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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. Sum of consecutive numbers
14 liters
16.6%
sum = (average)(number of terms)
P(E) + P(F) - P(E and F)

2. How to check for a prime number.

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3. Prime Factorization to find Greatest Common Factor
1.7
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 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. 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.

4. 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
Balancing
Purchase price
(x-n(n)y-n)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

5. Odd Factors
4/3 TT r ^3
1st Rule of Probability: Basic Rule is what?
Odd numbers only have ___________
Balancing

6. Indistinguishable events how to find the number of permutations

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7. (1/4)^2
1/16
s Sq. rt (x^r)
Find all prime factors
3 - 6 - 9 - 12

8. Compound interest rule
s Sq. rt (x^r)
n! / (n - r)!
2 steps
Find simple interest then look for the answer that is a little bigger

9. Percent Formula
1 - P(E)
P(E)P(F)
83.3%
p/100 = is/of

10. Gross
n! / (n - r)!
12^3
market value
The total amount before any deductions

11. 5/6 = what %
market value
1 - P(E)
83.3%
______ |m-n|

12. 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.
4/3 TT r ^3
The total amount before any deductions
p/100 = is/of
1st Rule of Probability: Basic Rule is what?

13. Permutations: Order Matters
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
347
______ |m-n|
n! / (n - r)!

14. To determine multiple-event probability where each individual event must occur in a certain way.
A = P(1 + r) ^n
s Sq. rt (x^r)
Figure out the probability for each individual event. Multiply the individual probabilities together.
at least 3 steps

15. 4th rule of Probability
P(event NOT occurring) = 1 - P(event occurring)
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)
______ |m-n|

16. To determine the number of integers less than 5000 that are evenly divisible by 15...?
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
If the outcome of one event affects the outcome of the other event.
The probability of an event occurring plus the probability of the event not occurring = 1
Divide 4999 by 15 => 333 integers

17. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
(n-1)!
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
Any multiplication involving an even number creates an even product.
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

18. 2nd Rule of Probability: P(E) = 1 - P(not E)
p/100 = is/of
1 - P(E)
Purchase price
The probability of an event occurring plus the probability of the event not occurring = 1

19. Multiplication principle
(n-1)!
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 total amount before any deductions
x(sq. rt 3) - x - 2x

20. Compound interest formula
Number is a multiple of 3 and 2
Principal (1 + interest/number times compounded)^(t)(n)
Odd
Immediately try factoring/simplifying when possible

21. x^r/s = ?
p/100 = is/of
Sum of digits is multiple of 3
s Sq. rt (x^r)
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.

22. 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.
at least 3 steps
y2 - y1 / x2 - x1
Number is a multiple of 3 and 2

23. 3^3 x 4^3 = ?
at least 3 steps
12^3
Find simple interest then look for the answer that is a little bigger
Odd numbers only have ___________

24. 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?
Sum of digits is multiple of 9
14 liters
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
Divide 4999 by 15 => 333 integers

25. Properties of 0
p/100 = is/of
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)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

26. 1/6 = what %
The probability of event occurring is...
Sum of digits is multiple of 3 - last two digits multiple of 4.
Figure out the probability for each individual event. Multiply the individual probabilities together.
16.6%

27. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
D or E
s Sq. rt (x^r)
1/16
$11 - 025

28. Set Problems formula
2 steps
1
(x-n(n)y-n)
The probability of an event occurring plus the probability of the event not occurring = 1

29. What to do with equations that have fractions
Immediately try factoring/simplifying when possible
(amount of change) / (original amount)
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.
sum = (average)(number of terms)

30. How to check whether number is multiple of 9
Sum of digits is multiple of 9
16.6%
Sum of digits is multiple of 3
22

31. Sq. rt(2)
1.4
x(sq. rt 3) - x - 2x
14 liters
16.6%

32. How to check whether a number is a multiple of 6
Number is a multiple of 3 and 2
-b +- sq. rt(b^2 - 4ac) / 2a
x - x - x(sq. rt 2)
1.7

33. Odd and Even rule.
sum = (average)(number of terms)
Any multiplication involving an even number creates an even product.
(amount of change) / (original amount)
(sum of bases)(height) / 2

34. Triangle abc with d on the outside with a line. What does d = ?
Exterior angle d is equal to the sum of the two remote interior angles a and b
x(sq. rt 3) - x - 2x
1
-b +- sq. rt(b^2 - 4ac) / 2a

35. Three triangle length patterns
Sum of digits is multiple of 9
n! / (n - r)!
Gross Profit = Selling Price - Cost
3-4-5 - 5-12-13 - 9-12-15

36. Formula for Mixed Group problems (involving Both/Neither)
Odd
Group 1 + Group 2 + Neither - Both = Total
1.7
principle (interest rate - in decimal form) (time - in years)

37. 1/8 = what %
22
-b +- sq. rt(b^2 - 4ac) / 2a
83.3%
12.5%

38. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
22
The probability of an event occurring plus the probability of the event not occurring = 1
at least 3 steps
-b +- sq. rt(b^2 - 4ac) / 2a

39. Percent increase = ?
1
gcd(m,n)*lcm(m,n) = mn
3 - 6 - 9 - 12
(amount of change) / (original amount)

40. 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.
principle (interest rate - in decimal form) (time - in years)
(total distance) / (total time)
Organize into a grid.
Purchase price

41. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
$11 - 025
1 - P(E)
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
always try to factor

42. Gross Profit formula
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.
12^3
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.

43. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
______ |m-n|
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
The amount after deductions
Odd

44. Combined Events: E and F
market value
180(n-2)
D or E
P(E)P(F)

45. Number added or deleted
83.3%
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
If the outcome of one event affects the outcome of the other event.
gcd(m,n)*lcm(m,n) = mn

46. The number of ways independent events can occur together.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
3 - 6 - 9 - 12
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 number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

47. 2n - 2n+2 - 2n+4
p/100 = is/of
Principal (1 + interest/number times compounded)^(t)(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.
Even

48. Quadratic formula
-b +- sq. rt(b^2 - 4ac) / 2a
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
P(E)P(F)
D or E

49. Intersecting Sets
| A union B| = |A| + |B| - |A intersect B|
gcd(m,n)*lcm(m,n) = mn
sum = (average)(number of terms)
x - x - x(sq. rt 2)

50. Dependent events: When are two events said to be dependent events?
Sum of digits is multiple of 3 - last two digits multiple of 4.
Divide 4999 by 15 => 333 integers
If the outcome of one event affects the outcome of the other event.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs