Essential GMAT Quant Skills Flashcards
(27 cards)
Proper Fraction
Numerator < Denominator
1
2
Improper Fraction
Numerator > Denominator
[Are sometimes expressed as mixed numbers – 1 1/3]
5
3
Least Common Denominator (LCD)
Smallest non-zero whole number that is divisible by each of the denominators
1/6, 1/5 —- LCD = 1/30
Equivalent Fractions
Fractions that have the same value.
A/B and C/D:
AxD = CxB
Reciprocal
The multiplicative, INVERSE of a number.
“1 over that number”
Reciprocal of 5 = 1/5
Special Rules for Reciprocals
- The reciprocal of 1 = 1
- The reciprocal of -1 = 1
- 0 DOES NOT have have reciprocal
Reference Points
Use when determining larger/smaller fractions
1/2 = good reference point
Bow Tie Method
The larger product is over the larger fraction.
7/9 and 6/8 =
7x8 = 56
6*9 = 54
Therefore 7/9 > 6/8
If a/b > c/d, then ad > cd
Common DENOMINATOR to Compare Size of Fractions
In a set of positive fractions, if all fraction share common denominator –
largest = greatest numerator.
5/6 > 4/6
Common NUMERATOR to Compare Size of Fractions
If positive fractions share a common numerator, the GREATER one has the LARGER DENOMINATOR.
10/20 > 10/30
1/2 > 1/3
Simple Rules of +/- Constant to Numerator and Denominator of Fractions
ONLY IF FRACTION IS BETWEEN 0 and 1:
+: adding a positive constant will bring the fraction CLOSER to 1
-: subtractive a positive constant will bring fraction FURTHER from 1
1 + 6
2 + 6 = 7/8
3 - 2
5 - 2 = 1/3
Converting Fraction to Percent
Multiply Fraction by 100 and add the % sign
1/4 x 100 = 25%
Converting Decimal to Percent
Move decimal 2 places to the right and attach the % sign.
0.125 = 12.5%
Converting Percent to Decimal
Drop the % sign and move decimal 2 places to the left.
12.5% = 0.125
Converting a Fraction to a Decimal
Use LONG DIVISION
5/8 = 0.625
Three Types of Decimals
- Terminating Decimals [3.4, 0.65]
- Repeating Decimals [3.33333]
- Non-Terminating and Non-Repeating Decimals [3.1415926535….]
Base Fractions
Every fraction has a base fraction.
Ex: All of the fraction with a denominator of 8, 1/8 is the BASE FRACTION. Easier to find multiples.
1/8 = 0.125
Important Base Fractions – Decimals
1/2 = 0.5
1/3 = 0.33..
1/4 = 0.25
1/5 = 0.20
1/6 = 0.167
1/7 = 0.143
1/8 = 0.125
1/9 = 0.111
1/10 = 0.10
Principal Square Root
The non-negative square root of a number (the square root that is either 0 or a positive number)
When the Square Root sign is used, the answer is ALWAYS a POSITIVE number.
Principal square root of 4 = 2
Squares and Square Roots of Fractions
- If B is not 0, the (a/b)^2 = a^2/b^2
- If x is equal to or greater than 0 and y is greater than 0, sqrt(x/y), then it is the same as sqrt(x)/sqrt(y)
True or False: If 0 < x < 1, it MUST BE TRUE that x^2 < x < sqrt(x)
TRUE
Multiplying Two Square Roots
sqrt(a) x sqrt(b) = sqrt(axb)
Strategic Numbers
Use an easier / simpler number to figure out complex problems.
Ex: use 1/4 instead of 0.2345
Clever, Time-Saving Strategies
- Strategic Numbers
- Estimation
- Use Units Digits of Numbers to Efficiently solve problems
- Re-Express Numbers to make problems simpler
- Factor out!
- Break it down into SIMPLE steps, but DON’T oversimplify!
- Picturization
