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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. Volume of a sphere
______ |m-n|
4/3 TT r ^3
1 - P(E)
y2 - y1 / x2 - x1

2. 4th rule of Probability
at least 3 steps
(x-n(n)y-n)
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)
p/100 = is/of

3. When you see an equation in factored form in a question?
3-4-5 - 5-12-13 - 9-12-15
Find all prime factors
Find simple interest then look for the answer that is a little bigger
Immediately UNFACTOR or vice versa

4. How to check whether a number is a multiple of 6
4/3 TT r ^3
3 - 6 - 9 - 12
Number is a multiple of 3 and 2
Group 1 + Group 2 + Neither - Both = Total

5. The average of consecutive numbers
-b +- sq. rt(b^2 - 4ac) / 2a
347
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Principal (1 + interest/number times compounded)^(t)(n)

6. Set Problems formula
| A union B| = |A| + |B| - |A intersect B|
Principal (1 + interest/number times compounded)^(t)(n)
(x-n(n)y-n)
at least 3 steps

7. 5/6 = what %
always try to factor
83.3%
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
16.6%

8. gcd(m,n)
______ |m-n|
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)
1.7
always try to factor

9. 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.
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.
______ |m-n|
Sum of digits is multiple of 9
1st Rule of Probability: Basic Rule is what?

10. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
(total distance) / (total time)
principle (interest rate - in decimal form) (time - in years)
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.
gcd(m,n)*lcm(m,n) = mn

11. Combined Events: E or F
sum = (average)(number of terms)
12.5%
P(E) + P(F) - P(E and F)
x(sq. rt 3) - x - 2x

12. x^r/s = ?
1.7
Immediately UNFACTOR or vice versa
1st Rule of Probability: Basic Rule is what?
s Sq. rt (x^r)

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
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
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 probability of an event occurring plus the probability of the event not occurring = 1
(x-n(n)y-n)

14. 3^3 x 4^3 = ?
Figure out the probability for each individual event. Multiply the individual probabilities together.
12^3
sum = (average)(number of terms)
Group 1 + Group 2 + Neither - Both = Total

15. 3rd Rule of Probability: Conditional Probability
1st Rule of Probability: Basic Rule is what?
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 A AND event B occurring is the probability of event A times the probability of event B - given that A has already occurred.
Odd numbers only have ___________

16. To determine multiple-event probability where each individual event must occur in a certain way.
Immediately try factoring/simplifying when possible
| A union B| = |A| + |B| - |A intersect B|
Figure out the probability for each individual event. Multiply the individual probabilities 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

17. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
If the outcome of one event affects the outcome of the other event.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
s Sq. rt (x^r)

18. In general - difficult questions require how many steps to solve?
at least 3 steps
gcd(m,n)*lcm(m,n) = mn
Group 1 + Group 2 + Neither - Both = Total
always try to factor

19. In general - medium questions require how many steps to solve?
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)
2 steps
at least 3 steps

20. To determine the number of integers less than 5000 that are evenly divisible by 15...?
Divide 4999 by 15 => 333 integers
180(n-2)
x(sq. rt 3) - x - 2x
83.3%

21. How do you multiply roots together.
always try to factor
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
180(n-2)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

22. Sq. rt(3)
Find simple interest then look for the answer that is a little bigger
1 - P(E)
1.7
Exterior angle d is equal to the sum of the two remote interior angles a and b

23. 30-60-90 triangle basic lengths of sides
principle (interest rate - in decimal form) (time - in years)
14 liters
sum = (average)(number of terms)
x(sq. rt 3) - x - 2x

24. Triangle abc with d on the outside with a line. What does d = ?
Sum of digits is multiple of 3 - last two digits multiple of 4.
Find all prime factors
16.6%
Exterior angle d is equal to the sum of the two remote interior angles a and b

25. Multiplication principle
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
D or E
83.3%
Odd numbers only have ___________

26. How to check whether a number is a multiple of 3.
market value
Sum of digits is multiple of 3
s Sq. rt (x^r)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

27. Sq. rt(2)
1.4
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Organize into a grid.

28. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
A = P(1 + r) ^n
at least 3 steps
Group 1 + Group 2 + Neither - Both = Total
16.6%

29. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
(x-n(n)y-n)
Immediately try factoring/simplifying when possible
22
347

30. Permutations: Order Matters
The probability of event occurring is...
P(E)P(F)
Immediately try factoring/simplifying when possible
n! / (n - r)!

31. Dependent events: When are two events said to be dependent events?
at least 3 steps
If the outcome of one event affects the outcome of the other event.
s Sq. rt (x^r)
83.3%

32. Inscribed Angle - Minor Arc
Sum of digits is multiple of 9
83.3%
Minor arc = 2(inscribed angle)
Find simple interest then look for the answer that is a little bigger

33. How to check whether a number is a multiple of 4.
180(n-2)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
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.
(x-n(n)y-n)

34. Gross Profit formula
Gross Profit = Selling Price - Cost
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
(sum of bases)(height) / 2
-b +- sq. rt(b^2 - 4ac) / 2a

35. How to check whether number is multiple of 9
P(E) + P(F) - P(E and F)
Sum of digits is multiple of 9
market value
Balancing

36. Three triangle length patterns
3-4-5 - 5-12-13 - 9-12-15
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.
347
(n-1)!

37. 45-45-90 triangle basic lengths of sides
s Sq. rt (x^r)
x - x - x(sq. rt 2)
at least 3 steps
| A union B| = |A| + |B| - |A intersect B|

38. 1/6 = what %
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
1st Rule of Probability: Basic Rule is what?
x - x - x(sq. rt 2)
16.6%

39. (1/4)^2
4/3 TT r ^3
1/16
always try to factor
347

40. Sum of consecutive numbers
(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
sum = (average)(number of terms)
(# of favorable outcomes) / (# of possible outcomes)

41. Percent increase = ?
y2 - y1 / x2 - x1
Last two digits are multiple of 4 or the number can be divided by 2 twice.
(amount of change) / (original amount)
Sum of digits is multiple of 9

42. Intersecting Sets
Even
The amount after deductions
| A union B| = |A| + |B| - |A intersect B|
1.4

43. Compound interest formula
Principal (1 + interest/number times compounded)^(t)(n)
1st Rule of Probability: Basic Rule is what?
3 - 6 - 9 - 12
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

44. Net
The amount after deductions
1st Rule of Probability: Basic Rule is what?
Even
14 liters

45. Number added or deleted
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
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.
Find all prime factors
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

46. Multiples of 3
Any multiplication involving an even number creates an even product.
(sum of bases)(height) / 2
3 - 6 - 9 - 12
P(E) + P(F) - P(E and F)

47. Odd and Even rule.
Any multiplication involving an even number creates an even product.
Immediately UNFACTOR or vice versa
P(E)P(F)
12.5%

48. Price purchased for by wholesaler
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)
s Sq. rt (x^r)
Purchase price
Find all prime factors

49. Formula for Mixed Group problems (involving Both/Neither)
n! / (n - r)!
Any multiplication involving an even number creates an even product.
Group 1 + Group 2 + Neither - Both = Total
(total A) / (total B)

50. Combined Events: Not E = P(not E) = ?
1 - P(E)
Gross Profit = Selling Price - Cost
1st Rule of Probability: Basic Rule is what?
sum = (average)(number of terms)

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GMAT Quantitative General

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