OG 12th Data Sufficiency 141-160

Question 141 – “Committee X and Committee Y…”
OG Explanation is okay. This is basically a weighted average problem. Statement 1 gives us the “weights” but not the average of committee Z. Statement 2 gives us the average but not the weights. Combining both statements: If committee Z has an equal number of members from X and Y, the average age would be (25.7+29.3)/2 or 27.5. But 26.6 is less than an equally weight average of 27.5. Also, 26.6 is closer to 25.7 than it is to 29.3, so there is more weight on the 25.7 side, and thus more members come from committee X.


Question 142 – “What amount did Jean earn from the commission…”
OG Explanation is fine. Combining both statements, all we know is that her commission was 5% of total sales and that her sales were $10,000 more per month in the second half per month on average. But we know nothing of her total sales for the first half of the year. During the first half of the year, Jean’s sales could be $100,000 or $1,000,000. Both statements together are INSUFFICIENT. The answer is E.

Question 143 – “The price per share of Stock X increased by…”
OG Explanation is fine.
Khan Academy (OG 11th) Question 111 – Begins at 3:35

Question 144 – “In the figure above, if the area of triangular region D….”
OG Explanation is too complicated.
Let a = the length of a side of Square A (the hypotenuse of D)
Let b = the length of a side of Square B (the height of D)
Lec c = the length of a side of Square C (the base of D)
Because the area of the triangle is 4, bc=8.
Statement 1: The area of square B is 9, so b=3. If b=3, c=8/3 because bc=8. We have two sides of a right triangle. We can use the Pythagorean Theorem to solve for a. SUFFICIENT
Statement 2: The area of Square C is 64/9, so taking the square root, c = 8/3. If c = 8/3, then b=3 because bc=8. We have two sides of a right triangle. We can use the Pythagorean Theorem to solve for a. SUFFICIENT

Question 145 – “If Sara’s age is exactly twice Bill’s age…”
OG Explanation is fine.
Khan Academy (OG 11th Edition) Question 115 – Begins at 7:20

Question 146 – “A report consisting of 2,600 words is divided into…”
OG Explanation is fine. “Is the average number of words per paragraph less than 120?” Since there are 25 paragraphs, the average will be less than 120, if the total number of words is less than 25 x 120 = 3,000 words. To rephrase the question, “is the total number of words less than 3,000?

Statement 1: 2,600 words from the original and two more paragraphs have at least 100 words. If each preface paragraph has 150 words, we would have 2,900 words. If each paragraph paragraph has 300 words we would have 3,200 words total. INSUFFICIENT.

Statement 2: Each paragraph of the preface has fewer than 150 words. The total number of words must therefore be less than 2,900 SUFFICIENT.

Question 147 – “A certain bookcase has 2 shelves of books…”
OG Explanation is fine.

Question 148 – “The figure above shows the number…”
OG Explanation is fine.

Question 149 – “In the rectangular coordinate system above…”
OG Explanation is fine.
Khan Academy (OG 11th Edition) Question 124 – Begins at 7:40

Question 150 – “In the expression above if xn…”
OG Explanation is fine.


Question 151 – “If n is a positive integer and k…”
OG Explanation is fine. For statement 2, you do not need to solve for k. k is always positive, since both 5 and 10^n are both always positive. The square root of a number will always have only one positive number.

Question 152 – “If Carmen had 12 more tapes…”
OG Explanation is fine.

Question 153 – “If x is an integer…”

Khan Academy (OG 11th) Question 128 – Begins at 7:35
Note: In the OG 11th Edition (Yellow/Gold Color Book, there seems to be a typo, it should be 2^x instead of 2x). -

Question 154 – “If n is a positive integer is the value of b – a…”

Khan Academy (OG 11th) Question 129 – Begins at 0:00

Question 155 – “The inflation index for the year 1989 relative to the year 1970…”
OG Explanation is fine. An easier way to set up statement 1 would be:
Given: let p be the 1970 price. The 1989 price is 3.56p.
Statement 1: 1989 price – 1970 price = 3.56p – p = $102.40 This equation can easily be solved.
Khan Academy (OG 11th) Question 130 – Begins at 3:30

Question 156 – “If 5^k less than 1000”
OG Explanation is fine.

Question 157 – “The hypotenuse of a right triangle…”
OG Explanation is fine.

Question 158 – “Every member of a certain club volunteers to contribute equally…”
OG Explanation is fine. Let m be the number of members.
Statement 1: Quite easily, m = 15.
Statement 2: Strategic Alternative: Because GMAT Data Sufficiency questions cannot contradict each let m=15, $4 per person, if there are 5 fewer members, m=10, $6 per person. We get the same answer. Now think intuitively. Suppose we start with more than 15 members. If we drop 5 members, the increase for each member will not be as much since the loss of 5 numbers will not be as relatively large. Example: If m=20, $3 per person, drop 5 members, we have 15 each paying $4. This is increase of $1 per person. Suppose we start with less than 15 members. Suppose there are 10 members each paying $6. Drop by 5 and each member is paying $10. It follows that m=15 is the only value for m where if we drop 5 members, each member would pay $2 more.
Khan Academy (OG 11th) – Question 133 – Begins at 3:45

Question 159 – “If x < 0, is y…”
OG Explanation is fine.
Khan Academy (OG 11th) – Question 135

Question 160 – “What is the circumference of the circle…”
OG Explanation is fine. Notice that OX and OZ are both the radius. Since we have an isosceles right triangle, triangle OXZ must be 45:45:90. The perimeter is therefore: 2r+(√2)r
Khan Academy Question 136 – Begins at 2:20

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