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Test your basic knowledge |
GMAT Quantitative General
Start Test
Study First
Subjects
:
gmat
,
math
Instructions:
Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can
study here
.
Match each statement with the correct term.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.
This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.
1. The number of outcomes that result in A divided by the total number of possible outcomes.
The probability of event occurring is...
2 steps
Find all prime factors
the probability of event A AND event B occurring is the probability of event A times the probability of event B - given that A has already occurred.
2. In general - difficult questions require how many steps to solve?
at least 3 steps
If a point is chosen at random within a space with an area - volume - or length of Y and a space with a respective area - volume - or length of X lies within Y - the probability of choosing a random point within Y is the area - volume - or length of
(x-n(n)y-n)
The amount after deductions
3. Combined Events: Not E = P(not E) = ?
Principal (1 + interest/number times compounded)^(t)(n)
1 - P(E)
the probability of event A AND event B occurring is the probability of event A times the probability of event B - given that A has already occurred.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
4. Set Problems formula
x(sq. rt 3) - x - 2x
(x-n(n)y-n)
Sum of digits is multiple of 3
Purchase price
5. Gross
The total amount before any deductions
Organize into a grid.
at least 3 steps
Number is a multiple of 3 and 2
6. How to check for a prime number.
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7. How to check whether a number is a multiple of 6
P(E)P(F)
Principal (1 + interest/number times compounded)^(t)(n)
Group 1 + Group 2 + Neither - Both = Total
Number is a multiple of 3 and 2
8. Some GMAT word problems involve groups with distinct 'either/or' categories (male/female - blue collar/white collar - etc.) The key is to do what with the information? 1. Find total number of possible outcomes. 2. Find the number of desired outcomes.
sum = (average)(number of terms)
Organize into a grid.
y2 - y1 / x2 - x1
Number is a multiple of 3 and 2
9. Permutations: Order Matters
Balancing
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
P(E)P(F)
n! / (n - r)!
10. Formula for area of a Trapezoid
D or E
(sum of bases)(height) / 2
P(event NOT occurring) = 1 - P(event occurring)
y2 - y1 / x2 - x1
11. 2nd Rule of Probability: P(E) = 1 - P(not E)
The probability of an event occurring plus the probability of the event not occurring = 1
(x-n(n)y-n)
Check each prime number up to the approximate square root of the number. If you haven't found a number less than or equal to the square root of the number - then the number is prime.
1. Start by writing each number as product of primes. 2. Write so that each new prime factor begins in the same place. 3. Greatest Common Factor is found by multiplying all factors appearing in BOTH lists
12. Multiples of 3
3 - 6 - 9 - 12
1. Start by writing each number as product of primes. 2. Write so that each new prime factor begins in the same place. 3. Greatest Common Factor is found by multiplying all factors appearing in BOTH lists
The amount after deductions
A = P(1 + r) ^n
13. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
always try to factor
n! / (n - r)!
P(E)P(F)
347
14. How to check whether a number is a multiple of 12.
Odd
Odd numbers only have ___________
the probability of event A AND event B occurring is the probability of event A times the probability of event B - given that A has already occurred.
Sum of digits is multiple of 3 - last two digits multiple of 4.
15. How many liters of a solution that is 10% alcohol by volume must be added to 2 liters of a solution that is 50% alcohol by volume to create a solution that is 15% alcohol by volume?
(x-n(n)y-n)
4/3 TT r ^3
14 liters
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
16. Combined Events: E and F
(x-n(n)y-n)
P(E)P(F)
1. Start by writing each number as a product of primes. 2. Write so that each new prime factor begins in the same place. 3. Lowest common multiple is found by multiplying all factors in either list.
x(sq. rt 3) - x - 2x
17. Think of averages as what? The average of 3 - 4 - 5 - and x is 5. What is x? 3 is 2 less than 5 4 is 1 less than 5 - 5 is the average - x = 5 + 3 = 8
Balancing
P(event NOT occurring) = 1 - P(event occurring)
3 - 6 - 9 - 12
(amount of change) / (original amount)
18. What does the Sum of the angles in a Regular Polygon formula look like?
-b +- sq. rt(b^2 - 4ac) / 2a
180(n-2)
347
Last two digits are multiple of 4 or the number can be divided by 2 twice.
19. How to check whether a number is a multiple of 3.
Sum of digits is multiple of 3
1. Start by writing each number as product of primes. 2. Write so that each new prime factor begins in the same place. 3. Greatest Common Factor is found by multiplying all factors appearing in BOTH lists
______ |m-n|
1.7
20. gcd(m,n)*lcm(m,n)
$11 - 025
gcd(m,n)*lcm(m,n) = mn
(total A) / (total B)
Consider work done in one hour. Inverse of the time it takes everyone working together = Sum of the inverse of the times it would take each person working individually.
21. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Exterior angle d is equal to the sum of the two remote interior angles a and b
if a first object may be chosen in m ways and a second object may be chosen in n ways - then there are mn ways of choosing both objects
principle (interest rate - in decimal form) (time - in years)
22. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
$11 - 025
(amount of change) / (original amount)
Even
P(E)P(F)
23. Inscribed Angle - Minor Arc
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
P(event NOT occurring) = 1 - P(event occurring)
Minor arc = 2(inscribed angle)
3 - 6 - 9 - 12
24. Volume of a sphere
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
4/3 TT r ^3
Sum of digits is multiple of 3
1/16
25. Average Rate: Average speed
Sum of digits is multiple of 3 - last two digits multiple of 4.
