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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. 1/8 = what %
12.5%
(total A) / (total B)
180(n-2)
P(E)P(F)

2. Price sold for by retailer (after markup)
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.
n! / (n - r)!
Principal (1 + interest/number times compounded)^(t)(n)
market value

3. Gross Profit formula
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.
The amount after deductions
market value

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
Purchase price
D or E
n! / (n - r)!
Balancing

5. 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 number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
3-4-5 - 5-12-13 - 9-12-15
always try to factor
Organize into a grid.

6. 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
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
(total distance) / (total time)

7. Sq. rt(2)
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 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
(amount of change) / (original amount)

8. How to check whether a number is a 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.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
gcd(m,n)*lcm(m,n) = mn
Odd numbers only have ___________

9. 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.
The probability of an event occurring plus the probability of the event not occurring = 1
The probability of event occurring is...
1st Rule of Probability: Basic Rule is what?
s Sq. rt (x^r)

10. When you see an equation in factored form in a question?
Divide 4999 by 15 => 333 integers
Figure out the probability for each individual event. Multiply the individual probabilities together.
14 liters
Immediately UNFACTOR or vice versa

11. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
Principal (1 + interest/number times compounded)^(t)(n)
A = P(1 + r) ^n
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
s Sq. rt (x^r)

12. What to do with equations that have fractions
The total amount before any deductions
2 steps
Immediately try factoring/simplifying when possible
always try to factor

13. Multiples of 3
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
12^3
3 - 6 - 9 - 12
0.15n + 0.08(5) = 0.1(n+5)

14. Price purchased for by wholesaler
Odd numbers only have ___________
Minor arc = 2(inscribed angle)
Purchase price
4/3 TT r ^3

15. Triangle abc with d on the outside with a line. What does d = ?
(amount of change) / (original amount)
Find all prime factors
Exterior angle d is equal to the sum of the two remote interior angles a and b
16.6%

16. x^r/s = ?
1
s Sq. rt (x^r)
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.
Figure out the probability for each individual event. Multiply the individual probabilities together.

17. Percent Formula
12.5%
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.
Odd
p/100 = is/of

18. Average Rate: Average speed
1/16
347
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
(total distance) / (total time)

19. In general - medium questions require how many steps to solve?
The probability of event occurring is...
(x-n(n)y-n)
3 - 6 - 9 - 12
2 steps

20. Intersecting Sets
1st Rule of Probability: Basic Rule is what?
| A union B| = |A| + |B| - |A intersect B|
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

21. How to check whether a number is a multiple of 6
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
$11 - 025
1.4
Number is a multiple of 3 and 2

22. Set Problems formula
(amount of change) / (original amount)
3-4-5 - 5-12-13 - 9-12-15
(x-n(n)y-n)
$11 - 025

23. 5/6 = what %
p/100 = is/of
Immediately UNFACTOR or vice versa
83.3%
3-4-5 - 5-12-13 - 9-12-15

24. 4th rule of Probability
(total A) / (total B)
Sum of digits is multiple of 3
Group 1 + Group 2 + Neither - Both = Total
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)

25. How to find the slope.
The amount after deductions
2 steps
y2 - y1 / x2 - x1
4/3 TT r ^3

26. Sq. rt(3)
s Sq. rt (x^r)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
The probability of an event occurring plus the probability of the event not occurring = 1
1.7

27. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
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.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
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
(total A) / (total B)

28. Compound interest formula
Immediately UNFACTOR or vice versa
P(event NOT occurring) = 1 - P(event occurring)
Principal (1 + interest/number times compounded)^(t)(n)
Sum of digits is multiple of 3 - last two digits multiple of 4.

29. 2nd Rule of Probability: P(E) = 1 - P(not E)
The probability of an event occurring plus the probability of the event not occurring = 1
Immediately UNFACTOR or vice versa
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
n! / (n - r)!

30. 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)
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
Organize into a grid.
Figure out the probability for each individual event. Multiply the individual probabilities together.

31. 2n - 2n+2 - 2n+4
Even
1.7
14 liters
Divide 4999 by 15 => 333 integers

32. Combined Events: Not E = P(not E) = ?
1 - P(E)
Gross Profit = Selling Price - Cost
1.4
Find all prime factors

33. Number added or deleted
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
(# of favorable outcomes) / (# of possible outcomes)
Group 1 + Group 2 + Neither - Both = Total
(n-1)!

34. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
(x-n(n)y-n)
Sum of digits is multiple of 3 - last two digits multiple of 4.
D or 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

35. Dependent events: When are two events said to be dependent events?
Number is a multiple of 3 and 2
0.15n + 0.08(5) = 0.1(n+5)
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.
If the outcome of one event affects the outcome of the other event.

36. Properties of 0
3 - 6 - 9 - 12
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
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)
3-4-5 - 5-12-13 - 9-12-15

37. Permutations: Order Matters
Any multiplication involving an even number creates an even product.
(total distance) / (total time)
Gross Profit = Selling Price - Cost
n! / (n - r)!

38. How do you multiply roots together.
| A union B| = |A| + |B| - |A intersect B|
$11 - 025
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

39. gcd(m,n)*lcm(m,n)
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.
A = P(1 + r) ^n
-b +- sq. rt(b^2 - 4ac) / 2a
gcd(m,n)*lcm(m,n) = mn

40. The number of outcomes that result in A divided by the total number of possible outcomes.
The probability of event occurring is...
(x-n(n)y-n)
1st Rule of Probability: Basic Rule is what?
sum = (average)(number of terms)

41. 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
Odd numbers only have ___________
s Sq. rt (x^r)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

42. Three triangle length patterns
1.4
Balancing
3-4-5 - 5-12-13 - 9-12-15
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

43. Indistinguishable events how to find the number of permutations

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44. Work problem rule
Odd
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.
______ |m-n|
at least 3 steps

45. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
22
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.
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.
180(n-2)

46. How to check whether number is multiple of 9
Find simple interest then look for the answer that is a little bigger
(sum of bases)(height) / 2
Sum of digits is multiple of 9
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

47. Gross
2 steps
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
sum = (average)(number of terms)

48. Average Rate: Average A per B
(total A) / (total B)
Sum of digits is multiple of 3 - last two digits multiple of 4.
Even
Sum of digits is multiple of 9

49. Quadratic formula
Number is a multiple of 3 and 2
2 steps
n! / (n - r)!
-b +- sq. rt(b^2 - 4ac) / 2a

50. 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
Exterior angle d is equal to the sum of the two remote interior angles a and b
(amount of change) / (original amount)
The probability of an event occurring plus the probability of the event not occurring = 1