**Question 41 – “What is the value of the two-digit…”
** OG Explanation is fine.

Khan Academy (OG 11th) Question 45 – Begins at 6:30

**Question 42 – “The figure above shows the circular cross section of a concrete water…”
** OG Explanation is fine.

**Question 43 – “What is the tenths digit in the decimal representation….”
** OG Explanation is fine.

Khan Academy (OG 11th) Question 46 – Begins at 6:40

**Question 44 – “Robots X, Y, Z each assemble components at their respective…”
** OG Explanation is fine.

**Question 45 – “If r is a constant and an = rn……”
** OG Explanation is fine.

**Question 46 – “If r is represented by the decimal 0.t5….”
** OG Explanation is fine though their explanation for statement 2 is a little awkward. If r < 1/10, then r < 0.1 if r = 0.t5 then t can only be 0.

**Question 47 – “If the two floors in a certain building are 9 feet apart…”
** OG Explanation is fine.

Khan Academy (OG 11th) Question 47 – Begins at 0:00

**Question 48 – “In June 1989, what was the ratio of the number…”
** OG Explanation is fine though the subscripts are annoying.

**Question 49 – “If a < x < b and ….”
** OG Explanation is fine. For statement 2, if b < c, then x must be less than b and c. Since y > c, y is greater than b and c. So y must be greater than x. SUFFICIENT.

**Question 50 – “How many people are directors of both….”
** OG Explanation is fine but I would recommend a Venn Diagram Approach. See Khan Academy for the Venn diagram Approach

Khan Academy (OG 11th) Question 49 -Begins at 4:20

**Question 51 – “If x and y are positive…”
** OG Explanation is fine.

Khan Academy (OG 11th) Question 50 – Begins at 8:35

**Question 52 – “A clothing store acquired an item…”
** OG Explanation is fine.

**Question 53 – “What is the value of the expression…”
** OG Explanation is fine.

**Question 54 – “A taxi company charges f cents for the…”
** OG Explanation is fine. Combining both statements gives you a linear system of equations.

**Question 55 – “Guy’s net income equals his gross income…”
** OG Explanation is okay. It is easy to see why statements 1 and 2 are each insufficient. Combining both, you don’t have the ratio of the deductions to gross income. For example: suppose his gross income starts at $100. It increases to $104. His deductions increase by 15%. But his deductions could initially be at say $10 or $20. If his deductions start at $10, then in January there are $11.50 and he has a net income is $104 – $11.50 = $92.50 vs $90 before. If his deductions were $20 and are now $23, then he has $81 versus $80 before. We can see that the percent increase from $90 to $92.50 does not equal the percent increase from $80 to $81. Both statements together are INSUFFICIENT.

**Question 56 – “What is the value of z in the…”
** OG Explanation is fine.

Khan Academy (OG 11th) Question 51 – Begins at 0:00

**Question 57 – “Max has $125 consisting of bills each…”
** OG Explanation is fine.

**Question 58 – “If the ratio of the number of teachers to the number of students…”
** OG Explanation is okay. Alternatively, the question tells us the teacher to student ratio is the same for both districts. We need to find out the relationship between the number of students in each district (i.e. the ratio).

Statement 1: There are 10,000 more students in M than in P. INSUFFICIENT. There could be 110,000 in M and 100,000 in P or 20,000 in M and 10,000 in P. The ratios is 11:1 in the former and 2:1 in the latter.

Statement 2: This tells us there is 1 teacher per 20 students in district M and thus also in district P. But the scenario in statement 1 is still possible.

Combining both statements, the scenario in statement 1 is still possible. INSUFFICIENT.

**Question 59 – “If a total of 84 students are enrolled…”
** OG Explanation is fine.

**Question 60 – “What is the value of n in the…”
** OG Explanation is fine.

Khan Academy (OG 11th) Question 54 – Begins at 7:15

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