One type of question in which "plugging in" values is quite helpful is when you have variable expressions in all five answer choices. These can be word problems or algebraic manipulation problems. The plug-in technique is particularly helpful, I find, with the algebraic manipulation proble...

If you are composing a list, you should separate the elements of the list with commas and include "and" only before the final item in the list. (You're also allowed to use semicolons instead of commas when the members of the list are especially long and/or and contain commas themselves. No...

You're right, Hei, a comma would be necessary before the participial modifier, as in: The lawyer slammed her briefcase on the table, making it clear to everyone that she was unhappy. To your other point, I think "Having V-ed, S V O" clearly shows a sequence of events, specifically that the...

Aritro,

We're happy to provide assistance through this forum, but your question is too broad. Can you narrow your scope a bit? For example: Are there particular kinds of questions that are troubling you? Do you have specific content questions?

Rey

The original question was deleted because the poster did not cite the question's source.

You're welcome (on behalf of Stacey).

You're welcome (on behalf of Ron).

You're welcome (on behalf of Ron).

Could you explain the difference in meaning between the following two phrases 1) A is only surpassed by B vs. 2) A is surpassed only by B I disagree. As I read them, there is a difference between the two sentences. In #1, we learn that the only thing that B does relative to A is surpass it. In othe...

Nice solutions, David.

Bangu, You used the permutation formula: P(n,r) = n!/(n-r)!. And this formula assumes that once an element is picked (in this case, a digit between 1 and 5) it can't be picked again. That's why you get 20 right away with the formula and don't have to subtract the 5 double-digit numbers. Another appr...

I think your question stems from how to solve absolute value equations in general. Let's start with the definition of absolute value: |x| = x, if x>0 or -x, if x<0. Let's try it out... |3| = 3; because the number inside the absolute value was already positive, all we needed to do was drop the ...

Good luck!

can someone pls explain how to understand the ratios. In this case 1:2:3:5, if the given ratio is the no. of hrs a machine takes to sew a shirt, then isnt "1" the fastest machine? No. The numbers tell us, proportionately, the number of shirts per unit time the four machines are able to pr...

I find using the phrase "at least" helps for these problems. If we are told that j is divisible by 12, then that means that j has at least two 2s and one 3 in its prime box. There could be other prime factors in j, including some more 2s and 3s, but we're not sure about them. Similarly, j ...