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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
Find simple interest then look for the answer that is a little bigger
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
The probability of event occurring is...
always try to factor

2. gcd(m,n)*lcm(m,n)
gcd(m,n)*lcm(m,n) = mn
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
$11 - 025
3 - 6 - 9 - 12

3. Triangle abc with d on the outside with a line. What does d = ?
1
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.
Exterior angle d is equal to the sum of the two remote interior angles a and b
Balancing

4. 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?
x(sq. rt 3) - x - 2x
0.15n + 0.08(5) = 0.1(n+5)
Divide 4999 by 15 => 333 integers
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.

5. Formula for Mixed Group problems (involving Both/Neither)
Exterior angle d is equal to the sum of the two remote interior angles a and b
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Group 1 + Group 2 + Neither - Both = Total
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.

6. Permutations: Order Matters
n! / (n - r)!
Divide 4999 by 15 => 333 integers
$11 - 025
x(sq. rt 3) - x - 2x

7. 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
Odd
Minor arc = 2(inscribed angle)
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 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)

8. Intersecting Sets
| A union B| = |A| + |B| - |A intersect B|
(# of favorable outcomes) / (# of possible outcomes)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
D or E

9. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
A = P(1 + r) ^n
1.7
If the outcome of one event affects the outcome of the other event.

10. 30-60-90 triangle basic lengths of sides
x(sq. rt 3) - x - 2x
(total distance) / (total time)
______ |m-n|
$11 - 025

11. Sq. rt(2)
1.4
principle (interest rate - in decimal form) (time - in years)
market value
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

12. Work problem rule
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.
1 - P(E)
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.

13. 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.
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
(# of favorable outcomes) / (# of possible outcomes)
1st Rule of Probability: Basic Rule is what?
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.

14. 2n+1 - 2n+3 - 2n+5
Immediately UNFACTOR or vice versa
12.5%
(amount of change) / (original amount)
Odd

15. Combined Events: Not E = P(not E) = ?
Sum of digits is multiple of 9
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.
1 - P(E)
Group 1 + Group 2 + Neither - Both = Total

16. Sum of consecutive numbers
1
Odd
sum = (average)(number of terms)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

17. Dependent events: When are two events said to be dependent events?
If the outcome of one event affects the outcome of the other event.
$11 - 025
Organize into a grid.
16.6%

18. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
4/3 TT r ^3
Exterior angle d is equal to the sum of the two remote interior angles a and b
Find all prime factors
(n-1)!

19. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
Balancing
Sum of digits is multiple of 3 - last two digits multiple of 4.
347
14 liters

20. 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. 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
| A union B| = |A| + |B| - |A intersect B|
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)

21. Average Rate: Average speed
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.
347
(total distance) / (total time)
Gross Profit = Selling Price - Cost

22. Combined Events: E or F
16.6%
gcd(m,n)*lcm(m,n) = mn
P(E) + P(F) - P(E and F)
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.

23. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
16.6%
D or E
Exterior angle d is equal to the sum of the two remote interior angles a and b

24. 5/6 = what %
(sum of bases)(height) / 2
Balancing
83.3%
Purchase price

25. To determine the number of integers less than 5000 that are evenly divisible by 15...?
(x-n(n)y-n)
Find simple interest then look for the answer that is a little bigger
Organize into a grid.
Divide 4999 by 15 => 333 integers

26. Properties of 0
-b +- sq. rt(b^2 - 4ac) / 2a
If the outcome of one event affects the outcome of the other event.
3 - 6 - 9 - 12
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

27. Average Rate: Average A per B
(total A) / (total B)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Divide 4999 by 15 => 333 integers
1 - P(E)

28. How to find all divisors of a number
Exterior angle d is equal to the sum of the two remote interior angles a and b
1.4
P(E)P(F)
Find all prime factors

29. How to check whether a number is a multiple of 3.
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.
If the outcome of one event affects the outcome of the other event.
Sum of digits is multiple of 3
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

30. 0! = ?
1
Balancing
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.
n! / (n - r)!

31. Odd Factors
Odd numbers only have ___________
347
Divide 4999 by 15 => 333 integers
n! / (n - r)!

32. What to do with equations that have fractions
A = P(1 + r) ^n
Sum of digits is multiple of 3 - last two digits multiple of 4.
Immediately try factoring/simplifying when possible
Figure out the probability for each individual event. Multiply the individual probabilities together.

33. Gross
0.15n + 0.08(5) = 0.1(n+5)
The total amount before any deductions
Figure out the probability for each individual event. Multiply the individual probabilities together.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

34. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
principle (interest rate - in decimal form) (time - in years)
1 - P(E)
The probability of an event occurring plus the probability of the event not occurring = 1
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

35. 1/8 = what %
Last two digits are multiple of 4 or the number can be divided by 2 twice.
12.5%
market value
Even

36. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
Even
3 - 6 - 9 - 12
22
Figure out the probability for each individual event. Multiply the individual probabilities together.

37. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
The probability of an event occurring plus the probability of the event not occurring = 1
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
(n-1)!
Purchase price

38. How to check whether a number is a multiple of 6
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Number is a multiple of 3 and 2
Find simple interest then look for the answer that is a little bigger
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

39. 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
3 - 6 - 9 - 12
Balancing
2 steps
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.

40. x^r/s = ?
(# of favorable outcomes) / (# of possible outcomes)
3-4-5 - 5-12-13 - 9-12-15
s Sq. rt (x^r)
Sum of digits is multiple of 3 - last two digits multiple of 4.

41. What does the Sum of the angles in a Regular Polygon formula look like?
180(n-2)
The probability of an event occurring plus the probability of the event not occurring = 1
4/3 TT r ^3
sum = (average)(number of terms)

42. Price sold for by retailer (after markup)
market value
180(n-2)
Gross Profit = Selling Price - Cost
Find simple interest then look for the answer that is a little bigger

43. How to check for a prime number.

44. 4th rule of Probability
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.
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 an event occurring plus the probability of the event not occurring = 1

45. Inscribed Angle - Minor Arc
(total A) / (total B)
market value
14 liters
Minor arc = 2(inscribed angle)

46. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
$11 - 025
Purchase price
x(sq. rt 3) - x - 2x
s Sq. rt (x^r)

47. The number of outcomes that result in A divided by the total number of possible outcomes.
Immediately UNFACTOR or vice versa
(total distance) / (total time)
D or E
The probability of event occurring is...

48. To determine multiple-event probability where each individual event must occur in a certain way.
3 - 6 - 9 - 12
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
2 steps
Figure out the probability for each individual event. Multiply the individual probabilities together.

49. The average of consecutive numbers
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
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Balancing

50. Set Problems formula
Gross Profit = Selling Price - Cost
(x-n(n)y-n)
The total amount before any deductions
The probability of an event occurring plus the probability of the event not occurring = 1