SAT Question of the Day June 18 2013

y = (negative 2 times x^2) + (b times x) + 5

In the xy-plane, the graph of the equation above assumes its maximum value at x = 2. What is the value of b?

A.     negative 8

B.     negative 4

C.     4

D.     8

E.     10

We have a quadratic equation (X to the 2nd). The X coordinate of the vertex (where the quadratic equation obtained its max or min value) is determined by X=(-b)/(2a) where b is the number coefficient of the X and a is the number coefficient of the X^2

b=? a=(-2) and we know X=2

plugging in we have: 2=(-b)/[2*(-2)]

or 2=(-b)/(-4)

-8=-b

or b=8

You can also use your TI calculator to plug numbers in and find, using the min/max functions which value satisfies the conditions – but this is much more difficult.

36% out of 145,000 got it right.

SAT Question of the Day June 15 2013

Four distinct lines lie in a plane, and exactly two of them are parallel. Which of the following could be the number of points where at least two of the lines intersect?

Roman numeral 1. Three

Roman numeral 2. Four

Roman numeral 3. Five

A.     Roman numeral 1 only

B.     Roman numeral 3 only

C.     Roman numeral 1 and Roman numeral 2 only

D.     Roman numeral 1 and Roman numeral 3 only

E.     Roman numeral 1Roman numeral 2, and Roman numeral 3

In a math question concentrated on Geometry I recommend to make a little diagram.

We have 4 lines in the plane. Exactly two of them are parallel – implying they never cross.

Now lets call these lines A and B and lets draw them parallel to the bottom of the page.

————————————————————————

————————————————————————

The remaining two lines (C and D) are not parallel to one another or to A or B.

This mean we can imagine they are forming a gigantic

\                /

   \           /

      \     /

         X

       /    \

    /          \

/                 \

Now lets move this X up.

It is clear C and D meet exactly once. C intersect A once and intersect B once. The same is true for D.

We have an option of 1+2+2 intersections.

However, if we continue to move the X up and the intersection between C and D is now overlapping one of the parallel lines we reduced two points.

We conclude there are either 5 or 3 points were the lines intersect.

30% out of 218,000 got it right – a surprisingly difficult question.

SAT Question of the Day June 12 2013

A geologist has 10 rocks of equal weight. If 6 rocks and a 10-ounce weight balance on a scale with 4 rocks and a 22-ounce weight, what is the weight, in ounces, of one of these rocks?

A.     4

B.     5

C.     6

D.     7

E.     8

All we need to do is to set an equation – one rock will weigh X ounces.

6X+10=4X+22

It is clear we have two more rocks on one side and 12 ounce more on the other.

This implies each rock weighs 6 ounces.

71% out of 128,000 got it right – indeed a relatively simple question.

SAT Question of the Day June 09 2013

A, B, C, and D are points on a line, with D the midpoint of segment line B C. The lengths of segments line A B, line A C, and line B C are 10, 2, and 12, respectively. What is the length of segment line A D?

A.     2

B.     4

C.     6

D.     10

E.     12

This is a reading comprehension question as much as it is a mathematical question.

Notice that the assumption that the points are in order from A to B to C to D is challenged by the statement that D is actually exactly in the middle between B and C.

Now, what we want to do is create a diagram that will help us solve the important question – what is the distance between A and D?

Lets start with what we know to be true – D is in the middle between B and C.

Draw a line and two points on it and name them B and C (for the sake of simplicity let’s call the left one B and the right one C). Mark the middle of the segment as point D.

Now point A can be either on the left side of B, between B and D, between D and C, or on the right side of C.

(A)—B—(A)—D—(A)—C—(A)

Now, let us look on the distances between the points: BC is 12 – so BD=DC=6 We know AB is 10 – which places A either on the left of B or between D and C (10 is not far enough from B to be on the other side of C). We also know that the distance between A and C is 2 units – this leaves us only one option –  A is between D and C – and is located 4 units from D.

