Just A Bit More Math Help

Discus: SAT/ACT Tests and Test Preparation: June 2004 Archive: Just A Bit More Math Help
 By Ladybajan (Ladybajan) on Wednesday, June 02, 2004 - 03:48 pm: Edit

Can you all please help me with this problem? I'm taking the SAT on Saturday so these questions will be the last for a while. Thanks!

This is a grid-in:
The average (arithmetic mean) of the test scores of a class of p students is 70, and the average of the test scores of a class of n students is 92. When the scores of both classes are combined, the average score is 86. What is the value of p/n?

 By Qwert271 (Qwert271) on Wednesday, June 02, 2004 - 04:01 pm: Edit

Average: [(70)(p) + (92)(n)] / (p + n) = 86. Do some algebra and get 6n = 16p, then get p/n = 3/8.

Alternately, realize that 92 is 8/3 times as close to 86 as 70 is. Therefore, n must have 8/3 as many people as p.

 By Manyzhka (Manyzhka) on Wednesday, June 02, 2004 - 04:10 pm: Edit

Let x be the sum of all scores in the first class. And let y be the sum of all scores in the second class. You get:

x/p = 70
y/n = 92

So, x=70p and y=92n
Then for the combined thing you get
(70p+92n)/(p+n)=86
70p+92n = 86p+86n
6n=16p
n=16p/6

So, p/n= p/(16p/6)= p*(6/16p)=6/16=3/8

 By Ladybajan (Ladybajan) on Thursday, June 03, 2004 - 10:03 am: Edit

I don't know what this question is asking for me to do. Before you solve it, can you decipher it for me? I had thought it meant 12 times what equals a cube of an integer but no. It is a Grid-In.

24. What is the least positive integer n for which 12n is the cube of an integer?

This is a Quantitative Comparison. I wanted to know how you find how many cubes are in the column or row and the corners. Like a place said that 3 smaller cubes are along each side but how do you know? And then solve it after telling me, please.

Twenty-seven white cubes of the same size are put together to form a larger cube. The larger cube is painted blue.
A) The number of smaller cubes that have exactly three blue faces.
B) 9

This one I just don't know how to solve. I think it is the answer choices that are confusing me.

8. After Jean gave \$10 to Irene and Irene gave \$6 dollars to Todd, Jean had \$10 more than Irene and \$20 more than Todd. Originally, how much more did Jean have than Irene and Todd?

A) \$14 more than Irene and \$16 more than Todd
B) \$18 more than Irene and \$24 more than Todd
C) \$18 more than Irene and \$26 more than Todd
D) \$24 more than Irene and \$36 more than Todd

 By Optimizerdad (Optimizerdad) on Thursday, June 03, 2004 - 10:57 am: Edit

24. 'I had thought it meant 12 times what equals a cube of an integer' is indeed correct. Look at it this way: 12 is 2*2*3, so look for a value n such that 12n = 2*2*2 *3*3*3 = 2^3 * 3^3 or (2*3)^3 .
n = 2*2*2 *3*3*3 /12 = 2 *3*3 = 18

Q2. Think of the 27 small cubes as each being 1" x 1" x 1". Then the total volume of 27 such cubes is 27 * (1*1*1) = 27 * 1 = 27 = volume of the large cube. If the big cube is x" long on each side, x*x*x is its volume, which is 27; so x^3 = 27 and x=3, so there are 3 small cubes on each side of the big cube.
If you paint all faces of the big cube blue, the only small cubes with 3 blue faces will be those at the corners of the big cube (those along the edges but not at the corners will have two blue faces, all others on the faces of the big cube will have one blue face). Any cube has 8 corners, so the answer should be 8, not 9 (unless I'm missing something).

8. Suppose Jean originally had x dollars, Irene had \$y, and Todd had \$z. Jean finishes with x-10 dollars, Irene ends up with y+10-6 = y+4, and Todd ends up with z+6 dollars.
Jean now has \$10 more than Irene, so x-10 = 10 + y+4, or x = y+24. Similarly, Jean also ends up with \$20 more than Todd, so x-10 = 20+z+6, or x=z+36. The correct answer is D)

 By Ladybajan (Ladybajan) on Thursday, June 03, 2004 - 11:54 am: Edit

Thanks so much for the thorough explanations.

 By Eecs (Eecs) on Thursday, June 03, 2004 - 02:19 pm: Edit

for 24, a faster (but less mathematical way) would be just to take your graphing calculator, graph y= cuberoot(12x) and then go to that table of values thing, and scroll down until you seen an integer in the y column. the answer is in the x column.

of course this way is just in case you didn't know how to do it the mathematical way. you could really brute force quite a few SAT questions with a graphing calc.

 By Mhawk177 (Mhawk177) on Thursday, June 03, 2004 - 03:12 pm: Edit

The money one, the answer is D... one of the easiest ways for people to do these problems if they dont like to use many variables is to assign each person an ammount.

Jean gave \$10 to Irene.. therefore Jean was originally at \$40

Irene recieved \$10 from Jean and then gave \$6 to Todd meaning she is +\$4 after that... 20-4= \$16

Now for Todd.. we know that Jean has \$30 at the end (theoretically) and he has \$10 since he is \$20 down. Therefore since he recieved \$6 he originally had \$4.

Jean started with \$40, Irene started with \$16 and Todd started with \$4

The difference between \$40 and \$16 being \$24 and between \$40 and \$4 being \$36. Therefore the answer is D