GMAT Flashcards
What are the 2 top tips for the GMAT?
- Spend extra time on the first 10 questions. They are absolutely crucial
- You are always better off making your best guess ⇒ the best guess can often be determined by which answer option that has the most in common with the rest (the most common answer theorem)
What are the question types in the quantitative test and what share do they account for? (old test)
Data sufficiency questions = 40 %
When are you trying to find a Yes/No answer for data sufficiency questions?
If the question asked starts with “is”, “are” or “does” you look for a yes/no answer rather than a number.
What are integers?
What are whole numbers?
What are irrational numbers?
Numbers that canNOT be expressed as a fraction or ratio.
Examples: π and √2
When do you know that the GMAT is testing you in imaginary numbers?
If they ask you to take any EVEN ROOT OF A NEGATIVE NUMBER.
√-100 or √-8 fx.
What are the prime numbers up until 130
2, 3, 5, 7,
11, 13, 17, 19,
23, 29,
31, 37,
41, 43, 47,
53, 59,
61, 67,
71, 73, 79,
83, 89,
97,
101, 103, 107, 109,
113,
127.
What does “absolute value” mean and how is it expressed?
A number’s absolute value is its distance from zero on the number line, and like any distance, its ALWAYS positive.
Absolute value of 3 is 3. Absolute value of -8 is 8.
What is the order to work in maths?
PEMDAS
Parantheses
Exponents
Multiplication
Division
Addition
Subtraction
What is (x + y)*(x + y)?
(x + y)^2
x^2 + 2xy + y^2
What is (x - y)*(x - y)?
(x - y)^2
x^2 - 2xy + y^2
What is (x + y)*(x - y)?
x^2 - y^2
What is
How do you multiply exponent together? fx: x^3 * x^5
X^3 * X^5
Simply add the exponents together: X^3 * X^5 = X^8
is the same as: (x*x*x) * (x*x*x*x*x) = x^3 * x^5 = X^8
How do you divide exponents together? fx: y^3 / y^5
Simply subtract the denominator from the numerator.
y^3 / y^5 = (y3 - y5) = y^-2
What is the value of one exponent raised to another exponent? such as: (x^6)^3
Just multiply the two exponents
(X^6)^3 = x^18
What is 355^0?
1
ALL real numbers raised to the power of 0 = 1
What is x^0?
1
ALL real numbers raised to the power of 0 = 1
What is 3^-4?
which is = 1 / 3^4
which is 1 / 81
What can be said about “any number greater than 1 raised to a negative exponent”?
It will be a number greater than 0 but less than 1.
What is a number raised to a fractional power? such as X^⅙
ALL real numbers raised to the power of 0 = 1
X^⅙ =
What is the result of 2^2, 2^3, 2^4, 2^5, 2^6, 2^7, 2^2, 2^9, 2^10
What is the result of 3^2, 3^3, 3^4, 3^5?
What is the result of 5^2, 5^3, 5^4?
What is the result of 6^2, 6^3?
What is the result of 7^2, 8^2, 9^2, 10^2, 11^2, 12^2, 13^2, 14^2, 15^2, 16^2?
7^2 = 49
8^2 = 64
9^2 = 81
10^2 = 100
11^2 = 121
12^2 = 144
13^2 = 169
14^2 = 196
15^2 = 225
16^2 = 256
What is the difference between a finding the factors of a number and finding the prime factors? The processes?
Factors = all numbers can be used
Prime factors = only prime factors can be used
What is basis points?
It is 1 of 100.
0.45 % = 45 basis points.
What percent is 600 of 200?
300 %
but percentage increase from 200 to 600 is 200%
What is the percentage increase from 300 to 600?
100 %
but 600 is 300 % of 200.
How can you easily simplify a complex fraction? such as 210/2,772
Divide by 2 if possible, then 3, then 5, then 7
(210 / 2) / (2772 / 2) = 105 / 1386
(105 / 3) / (1386/3) = 35 / 462
(35 /7) / (462/7) = 5 / 66
How do you know if a number is divisible by a prime number?
Take the number, fx. 2772
then write it out as 2+7+7+2 = 14
Any prime number going to 14 will work = either 2 or 7.
What are the six main rules to remember in terms of exponents and roots?
