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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. Indistinguishable events how to find the number of permutations

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2. Quadratic formula
-b +- sq. rt(b^2 - 4ac) / 2a
always try to factor
1 - P(E)
(total A) / (total B)

3. Compound interest rule
(x-n(n)y-n)
x - x - x(sq. rt 2)
14 liters
Find simple interest then look for the answer that is a little bigger

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?
The amount after deductions
0.15n + 0.08(5) = 0.1(n+5)
Exterior angle d is equal to the sum of the two remote interior angles a and b
1

5. 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.
(sum of bases)(height) / 2
3 - 6 - 9 - 12
1st Rule of Probability: Basic Rule is what?
Principal (1 + interest/number times compounded)^(t)(n)

6. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
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
A = P(1 + r) ^n
Sum of digits is multiple of 9
(total A) / (total B)

7. The number of ways independent events can occur together.
The total amount before any deductions
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
s Sq. rt (x^r)
Minor arc = 2(inscribed angle)

8. Properties of 0
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
1/16
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
1st Rule of Probability: Basic Rule is what?

9. Gross Profit formula
Gross Profit = Selling Price - Cost
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.
3 - 6 - 9 - 12

10. Always try to factor
The amount after deductions
Purchase price
1st Rule of Probability: Basic Rule is what?
always try to factor

11. How to check for a prime number.

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12. Trial Problems: look at the probability of NOT OCCURRING
Figure out the probability for each individual event. Multiply the individual probabilities together.
P(event NOT occurring) = 1 - P(event occurring)
347
The total amount before any deductions

13. Simple probability
(# of favorable outcomes) / (# of possible outcomes)
12.5%
Sum of digits is multiple of 3
sum = (average)(number of terms)

14. 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.
22
(n-1)!
Gross Profit = Selling Price - Cost

15. Price sold for by retailer (after markup)
market value
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
$11 - 025
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

16. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
(total A) / (total B)
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
principle (interest rate - in decimal form) (time - in years)
Purchase price

17. Intersecting Sets
12^3
(total distance) / (total time)
Odd numbers only have ___________
| A union B| = |A| + |B| - |A intersect B|

18. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
D or 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.
180(n-2)
Odd numbers only have ___________

19. Volume of a sphere
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
16.6%
4/3 TT r ^3
Immediately try factoring/simplifying when possible

20. How to check whether a number is a multiple of 12.
Immediately try factoring/simplifying when possible
s Sq. rt (x^r)
Sum of digits is multiple of 3 - last two digits multiple of 4.
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

21. How to find all divisors of a number
P(E) + P(F) - P(E and F)
Find all prime factors
Minor arc = 2(inscribed angle)
$11 - 025

22. 4th rule of Probability
Divide 4999 by 15 => 333 integers
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)!
Last two digits are multiple of 4 or the number can be divided by 2 twice.

23. Combined Events: E or F
P(E) + P(F) - P(E and F)
Purchase price
16.6%
Divide 4999 by 15 => 333 integers

24. Triangle abc with d on the outside with a line. What does d = ?
Organize into a grid.
(n-1)!
Divide 4999 by 15 => 333 integers
Exterior angle d is equal to the sum of the two remote interior angles a and b

25. In general - medium questions require how many steps to solve?
______ |m-n|
1 - P(E)
2 steps
-b +- sq. rt(b^2 - 4ac) / 2a

26. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
22
principle (interest rate - in decimal form) (time - in years)
The probability of an event occurring plus the probability of the event not occurring = 1
A = P(1 + r) ^n

27. 3rd Rule of Probability: Conditional Probability
A = P(1 + r) ^n
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 AND event B occurring is the probability of event A times the probability of event B - given that A has already occurred.
Organize into a grid.

28. Percent Formula
(amount of change) / (original amount)
Sum of digits is multiple of 3
Immediately UNFACTOR or vice versa
p/100 = is/of

29. 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.
Organize into a grid.
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
Sum of digits is multiple of 9

30. 2n - 2n+2 - 2n+4
D or E
y2 - y1 / x2 - x1
Even
12^3

31. 45-45-90 triangle basic lengths of sides
180(n-2)
x - x - x(sq. rt 2)
Divide 4999 by 15 => 333 integers
Principal (1 + interest/number times compounded)^(t)(n)

32. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Any multiplication involving an even number creates an even product.
0.15n + 0.08(5) = 0.1(n+5)
$11 - 025

33. Probability and Geometry.
22
(# of favorable outcomes) / (# of possible outcomes)
(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

34. Percent increase = ?
n! / (n - r)!
Find simple interest then look for the answer that is a little bigger
(total A) / (total B)
(amount of change) / (original amount)

35. 30-60-90 triangle basic lengths of sides
1st Rule of Probability: Basic Rule is what?
x(sq. rt 3) - x - 2x
3-4-5 - 5-12-13 - 9-12-15
Group 1 + Group 2 + Neither - Both = Total

36. Average Rate: Average speed
(total distance) / (total time)
at least 3 steps
347
1.4

37. Formula for area of a Trapezoid
3 - 6 - 9 - 12
(sum of bases)(height) / 2
always try to factor
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)

38. What to do with equations that have fractions
Immediately try factoring/simplifying when possible
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
______ |m-n|
(sum of bases)(height) / 2

39. Multiplication principle
180(n-2)
The probability of event occurring is...
1.7
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

40. 2n+1 - 2n+3 - 2n+5
22
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Odd
x - x - x(sq. rt 2)

41. In general - difficult questions require how many steps to solve?
at least 3 steps
always try to factor
s Sq. rt (x^r)
1 - P(E)

42. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
(# of favorable outcomes) / (# of possible outcomes)
Immediately UNFACTOR or vice versa
The amount after deductions
347

43. Odd Factors
12^3
12.5%
$11 - 025
Odd numbers only have ___________

44. 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 probability of event occurring is...
Organize into a grid.
Group 1 + Group 2 + Neither - Both = Total
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.

45. Sq. rt(3)
x(sq. rt 3) - x - 2x
gcd(m,n)*lcm(m,n) = mn
1 - P(E)
1.7

46. How to check whether number is multiple of 9
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Even
Figure out the probability for each individual event. Multiply the individual probabilities together.
Sum of digits is multiple of 9

47. To determine the number of integers less than 5000 that are evenly divisible by 15...?
x(sq. rt 3) - x - 2x
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.
3 - 6 - 9 - 12
Divide 4999 by 15 => 333 integers

48. gcd(m,n)
| A union B| = |A| + |B| - |A intersect B|
Any multiplication involving an even number creates an even product.
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.
______ |m-n|

49. Dependent events: When are two events said to be dependent events?
Number is a multiple of 3 and 2
If the outcome of one event affects the outcome of the other event.
(total A) / (total B)
1st Rule of Probability: Basic Rule is what?

50. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
Odd
D or E
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
| A union B| = |A| + |B| - |A intersect B|