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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. Prime Factorization to find Greatest Common Factor
Immediately try factoring/simplifying when possible
1.4
Exterior angle d is equal to the sum of the two remote interior angles a and b
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

2. When you see an equation in factored form in a question?
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Immediately UNFACTOR or vice versa
16.6%
Gross Profit = Selling Price - Cost

3. 5/6 = what %
1.7
P(E)P(F)
83.3%
Gross Profit = Selling Price - Cost

4. How to check whether a number is a multiple of 3.
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
Sum of digits is multiple of 3
2 steps
Sum of digits is multiple of 9

5. What to do with equations that have fractions
Immediately try factoring/simplifying when possible
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 AND event B occurring is the probability of event A times the probability of event B - given that A has already occurred.
| A union B| = |A| + |B| - |A intersect B|

6. Gross Profit formula
A = P(1 + r) ^n
Figure out the probability for each individual event. Multiply the individual probabilities together.
| A union B| = |A| + |B| - |A intersect B|
Gross Profit = Selling Price - Cost

7. Sq. rt(3)
Odd
The total amount before any deductions
1.7
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. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
(n-1)!
$11 - 025
1/16
principle (interest rate - in decimal form) (time - in years)

9. 0! = ?
Find all prime factors
always try to factor
180(n-2)
1

10. 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.
P(E) + P(F) - P(E and F)
The amount after deductions
1st Rule of Probability: Basic Rule is what?
D or E

11. Inscribed Angle - Minor Arc
Principal (1 + interest/number times compounded)^(t)(n)
12.5%
Minor arc = 2(inscribed angle)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

12. How to find the slope.
1.4
x - x - x(sq. rt 2)
y2 - y1 / x2 - x1
12.5%

13. Quadratic formula
Group 1 + Group 2 + Neither - Both = Total
Find simple interest then look for the answer that is a little bigger
Divide 4999 by 15 => 333 integers
-b +- sq. rt(b^2 - 4ac) / 2a

14. 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 average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
(total distance) / (total time)
0.15n + 0.08(5) = 0.1(n+5)
Immediately try factoring/simplifying when possible

15. What does the Sum of the angles in a Regular Polygon formula look like?
x - x - x(sq. rt 2)
180(n-2)
If the outcome of one event affects the outcome of the other event.
Minor arc = 2(inscribed angle)

16. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
83.3%
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
______ |m-n|
-b +- sq. rt(b^2 - 4ac) / 2a

17. Percent Formula
p/100 = is/of
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)
| 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.
(sum of bases)(height) / 2
D or E
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)

19. 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.
principle (interest rate - in decimal form) (time - in years)
P(E) + P(F) - P(E and F)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

20. Gross
market value
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
sum = (average)(number of terms)
The total amount before any deductions

21. How do you multiply roots together.
3-4-5 - 5-12-13 - 9-12-15
(amount of change) / (original amount)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
1 - P(E)

22. Price sold for by retailer (after markup)
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
market value
The total amount before any deductions
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)

23. Dependent events: When are two events said to be dependent events?
If the outcome of one event affects the outcome of the other event.
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)!
2 steps

24. Triangle abc with d on the outside with a line. What does d = ?
Find all prime factors
Exterior angle d is equal to the sum of the two remote interior angles a and b
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
2 steps

25. Sum of consecutive numbers
Gross Profit = Selling Price - Cost
12^3
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
sum = (average)(number of terms)

26. 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
(total A) / (total B)
(total distance) / (total time)
If the outcome of one event affects the outcome of the other event.
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.

27. Always try to factor
The probability of event occurring is...
always try to factor
(sum of bases)(height) / 2
Group 1 + Group 2 + Neither - Both = Total

28. How to find all divisors of a number
P(E) + P(F) - P(E and F)
Find all prime factors
347
0.15n + 0.08(5) = 0.1(n+5)

29. 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.
(sum of bases)(height) / 2
principle (interest rate - in decimal form) (time - in years)
x - x - x(sq. rt 2)

30. Price purchased for by wholesaler
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Purchase price
(x-n(n)y-n)
Number is a multiple of 3 and 2

31. 2nd Rule of Probability: P(E) = 1 - P(not E)
The total amount before any deductions
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 an event occurring plus the probability of the event not occurring = 1
(x-n(n)y-n)

32. 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
Balancing
1st Rule of Probability: Basic Rule is what?
Any multiplication involving an even number creates an even product.

33. Multiples of 3
3 - 6 - 9 - 12
If the outcome of one event affects the outcome of the other event.
(# of favorable outcomes) / (# of possible outcomes)
1/16

34. 45-45-90 triangle basic lengths of sides
Odd
Even
Principal (1 + interest/number times compounded)^(t)(n)
x - x - x(sq. rt 2)

35. 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.
Gross Profit = Selling Price - Cost
0.15n + 0.08(5) = 0.1(n+5)
1

36. 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.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
P(E)P(F)
(n-1)!

37. Odd and Even rule.
Sum of digits is multiple of 3
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.
Any multiplication involving an even number creates an even product.
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

38. 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
(sum of bases)(height) / 2
Odd
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

39. Intersecting Sets
83.3%
Principal (1 + interest/number times compounded)^(t)(n)
| A union B| = |A| + |B| - |A intersect B|
D or E

40. Compound interest rule
s Sq. rt (x^r)
Find all prime factors
1st Rule of Probability: Basic Rule is what?
Find simple interest then look for the answer that is a little bigger

41. 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
Odd numbers only have ___________
y2 - y1 / x2 - x1
Balancing
p/100 = is/of

42. How to check whether number is multiple of 9
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Sum of digits is multiple of 3
Sum of digits is multiple of 9
12.5%

43. Compound interest formula
12.5%
Principal (1 + interest/number times compounded)^(t)(n)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
3-4-5 - 5-12-13 - 9-12-15

44. Combined Events: Not E = P(not E) = ?
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
x - x - x(sq. rt 2)
Find simple interest then look for the answer that is a little bigger
1 - P(E)

45. Work problem rule
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
The probability of event occurring is...
Organize into a grid.
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.

46. Number added or deleted
Even
gcd(m,n)*lcm(m,n) = mn
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
P(event NOT occurring) = 1 - P(event occurring)

47. Average Rate: Average speed
Immediately UNFACTOR or vice versa
(# of favorable outcomes) / (# of possible outcomes)
(total distance) / (total time)
Even

48. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
22
1st Rule of Probability: Basic Rule is what?
P(E) + P(F) - P(E and F)
If the outcome of one event affects the outcome of the other event.

49. 2n - 2n+2 - 2n+4
Organize into a grid.
Gross Profit = Selling Price - Cost
16.6%
Even

50. Formula for Mixed Group problems (involving Both/Neither)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
1 - P(E)
Group 1 + Group 2 + Neither - Both = Total
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs