@kunkunta I certainly did. Notice that the exponents originally on a and b are 1/2 and 1/3. Raise those to the 6th power and…
What I didn’t notice was the number 438.
Never mind, you’re correct.
It is 432,not 438. Sorry.
@kunkunta thought so. But no worries.
I recommend finding the prime factorization of 432. From there, you should be able to find a and b such that a^3 * b^2 = 432.
@MITer94 , thanks. If you don’t mind me asking, are you a tutor?
@kunkunta I don’t tutor for the SAT or ACT specifically, but I have tutored up to and including calculus, as well as for some math competitions.
@kunkunta
I could PM this to you, but I want to apologize to you publicly.
First, I am sorry for giving you a lecture and sounding like a condescending jerk.
Instead of scolding you for the high number of questions you dropped in your thread, I could’ve just said what @DrSteve tactfully wrote: “ In the future you might want to post one at a time. You’re more likely to get a faster response that way.”
Also, I made it look like you just need to give up at this point: it’s too late to do anything to improve.
I let my frustration cloud my mind and unleashed my emotions on you. Sorry for that again.
You can accomplish a lot in the remaining 1.5 days if your work efficeintly.
What often frustrates me (I know I should keep it better under check) is when questions are asked without prior attempts to try to come to the answers or look for them elsewhere.
Answers to all the questions from the BB can be found on www.collegeboard.org/satstudy. Some of the explanations there are okay, some – so-so, and some – quite bad. Still, it makes sense to look there first and then decide if additional help is needed.
Here’s a solution from that site to your last question:
Simplifying the exponential part of the expression gives
(a(6/2) b^(6/3)) = (a^3)(b^2) =432.
The prime factorization of 432 is (3^3)(2^4), so (a^3)(b^2) = (3^3)(2^4).
Since a and b are positive integers, it follows that a^3 = 3^3 and
b^2 = 2^4 = (2^2)^2. This yields a =3 and b = 2^2 = 4.
The question asks for the product of a and b, which is
3x4 = 12.
A bit too wordy, but easy to follow.
@gcf101 , you are super nice!! I appreciate it. But those sites provide answer explanations only upto practice test 4.
@MITer94 , I was wondering , are we supposed to take time literally only on clock involving questions? Are A.M.s and P.M.s insignificant then?
Here’s another solution.
(a^3)(b^2) =432.
a (ab)^2 = 432.
a = 432/(ab)^2 - has to be an integer.
.
There are five answer choices for ab: 6, 12, 18, 24, and 36.
Let’s start in the middle.
If ab = 18, then (ab)^2 = 324; 432 / 324 = 1.333… Not good
If ab = 12 then (ab)^2 = 144; 432 / 144 = 3 = a.
Let’s make sure that b is an integer as well:
b = 12 /a = 12/3 = 4. Yes, it is.
Done.
@kunkunta Sorry, I’m not exactly sure what you mean by “take time literally” (could you elaborate?). But when it says that the plane landed in San Francisco at 4:00 PM that same day, it is presumed to be 4:00 PM local time (i.e. 4:00 PM PST).
I would at least take note of the AM and PM (just in case two answer choices differ by AM/PM), but I was a tad sloppy and didn’t always include AM or PM.
@kunkunta You must’ve looked at some other site which explains only four tests.
The college board’s one provides explanations from “Official Practice Test #1” through
“Official Practice Test #10”.
Often overlooked is a very useful feature of that site: for each BB test’s essay prompt there are given 6 sample essays - one per score from 1 to 6 - with score explanations. You can even click on “Hand-written Essay” and see the original of each essay; that means all the essays there are from real test take-takers.
@gcf101, thanks. @MITer94 , when a clock says 7 P.M , we could either take it as 1 P.M. or just take 7 as it is. For the latter, P.M. And A.M. are insigninficant. On question #5 above, it was not a clock question so we took 9 A.M. as 3. Am i making sense?
@kunkunta I’m sorry, I’m confused.
When a clock says 7 PM, then (assuming it’s right) it is 7 PM. Not sure where you get 1 PM from? Different time zone?
Think of it like this:* New York is three hours ahead of San Francisco*, as given by the first sentence in #5 (this is always true in real life). So when it is noon (12 PM) in NYC, it is 9 AM in SFO; when it is 2 AM in NYC, it is 11 PM in SFO.
Ok. Forget every thing I have said. There is a time zone difference between USA and my country. Anywho, when it’s 3:00 A.M. ,on what does the hour hand point?
@Drsteve , two more please.
Page 731 #10
page 738 #12
@Drsteve ,sorry its page 732 not 738.
Um, the hour hand points on the 3 at 3:00 AM (or 3:00 PM).
Page 731 #10
Solution by process of elimination:
We can eliminate choices (A), © and (E) because 10, 18 and 30 are not divisible by 4. We can eliminate choice (D) because 20 is not divisible by 6. Therefore the answer is choice (B).
Verification that choice (B) works:
Let’s guess that there are a total of 12 marbles in the bag. Since the probability of selecting a red marble is 1/4, there are 12/4 = 3 red marbles in the bag. Since the probability of selecting a blue marble is 1/6, there are 12/6 = 2 blue marbles in the bag. This means that there must be 12 – 3 – 2 = 7 yellow marbles in the bag. So 7/12 of the marbles are yellow. Also, 1/4+1/6+7/12 = 1. Therefore the answer is choice (B).
Remark: To compute 1/4+1/6+7/12 simply type the following into your calculator: 1/4 + 1/6 + 7/12 ENTER. The output will be 1.
732 #12
Since the area of the square is 81, each side of the square has length 9. The perimeter of the figure outlined by the solid line is the sum of the perimeters of the 4 triangles minus the perimeter of the square (the dashed lines). This is 4(30) – 4(9) = 84, choice (D).
Remark: The area of a square is A = s^2 where s is the length of a side of the square. So if the area A is known, then s = √A. In this problem, the side length of the square is √81 = 9.
Just noticed a truncated link in my old (#26) post.
It should be https://sat.collegeboard.org/practice/sat-study-guide-owners-area?excmpid=CBP6-ST-2-guide.