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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. How to find all divisors of a number
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.
p/100 = is/of
Find all prime factors
______ |m-n|

2. Triangle abc with d on the outside with a line. What does d = ?
p/100 = is/of
Exterior angle d is equal to the sum of the two remote interior angles a and b
(n-1)!
Immediately UNFACTOR or vice versa

3. gcd(m,n)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
1.7
| A union B| = |A| + |B| - |A intersect B|
______ |m-n|

4. Inscribed Angle - Minor Arc
0.15n + 0.08(5) = 0.1(n+5)
Minor arc = 2(inscribed angle)
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.
Purchase price

5. 2nd Rule of Probability: P(E) = 1 - P(not E)
sum = (average)(number of terms)
gcd(m,n)*lcm(m,n) = mn
x - x - x(sq. rt 2)
The probability of an event occurring plus the probability of the event not occurring = 1

6. How to check whether number is multiple of 9
Sum of digits is multiple of 9
The amount after deductions
83.3%
Number is a multiple of 3 and 2

7. How to find the slope.
347
Find all prime factors
y2 - y1 / x2 - x1
Find simple interest then look for the answer that is a little bigger

8. 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 digits is multiple of 9
P(E) + P(F) - P(E and F)
1.4

9. 2n - 2n+2 - 2n+4
Principal (1 + interest/number times compounded)^(t)(n)
P(E) + P(F) - P(E and F)
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.
Even

10. How do you multiply roots together.
Immediately try factoring/simplifying when possible
Find simple interest then look for the answer that is a little bigger
Group 1 + Group 2 + Neither - Both = Total
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

11. 1/6 = what %
Immediately try factoring/simplifying when possible
16.6%
Balancing
(# of favorable outcomes) / (# of possible outcomes)

12. Formula for area of a Trapezoid
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
(sum of bases)(height) / 2
Organize into a grid.
2 steps

13. Combined Events: Not E = P(not E) = ?
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
180(n-2)
1 - P(E)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

14. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
always try to factor
22
14 liters
P(E)P(F)

15. 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
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.
market value
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Balancing

16. Combined Events: E or F
principle (interest rate - in decimal form) (time - in years)
P(E) + P(F) - P(E and F)
The probability of event occurring is...
P(E)P(F)

17. How to check whether a number is a multiple of 12.
Sum of digits is multiple of 3 - last two digits multiple of 4.
1st Rule of Probability: Basic Rule is what?
1.4
______ |m-n|

18. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
347
Figure out the probability for each individual event. Multiply the individual probabilities together.
3 - 6 - 9 - 12
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

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.
The probability of event occurring is...
0.15n + 0.08(5) = 0.1(n+5)
Organize into a grid.
always try to factor

20. 4th rule of Probability
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)
1.4
Minor arc = 2(inscribed angle)
347

21. 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?
83.3%
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
14 liters
Immediately UNFACTOR or vice versa

22. Always try to factor
always try to factor
180(n-2)
Odd numbers only have ___________
Sum of digits is multiple of 3

23. 3^3 x 4^3 = ?
Find simple interest then look for the answer that is a little bigger
y2 - y1 / x2 - x1
12^3
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

24. 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.
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.
1st Rule of Probability: Basic Rule is what?
Immediately UNFACTOR or vice versa
s Sq. rt (x^r)

25. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
x(sq. rt 3) - x - 2x
If the outcome of one event affects the outcome of the other event.
principle (interest rate - in decimal form) (time - in years)
Principal (1 + interest/number times compounded)^(t)(n)

26. How to check whether a number is a multiple of 6
(sum of bases)(height) / 2
22
The probability of an event occurring plus the probability of the event not occurring = 1
Number is a multiple of 3 and 2

27. Permutations: Order Matters
n! / (n - r)!
(x-n(n)y-n)
4/3 TT r ^3
Group 1 + Group 2 + Neither - Both = Total

28. What does the Sum of the angles in a Regular Polygon formula look like?
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
180(n-2)
Sum of digits is multiple of 3
Even

29. Volume of a sphere
Even
4/3 TT r ^3
Immediately UNFACTOR or vice versa
Exterior angle d is equal to the sum of the two remote interior angles a and b

30. The number of ways independent events can occur together.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
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.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
2 steps

31. Compound interest rule
principle (interest rate - in decimal form) (time - in years)
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.
n! / (n - r)!
Find simple interest then look for the answer that is a little bigger

32. 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
3 - 6 - 9 - 12
1 - P(E)
2 steps
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.

33. Indistinguishable events how to find the number of permutations

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34. Formula for Mixed Group problems (involving Both/Neither)
Immediately try factoring/simplifying when possible
Group 1 + Group 2 + Neither - Both = Total
p/100 = is/of
3-4-5 - 5-12-13 - 9-12-15

35. Odd and Even rule.
P(E)P(F)
Any multiplication involving an even number creates an even product.
D or E
(amount of change) / (original amount)

36. Gross Profit formula
gcd(m,n)*lcm(m,n) = mn
Gross Profit = Selling Price - Cost
P(E)P(F)
Odd numbers only have ___________

37. Sum of consecutive numbers
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Odd numbers only have ___________
sum = (average)(number of terms)
Find simple interest then look for the answer that is a little bigger

38. Combined Events: E and F
P(E)P(F)
180(n-2)
Group 1 + Group 2 + Neither - Both = Total
(total distance) / (total time)

39. Net
n! / (n - r)!
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
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
The amount after deductions

40. 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
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
2 steps
n! / (n - r)!

41. When you see an equation in factored form in a question?
1st Rule of Probability: Basic Rule is what?
always try to factor
Immediately UNFACTOR or vice versa
Any multiplication involving an even number creates an even product.

42. Three triangle length patterns
Odd
3-4-5 - 5-12-13 - 9-12-15
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.

43. Number added or deleted
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
3-4-5 - 5-12-13 - 9-12-15
1.4
(total A) / (total B)

44. What to do with equations that have fractions
always try to factor
Number is a multiple of 3 and 2
n! / (n - r)!
Immediately try factoring/simplifying when possible

45. Sq. rt(2)
Find all prime factors
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
gcd(m,n)*lcm(m,n) = mn

46. Percent Formula
always try to factor
4/3 TT r ^3
The total amount before any deductions
p/100 = is/of

47. gcd(m,n)*lcm(m,n)
12^3
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
2 steps
gcd(m,n)*lcm(m,n) = mn

48. x^r/s = ?
1 - P(E)
12^3
s Sq. rt (x^r)
16.6%

49. Compound interest formula
0.15n + 0.08(5) = 0.1(n+5)
Immediately UNFACTOR or vice versa
Principal (1 + interest/number times compounded)^(t)(n)
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)

50. Multiples of 3
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?
2 steps
3 - 6 - 9 - 12