| Two essay questions (one Analysis of Issue, one Analysis of Argument) | 30 minutes per essay |
| An optional 5 minute break | Please do take this. (You'll thank me!) |
| 41 Verbal reasoning questions (a mixture of critical reasoning, reading comprehension and sentence correction). | 75 minutes |
| An optional 5 minute break | |
| 37 Mathematics questions (a mixture of problem solving and data sufficiency). | 75 minutes |
Sentence correction: (which option should replace the underlined section to correct the sentence. Choose (A) if you think the original is correct).
An early example of 'rescue opera' was Gretry's Richard Coeur de Lion where King Richard is rescued by his minstrel, Blondel.
Critical reasoning: (testing your powers of logic and your ability to examine statements for hidden assumptions)
A desert-dweller showing an umbrella to his friend: "I bought it in Britain. When you want it to rain, you leave it at home!"
What logical flaw is the desert-dweller making?
Problem solving: x lb of sugar costing m cents an ounce is mixed with y lb of sugar costing n cents an ounce. What is the cost per ounce of the mixture?
(x + y) |
(m + n) |
(m + n) |
(x + y) |
16 |
Data sufficiency: The average height of a class of boys is 1.45m. What is the average height of the tallest 10 children?
In this case, the word "where" is wrong, as it refers to physical places. The scene is in the opera, so the correct wording is "in which". Answer (B) is correct.
The desert-dweller has found out that it often rains when people leave their umbrellas at home, but he has not realised that leaving the umbrella at home doesn't cause the rain. He assumes that leaving the umbrella at home is the "magic spell" that makes the rain happen. This is assuming cause and effect where there isn't any - the correct answer is (C)
The cost of the first type of sugar must be 16xm as it costs m cents per ounce and there are 16x ounces altogether. The question tried to fool us by stating that there were x lb (pounds weight) of sugar. We have to multiply that by 16 to convert it to ounces.
Similarly, the cost of the second type of sugar is 16yn as there are y lb (= 16y ounces) at n cents an ounce. Therefore the total cost of the sugar is 16xm + 16yn = 16(xm + yn).
The total number of ounces in the mixture is 16x + 16y = 16(x + y). Doing the division makes the 16s cancel from the numerator and denominator, and gives (D) as the correct answer.
Two points to note here:
Could the answer be (A)?: Statement (1) tells us that there are 30 children in the class. Note that the question stem tells us that it is a "class of boys", so we needn't worry about whether there are any girls or not - we can assume that "children" and "boys" are synonymous here.
However, although that lets us work out the sum of all the heights of all the children (from the average and the number of children), it doesn't allow us to work out the average height of the ten tallest boys. Statement (1) on its own is not enough to answer the question, and the answer cannot be (A). Similarly, the answer cannot be (D), as that says that either statement on its own is enough to answer the question, and we know that isn't true of statement (1). In a data sufficiency question, when you delete answer (A) as a possible answer, then (D) always goes with it!
Could the answer be (B)?: Statement (2) allows us to work out the sum of the heights of the shortest 20 boys in the class. However, if we just take statement (2) on its own, then we can't work out the average height of the ten tallest boys as we don't know how many boys there are in the class. Remember, if the answer is to be (B), then we have to pretend that we haven't seen statement (1)! Statement (2) on its own is not enough to answer the question, and the answer cannot be (B). We have already proved that the answer cannot be (D), but the fact that it can't be (B) gives us added confirmation.
Could the answer be (C)?: Statement (1) lets us work out the sum of the heights of all 30 boys in the class. Statement (2) lets us work out the sum of the heights of the shortest 20 boys, so the difference between these must be the sum of the heights of the tallest 10 boys. Now that we know the sum of the heights of the ten tallest boys, a quick division gives the average height of those boys. Statements (1) and (2) are sufficient to answer the question when they are put together. The answer is (C).
The only answer that we never considered was (E). If we had found that the correct answer hadn't been (C) (i.e. we still couldn't answer the question with all the information that we had been given), then we would have concluded that the answer was (E). Distinguishing between a correct (C) answer and a correct (E) answer is one of the hardest parts of data sufficiency questions.
One other thing to point out: We didn't actually work out what the average height of the tallest ten boys was. That's not the point! All we had to do was work out whether it was possible to do so. What is the average height of the tallest 10 children? Who cares? The fact is that we found we could do it, and that told us which option to choose!
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