OG 12th Problem Solving 61-80

Question 61 – “A glucose solution contains 15 grams…”
OG Explanation is fine
Khan Academy Link OG 11th #59 – Begins at 5:25

Question 62 – “In the figure above, if PQRS….”
OG Explanation is fine. It might be helpful for you to draw out the sides to create transversal parallel lines.
Khan Academy Link OG 11th #60 – Begins at 7:20

Question 63 – “If 1 kilometer is approximately…”
OG Explanation is fine.
Khan Academy Link OG 11th #61 Begins at 0:00
Question 64 – “Lucy invested $10,000 in a new mutual fund account….”
OG Explanation is fine.
Khan Academy Link OG 11th #62 – Begins at 1:30

Question 65 – “A certain fruit stand sold apples…”
OG Explanation is complicated. Note that the number of apples and bananas must be whole numbers. The question is telling you 0.70 a + 0.50 b = $6.30 and asking you, what is a + b?

To make it simpler,
7a + 5b = 63
a + b = ?

Going to the answer choices, and by multiplying by -5, we can solve the equation
(A) a + b = 10 becomes -5a + -5b = -50
(B) a + b = 11 “ “ = -55
(C) a + b = 12 “ “ = -60
(D) a + b = 13 “ “ = -65
(E) a + b = 14 “ “ = -70

Combining that with 7a + 5b = 63
(A) 2a = 13
(B) 2a = 8
(C) 2a = 3
(D) 2a = -2
(E) 2 a = -7
Because a is the number of apples, a must be both an integer and positive. Only choice b satisifies this requirement.

Alternatively, you could look at extremes. If there are all apples, we would have 9 apples = $6.30. If we were to subtract apples and add bananas, they would have to be an equal dollar amount. Looking at prices of 70 cents and 50 cents, If we remove 5 apples (value $3.50), we can add 7 bananas (value $3.50). Thus we have 4 apples and 7 bananas.
If we look at the other extreme (i.e. only bananas), $6.30 divided by 50 cents = 12.6 bananas. Since bananas are the cheapest and we must have both apples and bananas, we can’t have more than 12.6 fruits in total. So we can eliminate D and E.

Question 66 – “At a certain school, the ratio….”
OG Explanation is fine. You could also pick numbers but you must pick a good number. A good number to pick would be 60 because it is divisible by 4, 3, and 5.
Ratios:
2nd to 4th = 8 to 5
1st to 2nd = 3 to 4
3rd to 4th = 3 to 2
1st to 3rd = ?
From here we must go 1st to 2nd to 4th to 3rd
If we have 60 first graders, then we have 80 second graders (ratio is 3 to 4)
If we have 80 second graders, then we have 50 fourth graders (ratio is 8 to 5)
If we have 50 fourth graders, then we have 75 third graders (remember the ratio here is third grade to fourth grade and we only know the number of fourth graders. i.e. we have 3 third graders for every 2 fourth graders)
We have 60 first graders and 75 third graders, so the ratio of first graders to third graders is 4 to 5.

Question 67 – “Two integers will be randomly…”
Personally, I don’t like the OG Explanation. I think it is easier to realize no matter what I choose from Set A, there is one corresponding choice from Set B. (e.g. if I pick 2 from A, I must pick 7 from B, if I pick 3 from A, I must pick 6 from B, etc.) So there are 5 choices in B, and no matter what is picked in set A, exactly one will sum to 9. So the probability is 1/5th or 0.2.
Khan Academy Link OG 11th #64, 8:10

Question 68 – “At a certain instant in time, the number…”
OG Explanation is fine.

Question 69 – “According to the chart shown, which of the following…”
OG Explanation is fine. However, since you know there are 11 years, you can just use your eyes to evaluate the 6th shortest (or tallest) bar in the graph. This way you do not have to write the value of every year.

Question 70 – “If y(3x-5……”
OG Explanation is fine.
Khan Academy Link OG 11th #69, Begins at 9:05

Question 71 – “If x + 5 > 2 and x – 3 < 7 ….”
OG Explanation is fine.
Khan Academy Link OG 11th #70, Begins at 0:00

Question 72 – “A gym class…”

OG Explanation is fine.
Khan Academy Link OG 11th #71, Begins at 1:00

Question 73 – “If r = 0.345, s = …”
OG Explanation is fine.

Question 74 – “A total of n trucks…”
OG Explanation is fine. You could also pick numbers and see which answer choices match your calculation. If the number of cars is ¼ the number of trucks (i.e. there are 4 trucks to every 1 car), then cars make up 1/5th of all vehicles and trucks make up 4/5th of all vehicles. Two thirds of the trucks are pick-up so we could multiply it out.

Question 75 – “At least 2/3 of the 40 members….”
OG Explanation is fine.
Khan Academy Link OG 11th #72, begins at 2:00

Question 76 – “In the Johnson’s monthly budget, the dollar…”
OG Explanation is fine.
Khan Academy Link OG 11th #73, begins at 3:45

Question 77 – “There are 4 more women than men….”
OG Explanation is fine.
Khan Academy Link OG 11th #74 begins at 5:55

Question 78 – “Leona bought a….”
OG Explanation is okay. An annual rate of 8% compounded semiannually means 4% every six months.
$10,000(1.04) = $10,400
$10,400(1.04) = $10,000(1.04) + $400(1.04) = $10,400 + $416 = $10816. The interest is $816.
Khan Academy Link OG 11th #75, begins at 7:00

Question 79 – “(0.0036)….”
OG Explanation is fine.

Question 80 – “Machine A produces bolts….”
OG Explanation is okay. Machine A produces 120 bolts every 40 seconds. Machine B produces 100 every 20 seconds or 200 every 40 seconds. Combined, they produce 320 every 40 seconds.
Solving the proportion for x seconds….

Khan Academy Link OG 11th #82 - Begins at 1:25


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