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SAT Question of The Day June 24th 2013

### It costs dollars to ship a package that weighs pounds if and only if . If Alan’s package weighs pounds and costs dollars to ship, which of the following must be true?

### A.

### B.

### C.

### D.

### E.

### The wording of this question is horrible. It tells you about Allan who shipped a package and it cost him d Dollars to ship.

### It wastes your time to try and understand what d has to do with the question (hint: NOTHING).

### You have a package that weighs anything between 6 and 10 pounds. Shipping packages that weigh in between 6 and 10 pounds cost the same (d) regardless of the actual weight of the package.

### That means Allan’s package must weigh something between 6 and 10 pounds.

### You are asked to find the expression that best describe the relation between the data above and the weight (p) of this specific package.

### All the answers have absolute value in them – that is they strip the expression inside of them of it’s sign (be it positive or negative) and place a positive sign instead.

### Now Allan’s package can weigh 6, 7.5, 7.8, 9.9 or 10 pounds – all are OK.

### The answer, in this question, must always be true (think why). You can plug in 6, 8, and 10. This will nullify A, B, D, and E.

### Another way to think about it is that with absolute value expression we are measuring the distance (positive) from a mid point. In our case the difference between 10 and 6 is 4 and the mid-point is 8. If we measure the difference between the actual weight of Allan’s package and 8 – it’s absolute value must always be smaller or equal to 2.

### 50% out of 145,000 got it right.

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