine.
Khan Academy 207 – Begins at 0.00 (I think there is an error in this video)

Question 198 – “If n = 4p where p is a prime…”
OG Explanation is fine. Alternatively, you could pick a number, say let p = 12. Divisors of 12 are 1, 2, 3, 4, 6, and 12. There are four even factors here. (i.e. 2, 4, 6, and 12)

Question 199 – “The data sets I, II, and II above….”
The OG Explanation is doing unnecessary calculations. There is no need to compute the standard deviation here. Starting with set II, the standard deviation here is 0 because none of the terms deviate from the mean. The standard deviation in I is smaller than the standard deviation than III because 62 and 89 deviate so far out from the mean.

Thus, the answer is III, I, II (D)
Khan Question 212 – 3.05

Question 200 – “Of the 50 researches in a workgroup….”
OG Explanation is fine.
Khan #214 – Begins at 0:00


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