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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. Combined Events: E and F
P(E)P(F)
principle (interest rate - in decimal form) (time - in years)
x - x - x(sq. rt 2)
Any multiplication involving an even number creates an even product.

2. How to check whether number is multiple of 9
Sum of digits is multiple of 9
4/3 TT r ^3
1.4
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)

3. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
Divide 4999 by 15 => 333 integers
0.15n + 0.08(5) = 0.1(n+5)
(n-1)!
Last two digits are multiple of 4 or the number can be divided by 2 twice.

4. 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?
14 liters
1st Rule of Probability: Basic Rule is what?
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.
Balancing

5. Quadratic formula
(total A) / (total B)
-b +- sq. rt(b^2 - 4ac) / 2a
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 average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

6. Volume of a sphere
The amount after deductions
4/3 TT r ^3
P(E) + P(F) - P(E and F)
Find all prime factors

7. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
(x-n(n)y-n)
$11 - 025
347
y2 - y1 / x2 - x1

8. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
22
(# of favorable outcomes) / (# of possible outcomes)
0.15n + 0.08(5) = 0.1(n+5)
Divide 4999 by 15 => 333 integers

9. To determine multiple-event probability where each individual event must occur in a certain way.
P(E)P(F)
Figure out the probability for each individual event. Multiply the individual probabilities together.
The amount after deductions
Even

10. 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
Sum of digits is multiple of 3
A = P(1 + r) ^n
Balancing
Last two digits are multiple of 4 or the number can be divided by 2 twice.

11. Sq. rt(3)
always try to factor
1.7
14 liters
Any multiplication involving an even number creates an even product.

12. 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.
always try to factor
y2 - y1 / x2 - x1
Organize into a grid.
Odd

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.
1st Rule of Probability: Basic Rule is what?
Sum of digits is multiple of 3
Last two digits are multiple of 4 or the number can be divided by 2 twice.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

14. (1/4)^2
Divide 4999 by 15 => 333 integers
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
(x-n(n)y-n)
1/16

15. Properties of 0
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any 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.
Figure out the probability for each individual event. Multiply the individual probabilities together.
1st Rule of Probability: Basic Rule is what?

16. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
P(event NOT occurring) = 1 - P(event occurring)
D or E
(# of favorable outcomes) / (# of possible outcomes)

17. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
16.6%
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
at least 3 steps
A = P(1 + r) ^n

18. How to check whether a number is a multiple of 6
(# of favorable outcomes) / (# of possible outcomes)
83.3%
1
Number is a multiple of 3 and 2

19. Average Rate: Average A per B
12^3
P(E) + P(F) - P(E and F)
(total A) / (total B)
market value

20. 4th rule of Probability
always try to factor
1/16
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)
-b +- sq. rt(b^2 - 4ac) / 2a

21. Intersecting Sets
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.
| A union B| = |A| + |B| - |A intersect B|
The amount after deductions
1st Rule of Probability: Basic Rule is what?

22. Multiplication principle
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
P(E) + P(F) - P(E and F)
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
347

23. Formula for area of a Trapezoid
1st Rule of Probability: Basic Rule is what?
1.7
Purchase price
(sum of bases)(height) / 2

24. Trial Problems: look at the probability of NOT OCCURRING
P(event NOT occurring) = 1 - P(event occurring)
83.3%
always try to factor
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. 1/8 = what %
Figure out the probability for each individual event. Multiply the individual probabilities together.
always try to factor
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
12.5%

26. What to do with equations that have fractions
Balancing
A = P(1 + r) ^n
Sum of digits is multiple of 9
Immediately try factoring/simplifying when possible

27. Sum of consecutive numbers
$11 - 025
12^3
sum = (average)(number of terms)
Find all prime factors

28. Gross Profit formula
P(E) + P(F) - P(E and F)
Gross Profit = Selling Price - Cost
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
market value

29. To determine the number of integers less than 5000 that are evenly divisible by 15...?
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
| A union B| = |A| + |B| - |A intersect B|
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Divide 4999 by 15 => 333 integers

30. Work problem rule
Sum of digits is multiple of 9
Any multiplication involving an even number creates an even product.
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.
s Sq. rt (x^r)

31. gcd(m,n)
______ |m-n|
s Sq. rt (x^r)
12.5%
Find simple interest then look for the answer that is a little bigger

32. 30-60-90 triangle basic lengths of sides
Immediately UNFACTOR or vice versa
x(sq. rt 3) - x - 2x
Minor arc = 2(inscribed angle)
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.

33. Compound interest rule
16.6%
y2 - y1 / x2 - x1
1
Find simple interest then look for the answer that is a little bigger

34. Compound interest formula
Number is a multiple of 3 and 2
Figure out the probability for each individual event. Multiply the individual probabilities together.
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
Principal (1 + interest/number times compounded)^(t)(n)

35. What does the Sum of the angles in a Regular Polygon formula look like?
180(n-2)
Purchase price
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.
always try to factor

36. gcd(m,n)*lcm(m,n)
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.
market value
p/100 = is/of
gcd(m,n)*lcm(m,n) = mn

37. Indistinguishable events how to find the number of permutations

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38. Prime Factorization to find Greatest Common Factor
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
P(E) + P(F) - P(E and F)
12^3
Find simple interest then look for the answer that is a little bigger

39. Three triangle length patterns
n! / (n - r)!
x(sq. rt 3) - x - 2x
The amount after deductions
3-4-5 - 5-12-13 - 9-12-15

40. Price purchased for by wholesaler
(n-1)!
Any multiplication involving an even number creates an even product.
0.15n + 0.08(5) = 0.1(n+5)
Purchase price

41. 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)
3-4-5 - 5-12-13 - 9-12-15
14 liters
Odd

42. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
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.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
(total distance) / (total time)

43. 2nd Rule of Probability: P(E) = 1 - P(not E)
market value
The probability of an event occurring plus the probability of the event not occurring = 1
Immediately UNFACTOR or vice versa
3-4-5 - 5-12-13 - 9-12-15

44. Always try to factor
s Sq. rt (x^r)
2 steps
Group 1 + Group 2 + Neither - Both = Total
always try to factor

45. The number of ways independent events can occur together.
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 occurring is...
1.4
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

46. In general - difficult questions require how many steps to solve?
180(n-2)
sum = (average)(number of terms)
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.
at least 3 steps

47. 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
principle (interest rate - in decimal form) (time - in years)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
347

48. The number of outcomes that result in A divided by the total number of possible outcomes.
1.4
1.7
The probability of event occurring is...
0.15n + 0.08(5) = 0.1(n+5)

49. Gross
The total amount before any deductions
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Purchase price
Sum of digits is multiple of 3

50. Net
(n-1)!
______ |m-n|
The amount after deductions
Find all prime factors