Answer:
Question:
Answer:
(3* 7) + (7* 3) = 21 +21 = 42 = D.
Makes sense, since you have 3 / (1 / 7), as 1/7 naturally goes into 1 seven times. And 3 is in the numerator, so it has to go up to three (which is three times as much as 1, i.e. 3 * 7 = 21).
The same logic can be applied for the other part.
Question:
Answer:
64^k is the same as (4^3)^k
So following the rule of multiplying exponents when one exponent is raised to another, we simply have to figure out what:
3* k > 14
k > 14/3
k > 4,67
K must be B = 5.
Question:
answer:
the prime numbers less than 10 are: 2, 3, 5 , 7
2*3 = 6 so cannot be A
Nothing can be multiplied to B as it has to be DISTINCT numbers = B
2*5 = 10
2*7 = 14
3*5 = 15
What are the rules of the cube root table and how does the table look?
- Take the last digit in a number: for example 6 in 636,056 and find that digit in the last digit column.
- Look at the three first digits in a number and find the digit in the table where they do NOT exceed the cube. For example 636 in 636,056.
So cube root of 636,056 would be 86
What are the solutions to the equation x^2 + -2x = 15?
First, re-order to separate 0.
x^2 - 2x - 15 = 0
Now factor (-15)
- 1 and 15 1 and -15
- 3 and 5 3 and -5
Which pair can you manipulate to get to -2?
-1 + 15 = 14 so no
1 -15 = -14 so no
-3 + 5 = 2 so no
3 - 5 = -2 so YES
(x - 3) * (x + 5)
x + 3 = 0, then x = -3
x - 5 = 0, then x = 5
What is the median of 105, 106, 107, 108, 109, 110, 111, 112, 113?
The middle value which in this range of 9 values will be the 5th value = 109.
What is the median of 105, 108, 110, 112, 114, 115?
6 different numbers so the median is the average of the 3rd and 4th number.
(110 + 112) / 2 = 111
What is the mode?
The most common element in a set
NOTE!!! A set can have more than one mode.
NOTE NOTE!!! A set can also NOT have a mode if no number occurs more than once
What is the range?
The difference between the largest and the smallest number.
How is the standard deviation calculated? and how is it useful to know?
The standard deviation is the square root of the result of the summation of the squares of the differences between the individual values of the set and the mean, divided by the number of items in the set.
You will not have to calculate this on the GMAT.
But… you might be asked which set of numbers has the largest standard deviation.
What is the formula for calculating the third side of a right triangle?
A^2 + B^2 = C^2 (pythagoras)
What are parallel lines?
Lines that if extended to infinity, would never intersect.
How do you calculate the area of a triangle?
½ * Base * Height
How do isosceles triangles look and what are their properties?
- Two sides of equal length
- The two angles opposite the sides of equal length are also of equal degree
How do equilateral triangles look and what are their properties?
- All sides of equal length
- All angles have 60 degrees
How do you calculate the area of an equilateral triangle?
(√3 / 4) * s^2
(1. 732 / 4) * s^2
0. 433 * s^2
How do right triangles look and what are their properties?
- One angle is 90 degrees
- The third side (hypotenuse) can be calculated by A^2 + B^2 = C^2
How do right isosceles triangles look and what are their properties?
- one angle with 90 degrees
- Two sides of equal length
What is the 3-4-5 triangle type?
A common ratio used on the GMAT.
RIGHT triangles with the ratio of 3,4 and 5.
- A is 3, B is 4 then C = 5
- A is 6, B is 8, then C = 10
- A is 9, B is 12, then C = 15
- A is 12, B is 16, then C = 20
What is the 5-12-13 triangle type?
A common RIGHT triangle ratio:
- A is 5, B is 12, then C = 13
- A is 10, B is 24, Then C = 26
What is the 30 degrees, 60 degrees and 90 degrees triangle?
The 1 - √3 - 2
- If A is 1, B is √3, then c = 2
- If A is 5, B is 5*√3, then c = 10
- If A is 8, B is 8* √3, then c = 16
What is the perimeter?
How far there is around a triangle, square etc.
The sum of the sides.
How do a rhombus look and what are their properties?
