SAT Math Problems Thread

cheating :slight_smile:

Although in reality, I don’t think you’ll save much time by using a calculator program on SAT math.

Well, I wouldn’t call it that… :stuck_out_tongue:
The DIstance Formula and the Quadratic Equation solver were the only ones that were really useful for me.

Please someone answer my question… A game has 60 min of playing time. What percent of the game has been played if the playing time remaining is one forth of the time already played?
1- 20%
2-25%
3-35%
4-75%
5-80%
Please i need a help

80%, you just have to read carefully.

@MITer94 can you please show the steps :confused:

Let the time already played be ‘x’

One fourth of the played time is left, so

x + (1/4)x = 60, because the sum of the ‘time already played’ and ‘one fourth of the time already played’ is equal to the total time to be played, 60 minutes

If you solve the equation, you get x = 48.

Then calculate 48 as a percentage of 60.

48/60 * 100 = 80%

@hardwork213 in short, read the question really carefully. Then the question is easy.

Playing time remaining = x, then time played so far = 4x. Percent of game played so far is 4x/(4x+x) = 80%

Thanks DVD and MITer …yeah understanding the question is quite important

A bakery sells donuts for $0.60 each or a box of 12 for C dollars. A customer can save $1.80 by buying a box of 12 rather than individually. What is the value of C? (pdf says the answer is 5.4) (my answer is $9)

I think you added $1.80 instead of subtracted $1.80.

A fast way to check is $9/12 = $0.75/donut but this doesn’t save you money.

@MITer94 : Thanks!

What do you guys think is the best way to attack this problem?

(X-8) (X-K) = X^2 - 5KX + M

In the equation above, K and M are constants. If the equation is true for all values of X, what is the value of M?

The sum of the roots is 5K = K + 8. So 4K = 8 and therefore K = 2.

The product of the roots is M = 8K = 16.

Thanks. Does anyone know how typical it is for the SAT to test if a student knows how use the sum and product of roots to find the value of a variable?

Oh, one more question on the problem in post 511. Is there another reasonable approach to that problem?

@CHD2013 There is no question on the current SAT where you NEED to know about the sum and product of roots. But you asked for the best way to do that particular problem, and in my opinion that is the best way. There are several other ways that work well too such as (i) picking numbers and (ii) multiplying out the left hand side and equating coefficients of powers of x.

@DrSteve @CHD2013 kind of curious, (i) picking numbers leaves me with some mixed results here. My first solution would be to use the sum/product of roots.

Intuitively I would substitute x = 8 and x = k since LHS vanishes:

x = 8 --> 0 = 64 - 40k + m <–> 40k - m = 64
x = k --> 0 = k^2 - 5k^2 + m <–> 4k^2 = m

But once you solve for m and k, you get (k,m) = (16,2) or (256,8), in which you introduce an extraneous solution.

I believe if you plug in one more number (say x = 0), then you will eliminate the extraneous solution. It seems that what happened is that the two x values you chose were not enough to narrow it down to a single solution. Remember that the equation must be true for all x, not just for 2 values of x.

It seems like an unusual problem to me. Either a student needs to use math concepts that are beyond the scope of what is considered necessary for the SAT, or it requires a lot of brute force requiring much more than the usual max of 30 seconds per question for most students.

Ah yes - plugging in x = 0 gives m = 8k which reduces the # of solutions to 1. Basically what I was trying to get at is, x = k is probably not the best choice, although if I did this entirely by plugging in, 8 and k would intuitively be my first two choices.