10 HARD ACT Math Problems | ACT MATH | 5 Academy | 2024

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[@5Academy]

Hey guys! Correction to problem 51. The answer should be D. Since this is a replacement problem with two draws, you should add 10/810 + 10/810 to get 20/810. Apologies for the confusion and thanks to those of you who pointed it out!

[@5Academy]

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[@OverclockingCowboy]

The comment by @zackhockey10 is the correct answer. You did not consider AT LEAST ONE for the extra piece. Not having an extra piece on the first draw is a desired outcome, as long as your second draw is an extra piece. Your answer happens to be “numerically” close to the correct answer D. The desired outcomes are 01, 10, 11 for 2 draws, where 1 means an extra piece. If we enumerate these outcomes, we have (800/810)(10/810) + (10/810)(800/810) + (10/810)(10/810) = (10/810)(800/810 + 800/810 + 10/810) = (10/810)(1 + 800/810) The last expression can also be interpreted as having an extra piece on the first draw (the 1 term) plus having an extra piece on the second draw “given” that the first draw is not an extra piece (the 800/810 term), satisfying the condition of at least one extra piece. The last expression can be further manipulated as (1 - 800/810)(1 + 800/810) = 1 - (800/810)^2 which has the meaning 1 minus probability of not having an extra piece for 2 draws as given by @zackhockey10 The BOTTOMLINE is you cannot just multiply 10/810 by the number of draws. If that is true, you will get probability 1 after 81 draws and probability exceeding 1 after more than 81 draws.

[@hqs9585]

problem 51: you have two trials not 1 so the correct answer is double from what you mistakenly got, i.e. P = 0.025

[@zackhockey10]

Isn't Q51 D? Since we are looking for at least 1 of the extra pieces, we can subtract getting no extra pieces from 1 to get the final percent. Getting no extra pieces would be (800/810)^2. Then 1- (800/810)^2 would be your answer. Comes out to 0.024538... rounding to .0250. Answer is D. Am I missing something?

[@top10trending41]

Yes I thought so too

[@kadinnguyen3930]

@@top10trending41 fr me too

[@OverclockingCowboy]

You did not miss anything. You are the only one who considered AT LEAST ONE of the extra pieces.

[@dhivyasahiram5727]

Please correct Me if I'm wrong but for the first question wouldn't the answer be D? Because 10/810 is the probability for picking one extra piece but they are asking about selecting two pieces?

[@top10trending41]

That’s what I thought too

[@rheagovindaraj6913]

thats what i was confused about as well, but I think because it is asking for at least one of the two selections to be the extra piece it would only be 10/880.

[@krillan6692]

Thank you so much bro you are helping this next generation more than Tate and all these other pinballs can dream of

[@StudsMac]

23:15 pretty sure if the moon was 2531 ft away we would not be having a fun time

[@mangler241]

Not only was Problem 51 poorly composed, the answer is incorrect; the correct answer is ~0.0245.

[@hqs9585]

Problem 53: N = number of applicants; 30% interview and 2/3 of this are hired . so .3(2/3) = .2 or 20% hired or 90 . So 20/90 = 100/N. So N= 450

[@5Academy]

That's a valid way to do the problem 👍

[@hqs9585]

last problem you really did not solve it or told how to go about it?

[@davidmunoz4223]

"Whoever wrote the problem... good job don't know what planet you're on" 😂

[@mangler241]

Problem 56 was also poorly composed.

[@user-tg3du6rt6m]

Is This ACT 2 math level 2?

[@5Academy]

I'm not sure