A rhombus is a quadrilateral with sides of equal length and two sets of opposite angles with equal measures.
How do a parallelogram look and what are their properties?
Two sets of parallel lines
The two sets have different length
How do you calculate the area of a parallelogram?
If you recognize that it is simply a square and two triangles of equal size, the calculation simply become
AREA = BASE * HEIGHT
How do trapezoids look and what are their properties?
One pair of parallel lines
The two other sides have equal length but are not parallel
How do you calculate the area of a trapezoid?
Recognize that a trapezoid is a square with two equal triangles.
AREA = HEIGHT * ((A + C) / 2)
Thus we just take the height and the average of the length of the two parallel lines. Then it is essentially just as calculating a rectangle.
How do you calculate the circumference?
The circumference is the distance around a circle (what we call a perimeter in a polygon).
It is simply:
Diameter * π
or: 2 * r * π
What is the area of a circle?
A = r^2 * π
How do you calculate the volume and surface area of a right circular cylinder?
How do you calculate the volume and surface area of a square pyramid?
How do you calculate the volume and the surface area of a cube?
How do you calculate the volume and the surface area of a rectangular solid?
How do you calculate the volume of a general cone/pyramid?
For a right circular cone, you would obviously find A by taking r^2*π
How do you calculate the volume and surface area of a sphere?
What is the result of “even*even”?
Even
4*4 = 16
What is the result of “even*odd”?
Even
4*5 = 20
What is the result of “odd*odd”?
odd
13*13 = 169
What is the result of “even + even”?
Even
22 + 36 = 58
What is the result of “odd + odd”?
Even
17 + 19 = 38
What is the result of “odd + even”?
odd
21 + 22 = 43
What is the result of “negative * negative”?
Positive
-4 * -5 = 20
What is the result of “positive * negative”?
Negative
5 * -6 = -30
What is the result of “positive + negative”?
It depends.
on which one is biggest.
When an odd number is raised to an exponent, what will it result in?
It will still be an ODD number.
13*13 = 169.
No matter if it is raised to 2, 3, 4, 5, 6 etc., it will always be an odd number
When an even number is raised to an exponent, what will it result in?
It will still be an EVEN number.
12*12 = 144.
No matter if it is raised to 2, 3, 4, 5, 6 etc., it will always be an even number
What is the result of “non-integer * non-integer”?
It will always be a NON-INTEGER
0.5 * 0.5 = 0.25.
What is the result of “integer * non-integer”?
It depends.
What is the key component of combinatorial math and what is the formula used?
Factorials.
n! = n* (n - 1) * (n- 2) * - (n - 3) * ….
So
- 2! = 2* 1 = 2
- 3! = 3 * 2 * 1 = 6
- 4! = 4 * 3 * 2 * 1 = 24
- 5! = 5 * 4 ‘ 3 * 2 *1 = 120
- 6! = 6* 5 * 4* 3 * 2 ‘ 1 = 720
- 7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5,040
What is the formula for combinations and what does combinations refer to?
Combinations regards groupings where ORDER DOES NOT MATTER
What is the formula for permutations and what does permutations refer to?
Permutation regards groupings where ORDER MATTERS.
How do you multiply fractions? for example 4/9 x 3/2?
4/9 * 3/2
4*2 / 9*2 = 12/18 = 2/3
What should you ask yourself for inference questions?
- If the statements in the passage are true, what else has be true?
- When having found potential answers, ask yourself “what if the opposite of this answer were true?”
ALWAYS Pick the moderate statement over the extreme.
What are the three main ways in which an answer can be wrong for sentence correction questions?
It violates a rule of grammar
It is worded in an unclear way
It is worded in a “nonstandard” way; i.e. it sounds funny
Which words should you look for to avoid being trapped by pronouns errors?
- He
- She
- It
- they
- them
Ask yourself whether
- is it clear who the referent is?
- is it the right pronoun for that referent?
What are some of the most frequent quantity-words used in the GMAT?
What are some of the most frequent countable/non-countable words used in the GMAT?
Countable words should be used when you can normally assign a whole number to it. Such as six cars.
Non-countable items are for example a little soup as you cannot quantify “a little soup”.
A cup of soup, of course, would be countable = 1.
What is the most common error in sentence correction questions?
