Nov 12

Transition to the redesigned SAT – first PSAT in the new format

Below is the link to an article which was in the New York Times regarding the new SAT. I think students and parents will find it very helpful!

http://www.nytimes.com/2015/11/01/education/edlife/everything-you-need-to-know-about-the-new-sat.html?_r=1#story-continues-1

 

Aug 18

SAT Question of the Day transition from email to app.

Well, it seems the makers of the SAT do not want to send us emails any more.

If you have an Apple phone or tablet there is an App for you. For the rest of us with Android based machines the College board seems to think we will run and buy one?

I would expect the College board to be more mature and design the transition better.

Hopefully someone there will realize they need to provide a platform for all users.

I will visit the SAT official website and continue to post the SAT question of the day.

Good luck.

Hanan

Aug 11

SAT Question of the Day August 11th 2013

If Kelly buys t pens priced at 2 dollars each and u pens priced at 4 dollars each, which of the following expresses, in terms of t and u, the average (arithmetic mean) price, in dollars, of these pens?

A.     (3 times t) + (3 times u) over (t + u)

B.     (3 times t) + (3 times u) over (t imes u)

C.     (3 times t times u) over (t + u)

D.     ((2 times t) + (4 times u)) over (t + u)

E.     ((2 times t) + (4 times u)) over (t times u)

Very similar to the question discussed in the previous post, we have a word to equation problem.

One way (not recommended) is plug in and see that you obtain the number you expect to get.

The better way, in my opinion, is to try and translate the problem.

Lets say Kelly buys 4 pens, each for $2. She will pay for them $8. If she buys the other kind, lets say 5 of them, she will pay for each $4 and for these $4 pens she’ll pay $20.

She bought 9 pens for a total of $28.

Each pen, on average, will cost $28/9 which is a little less than $3.5

This is the way to calculate a weighted average (where we care about the amount we have of each ingredient).

If we follow the steps we just took using the letters t and u instead of the actual numbers it is clear we should mark D.

68% got it right.

Aug 11

SAT Question of the Day August 8th 2013

For every 10 dollars Ken earns mowing lawns, he gives 3 dollars to his younger brother, Tim, who helps him. Which of the following gives the relationship between d, the number of dollars Ken earns, and t, the number of dollars he gives to Tim?

A.     d equals (3 times t) over 10

B.     d equals (10 times t) over 3

C.     d equals 3 over (10 times t)

D.     d equals 10 over (3 times t)

E.     d equals (3 times t) minus 10

Yet another reading and understanding question.

We don’t need to do any calculations – just write down an equation.

We have two brothers (Ken and Tim). They earn d dollars mowing the lawn.

For every 10 dollars they earn Tim gets 3 . If Tim got T dollars how can we calculate d?

Well, if Tim got 3 dollars d must be $10. if Tim got 6, d must be $20 and so on.

That means we need to divide the t dollars tim gets by 3 and multiply it by 10 to obtain the d dollars they earned all together.

Answer b should do the trick.

Another way is to plug in 6 as the number of dollars tim earns and see that we get 20 as the d dollars they earn together.

46% of 170,000 got it right !

Aug 11

SAT Question of the Day August 05 2013

 

8-5-2013-M112209.png

 

The graph above shows the distribution of the number of days spent on business trips in 2010 by a group of employees of Company W. Based on the graph, what is the median number of days spent on business trips in 2010 for these employees?

 

A.     22

B.     22.5

C.     22.75

D.     23

E.     23.5

This is a typical reading comprehension question – the fact that it is in the math section indicates we need to be familiar with key concepts of graph reading and in this case with the definition of the median.

The median is a statistic (a number that represents a group that can be ordered and ranked) which has half the group members above it and half below it. In case we have an even number of group members it will be the average of the two members that are closest to the middle.

As we discussed in previous posts, we first want to be able to read the data in the graph. Choosing randomly the third bar from the left we make sure we read it as: “5 employees spent 22 days  on business trips in 2010”.

Now, the median will be the number of days spent on business trips in 2010 that half the employees traveled less than and half traveled more than.

How many employees do we have presented in the graph?

5+6+5+8+6+1=31

That mean we are looking for the number of days the 16th worker traveled (15 employees or half traveled less or the same and 15 employees – or the other half traveled more).

Counting from the left 5+6+5=16.

The 16th employee traveled then 22 days.

34% out of 218,000 got it right.

 

Aug 04

SAT Question of the Day August 2nd 2013

A 25-foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on concrete 7 feet from the base of the building. If the top of the ladder slips down 4 feet, then the bottom of the ladder will slide out

A.     4 feet

B.     5 feet

C.     6 feet

D.     7 feet

E.     8 feet

One of the hardest SAT questions of the day I’ve seen so far.

