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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. Percent increase = ?
12^3
s Sq. rt (x^r)
(amount of change) / (original amount)
n! / (n - r)!

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?
0.15n + 0.08(5) = 0.1(n+5)
12.5%
______ |m-n|
Organize into a grid.

3. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
x(sq. rt 3) - x - 2x
22
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.
14 liters

4. How to find all divisors of a number
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.
Find all prime factors
| A union B| = |A| + |B| - |A intersect B|
-b +- sq. rt(b^2 - 4ac) / 2a

5. 2n - 2n+2 - 2n+4
Number is a multiple of 3 and 2
1.4
If the outcome of one event affects the outcome of the other event.
Even

6. 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
1.4
Balancing
(# of favorable outcomes) / (# of possible outcomes)
Gross Profit = Selling Price - Cost

7. How to check whether a number is a multiple of 4.
Number is a multiple of 3 and 2
Last two digits are multiple of 4 or the number can be divided by 2 twice.
22
Odd numbers only have ___________

8. gcd(m,n)*lcm(m,n)
16.6%
gcd(m,n)*lcm(m,n) = mn
s Sq. rt (x^r)
Sum of digits is multiple of 9

9. 5/6 = what %
Immediately try factoring/simplifying when possible
The probability of event occurring is...
83.3%
s Sq. rt (x^r)

10. What does the Sum of the angles in a Regular Polygon formula look like?
Divide 4999 by 15 => 333 integers
gcd(m,n)*lcm(m,n) = mn
Sum of digits is multiple of 3 - last two digits multiple of 4.
180(n-2)

11. The number of outcomes that result in A divided by the total number of possible outcomes.
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 probability of event occurring is...
P(E)P(F)
1.4

12. How to check for a prime number.

13. How do you multiply roots together.
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
D or E
(n-1)!
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

14. Sq. rt(3)
principle (interest rate - in decimal form) (time - in years)
(# of favorable outcomes) / (# of possible outcomes)
1.7
Group 1 + Group 2 + Neither - Both = Total

15. Average Rate: Average speed
Sum of digits is multiple of 3
P(event NOT occurring) = 1 - P(event occurring)
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.
(total distance) / (total time)

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

17. Price sold for by retailer (after markup)
x - x - x(sq. rt 2)
The amount after deductions
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.
market value

18. In general - medium questions require how many steps to solve?
P(event NOT occurring) = 1 - P(event occurring)
2 steps
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
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.

19. Sum of consecutive numbers
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)
Figure out the probability for each individual event. Multiply the individual probabilities together.
sum = (average)(number of terms)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

20. Multiples of 3
4/3 TT r ^3
3 - 6 - 9 - 12
Organize into a grid.
| A union B| = |A| + |B| - |A intersect B|

21. Multiplication principle
12.5%
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
1.7
The total amount before any deductions

22. 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?
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 liters
p/100 = is/of
(# of favorable outcomes) / (# of possible outcomes)

23. Odd Factors
Even
Odd numbers only have ___________
Any multiplication involving an even number creates an even product.
0.15n + 0.08(5) = 0.1(n+5)

24. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
$11 - 025
83.3%
347

25. Permutations: Order Matters
Exterior angle d is equal to the sum of the two remote interior angles a and b
n! / (n - r)!
market value
D or E

26. Set Problems formula
P(E)P(F)
Sum of digits is multiple of 3 - last two digits multiple of 4.
(x-n(n)y-n)
principle (interest rate - in decimal form) (time - in years)

27. 2n+1 - 2n+3 - 2n+5
Immediately UNFACTOR or vice versa
Odd
sum = (average)(number of terms)
(# of favorable outcomes) / (# of possible outcomes)

28. Combined Events: E and F
Principal (1 + interest/number times compounded)^(t)(n)
P(E)P(F)
at least 3 steps
A = P(1 + r) ^n

29. Quadratic formula
-b +- sq. rt(b^2 - 4ac) / 2a
1.4
(# of favorable outcomes) / (# of possible outcomes)
P(event NOT occurring) = 1 - P(event occurring)

30. 3^3 x 4^3 = ?
(total distance) / (total time)
12^3
The probability of event occurring is...
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)

31. 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
Find all prime factors
at least 3 steps
347

32. 0! = ?
(amount of change) / (original amount)
1
Odd
180(n-2)

33. What to do with equations that have fractions
Immediately try factoring/simplifying when possible
Immediately UNFACTOR or vice versa
-b +- sq. rt(b^2 - 4ac) / 2a
P(E)P(F)

34. Trial Problems: look at the probability of NOT OCCURRING
Sum of digits is multiple of 3
at least 3 steps
P(event NOT occurring) = 1 - P(event occurring)
Sum of digits is multiple of 3 - last two digits multiple of 4.

35. Volume of a sphere
Purchase price
The total amount before any deductions
4/3 TT r ^3
Sum of digits is multiple of 3

36. Compound interest rule
1.7
Gross Profit = Selling Price - Cost
______ |m-n|
Find simple interest then look for the answer that is a little bigger

37. 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.
Sum of digits is multiple of 9
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
4/3 TT r ^3

38. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
1 - P(E)
Exterior angle d is equal to the sum of the two remote interior angles a and b
principle (interest rate - in decimal form) (time - in years)
16.6%

39. 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
Any multiplication involving an even number creates an even product.
1st Rule of Probability: Basic Rule is what?
The amount after deductions

40. Intersecting Sets
P(E)P(F)
Sum of digits is multiple of 3 - last two digits multiple of 4.
(x-n(n)y-n)
| A union B| = |A| + |B| - |A intersect B|

41. 4th rule of Probability
1/16
2 steps
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 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)

42. How to check whether a number is a multiple of 6
Number is a multiple of 3 and 2
(# of favorable outcomes) / (# of possible outcomes)
(x-n(n)y-n)
D or E

43. Sq. rt(2)
Purchase price
Find simple interest then look for the answer that is a little bigger
Group 1 + Group 2 + Neither - Both = Total
1.4

44. Odd and Even rule.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
y2 - y1 / x2 - x1
Immediately UNFACTOR or vice versa
Any multiplication involving an even number creates an even product.

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

46. 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.
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?
1.7

47. 45-45-90 triangle basic lengths of sides
x - x - x(sq. rt 2)
0.15n + 0.08(5) = 0.1(n+5)
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.
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

48. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
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.
A = P(1 + r) ^n

49. Properties of 0
principle (interest rate - in decimal form) (time - in years)
A = P(1 + r) ^n
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Divide 4999 by 15 => 333 integers

50. Dependent events: When are two events said to be dependent events?
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.
If the outcome of one event affects the outcome of the other event.
180(n-2)
Find all prime factors