B——D—-A–C

46% out of 150,000 got it right.

SAT Question of the Day June 6th 2013

Milk costs x cents per half-gallon and y cents per gallon. If a gallon of milk costs z cents less than 2 half-gallons, which of the following equations must be true?

A.     x minus (2 times y) + z = 0

B.     (2 times x) minus y plus z equals 0

C.     x minus y minus z equals 0

D.     (2 times x) minus y minus z equals 0

E.     x + (2 times y ) minus z = 0

We can buy milk either in one or half gallon containers.

We pay Y cents per one gallon and X cents per half gallon.

If we buy two half gallons of milk we pay another Z cents  than if we buy a one gallon container.

In Math we will write 2X=Y+Z or 2X-Y-Z=0

You can try it with numbers: 10 cents for a gallon 6 cents for each half gallon and 2 cents for the difference between buying a gallon or buying two half gallons.

57% out of 141,000 got it right.

SAT Question of the Day June 3rd 2013

2013-M37917.png

In the triangles above, 3 times (y minus x) =

A.     15

B.     30

C.     45

D.     60

E.     105

The triangle on the left is an isosceles right triangle (two legs are equal and one angle is 90 degrees). This means X=45

The triangle on the right is equilateral – each angle is 60 degrees.

y-x=15 so 3(Y-X)=3 times 15 = 45

74% out of 160,000 got it right.

SAT Question of the Day May 31st 2013

The stopping distance of a car is the number of feet that the car travels after the driver starts applying the brakes. The stopping distance of a certain car is directly proportional to the square of the speed of the car, in miles per hour, at the time the brakes are first applied. If the car’s stopping distance for an initial speed of 20 miles per hour is 17 feet, what is its stopping distance for an initial speed of 40 miles per hour?

A.     34 feet

B.     51 feet

C.     60 feet

D.     68 feet

E.     85 feet

Lets read the question and highlight the critical words:

The stopping distance of a certain car is directly proportional to the square of the speed.

That is – the distance equals a constant times the speed squared.

If we double the speed the distance of 17 feet would be quadrupled (2 square is 4) and will equal 68 feet.

38% out of 258,000 got it right.

SAT Question of the Day May 28th 2013

Miguel is 180 centimeters tall. At 2:00 p.m. one day, his shadow is 60 centimeters long, and the shadow of a nearby fence post is t centimeters long. In terms of t, what is the height, in centimeters, of the fence post?

A.     t + 120

B.     t over 3

C.     3 times t

D.     3 times (square root t)

E.     (t over 3)^2

Miguel shadow is 1/3 of his height. If we are given the shadow length (t) the true height must be 3 times as big or 3t.

52% out of 235,000 got it right.

SAT Question of the Day May 25th 2013

In a community of 416 people, each person owns a dog or a cat or both. If there are 316 dog owners and 280 cat owners, how many of the dog owners own no cat?

 

A.     36

B.     100

C.     136

D.     180

E.     316

This is a “set theory” question – best solved by drawing a Venn diagram.

Write in the left circle dog owners.Write in the right circle cat owners.

In the middle circle are people who own both.

If there are 416 people all together and there are 316+280=596 pets – that means there are 180 who are double counted.

Out of the 316 dog owners 180 have a cat. That implies there are 136 that own only a dog.

45% out of 275,000 got it right.

SAT Question of the Day May 22nd 2013

If 24 over 15 = 4 over n, what is the value of 4 times n?

A.     6

B.     10

C.     12

D.     30

E.     60

We know 24/15 equals 4/n what is the value of 4n?

4/n=16/4n (expand both top and bottom by 4) – the idea is we will find what is the value of 4n directly.

24/15=16/4n – lets flip both sides 15/24=4n/16 multiply both sides by 16.

15*16/24= 5*3*8*2/(3*8)=10=4n

63% of 236,000 got it right – relatively easy with a calculator.