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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. Compound interest rule
n! / (n - r)!
Find simple interest then look for the answer that is a little bigger
4/3 TT r ^3
180(n-2)

2. How to check whether a number is a multiple of 3.
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
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
(n-1)!

3. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
(amount of change) / (original amount)
The probability of an event occurring plus the probability of the event not occurring = 1
12^3
22

4. 45-45-90 triangle basic lengths of sides
x - x - x(sq. rt 2)
3 - 6 - 9 - 12
$11 - 025
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

5. Properties of 0
3-4-5 - 5-12-13 - 9-12-15
s Sq. rt (x^r)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
(total A) / (total B)

6. Volume of a sphere
4/3 TT r ^3
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
(# of favorable outcomes) / (# of possible outcomes)
1 - P(E)

7. 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?
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
0.15n + 0.08(5) = 0.1(n+5)
Exterior angle d is equal to the sum of the two remote interior angles a and b
1 - P(E)

8. Intersecting Sets
P(E) + P(F) - P(E and F)
12.5%
| A union B| = |A| + |B| - |A intersect B|
3 - 6 - 9 - 12

9. 5/6 = what %
83.3%
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
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.
1st Rule of Probability: Basic Rule is what?

10. Gross Profit formula
P(E)P(F)
4/3 TT r ^3
Gross Profit = Selling Price - Cost
1 - P(E)

11. Net
Organize into a grid.
0.15n + 0.08(5) = 0.1(n+5)
always try to factor
The amount after deductions

12. 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.
| A union B| = |A| + |B| - |A intersect B|
at least 3 steps
347

13. 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
______ |m-n|
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.
sum = (average)(number of terms)
(total A) / (total B)

14. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
Immediately UNFACTOR or vice versa
1.7
principle (interest rate - in decimal form) (time - in years)
16.6%

15. 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.
1st Rule of Probability: Basic Rule is what?
The probability of event occurring is...
Divide 4999 by 15 => 333 integers
Sum of digits is multiple of 3 - last two digits multiple of 4.

16. Multiplication principle
1.4
1st Rule of Probability: Basic Rule is what?
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
(n-1)!

17. Sq. rt(3)
1.7
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.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
P(E) + P(F) - P(E and F)

18. Sq. rt(2)
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.
Principal (1 + interest/number times compounded)^(t)(n)
1.4
Find simple interest then look for the answer that is a little bigger

19. Odd Factors
Odd numbers only have ___________
Organize into a grid.
Divide 4999 by 15 => 333 integers
x(sq. rt 3) - x - 2x

20. How to check whether a number is a multiple of 12.
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.
Sum of digits is multiple of 3 - last two digits multiple of 4.
Immediately UNFACTOR or vice versa

21. Inscribed Angle - Minor Arc
180(n-2)
Number is a multiple of 3 and 2
Odd
Minor arc = 2(inscribed angle)

22. How to find the slope.
y2 - y1 / x2 - x1
The amount after deductions
______ |m-n|
14 liters

23. gcd(m,n)
______ |m-n|
83.3%
| A union B| = |A| + |B| - |A intersect B|
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

24. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
Sum of digits is multiple of 9
1.7
The total amount before any deductions
A = P(1 + r) ^n

25. 1/8 = what %
2 steps
12.5%
12^3
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

26. Set Problems formula
1.7
(x-n(n)y-n)
If the outcome of one event affects the outcome of the other event.
83.3%

27. Always try to factor
22
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.
always try to factor
The probability of event occurring is...

28. When you see an equation in factored form in a question?
Immediately UNFACTOR or vice versa
1 - P(E)
x - x - x(sq. rt 2)
Minor arc = 2(inscribed angle)

29. Permutations: Order Matters
12^3
n! / (n - r)!
(amount of change) / (original amount)
Gross Profit = Selling Price - Cost

30. Triangle abc with d on the outside with a line. What does d = ?
Group 1 + Group 2 + Neither - Both = Total
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Sum of digits is multiple of 3 - last two digits multiple of 4.
Exterior angle d is equal to the sum of the two remote interior angles a and b

31. Percent Formula
Purchase price
p/100 = is/of
| A union B| = |A| + |B| - |A intersect B|
Immediately try factoring/simplifying when possible

32. 3rd Rule of Probability: Conditional Probability
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
(total A) / (total B)
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.
12^3

33. The number of ways independent events can occur together.
Odd numbers only have ___________
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
4/3 TT r ^3

34. 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
The probability of event occurring is...
Minor arc = 2(inscribed angle)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Balancing

35. 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
Sum of digits is multiple of 3
1st Rule of Probability: Basic Rule is what?
4/3 TT r ^3

36. What to do with equations that have fractions
Gross Profit = Selling Price - Cost
1.4
Immediately try factoring/simplifying when possible
gcd(m,n)*lcm(m,n) = mn

37. Trial Problems: look at the probability of NOT OCCURRING
P(event NOT occurring) = 1 - P(event occurring)
0.15n + 0.08(5) = 0.1(n+5)
P(E)P(F)
(sum of bases)(height) / 2

38. 3^3 x 4^3 = ?
Divide 4999 by 15 => 333 integers
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
12^3
(# of favorable outcomes) / (# of possible outcomes)

39. What does the Sum of the angles in a Regular Polygon formula look like?
180(n-2)
3-4-5 - 5-12-13 - 9-12-15
$11 - 025
Principal (1 + interest/number times compounded)^(t)(n)

40. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
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.
The total amount before any deductions
(n-1)!
Odd

41. Gross
A = P(1 + r) ^n
s Sq. rt (x^r)
83.3%
The total amount before any deductions

42. Formula for Mixed Group problems (involving Both/Neither)
y2 - y1 / x2 - x1
Immediately UNFACTOR or vice versa
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Group 1 + Group 2 + Neither - Both = Total

43. How to check whether a number is a multiple of 4.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
at least 3 steps
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
(n-1)!

44. How do you multiply roots together.
(x-n(n)y-n)
The amount after deductions
P(E) + P(F) - P(E and F)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

45. Quadratic formula
(amount of change) / (original amount)
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
1.7
-b +- sq. rt(b^2 - 4ac) / 2a

46. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
Find all prime factors
$11 - 025
Sum of digits is multiple of 3 - last two digits multiple of 4.
83.3%

47. Three triangle length patterns
1.7
3-4-5 - 5-12-13 - 9-12-15
Exterior angle d is equal to the sum of the two remote interior angles a and b
Find all prime factors

48. Price sold for by retailer (after markup)
(n-1)!
14 liters
market value
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.

49. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
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.
12^3
D or E
If the outcome of one event affects the outcome of the other event.

50. 30-60-90 triangle basic lengths of sides
347
Group 1 + Group 2 + Neither - Both = Total
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.
x(sq. rt 3) - x - 2x