Aug 04

## SAT Question of the Day July 15th 2013

### A number cube, with faces numbered through , is to be rolled twice. What is the probability that the number that comes up on the first roll will be less than the number that comes up on the second roll?

### A.

### B.

### C.

### D.

### E.

### We have a probability question on our hands.

### There are a few ways to attack this problem and get to the right answer.

### The easiest way, in my opinion, to solve this question is unfortunately the most time demanding.

### We have 6X6=36 possible outcomes – lets write them down:

### In the table we’ll make we will place the number that can come up in the first roll and we will mark the desired outcomes of the second roll (with a value less than and not including the value we got on the first roll) in parentheses.

### First roll Second roll number of options that satisfy the criteria

### 1 1, 2, 3, 4, 5, 6 0

### 2 (1), 2, 3, 4, 5, 6 1

### 3 (1, 2), 3, 4, 5, 6 2

### 4 (1, 2, 3), 4, 5, 6 3

### 5 (1, 2, 3, 4), 5, 6 4

### 6 (1, 2, 3, 4, 5), 6 5

### Summing up the desired outcomes we obtain 15 out of 36 or 5/12.

### This is one of those problems that can be solved theoretically using formulas but lend themselves to be solved by “brute force” which also allows for us to check our work.

### 47% out of 184,000 got it right.

Jul 13

## SAT Question of The Day July 12th 2013

### Triangle is isosceles, and the measure of angle is . What must be the measure of another angle of this triangle?

### A.

### B.

### C.

### D.

### E. It cannot be determined from the information given.

### If a triangle is an isosceles two of its sides are equal and two of his angles are equal.

### We are given one angle with a measure of 74. It could be that this is one of the base angles and thus the other base angle is equal to it and the head angle is 32. Another option is that 74 is the head angle and then each of the base angles is 53. Without additional information we can’t tell.

### We must therefore choose E.

### 38% out of 184,000 considered both options and choose the correct third option.

Jul 13

## SAT Question of The Day July 9th 2013

### If , what is the value of ?

### A.

### B.

### C.

### D.

### E.

### Yet again, in the SAT it is useful to think backwards.

### If b-3=6 it means that b=9

### If a-b=6 and b=9 then a must be 15.

### Simplify and solve – this question tries to confuse by a non standard layout of the mathematical information.

### Clean it up and you have it.

### 61% out of 171,000 did it.

Jul 13

## SAT Question of The Day 6th July 2013

### , , ,, …

### The first four terms of a sequence are shown above. Which of the following could be the formula that gives the th term of this sequence for all positive integers ?

### A.

### B.

### C.

### D.

### E.

### One approach is plug in – n stands for the position of the term in the sequence.

### If we plug in 1 to the formula instead of n we should obtain 3, when we plug in 2 we will get 6, 3 to give 11 and 4 to obtain 18.

### Only n^2+2 delivers each time.

### 52% of 172,000 got it right.

### P.S. in questions where plugging in seems to be the best option start from the last answer.

Jul 13

## SAT Question of The Day July 3rd 2013

### In the figure above, all intersecting sides of the polygon meet at right angles. What is the area of the polygon?

### A.

### B.

### C.

### D.

### E.

### My approach is to close the rectangle (12X9=108 units) and then subtract two small rectangles. One is 2X2 and the other is 2X3 or 4 and 6 units that are taken out – giving 98 units.

### 61% of 164,000 got it right

Jul 13

## SAT Question of The Day June 30th 2013

### Ten cars containing a total of people passed through a checkpoint. If none of these cars contained more than people, what is the greatest possible number of these cars that could have contained exactly people?

### A. One

### B. Two

### C. Three

### D. Four

### E. Five

### This is a “logic” question.

### We have 10 cars and 32 people. None of them contain more than 4 people. We need to find the MAXIMUM number of cars that contain exactly 2 people.

### Lets try and construct the ideal condition. If we had 10 cars with 2 people in them we will have the maximum number of cars. However, this scenario enables only 20 people to ride in the cars and 12 are left out. Now, if each car contains no more than 4 people we can sit another 2 people in each car until we sit the 12 people we left out. We need 6 cars to sit these people with 4 people in each of these cars. We are then left with 4 cars with 2 people in each.

### There are other legitimate logical approaches to this question – I shared the one that works best for me.

### 57% out of 162,000 got it right.

Jul 13

## SAT Question of The Day June 27th 2013

### In the quadratic equation above, is a constant. The graph of the equation in the contains the points and. What is the value of ?

### A.

### B.

### C.

### D.

### E.

### Well – this is a nice question as you are actually given too much information.

### We have the equation that correlates between X values and Y values.

### This relation is quadratic. We are missing the value of a number that is replaced by the letter C.

### It is clear that if the relation between X and Y is true then C must assumes a certain value.

### The graph of the equation passes through 6,0 that implies that when X=6 Y=0

### 0=6^2-4*6+C or 0=36-24+C

### That in turn means C=-12

### You could have come to the same conclusion using the other point – however – if you don’t like to work hard try to avoid negative numbers.

### 52% out of 143,000 got it right.

Jul 13

## 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.

Jul 13

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