# Tutor profile: Anshul B.

## Questions

### Subject: SAT

If n does not equal 3p and $$ s = (n^{2} + p)/(n - 3p) $$ then what is the value of p in terms of n and s?

Whenever we try to solve for an algebraic variable, we always need to remember the fundamental rule: bring similar variables on one side and all other variables on the other side. So, here, we need to get all p variables on one side, and only n and s variables on the other. How do we do this? Since we have the p term in both the numerator and the denominator, we should first cross-multiply to get rid of any denominator. So, we multiple both sides by n-3p. This gets us $$ s(n-3p) = (n^{2} + p) $$. This simplifies to $$ sn - 3ps = (n^{2} + p) $$. Now we can subtract p from both sides to get all the p terms on one side. This gets us $$ sn - 3ps - p = n^{2} $$. Now, we subtract by sn to get all the "non-p" terms on the right side. This gets us $$ - 3ps - p = n^{2} - sn $$. There is still a pesky s on the left side. To get rid of this, we can factor out the p, since p is being multiplied by s. This leads us to $$ p (-3s - 1) = n^{2} - sn $$. Now, all we need to is divide both sides by (-3s-1). This gets us to the final solution $$ p = (n^{2} - sn)/(-3s - 1) $$. This may seem very complicated, but if you take a moment to think about it, throughout the entire question, we are doing nothing more complicated than basic addition, subtraction, multiplication, and division. If you know how to do these four processes, you can answer this question. The only trick is knowing the order of the processes and when to use each one. This intuition can be developed with practice, and I promise you will start to see patterns emerge from the numbers!

### Subject: Chemistry

Based on the principles of polarity and hydrogen bonding, rank the following molecules in order of increasing solubility in water. Molecule A: CH3-CH2-CH2-OH Molecule B: CH3-CH2-CH2-CH2-OH Molecule C: CH3-CH2-CH2-(OH)2 Molecule D: CH3-CH2-CH2-CH3 Answers: 1. A<B<C<D 2. D<A<B<C 3. D<B<A<C 4. C<A<B<D

Whenever we try to determine solubility of various molecules, we should always remember the old adage "like likes like." So, of we are determining solubility of molecules in water (H20), then we should look for molecules that have similar properties as H2O, as these molecules would be more soluble in water. We know that water has many distinguishing properties, so what should we look for? The beginning portion of the question stem should narrow this down to two properties: polarity and hydrogen bonding. We know that water is polar (has an uneven distribution of electrons, as the more electronegative oxygen "hogs" all the electrons, giving it a partially negative charge, while giving the deficient hydrogen atoms partially positive charges. We know that CH groups are non-polar, as carbon and hydrogen have similar electronegativities, while OH groups are polar. A hint should be that (OH) groups even look somewhat like the formula for water (H20). So, we know that the most soluble molecule should be C, which has the most OH groups (2) and is thus most like water, while the least soluble molecule should be D, which has the least OH groups and is thus least like water (O). This narrows our choices to 2 and 3, in which case we need to determine whether A or B is more soluble in water. The only difference between molecules A and B is that B has an extra CH2 group, which we know is non-polar and thus not soluble in water. This should make B less soluble than A, so the correct answer is 3.

### Subject: ACT

Please fix the following sentence (if necessary): Whether its math, science, or English I can help. Choices: 1. NO CHANGE 2. Whether its math, science, or English, I can help. 3. Whether it's math, science, or English, I can help. 4. Whether it's math, science, or English I can help.

There are two problems with the current sentence. The first concerns the word "its." There is another commonly misused version of this word: it's. What is the difference between the two? "Its" is like the possessive words "her" and "his," but for objects that don't have a specified gender (for example, such as in the sentence "the rabbit placed its paw on my hand"). So, when "its" is being used, something actually needs to be the "it" to which the word is referring (in my example, the rabbit). This does not happen in the question that I have asked. The second form (it's) is a contraction (just a fancy term for a combination of two words) for the words "it is." A trick to determining when "it's" is necessary is if we can replace the former with the latter phrase and the sentence still makes sense. In the presented question, if we do this, the sentence instead reads "Whether it is math, science, or English I can help." This still makes sense, and so we know that "it's" is the right version and not "its". This narrows the choices to 3 and 4. By examining the differences between these two, we can see that the only change is that 3 includes an extra comma. We know that the term "I can help" is an independent clause (it can stand alone as its own sentence), and we also know that the phrase "Whether it's math, science, or English" is a dependent clause (it cannot stand alone as its own sentence). As a rule, whenever we have a dependent clause followed by an independent clause, we always separate them by a comma (note that I have done so in this sentence itself). Thus, 3 is the correct choice.

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