It requires knowledge of the pythagorean theorem and for most students, a use of a calculator.

Lets draw a diagram that will help us understand what is going on.

We have a 25 foot ladder (constant length) leaning against a wall. This creates a right triangle with the floor. The base is 7 feet from the wall. Using pythagorean theorem (the sum of the squares of the lengths of a right triangle equals the square of the length of it’s hypotenuse).

c^2=b^2+a^2

Using this theorem we conclude the ladder’s top is 24 feet from the ground.

25^2=7^2+a^2

625=49+a^2

576=a^2

24=a

Now the ladder slips down 4 feet – that means we now have a different right triangle. The length of the ladder did not change (25 feet) but the distance from the top of the ladder to the ground and from the bottom part of the ladder to the wall both do. Now we look for our b

25^2=20^2+b^2

625=400+b^2

225=b^2

15=b

The ladder then slides from it’s initial location, 7 feet from the wall, to a new location 15 feet from the wall. It was displaced 8 feet.

39% out of 151,000 got it right.

Aug 04

SAT Question of the Day July 30th 2013

All numbers divisible by both 4 and 15 are also divisible by which of the following?

A.     6

B.     8

C.     18

D.     24

E.     45

This is a number set property question asking us about the divisibility of a set of numbers that are divisible by both 4 and 15.

If a number is divisible by 4 it is also divisible by 2 (1, 2, 4, and the number itself). If this number is also divisible by 15 it is divisible by 3 and 5 (1, 3, 5, 15, and the number itself).

If it is divisible by both it is divisible by any combination of 4 and 15 prime divisors (1, 2, 2, 3, and 5).

The only number that does NOT have any additional prime divisors is 6. 8 (1, 2, 2, 2) has another 2 as its prime divisors. 18 has an additional 3 (1, 2, 3, 3). 24 has an additional 2 (1, 2, 2, 2, 3) and 45 has an additional 3 (1, 3, 3, 5).

56% of 192,000 got it right.

Aug 04

SAT Question of the Day July 27th 2013

What is the volume of a cube with surface area 54 times (x ^ 2)?

A.     9 times (x ^ 2)

B.     27 times (x^3)

C.     81 times (x ^ 2)

D.     81 times (x ^ 3)

E.     729 times (x ^ 3)

We have a geometry problem. Remember you have a formula sheet on the first page – if you don’t remember the formulas you can always go there and check.

A cube with a side of a has a volume equal to a^3 (aXaXa)

All we need to do is to find what is the value of a in terms of X.

We are given the surface area of the cube. This is the sum of the area of the six faces of cube – each is a^2 units.

Surface area is then 6Xa^2.

If we take 54X^2 and divide it to 6 we will obtain the value of one face.

a^2=9X^2

Lets take the sqrt of both sides

a=3X

Now we know the value (in terms of X) of the side of the cube. The volume is a^3:

3X times 3X times 3X or (3X)^3 = 27X^3

46% out of 190,000 got it right.

Aug 04

SAT Question of the Day July 24th 2013

A mechanic can install carburetors in 3 cars every 4 hours. At that rate, how long will it take the mechanic to install carburetors in 5 cars?

A.     6 hr 20 min

B.     6 hr 40 min

C.     7 hr 15 min

D.     7 hr 30 min

E.     7 hr 45 min

This is a work/rate problem. It is further complicated by the use of two types of units – hours in the question and a combination of hours and minutes in the answer.

I suggest you remember that every 15 minutes is 1/4 or 0.25 of an hour and 20 minute are one third of an hour.

Now lets get to work…

Our mechanic installs carburetors in 3 cars every 4 hours. It takes him then (without lunch breaks etc.) one hour and 20 minutes (a third) to install a carburetor in one car. Times five will give us 5 hours + 5X1/3 of an hour or another hour and forty minutes. Altogether 6 hours and forty minutes.

66% got it right out of 173,000.

Aug 04

SAT Question of the Day 21th July 2013

(absolute value of x minus 5) is less than or equal to 2

How many integers satisfy the inequality above?

A.     None

B.     One

C.     Two

D.     Three

E.     Five

We have an inequality on our hands (it has a < or a > sign) and also an absolute value hidden inside. We know that when we take an integer and subtract five of that number and change the sign of the answer to a positive we obtain a number that is smaller or equal to 2.

How many non-negative integers are there that are smaller or equal to 2? well there is 2 (equal), 1 (smaller), and 0 (a non negative). We obtain 0 by X=5, we obtain 1 by X=6 OR by X=4 (remember that absolute value function turns negative to positives), and the same for 2 – we will obtain it by X=7 or X=3.

We conclude there are 5 such integers.

43% out of 222,000 concluded the same.

Other techniques involve solving the inequality – I suggest the graphical approach since it is faster.

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