twinkletoes23

K, i got two wrong overall on the math section...

but here are the three i'm struggling on...

1. The average (arithmetic mean) of 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?

I just guessed and checked and got the right answer. Is there a simpler way?





2. Page 746, # 12.




3. A store charges 28 dollars for a certain type of sweater. This price is 40 percent more than the amount it costs the store to buy one of these sweaters. At an end-of-season sale, store employees can purchase any remaining sweaters at 30 perfect of the store's cost. How much would it cost an employee to purchase a sweater of this type at this sale?

HUH? i don't understand the question. None of my answers match the solution.


*mwah* thanx a ton!!!

setzwxman

If you provide the page numbers of these problems, it'd make it much more convenient for everyone so we could check the answers.

1. Let x = the sum of the test scores for the p number of students.
x/p = 70
x = 70p

Let y = the sum of the test scores for the n number of students.
y/n = 92
y = 92n

For the combined classes average,
(y + x)/(p + n) = 86
(92n + 70p)/(p + n) = 86
92n + 70p = 86p + 86n
6n = 16p
6 = 16(p/n)
6/16 = p/n
3/8 = p/n

2. This involves one of those things from geometry - perhaps it's a theorem; I'm not sure. Whenever you have a triangle like this, the segment connecting the two midpoints (in this case, points A and Q) is exactly half the length of the longer parallel segment (BR). We know that AB = 2, QR = 3, AQ = 4, and now that BR = 8. Perimeter = 2 + 3 + 4 + 8 = 17, answer E.

3. I might be able to decipher that awkward wording if I knew the answer.

ShadowOfAnEnigma

What I understand question 3 to say:

a store buys a sweater for cost X
a store sells said sweater for $28, which is 40% more than price X
employees can buy the sweater for price Y, which is 30% of X

That being said, I don't actually know how to solve it.

tanman

3. Retail price = $28
Retail price = 140% of store cost

$28 = 1.4 * (store cost), so store cost = $20

An employee can purchase at 30% of store cost so
Employee cost = .3 * (store cost) = .3 * 20 = $6

So the answer appears to be $6 (though I don't know why the store would sell something for so much below cost)

obsessedAndre

This should be the answer to #3:

they're telling you it's 40% more than the store's cost, so call the store's cost x

you know
28 = 1.4x

28/1.4 = x
28/1.4 = 20
20=x

Now BE CAREFUL, the question has tricky wording:

"30% OF the store's cost"

so 20 * 30% = 6 (or -70%, however you want to look at it)

The answer should be 6.

xiggi

I would really encourage anyone to read the past questions.

The students' grade question came up a few days ago:

Help with math problems from CB blue book!!

xiggi

Humm. The sweater problem would be a bit too simple for ETS if it was a mere 30% of the store price. ETS would like to test a bit more of your knowledge.

I think that the question should read "the employee can buy the remaining at 30% OFF the store price.

The answer to this problem should then be 20 x (100 - 30)% or 14 dollars.

PS Tanman was correct to wonder about the value of 6 bucks. It is worth remembering that ETS usually leaves an element of realism in its problems.

Flipsta_G

Yes Xiggi is correct, it should be 30% OFF the cost. I just took these questions in the Red book. Damnit, why does CB rip us off like this by repeating its material?

gcf101

Look up
http://talk.collegeconfidential.com/...78#post1113278
and
http://talk.collegeconfidential.com/...19#post1113919

Just to illustrate Ziggy's approach:

It's often helpful to visualize
1.numbers
and
2.their average
as
1.straight glasses with different levels of water
and
2.same glasses with equal volume of water in each,
total volume of water in these glasses being equal to
total volume of water in the original configiration of glasses.
This is actually an analogy to bar graphs.

In order to have all glasses filled equally we need to redistribute the water:
add to those where the level is below the average,
taking water out of those wth the level above the average.

You can see that "added volume" has to be equal to "removed volume".

So, if the average of p students' scores is 70, and the average score of another group of n students is 92, you can draw
p glasses with the level of 70 and n glasses in the same row with the level of 92.
Now draw the line through all the glasses at level 86.
In order to get a volume in each glass equal to 86, we'll pour out what's above 86 level into what's below it.
There are n glasses with the level above 86 by 6
(86+6=92), required loss = 6n,
and p glasses with the level below 86 by 16
(70+16=86), needed gain = 16p.
6*n = 16*p,
p/n = 6/16.
THE END.

This is a simplified situation (each of p glasses have the same volume of water; same is true for n glasses), but it visually confirms what Ziggy showed in his diagram:

"...CHANGES in scores

70................86......92
...........16...........6

... the gain of p students HAS to equal the loss of students of n students (no points vanish when averaging the scores)."

xiggi

gcf101

I wonder if somebody would try using this "glasses technique" (no equations) on the BB q.5 p.397:

The average of x and y is 5 and the avearage of x, y, and z is 8. What is the value of z?
A.19
B.14
C.13
D.11
E. 3

Nerj

it seems to complicates the question if u go the 'glases technique'.... (though i dont noe exactly wat tht is, but the explaination seems pretty long)

gcf101

First, an important tip for the SAT math questions in general:
if variables are given, but the answer is numeric, you can choose numeric values for variables that suit you best.

We can set x=5, y=5 (average of x and y is 5 with no restrictions on x and y).

Rephrazing the question:
two glasses filled to volume 5 and one to volume z.
------------z
---8---8---8---average
---5---5

8-5=3.
We need to pour out 3+3=6 out of glass "z" into the first two glasses to make volumes in all three glasses equal average 8, which means volume z is 6 above the average,
z = 8+6 = 14.

It takes literally seconds to answer the questions this way - just draw a diagram with glasses.

With some practice you'll be able to apply this technique to much more difficult questions.

Flipsta_G

Yea, that glasses technique confused me also. Wouldn't it be easier to use regular equations?

(x+y)/2 = 5
x+y = 10

(x+y+z)/3 = 8
x+y+z = 24
10 +z = 24
z = 14

gcf101

In this question there is a small time gain if you do it the "glasses" way, but chances of mistake are significantly reduced.
In more difficult questions the benefits of using the "glasses method" become quite obvious.

In general, given a choice between visual and algebraic solutions, I'd choose visual any time of day.