Mission 2- Quant Essentials

Question 1

What are 2 types of ways that you can simplify fractions?

Answer 1

Top-and-bottom simplification and cross-simplification

Question 2

What is a trick that you can use to compare the size of fractions, such as 499/1000, 61/120, 149/300

Answer 2

You can use referrence points, such as 1/2 AKA 500/1000 or 60/120

Question 3

What method could you use to compare these 2 fractions:

7/9 AND 6/8

Answer 3

Use the bowtie method multiply one top with another denominator. The larger fraction will be the one that has the larger product on its side.

Question 4

How do you compare 6/7 , 18/23 and 27/31?

Answer 4

You set the numerators euqal to the same thing, 54. For fractions, either set the numerators or the denominators ALL to the same value and then compare easily

Question 5

If a fraction is between 0 and 1, what will adding a positive constant to the numerator and denominator do? How about subtracting?

Answer 5

For fractions between 0 and 1, adding a constant to the top and bottom will bring it closer to 1. 2/3 –> add 4 to each term–> 6/7 which is closer to 1.

Subtracting will bring about the opposite effect–> brings it closer to 0.

Question 6

What is the difference between hundredths and hundreds?

Answer 6

A hundredth is 0.01 while hundreds are 100.

A tenth is 0.1 while the tens are 10.

A thousandth is 0.001 while the thousands are 1000.

Question 7

What is the shortcut for multiplying decimals and when should you not use it?

Answer 7

When multiplying decimals we obviously change to whole numbers and keep track of the decimal places. In fact no need to do the whole calculation if each answer choice have different number of decimal places.

However, don’t use the shortcut when the product of the 2 numbers ends in 0 as is with 0.5 x0.6.

Question 8

When dividing decimals, what is the best approach (in terms of restructuring the divisor and dividend)?

Answer 8

Turn the divisor into a whole number and move the same number of DPs in the numerator.

Question 9

In the following numbers, state which are the ones, tens, hundreds, thousands, and then the ones, tenths, hundredths, thousandths:

4928
0.123

Answer 9

4928–> 8- ones, 2, tens, 9, hundreds, 4 thousands

0.123–> 0-ones, 1-tenths, 2- hundredths, 3- thousandths

Question 10

What is 0.348 rounded to the nearest hundredth?

Answer 10

0.35

Question 11

How would you go about comparing decimals?

Answer 11

To compare decimals, compare each digit to the right of the decimal place, starting with the tenths then moving on. As soon as one digit in a number beats the other, it’s higher.

0.7007 is greater than 0.7000 because the ten thousandth digit is bigger in the first term. Super easy.

Question 12

Express x% as a fraction:

Answer 12

x%= x/100.

x% is simply x divided by 100

Question 13

Convert 3/2 to a percentage

Answer 13

Simply multiply by 100 and add % to the end of that number.

So 3/2*100= 300/2=150 =150 %

Question 14

Convert the decimal 0.003 to a percentage

Answer 14

To convert a decimal or integer to a percent simply move it two decimal places to the right and adjoin the % sign.

So 0.003–>0.3>0.3%

Question 15

How can you convert a fraction such as 5/8 to a decimal?

Answer 15

You just have to set up the long division. 8/~~5

Question 16

To convert decimals to fractions (only focus on terminating decimals):

Answer 16

This will depend on the number of decimal places in the fraction. Multiply by 10^ of however many decimals there are. Essentially multiply out the decimal (by a power of 10).

Eg 0.3 = 3/10

0. 31= 31/100
1. 6796=6796/10000

Then you can simply.
Don’t worry about repeating decimals and non-repeating non terminating decimals.

Question 17

What are base fractions?

List the base fractions for 1/6 and 1/7 and then all other fractions.

Answer 17

Base fractions are 1/2, 1/3, 1/4 and so on.

1/6= .167, 5/6= .833
1/7= .143, .286, .429, .571, .714, .857

Question 18

When a question asks for √x, how many answers are there?

Answer 18

Only the positive value. When you see the square root symbol only provide the positive root. √4 is 2. Not +-2

√100= 100 (ONLY), √81= 9 (ONLY), √1= 1 ONLY

Question 19

If x is between 0 and 1, how do x, √x and x² compare

Answer 19

If for numbers greater than 1, x² >x>√x, it is the opposite for numbers between 0 and 1

Question 20

Suppose you are given a number such as x=0.44432 and you are asked to compare x² , √x and x. What do you do?

Answer 20

You pick a strategic number between 0 and 1 because it will act the same. In this case choose 1/4 (notice that it works better than 1/2).

Question 21

10000+ 1/10000=

Answer 21

~10000.

Treat it as the same number. This showcases the strategy of estimation.

Question 22

(198*0.987)/311

Answer 22

=(200*1)/300

~~2/3

Question 23

When the GMAT is testing large numbers squared, what can you pay attention to in the answer choices/how do they vary?

Answer 23

These questions may be good indications of unit digit calculations.

Question 24

How do you compute 25.5² on the GMAT?

Answer 24

You don’t. You hope that there is only one answer choice with a 5 in the last decimal place

Question 25

Perfect squares always end in which numbers as the unit digits? Which do they not end in?

Answer 25

They end in 0,1,4,9,6,5

They cannot end in 2,3,7,8

Question 26

What is the easiest conceptual way to compare negative fractions (to see which is bigger/smaller)

Ex -5/8 v -3/8

Answer 26

Assume they were both positive fractions and see which is larger. At that point it’s just the opposite.

Well 5/8 is bigger than 3/8. So, -3/8 is closer to 0 than -5/8.

Question 27

What is the most basic conceptual definition of an absolute value?

Answer 27

A number without a negative sign

Question 28

Spell out PEMDAS

Where do absolute values and square roots fit into this order?

Answer 28

Parentheses, exponents, multiplication AND division, addition AND subtraction

Treat absolute values as parentheses and treat square roots as exponents.

PS. For multiplication/division and addition/subtraction, start from LEFT TO RIGHT.

Question 29

Compute 43(16) + 32(16) + 21(16) + 10(16) -6(16) in the right/clever way

Answer 29

16(43+32+21+10-6)= 16(100)=1600

Question 30

5+10+15+20….+55+60+65
____________________
6+12+18+……+ 66 +72 +78

Answer 30

5(1+2+3….+11+12+13)
=________________ = 5/6
6(1+2+3……11+12+13).

Question 31

Whats an easier way to perform 1005-672?

Answer 31

999-672 +6 because now you don’t need to carry over terms in the subtraction (999-672).

Question 32

What is 0!

What is 1!?

Answer 32

0!=1

1!=1

Question 33

10!
____
8!x3!

Answer 33

10! 10x9x8!
____. =. ______ =90/(3!)===90/6=15
8!x3! 8!x3!

Question 34

Remember that 8!= 876! or 56*6!. You can re-arrange these multiple different ways

Question 35

If a fraction is greater than 1, what will adding and subtracting do to the fraction?

Answer 35

Adding will make that fraction smaller, subtracting will make that fraction bigger so long as it stays positive.