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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. (1/4)^2
Principal (1 + interest/number times compounded)^(t)(n)
1/16
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

2. Set Problems formula
(x-n(n)y-n)
Odd numbers only have ___________
Group 1 + Group 2 + Neither - Both = Total
1

3. Sq. rt(3)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
(total A) / (total B)
______ |m-n|
1.7

4. 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
0.15n + 0.08(5) = 0.1(n+5)
If the outcome of one event affects the outcome of the other event.
(amount of change) / (original amount)

5. Properties of 0
1 - P(E)
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
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Sum of digits is multiple of 9

6. Number added or deleted
(sum of bases)(height) / 2
12^3
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Immediately UNFACTOR or vice versa

7. Indistinguishable events how to find the number of permutations

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8. How to check whether a number is a multiple of 6
180(n-2)
Number is a multiple of 3 and 2
12^3
Immediately UNFACTOR or vice versa

9. How to find the slope.
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.
y2 - y1 / x2 - x1
22
Odd

10. The number of ways independent events can occur together.
______ |m-n|
P(E)P(F)
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.

11. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
always try to factor
22
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Exterior angle d is equal to the sum of the two remote interior angles a and b

12. 30-60-90 triangle basic lengths of sides
A = P(1 + r) ^n
Immediately UNFACTOR or vice versa
x(sq. rt 3) - x - 2x
(total A) / (total B)

13. 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
83.3%
D or E
Odd

14. 1/8 = what %
12.5%
Odd
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
(total distance) / (total time)

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?
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
14 liters
2 steps
The probability of event occurring is...

16. Combined Events: E and F
Balancing
Last two digits are multiple of 4 or the number can be divided by 2 twice.
P(E)P(F)
Sum of digits is multiple of 3

17. The number of outcomes that result in A divided by the total number of possible outcomes.
1st Rule of Probability: Basic Rule is what?
The probability of event occurring is...
Any multiplication involving an even number creates an even product.
If the outcome of one event affects the outcome of the other event.

18. Three triangle length patterns
The total amount before any deductions
Purchase price
0.15n + 0.08(5) = 0.1(n+5)
3-4-5 - 5-12-13 - 9-12-15

19. Combined Events: E or F
P(E) + P(F) - P(E and F)
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
(amount of change) / (original amount)

20. Dependent events: When are two events said to be dependent events?
If the outcome of one event affects the outcome of the other event.
1
sum = (average)(number of terms)
Any multiplication involving an even number creates an even product.

21. Quadratic formula
Find simple interest then look for the answer that is a little bigger
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
(amount of change) / (original amount)
-b +- sq. rt(b^2 - 4ac) / 2a

22. How to find all divisors of a number
(x-n(n)y-n)
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
Find all prime factors
x - x - x(sq. rt 2)

23. To determine the number of integers less than 5000 that are evenly divisible by 15...?
Divide 4999 by 15 => 333 integers
83.3%
sum = (average)(number of terms)
1

24. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
n! / (n - r)!
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
principle (interest rate - in decimal form) (time - in years)
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.

25. gcd(m,n)*lcm(m,n)
Immediately try factoring/simplifying when possible
gcd(m,n)*lcm(m,n) = mn
sum = (average)(number of terms)
1

26. Work problem rule
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 probability of an event occurring plus the probability of the event not occurring = 1
Find all prime factors
(# of favorable outcomes) / (# of possible outcomes)

27. In general - medium questions require how many steps to solve?
2 steps
Gross Profit = Selling Price - Cost
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 of bases)(height) / 2

28. In general - difficult questions require how many steps to solve?
at least 3 steps
Immediately UNFACTOR or vice versa
p/100 = is/of
x - x - x(sq. rt 2)

29. How to check whether a number is a multiple of 12.
1
22
The probability of an event occurring plus the probability of the event not occurring = 1
Sum of digits is multiple of 3 - last two digits multiple of 4.

30. 3^3 x 4^3 = ?
The total amount before any deductions
16.6%
12^3
1/16

31. 2nd Rule of Probability: P(E) = 1 - P(not E)
1.4
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)
The probability of an event occurring plus the probability of the event not occurring = 1

32. Sum of consecutive 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
Find simple interest then look for the answer that is a little bigger
The probability of an event occurring plus the probability of the event not occurring = 1
sum = (average)(number of terms)

33. 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?
Principal (1 + interest/number times compounded)^(t)(n)
P(E) + P(F) - P(E and F)
______ |m-n|

34. 0! = ?
The total amount before any deductions
1
Principal (1 + interest/number times compounded)^(t)(n)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

35. gcd(m,n)
A = P(1 + r) ^n
Group 1 + Group 2 + Neither - Both = Total
always try to factor
______ |m-n|

36. Gross
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
1/16
The total amount before any deductions
16.6%

37. Odd Factors
Purchase price
Gross Profit = Selling Price - Cost
Odd numbers only have ___________
The total amount before any deductions

38. Prime Factorization to find Greatest Common Factor
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 average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
12.5%
Immediately try factoring/simplifying when possible

39. Average Rate: Average A per B
Odd
The amount after deductions
(total A) / (total B)
The total amount before any deductions

40. 4th rule of Probability
x(sq. rt 3) - x - 2x
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)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
A = P(1 + r) ^n

41. 5/6 = what %
Purchase price
Immediately try factoring/simplifying when possible
83.3%
3 - 6 - 9 - 12

42. How to check for a prime number.

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43. 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.
Balancing
sum = (average)(number of terms)
Exterior angle d is equal to the sum of the two remote interior angles a and b
Organize into a grid.

44. Percent increase = ?
(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.
The total amount before any deductions
83.3%

45. 3rd Rule of Probability: Conditional Probability
always try to factor
x(sq. rt 3) - x - 2x
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.
-b +- sq. rt(b^2 - 4ac) / 2a

46. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
180(n-2)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
gcd(m,n)*lcm(m,n) = mn
P(E) + P(F) - P(E and F)

47. Triangle abc with d on the outside with a line. What does d = ?
sum = (average)(number of terms)
Gross Profit = Selling Price - Cost
Exterior angle d is equal to the sum of the two remote interior angles a and b
| A union B| = |A| + |B| - |A intersect B|

48. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
(n-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.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
14 liters

49. 45-45-90 triangle basic lengths of sides
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
x - x - x(sq. rt 2)
Sum of digits is multiple of 9
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.

50. Percent Formula
p/100 = is/of
P(E) + P(F) - P(E and F)
y2 - y1 / x2 - x1
n! / (n - r)!