No error at all.
20 % has no errors at all.
What are 3 points that should raise an alarm for sentence correction questions?
A sentence does not have to be wrong when it includes any of the following but it often will be:
- Any answer that includes “being”
- Passive verb forms when active verbs would work just as well
- Words ending in “-ing” when there are simpler choices
If you have to give your best guess for sentence correction questions, which two rules should you follow?
- Pick the shortest answer
- Pick the “most common” answer.
- The one that has the most in common with the other options
What are good examples of phrases in which the writer CONTINUES his/her line of thought?
What are good examples of phrases in which the writer CHANGEs his/her line of thought?
How should your essay outline ideally look?
- Paragraph 1: INTRODUCTION
- State argument in a clear statement
- Acknowledge that the opposite position has merits, but that for the following X reasons (summarize your points), my position is the correct one
- Paragraph 2: REASON 1, with supporting evidence/examples/facts
- Paragraph 3: REASON 2, with supporting evidence/examples/facts
- Paragraph 4: REASON 3, with supporting evidence/examples/facts
- Paragraph 5: CONCLUSION
- For the X reasons previously stated, my argument is the correct one
- The argument would have been more persuasive if it ______.
What does bisect mean?
Divide (a line, angle, or shape) into TWO EXACTLY EQUAL parts.
XB bisects ABY only if it splits ABY into two exactly equal parts, meaning that there must be a 45 degree angle on both sides (given that ABY is a 90 degree angle).
How can you derive the side of a square from its diagonal?
The side of a square is it’s diagonal divided by 2 (derived from pythagoras)
How do you quickly add to fractions with different denominators?
Multiply the numerator of the first fraction with the denominator of the second fraction, which is equal to the numerator of the new fraction.
The same applies for the second part, multiply the numerator of the second fraction with the denominator of the first fraction, which is equal to the numerator of the new second fraction.
Lastly, you multiply the two denominators, which is equal to the new common denominator for the two new fractions.
Now you can just add them together normally.
How do you quickly subtract two fractions with different denominators?
Same methods as how you add them, you just subtract instead when you get the common denominator.
How do you multiply two fractions?
How do you divide a number (or fraction) with a fraction?
What does “place value” refer to?
What are inequalities in math?
Statements that involve “<” or “>”.
What is a “perfect square”?
What is a “perfect cube”?
What is LCD and what is the LCD of two numbers?
What are the results of (-3)^2 and -3^2 ?
(-3)^2 = -3 * -3 = 9
-3^2 = - 3*3 = - 9
How can you simplify exponent expression so they are easier to work with?
For negative exponents, you can always divide that expression by one and change the negative exponent to a positive.
Also, you can always move exponents from the numerator to denominator or vice versa by changing the sign.
- = 1 / 2^3 = 1 / 8
- ) (3^3 * 1) / 1 = 9 / 1 = 9
When do you make ADDITION and when do you make MULTIPLICATION of exponents?
How do you add or subtract terms when the bases are different? (working with exponents)
How can you rewrite the √5^12 ?
How do you multiply and divide square roots?
What should you do when you get to a result that is not an answer option when working with square root results such as √50 or √12?
How do you ADD or SUBTRACT under the square root symbol?
Do NOT get confused or fall in the trap of using the rules from multiplication and division under the square root symbol.
Instead…
What is 7^6 * 7^9?
7^15
when multiplying roots you can just add the roots together (when the base is the same)
What is (a^3)^2?
A^6
when multiplying roots you can just add the roots together (when the base is the same)
What is (3^2)^-3 ?
3^-6
What is 5^5 / 5^3?
5^2 = 25
When dividing roots, you can subtract them as long as the base is the same
What is 11^4 / 11^x ?
11^(4-x)
what is (5^2)^x ?
25^x OR 5^2*x
what is (5^6 * 5^4x) / 5^4 ?
We can simplify to:
5^2 * 5^4x
And then simplify to:
5^(4x + 2)
What is y^7 * y^8 * y^-6?
y^7+8-6 = y^9
What is y^4 / y^-3?
Y^(4-(-3) = y^7
What is (3^2x * 3^6x) / 3^-3y?
