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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. What to do with equations that have fractions
Immediately try factoring/simplifying when possible
x - x - x(sq. rt 2)
Find all prime factors
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

2. 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?
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.
0.15n + 0.08(5) = 0.1(n+5)
gcd(m,n)*lcm(m,n) = mn
p/100 = is/of

3. Price sold for by retailer (after markup)
market value
Group 1 + Group 2 + Neither - Both = Total
14 liters
P(E) + P(F) - P(E and F)

4. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
16.6%
x(sq. rt 3) - x - 2x
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Find all prime factors

5. 3rd Rule of Probability: Conditional Probability
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.
(amount of change) / (original amount)
Divide 4999 by 15 => 333 integers
Odd

6. Prime Factorization to find Greatest Common Factor
Balancing
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
Purchase price

7. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
Sum of digits is multiple of 3 - last two digits multiple of 4.
(n-1)!
Number is a multiple of 3 and 2
1st Rule of Probability: Basic Rule is what?

8. Three triangle length patterns
3-4-5 - 5-12-13 - 9-12-15
16.6%
Last two digits are multiple of 4 or the number can be divided by 2 twice.
market value

9. How to check whether number is multiple of 9
Divide 4999 by 15 => 333 integers
Exterior angle d is equal to the sum of the two remote interior angles a and b
22
Sum of digits is multiple of 9

10. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
1/16
A = P(1 + r) ^n
Number is a multiple of 3 and 2
Principal (1 + interest/number times compounded)^(t)(n)

11. 2nd Rule of Probability: P(E) = 1 - P(not E)
principle (interest rate - in decimal form) (time - in years)
The probability of an event occurring plus the probability of the event not occurring = 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.
Any multiplication involving an even number creates an even product.

12. Gross Profit formula
(n-1)!
1/16
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

13. Sum of consecutive numbers
1.4
sum = (average)(number of terms)
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.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

14. How do you multiply roots together.
n! / (n - r)!
A = P(1 + r) ^n
(# of favorable outcomes) / (# of possible outcomes)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

15. Dependent events: When are two events said to be dependent events?
______ |m-n|
Immediately UNFACTOR or vice versa
1/16
If the outcome of one event affects the outcome of the other event.

16. 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.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
sum = (average)(number of terms)

17. In general - difficult questions require how many steps to solve?
at least 3 steps
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)
(n-1)!
(amount of change) / (original amount)

18. 2n - 2n+2 - 2n+4
Even
y2 - y1 / x2 - x1
-b +- sq. rt(b^2 - 4ac) / 2a
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

19. Indistinguishable events how to find the number of permutations

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20. Trial Problems: look at the probability of NOT OCCURRING
(sum of bases)(height) / 2
Organize into a grid.
-b +- sq. rt(b^2 - 4ac) / 2a
P(event NOT occurring) = 1 - P(event occurring)

21. Set Problems formula
(x-n(n)y-n)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Odd numbers only have ___________

22. What does the Sum of the angles in a Regular Polygon formula look like?
The probability of an event occurring plus the probability of the event not occurring = 1
principle (interest rate - in decimal form) (time - in years)
Organize into a grid.
180(n-2)

23. Odd and Even rule.
Find simple interest then look for the answer that is a little bigger
Any multiplication involving an even number creates an even product.
Odd numbers only have ___________
(amount of change) / (original amount)

24. Simple probability
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 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)
Organize into a grid.
(# of favorable outcomes) / (# of possible outcomes)

25. 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.
n! / (n - r)!
A = P(1 + r) ^n
Organize into a grid.
gcd(m,n)*lcm(m,n) = mn

26. gcd(m,n)
12^3
______ |m-n|
2 steps
(# of favorable outcomes) / (# of possible outcomes)

27. 5/6 = what %
$11 - 025
83.3%
market value
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.

28. Sq. rt(3)
2 steps
Sum of digits is multiple of 3
n! / (n - r)!
1.7

29. How to check whether a number is a multiple of 3.
Number is a multiple of 3 and 2
Sum of digits is multiple of 3
s Sq. rt (x^r)
1

30. Permutations: Order Matters
Last two digits are multiple of 4 or the number can be divided by 2 twice.
y2 - y1 / x2 - x1
n! / (n - r)!
Even

31. 2n+1 - 2n+3 - 2n+5
n! / (n - r)!
Odd
1st Rule of Probability: Basic Rule is what?
Figure out the probability for each individual event. Multiply the individual probabilities together.

32. To determine the number of integers less than 5000 that are evenly divisible by 15...?
(total distance) / (total time)
Find all prime factors
3 - 6 - 9 - 12
Divide 4999 by 15 => 333 integers

33. 1/6 = what %
(total distance) / (total time)
16.6%
1st Rule of Probability: Basic Rule is what?
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

34. Intersecting Sets
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
y2 - y1 / x2 - x1
| A union B| = |A| + |B| - |A intersect B|
(total distance) / (total time)

35. The number of ways independent events can occur together.
______ |m-n|
14 liters
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 AND event B occurring is the probability of event A times the probability of event B - given that A has already occurred.

36. Gross
The total amount before any deductions
If the outcome of one event affects the outcome of the other event.
Balancing
The probability of event occurring is...

37. 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
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.
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?
D or E

38. Volume of a sphere
4/3 TT r ^3
always try to factor
(x-n(n)y-n)
14 liters

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
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
1.4
The total amount before any deductions
Balancing

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

41. Triangle abc with d on the outside with a line. What does d = ?
always try to factor
Exterior angle d is equal to the sum of the two remote interior angles a and b
Gross Profit = Selling Price - Cost
s Sq. rt (x^r)

42. How to check for a prime number.

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43. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
| A union B| = |A| + |B| - |A intersect B|
$11 - 025
(total A) / (total B)
Divide 4999 by 15 => 333 integers

44. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
22
1/16
347
(# of favorable outcomes) / (# of possible outcomes)

45. 4th rule of Probability
1.4
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
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)
A = P(1 + r) ^n

46. 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?
P(E)P(F)
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
83.3%
14 liters

47. The average of consecutive numbers
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
1/16
-b +- sq. rt(b^2 - 4ac) / 2a
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

48. Formula for area of a Trapezoid
(sum of bases)(height) / 2
Principal (1 + interest/number times compounded)^(t)(n)
22
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. 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.
Number is a multiple of 3 and 2
1st Rule of Probability: Basic Rule is what?
(x-n(n)y-n)
Sum of digits is multiple of 3 - last two digits multiple of 4.

50. To determine multiple-event probability where each individual event must occur in a certain way.
Odd
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Group 1 + Group 2 + Neither - Both = Total
Figure out the probability for each individual event. Multiply the individual probabilities together.