(total distance) / (total time)
2 steps
Minor arc = 2(inscribed angle)
26. Price sold for by retailer (after markup)
market value
The amount after deductions
1/16
gcd(m,n)*lcm(m,n) = mn
27. Percent Formula
Organize into a grid.
s Sq. rt (x^r)
Immediately UNFACTOR or vice versa
p/100 = is/of
28. Probability and Geometry.
If a point is chosen at random within a space with an area - volume - or length of Y and a space with a respective area - volume - or length of X lies within Y - the probability of choosing a random point within Y is the area - volume - or length of
1
1. Start by writing each number as a product of primes. 2. Write so that each new prime factor begins in the same place. 3. Lowest common multiple is found by multiplying all factors in either list.
s Sq. rt (x^r)
29. Work problem rule
P(event NOT occurring) = 1 - P(event occurring)
Consider work done in one hour. Inverse of the time it takes everyone working together = Sum of the inverse of the times it would take each person working individually.
Even
If a point is chosen at random within a space with an area - volume - or length of Y and a space with a respective area - volume - or length of X lies within Y - the probability of choosing a random point within Y is the area - volume - or length of
30. Prime Factorization to find Greatest Common Factor
the probability of event A AND event B occurring is the probability of event A times the probability of event B - given that A has already occurred.
(# of favorable outcomes) / (# of possible outcomes)
P(E)P(F)
1. Start by writing each number as product of primes. 2. Write so that each new prime factor begins in the same place. 3. Greatest Common Factor is found by multiplying all factors appearing in BOTH lists
31. Compound interest formula
Principal (1 + interest/number times compounded)^(t)(n)
x(sq. rt 3) - x - 2x
-b +- sq. rt(b^2 - 4ac) / 2a
(total distance) / (total time)
32. Sq. rt(2)
1.4
347
If the outcome of one event affects the outcome of the other event.
12.5%
33. How many liters of a solution that is 15% salt must be added to 5 liters of a solution that is 8% salt so that the resulting mixture is 10% salt?
always try to factor
0.15n + 0.08(5) = 0.1(n+5)
12.5%
y2 - y1 / x2 - x1
34. 1. A and B < A or B 2. A or B > Individual probabilities of A - B 3. P(A and B) = P(A) x P(B) <-- 'fewer options' 4. P(A or B) = P(A) + P(B) <-- 'more options' - Probability of multiple events rules.
(sum of bases)(height) / 2
1st Rule of Probability: Basic Rule is what?
Immediately UNFACTOR or vice versa
22
35. Gross Profit formula
principle (interest rate - in decimal form) (time - in years)
To find the number of distinct permutations of a set of items with indistinguishable ('repeat') items - divide the factorial of the items in the set by the product of the factorials of the number of indistinguishable elements.
Gross Profit = Selling Price - Cost
Sum of digits is multiple of 3 - last two digits multiple of 4.
36. Intersecting Sets
| A union B| = |A| + |B| - |A intersect B|
Balancing
if a first object may be chosen in m ways and a second object may be chosen in n ways - then there are mn ways of choosing both objects
Sum of digits is multiple of 9
37. x^r/s = ?
14 liters
s Sq. rt (x^r)
(total distance) / (total time)
D or E
38. Formula for Mixed Group problems (involving Both/Neither)
Exterior angle d is equal to the sum of the two remote interior angles a and b
x(sq. rt 3) - x - 2x
1
Group 1 + Group 2 + Neither - Both = Total
39. How to find the slope.
principle (interest rate - in decimal form) (time - in years)
| A union B| = |A| + |B| - |A intersect B|
y2 - y1 / x2 - x1
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
40. What to do with equations that have fractions
at least 3 steps
(total A) / (total B)
0.15n + 0.08(5) = 0.1(n+5)
Immediately try factoring/simplifying when possible
41. Always try to factor
22
always try to factor
1/16
If a point is chosen at random within a space with an area - volume - or length of Y and a space with a respective area - volume - or length of X lies within Y - the probability of choosing a random point within Y is the area - volume - or length of
42. Multiplication principle
______ |m-n|
(# of favorable outcomes) / (# of possible outcomes)
if a first object may be chosen in m ways and a second object may be chosen in n ways - then there are mn ways of choosing both objects
1. Start by writing each number as a product of primes. 2. Write so that each new prime factor begins in the same place. 3. Lowest common multiple is found by multiplying all factors in either list.
43. How to check whether number is multiple of 9
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Sum of digits is multiple of 9
(amount of change) / (original amount)
16.6%
44. 4th rule of Probability
1.4
(sum of bases)(height) / 2
The probability of event A OR B occurring is the probability of event A occurring plus the probability of event B occurring minus the probability of both events occurring. P(A or B) = P(A) +P(B) - P(A and B)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
45. Number added or deleted
16.6%
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
1
347
46. Price purchased for by wholesaler
1st Rule of Probability: Basic Rule is what?
(# of favorable outcomes) / (# of possible outcomes)
P(E) + P(F) - P(E and F)
Purchase price
47. 30-60-90 triangle basic lengths of sides
______ |m-n|
x(sq. rt 3) - x - 2x
The total amount before any deductions
(n-1)!
48. The number of ways independent events can occur together.
1.4
Immediately UNFACTOR or vice versa
the probability of event A AND event B occurring is the probability of event A times the probability of event B - given that A has already occurred.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
49. 2n - 2n+2 - 2n+4
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Purchase price
22
Even
50. In general - medium questions require how many steps to solve?
12.5%
Any multiplication involving an even number creates an even product.
(n-1)!
2 steps