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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. x^r/s = ?
Find all prime factors
s Sq. rt (x^r)
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(sq. rt 3) - x - 2x

2. 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.
P(E) + P(F) - P(E and F)
1st Rule of Probability: Basic Rule is what?
Balancing
2 steps

3. 3rd Rule of Probability: Conditional Probability
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
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.
16.6%

4. Price sold for by retailer (after markup)
The amount after deductions
Any multiplication involving an even number creates an even product.
(x-n(n)y-n)
market value

5. Probability and Geometry.
Find simple interest then look for the answer that is a little bigger
(total A) / (total B)
14 liters
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

6. How to check whether a number is a multiple of 6
1st Rule of Probability: Basic Rule is what?
Number is a multiple of 3 and 2
16.6%
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.

7. 2nd Rule of Probability: P(E) = 1 - P(not E)
347
The probability of an event occurring plus the probability of the event not occurring = 1
(total A) / (total B)
Any multiplication involving an even number creates an even product.

8. Sum of consecutive numbers
1/16
sum = (average)(number of terms)
3 - 6 - 9 - 12
12.5%

9. Average Rate: Average speed
p/100 = is/of
(total distance) / (total time)
Minor arc = 2(inscribed angle)
Balancing

10. (1/4)^2
Even
gcd(m,n)*lcm(m,n) = mn
1/16
1st Rule of Probability: Basic Rule is what?

11. How do you multiply roots together.
1.7
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Minor arc = 2(inscribed angle)
Balancing

12. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
347
principle (interest rate - in decimal form) (time - in years)
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
Balancing

13. Combined Events: Not E = P(not E) = ?
4/3 TT r ^3
1 - P(E)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
12.5%

14. Combined Events: E or F
P(E) + P(F) - P(E and F)
Any multiplication involving an even number creates an even product.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

15. Odd and Even rule.
The amount after deductions
market value
Balancing
Any multiplication involving an even number creates an even product.

16. Net
The amount after deductions
1.4
1
Immediately UNFACTOR or vice versa

17. How to check whether a number is a multiple of 12.
Number is a multiple of 3 and 2
Gross Profit = Selling Price - Cost
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 of digits is multiple of 3 - last two digits multiple of 4.

18. The number of outcomes that result in A divided by the total number of possible outcomes.
(total A) / (total B)
The probability of event occurring is...
The probability of an event occurring plus the probability of the event not occurring = 1
Divide 4999 by 15 => 333 integers

19. Volume of a sphere
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.
D or E
Purchase price
4/3 TT r ^3

20. gcd(m,n)
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
s Sq. rt (x^r)
______ |m-n|
3 - 6 - 9 - 12

21. Percent increase = ?
(amount of change) / (original amount)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
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.
A = P(1 + r) ^n

22. Dependent events: When are two events said to be dependent events?
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
0.15n + 0.08(5) = 0.1(n+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.
If the outcome of one event affects the outcome of the other event.

23. 3^3 x 4^3 = ?
(# of favorable outcomes) / (# of possible outcomes)
12^3
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 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

24. Odd Factors
Any multiplication involving an even number creates an even product.
A = P(1 + r) ^n
Odd numbers only have ___________
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. Price purchased for by wholesaler
Purchase price
x(sq. rt 3) - x - 2x
always try to factor
Group 1 + Group 2 + Neither - Both = Total

26. What to do with equations that have fractions
Divide 4999 by 15 => 333 integers
4/3 TT r ^3
Sum of digits is multiple of 3
Immediately try factoring/simplifying when possible

27. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
Divide 4999 by 15 => 333 integers
$11 - 025
1st Rule of Probability: Basic Rule is what?
principle (interest rate - in decimal form) (time - in years)

28. 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?
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)
$11 - 025
180(n-2)

29. Permutations: Order Matters
Find simple interest then look for the answer that is a little bigger
n! / (n - r)!
Immediately try factoring/simplifying when possible
Even

30. 1/8 = what %
347
12.5%
P(E)P(F)
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

31. Formula for area of a Trapezoid
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.
P(event NOT occurring) = 1 - P(event occurring)
at least 3 steps
(sum of bases)(height) / 2

32. Combined Events: E and F
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Odd
(n-1)!
P(E)P(F)

33. What does the Sum of the angles in a Regular Polygon formula look like?
3-4-5 - 5-12-13 - 9-12-15
P(E)P(F)
1.7
180(n-2)

34. How to find all divisors of a number
Find all prime factors
12^3
16.6%
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.

35. When you see an equation in factored form in a question?
y2 - y1 / x2 - x1
Immediately UNFACTOR or vice versa
Organize into a grid.
s Sq. rt (x^r)

36. Inscribed Angle - Minor Arc
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 amount after deductions
x(sq. rt 3) - x - 2x
Minor arc = 2(inscribed angle)

37. Gross Profit formula
| A union B| = |A| + |B| - |A intersect B|
Gross Profit = Selling Price - Cost
1.7
16.6%

38. Trial Problems: look at the probability of NOT OCCURRING
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
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
P(event NOT occurring) = 1 - P(event occurring)

39. 30-60-90 triangle basic lengths of sides
P(E)P(F)
D or E
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

40. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
(# of favorable outcomes) / (# of possible outcomes)
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.
Even

41. gcd(m,n)*lcm(m,n)
Immediately try factoring/simplifying when possible
12^3
Exterior angle d is equal to the sum of the two remote interior angles a and b
gcd(m,n)*lcm(m,n) = mn

42. 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
The amount after deductions
83.3%
Purchase price
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.

43. 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
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.
y2 - y1 / x2 - x1
Balancing
x - x - x(sq. rt 2)

44. Intersecting Sets
(n-1)!
Gross Profit = Selling Price - Cost
| A union B| = |A| + |B| - |A intersect B|
Even

45. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
D or E
P(E) + P(F) - P(E and F)
n! / (n - r)!
(x-n(n)y-n)

46. Gross
Purchase price
The total amount before any deductions
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.
sum = (average)(number of terms)

47. Multiplication principle
1.7
y2 - y1 / x2 - x1
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. 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.

48. Simple probability
Principal (1 + interest/number times compounded)^(t)(n)
(# of favorable outcomes) / (# of possible outcomes)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
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

49. To determine the number of integers less than 5000 that are evenly divisible by 15...?
1/16
Divide 4999 by 15 => 333 integers
Any multiplication involving an even number creates an even product.
2 steps

50. 2n+1 - 2n+3 - 2n+5
Principal (1 + interest/number times compounded)^(t)(n)
(n-1)!
83.3%
Odd