<p>Hello fellow members,</p>
<p>I need help in the following question:</p>
<p>A large cube, 5 cm x 5 cm x 5 cm is painted orange on all six faces, and then it is cut into 125 small cubes, each 1 cm by 1 cm by 1 cm. How many of the small cubes are not painted orange on any face?</p>
<p>A) 125
B) 64
C) 27
D) 24
E) 9</p>
<p>P.S. Don't simply post the answer. Please provide an explanation.</p>
<p>Only the interior cubes don’t get painted, right? What shape are they arranged in? And how big a shape is it? You’ll have to strip away all the cubes on the top and bottom faces, the front and back faces, and the left and right faces. When you do that, what are you left with?</p>
<p>Oh yes. I got it. You made it sound so simple. Thanks a ton. </p>
<p>We’ll be left with a 3x3x3 cube = 27</p>
<p>Another one:</p>
<p>A grocery customer spent a total of $17.50 for butter and peanut. The peanut costs 3 times as much per pound as the butter, and the customer bought four times as many pounds of butter as pounds of peanut. How much, in dollars, did the customer spend on butter?</p>
<p>Try setting it up as an algebraic relation, then simplify.</p>
<p>For mnemonic purposes, I’d suggest letting b be the number of pounds of butter, cb the cost of the butter per pound, p the number of pounds of peanuts, and cp the cost of the peanuts per pound. Since you know the total that was spent, you can set up an equation for it:</p>
<p>That would be $17.50 = cb * b + cp * p.</p>
<p>Now, what other information are you given? You know that peanuts cost 3 times as much per pound as butter. So cp = 3 * cb. Use that to replace cp in the equation.</p>
<p>Now you have
$17.50 = cb * b + 3 cb * p.</p>
<p>Next, you know that the customer bought 4 times as many pounds of butter as pounds of peanuts. So b = 4 p. However, looking ahead, you want to know how much the customer spent on butter. So rather than replacing b in terms of p, it would be better to replace p in terms of b. Therefore, convert the equation to p = b/4. Then put it back into the cost equation:</p>
<p>$17.50 = cb * b + 3 cb * (b/4) = 1.75 cb * b.</p>
<p>The amount that the customer spent on butter is cb * b. Solving for that, the result is $10.</p>
<p>There are other work-arounds that you can use in your head, but this approach will work every time, and in my opinion, it’s most likely to help you avoid arithmetic errors.</p>
<p>I would like to clarify this part-</p>
<p>The peanut costs 3 times as much per pound as the butter => cp = 3cb</p>
<p>The customer bought four times as many pounds of butter as pounds of peanut => 4p = b</p>
<p>I get the former; however, for the latter part, I am getting confused in the way the sentence is phrased. I end up writing 4b = p instead. Can you provide a clarification for this too? </p>
<p>Thanks for the lucid explanation.</p>
<p>Please QuantMech. Try to explain the last post too.</p>
<p>Question 3:</p>
<p>If 4√8 = m√n, and if n and m are positive integers, which of the following cannot be the value of m+n?</p>
<p>A- 129
B- 34
C-24
D- 12
E - 10</p>
<p>So what I can gauge is that 4√8 can be written as 8√2, which means m+n=10. What about the other options?</p>
<p>Hi IAMSTRONG95: It might be the wording of the statement that is confusing you. When it says “The customer bought four times as many pounds of butter as pounds of peanuts,” this means the following: Think of the number of pounds of peanuts the customer bought (p). How is the number of pounds of butter (b) related to that? It is supposed to be four times as many. So b = 4p.</p>
<p>This is a fairly common way of phrasing the relation. If you work through a few more examples, you will become familiar with it. Hope this helps.</p>
<p>In #8, you have simplified the square root in the normal direction, to get 8√2.</p>
<p>However, you could also take the 4 outside the square root in the expression 4√8, and figure out what you would need to put under the square root, to have everything under the square root. This would give you √(16)* 8 (with the whole expression 16*8 under the square root sign). That would be √128. In this case, m = 1 and n = 128, giving m + n = 129. So A is ok.</p>
<p>You could leave one factor of 2 in the 4 outside, and change the expression to pull the rest in under the square root. This would give 2 √(4) * 8 (with the (4) * 8 all under the square root). In this case, m =2 and n = 32, so m + n = 34. This means that B is ok.</p>
<p>At this point, there is nothing more that is obvious to do, there are two choices left, and you have to eliminate one choice. This is where the question is slightly sneaky. For 4√8 = m√n, you could also have m = 4 and n = 8 (no change in the expression). In that case m + n = 12, so D is ok.</p>
<p>The only option we didn’t find is C, 24. There are probably some other number-theory considerations that could give you the answer a bit faster, but this will work.</p>
<p>Thank you so much QuantMech. You’re such a great help. I get it now.</p>
<p>Sorry for the barrage of questions, but I have another doubt:</p>
<p>Ten to Fifteen tires out of 300 are defective. If there are 1800 tires in shipment, which of the following could be the number of defective tires?</p>
<p>A- 30
B- 35
C- 40
D- 50
E- 80</p>
<p>Okay, so the question is saying that there are about 10 to 15 defective tires every 300 tires. The question asks you approximately how many tires will be defective in a batch of 1800 tires. So, how many 300 tires make 1800 tires? To figure that out, you’ll need to divide 1800 by 300. The answer to that is 6. Since there are 10 to 15 defective tires per 300, you’ll need to multiply 6 times 10, which is 60, and 6 times 15, which is 90. That means that the amount of defective tires in a batch 1,800 will range from 60 to 90. Look at the choices, E (80) is the only number that is between 60 to 90. The answer must E!</p>
<p>Thank you so much labella. Got it! Great explanation.</p>
<p>Sure, I’ll try and check this thread often to see if I can help.</p>
<p>That’ll be great. Thanks labella.</p>
<p>QUESTION:</p>
<p>AGES NUMBER OF STUDENTS
18 2<br>
17 6<br>
16 12<br>
15 2</p>
<p>The chart above shows ages of 22 students enrolled in math class. What is the mean?</p>
<p>ages - 18 17 16 15
Number of students - 2, 6, 12, 2</p>
<p>Have a look at the corresponding values. I can’t post it in the form of a table.</p>
<p>My answer is 16.3, but the answer is 45.5. I don’t get it.</p>
<p>answer cannot be more than 18 and less than 15. It has to be within the data. So 45.5 is wrong. Your 16.36 is correct!</p>
<p>Thanks a lot Nebico. Got it! It must be a typographical error.</p>