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GMAT Quantitative General

Subjects : gmat, math

Instructions:

Answer 50 questions in 15 minutes.
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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. 5/6 = what %
12^3
Find all prime factors
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
83.3%

2. Multiplication principle
0.15n + 0.08(5) = 0.1(n+5)
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
3 - 6 - 9 - 12
Exterior angle d is equal to the sum of the two remote interior angles a and b

3. Always try to factor
1st Rule of Probability: Basic Rule is what?
always try to 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.
P(event NOT occurring) = 1 - P(event occurring)

4. Inscribed Angle - Minor Arc
Minor arc = 2(inscribed angle)
2 steps
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
3 - 6 - 9 - 12

5. Gross
16.6%
1 - P(E)
The total amount before any deductions
1.4

6. Compound interest rule
Find simple interest then look for the answer that is a little bigger
y2 - y1 / x2 - x1
83.3%
12.5%

7. In general - medium questions require how many steps to solve?
2 steps
$11 - 025
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

8. 1/8 = what %
P(E) + P(F) - P(E and F)
12.5%
Any multiplication involving an even number creates an even product.
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.

9. Net
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
Purchase price
The amount after deductions
12^3

10. 45-45-90 triangle basic lengths of sides
A = P(1 + r) ^n
x - x - x(sq. rt 2)
(amount of change) / (original amount)
Sum of digits is multiple of 9

11. Simple probability
Balancing
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)
gcd(m,n)*lcm(m,n) = mn
(# of favorable outcomes) / (# of possible outcomes)

12. Average Rate: Average speed
at least 3 steps
1st Rule of Probability: Basic Rule is what?
(total distance) / (total time)
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

13. 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?
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.
Divide 4999 by 15 => 333 integers
22
14 liters

14. x^r/s = ?
Odd
Exterior angle d is equal to the sum of the two remote interior angles a and b
s Sq. rt (x^r)
Minor arc = 2(inscribed angle)

15. How to check whether a number is a multiple of 3.
gcd(m,n)*lcm(m,n) = mn
Sum of digits is multiple of 3
s Sq. rt (x^r)
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)

16. Lowest Common Multiple 60: 2 x 2 x 3 x 5 - 72: 2 x 2 x 2 x 3 x 3 - LCM: 2 x 2 x 2 x 3 x 3 x 5
(amount of change) / (original amount)
Exterior angle d is equal to the sum of the two remote interior angles a and b
x - x - x(sq. rt 2)
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.

17. How do you multiply roots together.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
3 - 6 - 9 - 12
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
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.

18. Combined Events: E or F
(n-1)!
Gross Profit = Selling Price - Cost
P(E) + P(F) - P(E and F)
y2 - y1 / x2 - x1

19. 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
3 - 6 - 9 - 12
Figure out the probability for each individual event. Multiply the individual probabilities together.
14 liters

20. gcd(m,n)
1
Group 1 + Group 2 + Neither - Both = Total
______ |m-n|
Sum of digits is multiple of 9

21. Formula for area of a Trapezoid
A = P(1 + r) ^n
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Sum of digits is multiple of 9
(sum of bases)(height) / 2

22. Odd and Even rule.
1
Any multiplication involving an even number creates an even product.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Balancing

23. 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?
22
Gross Profit = Selling Price - Cost
0.15n + 0.08(5) = 0.1(n+5)
x(sq. rt 3) - x - 2x

24. Set Problems formula
Minor arc = 2(inscribed angle)
x(sq. rt 3) - x - 2x
P(E) + P(F) - P(E and F)
(x-n(n)y-n)

25. Triangle abc with d on the outside with a line. What does d = ?
(# of favorable outcomes) / (# of possible outcomes)
Minor arc = 2(inscribed angle)
Exterior angle d is equal to the sum of the two remote interior angles a and b
12^3

26. 0! = ?
12.5%
1
83.3%
| A union B| = |A| + |B| - |A intersect B|

27. Number added or deleted
The probability of event occurring is...
x - x - x(sq. rt 2)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Sum of digits is multiple of 3

28. How to check whether number is multiple of 9
p/100 = is/of
Immediately UNFACTOR or vice versa
Sum of digits is multiple of 9
3 - 6 - 9 - 12

29. Properties of 0
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
(amount of change) / (original amount)
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.
1.7

30. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
16.6%
Purchase price
22
(n-1)!

31. What does the Sum of the angles in a Regular Polygon formula look like?
180(n-2)
Gross Profit = Selling Price - Cost
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Balancing

32. When you see an equation in factored form in a question?
y2 - y1 / x2 - x1
The probability of event occurring is...
-b +- sq. rt(b^2 - 4ac) / 2a
Immediately UNFACTOR or vice versa

33. 3rd Rule of Probability: Conditional Probability
y2 - y1 / x2 - x1
12^3
Principal (1 + interest/number times compounded)^(t)(n)
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.

34. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
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.
Purchase price
principle (interest rate - in decimal form) (time - in years)
Immediately UNFACTOR or vice versa

35. How to check whether a number is a multiple of 6
Gross Profit = Selling Price - Cost
Number is a multiple of 3 and 2
2 steps
22

36. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
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
347
Immediately try factoring/simplifying when possible
x - x - x(sq. rt 2)

37. Dependent events: When are two events said to be dependent events?
Number is a multiple of 3 and 2
If the outcome of one event affects the outcome of the other event.
Purchase price
(amount of change) / (original amount)

38. Average Rate: Average A per B
Find simple interest then look for the answer that is a little bigger
______ |m-n|
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.
(total A) / (total B)

39. The number of ways independent events can occur together.
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
Divide 4999 by 15 => 333 integers
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Find all prime factors

40. The number of outcomes that result in A divided by the total number of possible outcomes.
Group 1 + Group 2 + Neither - Both = Total
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
The probability of event occurring is...

41. Trial Problems: look at the probability of NOT OCCURRING
1.7
P(event NOT occurring) = 1 - P(event occurring)
(total distance) / (total time)
s Sq. rt (x^r)

42. Prime Factorization to find Greatest Common Factor
x(sq. rt 3) - x - 2x
Balancing
Exterior angle d is equal to the sum of the two remote interior angles a and b
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

43. Price sold for by retailer (after markup)
market value
P(E) + P(F) - P(E and F)
Immediately UNFACTOR or vice versa
Last two digits are multiple of 4 or the number can be divided by 2 twice.

44. (1/4)^2
P(event NOT occurring) = 1 - P(event occurring)
1/16
3-4-5 - 5-12-13 - 9-12-15
1.7

45. 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.
Organize into a grid.
3-4-5 - 5-12-13 - 9-12-15
Figure out the probability for each individual event. Multiply the individual probabilities together.
Balancing

46. Sq. rt(2)
1.4
Group 1 + Group 2 + Neither - Both = Total
180(n-2)
Number is a multiple of 3 and 2

47. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
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
1/16
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.
D or E

48. The average of consecutive numbers
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.
1
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
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

49. Sq. rt(3)
0.15n + 0.08(5) = 0.1(n+5)
principle (interest rate - in decimal form) (time - in years)
1.7
Number is a multiple of 3 and 2

50. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
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 probability of event occurring is...
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Find all prime factors

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GMAT Quantitative General

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