Math trick need for TBR Gen Chem Sec 3, Passage 8

[davcro]

In order to solve this passage you have to order the following fractions:

7/100, 9/120, and 4/150

I couldn't think of a quick way to solve these and missed nearly every question in the passage. How do you solve the above fractions quickly?

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[MedPR]

In order to solve this passage you have to order the following fractions:

7/100, 9/120, and 4/150

I couldn't think of a quick way to solve these and missed nearly every question in the passage. How do you solve the above fractions quickly?

Are you sure there isn't another way? If not, those fractions still aren't all that difficult.

7/100 = .07
9/120 = less than .09 (9/100), but greater than .066 (8/120 = 2/30. Since 2/3 = .66, 2/30 must = .066),
4/150 = slightly more than .025 (4/160 = .025)

 

[davcro]

No other way. More than half the questions for that passage depend on the above three fractions. The crux is ordering 9/120 and 7/100.

In hindsight here is my solution:

9/120 = 9 / (12 * 10) = 3 / (4 * 10) = 0.75 x 10^-1 = 7.5 x 10^-2
4/150 = 8 / 300 = 8 / (3 * 100) = 8/3 x 10^-2 = 2.66 x 10^-2
7/100 = 7 x 10^-2

 

[MedPR]

No other way. More than half the questions for that passage depend on the above three fractions. The crux is ordering 9/120 and 7/100.

In hindsight here is my solution:

9/120 = 9 / (12 * 10) = 3 / (4 * 10) = 0.75 x 10^-1 = 7.5 x 10^-2
4/150 = 8 / 300 = 8 / (3 * 100) = 8/3 x 10^-2 = 2.66 x 10^-2
7/100 = 7 x 10^-2

Yes, those calculations are perfectly accurate, but I'd be willing to bet that you don't need to be that precise to answer the question. If you have a lot of extra time on PS, it doesn't hurt to do complete calculations, but you might want to consider saving time by estimating (e.g 9/120 is less than .09 but greater than .066. I don't have the problem in front of me though, so for all I know you do need to have exact decimals.

 

[chiddler]

In order to solve this passage you have to order the following fractions:

7/100, 9/120, and 4/150

I couldn't think of a quick way to solve these and missed nearly every question in the passage. How do you solve the above fractions quickly?

7/100 is simple.

you can simplify the second one: 9 / 3 = 3, 120 / 3 = 40. 1/40 is 2.5. 2.5*3 =7.5. Move the decimal.

4/150. this one must be the smallest one!

 

[davcro]

Yes, those calculations are perfectly accurate, but I'd be willing to bet that you don't need to be that precise to answer the question. If you have a lot of extra time on PS, it doesn't hurt to do complete calculations, but you might want to consider saving time by estimating (e.g 9/120 is less than .09 but greater than .066. I don't have the problem in front of me though, so for all I know you do need to have exact decimals.

You need to know if 9/120 is greater than 0.07. Knowing that it falls into the range of 0.09 - 0.066 doesn't help.

From what I've read so far, it appears that the MCAT will have a handful of tricky math calculations. I'm trying to learn all the little tricks I can to save time. Solving fractions quickly seems to be the biggest problem for me

 

[MedPR]

You need to know if 9/120 is greater than 0.07. Knowing that it falls into the range of 0.09 - 0.066 doesn't help.

From what I've read so far, it appears that the MCAT will have a handful of tricky math calculations. I'm trying to learn all the little tricks I can to save time. Solving fractions quickly seems to be the biggest problem for me

Estimating a small enough range is often enough for mcat math (at least in my experience), but in certain cases, like this one apparently, you do need to be more precise. Sometimes not rounding until the end makes the math simpler as well.

It also doesn't take long to do the long division for 9/120. 120 goes into 900 7 times, leaving 60, and 120 goes into 600 5 times. = .075

 

[ljc]

My method:

7/100 and 4/150 are obvious. The question is between 7/100 and 9/120. For me, I see that 120 is 100*1.2. So now multiply 7 by 1.2 = 8.4/120. Now order accordingly. 4/150, 8.4/120, 9/120.

 

[Ssina]

Estimating a small enough range is often enough for mcat math (at least in my experience), but in certain cases, like this one apparently, you do need to be more precise. Sometimes not rounding until the end makes the math simpler as well.

It also doesn't take long to do the long division for 9/120. 120 goes into 900 7 times, leaving 60, and 120 goes into 600 5 times. = .075

questions I have seen so far are all apart enough or numbers cancel each other out either way.... so I always write all the numbers out in calculations before doing fractions one by one and most of the time all the weird numbers cancel out and your left with easy ones.

with that said, I guess it's not bad to prep for that 1% chance you might end up with a math heavy physics! I round numbers a lot (a bit too much even) and so far it has only cost me couple of questions only in TBR (not AAMC, TPR, etc.)

 

[MedPR]

questions I have seen so far are all apart enough or numbers cancel each other out either way.... so I always write all the numbers out in calculations before doing fractions one by one and most of the time all the weird numbers cancel out and your left with easy ones.

with that said, I guess it's not bad to prep for that 1% chance you might end up with a math heavy physics! I round numbers a lot (a bit too much even) and so far it has only cost me couple of questions only in TBR (not AAMC, TPR, etc.)

I guess so, but the 1% of questions that require precise math will probably also require very simple math to get to the precise answer (e.g simple long division). I personally am going to practice and drill estimation (y is greater than x but less than z).

 

[bidiboom]

If its only about "ordering" then I would develop a rough approach: just drop the denominators to the least value possible (10, 12, 15) and find the least common multiple lcm(10, 12, 15)= 60

So to get the common denominator at 60, I need to multiply
7/10 with 6 = 42/60
9/12 with 5 = 45/60
4/15 with 4 = 16/60

Now disregarding the denominator parts (which are equal for all), I need to just compare the numerator parts : 16<42<45 .. so the last one(4/150) is the least, later comes the first(7/100), later the one in the middle(9/120).

This way, just by looking at the question roughly and from a distance, you can directly see the answer. No need to get in detailed calculations.

 

[muhali3]

TBH, the PS on the real mcat was so easy and very calculation-light compared to TBR. I only used scratch paper for maybe 4-5 questions, and that was just to confirm that I was right after I already did it in my head.