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GMAT Quantitative General

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. Set Problems formula
(x-n(n)y-n)
$11 - 025
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)
sum = (average)(number of terms)

2. How to find the slope.
4/3 TT r ^3
y2 - y1 / x2 - x1
The probability of event occurring is...
180(n-2)

3. Odd Factors
sum = (average)(number of terms)
(x-n(n)y-n)
Odd numbers only have ___________
Exterior angle d is equal to the sum of the two remote interior angles a and b

4. Gross
The total amount before any deductions
Find simple interest then look for the answer that is a little bigger
If the outcome of one event affects the outcome of the other event.
______ |m-n|

5. Multiples of 3
P(E) + P(F) - P(E and F)
3 - 6 - 9 - 12
$11 - 025
y2 - y1 / x2 - x1

6. 3rd Rule of Probability: Conditional Probability
always try to factor
1.4
14 liters
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.

7. Sq. rt(3)
3 - 6 - 9 - 12
1.7
Sum of digits is multiple of 3 - last two digits multiple of 4.
Balancing

8. 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
s Sq. rt (x^r)
Balancing
The amount after deductions
The probability of event occurring is...

9. 3^3 x 4^3 = ?
1
D or E
12^3
Divide 4999 by 15 => 333 integers

10. Quadratic formula
The amount after deductions
-b +- sq. rt(b^2 - 4ac) / 2a
principle (interest rate - in decimal form) (time - in years)
(amount of change) / (original amount)

11. 1/6 = what %
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
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.
0.15n + 0.08(5) = 0.1(n+5)
16.6%

12. 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
1.7
x - x - x(sq. rt 2)
4/3 TT r ^3

13. In general - difficult questions require how many steps to solve?
1st Rule of Probability: Basic Rule is what?
Sum of digits is multiple of 3
at least 3 steps
16.6%

14. 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.
Even
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.
Odd numbers only have ___________
Organize into a grid.

15. Intersecting Sets
1.7
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.
| A union B| = |A| + |B| - |A intersect B|
Sum of digits is multiple of 3

16. How to find all divisors of a number
2 steps
D or E
3-4-5 - 5-12-13 - 9-12-15
Find all prime factors

17. 2n+1 - 2n+3 - 2n+5
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.
Odd numbers only have ___________
Odd
Group 1 + Group 2 + Neither - Both = Total

18. Volume of a sphere
(total distance) / (total time)
(x-n(n)y-n)
4/3 TT r ^3
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.

19. The average of consecutive numbers
Minor arc = 2(inscribed angle)
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.
Any multiplication involving an even number creates an even product.
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

20. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
Even
3-4-5 - 5-12-13 - 9-12-15
Odd
(n-1)!

21. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
Gross Profit = Selling Price - Cost
D or E
______ |m-n|
3 - 6 - 9 - 12

22. Sum of consecutive numbers
Balancing
sum = (average)(number of terms)
p/100 = is/of
1.4

23. Inscribed Angle - Minor Arc
(amount of change) / (original amount)
| A union B| = |A| + |B| - |A intersect B|
Find all prime factors
Minor arc = 2(inscribed angle)

24. Formula for Mixed Group problems (involving Both/Neither)
4/3 TT r ^3
(x-n(n)y-n)
Group 1 + Group 2 + Neither - Both = Total
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

25. 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.
at least 3 steps
Even
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
1st Rule of Probability: Basic Rule is what?

26. In general - medium questions require how many steps to solve?
2 steps
0.15n + 0.08(5) = 0.1(n+5)
Immediately UNFACTOR or vice versa
| A union B| = |A| + |B| - |A intersect B|

27. Formula for area of a Trapezoid
(sum of bases)(height) / 2
| A union B| = |A| + |B| - |A intersect B|
Balancing
1.7

28. The number of outcomes that result in A divided by the total number of possible outcomes.
Group 1 + Group 2 + Neither - Both = Total
1 - P(E)
The probability of event occurring is...
-b +- sq. rt(b^2 - 4ac) / 2a

29. To determine multiple-event probability where each individual event must occur in a certain way.
The amount after deductions
Figure out the probability for each individual event. Multiply the individual probabilities together.
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.
If the outcome of one event affects the outcome of the other event.

30. Price purchased for by wholesaler
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
Purchase price
principle (interest rate - in decimal form) (time - in years)
Sum of digits is multiple of 9

31. 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
sum = (average)(number of terms)
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.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
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.

32. 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?
0.15n + 0.08(5) = 0.1(n+5)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
16.6%
83.3%

33. How to check for a prime number.

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34. 1/8 = what %
(total distance) / (total time)
P(event NOT occurring) = 1 - P(event occurring)
1 - P(E)
12.5%

35. When you see an equation in factored form in a question?
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.
22
Immediately UNFACTOR or vice versa
x - x - x(sq. rt 2)

36. Average Rate: Average speed
(total distance) / (total time)
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
The probability of an event occurring plus the probability of the event not occurring = 1
0.15n + 0.08(5) = 0.1(n+5)

37. x^r/s = ?
s Sq. rt (x^r)
at least 3 steps
n! / (n - r)!
principle (interest rate - in decimal form) (time - in years)

38. 45-45-90 triangle basic lengths of sides
x - x - x(sq. rt 2)
(sum of bases)(height) / 2
Minor arc = 2(inscribed angle)
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)

39. Sq. rt(2)
x(sq. rt 3) - x - 2x
Purchase price
1.4
| A union B| = |A| + |B| - |A intersect B|

40. Percent increase = ?
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
n! / (n - r)!
(amount of change) / (original amount)
1.7

41. Compound interest formula
12^3
______ |m-n|
16.6%
Principal (1 + interest/number times compounded)^(t)(n)

42. Percent Formula
p/100 = is/of
1.4
4/3 TT r ^3
2 steps

43. Properties of 0
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
347
0.15n + 0.08(5) = 0.1(n+5)
1.4

44. Prime Factorization to find Greatest Common Factor
Any multiplication involving an even number creates an even product.
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
(n-1)!
Balancing

45. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
Principal (1 + interest/number times compounded)^(t)(n)
347
Organize into a grid.
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

46. Net
22
The amount after deductions
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.
(total distance) / (total time)

47. Indistinguishable events how to find the number of permutations

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48. 30-60-90 triangle basic lengths of sides
x(sq. rt 3) - x - 2x
Principal (1 + interest/number times compounded)^(t)(n)
If the outcome of one event affects the outcome of the other event.
1st Rule of Probability: Basic Rule is what?

49. 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.
(sum of bases)(height) / 2
Last two digits are multiple of 4 or the number can be divided by 2 twice.
(amount of change) / (original amount)

50. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
$11 - 025
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Odd numbers only have ___________
The probability of event occurring is...