3^8x / 3^-3y
3^8x + 3^3y OR …. 3^(8x + 3y)
What is 27^⅓ + 9^½ + (3/9^0)
3 + 3 + 3/1 = 9
What is -3^4?
-3 * -3 * -3 * -3 = -81
Which of the following 5 options are equal to (⅖)^-3?
- -(⅔)^3
- (⅖)^⅓
- (- ⅖ )^3
- (5/2)^⅓
- (5/2)^3
The answer is option 5 such that (⅖)^-3 = (5/2)^3.
You can shift around the numerator and denominator IF you also change the plus/minus sign in the root.
What is 8^3 * 2^6?
(2^3)^3 * 2^6
2^9 * 2^6
2^9+6
2^15
What is 25^4 * 125^3?
(5^2)^4 * (5^3)^3
5^8 * 5*9
5*17
What is 9^-2 * 27^2?
(3^2)^-2 * (3^3)^2
3^-4 * 3^6
3^-4+6
3^2
9
What is 6^3 + 3^3?
6^3 + 3^3
(2 * 3)^3 + 3^3
2^3 * 3*3 + 3*3
3^3 (2^3 + 1)
3^3 (9)
3^3 (3^2)
3^5
What is (4^8 - 8^4) / (2^4 + 4^2)?
(4^8 - 8^4) / (2^4 + 4^2)
((2^2)^8 - (2^3)^4 ) / ( 2^4 + (2^2)^2 )
(2^16 - 2^12) / (2^4 + 2^4)
(2^12 (2^4 - 1)) / (2^4 (1+1))
(2^12 (15)) / (2^4 (2))
(2^12 (15)) / 2^5
2^7 * (15)
What is √5 * √45?
√5*45
√225
15
What is √3 * √27?
√3*27
√81
9
what is √5000 / √50?
√5000/50
√100
10
What is (√54 * √3) / √2 ?
√54 * 3 / √2
√168 / √2
√81
9
What is √32?
Divide up 32…..
32 = 2 * 16
√16 * √2
4 * √2
what is √180?
Divide up 180
2 * 90
3 * 60
4 * 45
5 * 36
The easiest is 5 * 36
√5 * √36
√5 * 6
What is √135?
Divide up 135
3 * 45
6 * 22.5
9 * 15
√9 * √15
3 * √15
What is √35^2 - 21^2?
Find a common ground…
35 = 5 * 7….. and 21 = 3 * 7
√7^2 (5^2 - 3^2)
√7^2 (25-9)
√7^2 (16)
√7^2 (4^2)
7 * 4
28
What is √6 * (5^6 + 5^7)?
√6* (5^6(1+5))
√6 * (5^6 (6))
√6^2 * 5^6
6 * 5^3
6 * 125
750
what is √(11^4 - 11^2)/ 30?
(11^2 (121 - 1)) / 30
(11^2 (120)) / 30
11^2 * 4
11^2 * 2^2
11 * 2
22
What is √5^7 - 5^5 + 5^4?
√5^4(5^3 - 5^1 + 5^0)
√5^4 (125 - 5 + 1)
√5^4 (121)
√5^4 (11^2)
5^2 * 11
25 * 11
275
What is the reciprocal?
The number (B) for any number (A) that makes A*B = 1.
5 = Reciprocal is ⅕ as 5*⅕ = 1
⅔ = reciprocal is 3/2 as ⅔ * 3/2 = 1
what is the reciprocal of -⅚?
The reciprocal will be the opposite so switching:
6/-5
(-5 / 6) * (6 / -5) = 1
How do you divide something by a fraction?
You simply multiply by that fraction’s reciprocal = you simply flip the numerator and denominator of that fraction.
What must you be aware of if there is addition or subtraction in the fraction’s NUMERATOR?
You MUST divide with the ENTIRE denominator. Thus, you have to find common factors and simplify.
You can split up into two fractions
What must you be aware of if there is addition or subtraction in the fraction’s DENOMINATOR?
You are NOT allowed to split up into two fractions in the same way. You ALWAYS have to divide the numerator by the ENTIRE denominator.
What is a/12 - b/6 - b/4?
First, find a common denominator
a/12 - 2b/12 - 3b/12
next, add it together:
(a - 5b) / 12
What is √3/2 - √2/3?