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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 the slope.
y2 - y1 / x2 - x1
Organize into a grid.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
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.

2. Formula for Mixed Group problems (involving Both/Neither)
Group 1 + Group 2 + Neither - Both = Total
1/16
1 - P(E)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

3. Simple probability
p/100 = is/of
market value
(# of favorable outcomes) / (# of possible outcomes)
12.5%

4. Sum of consecutive numbers
sum = (average)(number of terms)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Number is a multiple of 3 and 2
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

5. Price purchased for by wholesaler
Sum of digits is multiple of 3 - last two digits multiple of 4.
Purchase price
P(E) + P(F) - P(E and F)
22

6. 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
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.
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)
gcd(m,n)*lcm(m,n) = mn

7. Average Rate: Average speed
Minor arc = 2(inscribed angle)
1
(total distance) / (total time)
3-4-5 - 5-12-13 - 9-12-15

8. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
347
Organize into a grid.
22
180(n-2)

9. Percent increase = ?
14 liters
The probability of event occurring is...
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
(amount of change) / (original amount)

10. Percent Formula
Balancing
p/100 = is/of
Sum of digits is multiple of 3 - last two digits multiple of 4.
Gross Profit = Selling Price - Cost

11. How to find all divisors of a number
(sum of bases)(height) / 2
Group 1 + Group 2 + Neither - Both = Total
Find all prime factors
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.

12. To determine multiple-event probability where each individual event must occur in a certain way.
Figure out the probability for each individual event. Multiply the individual probabilities together.
83.3%
s Sq. rt (x^r)
Last two digits are multiple of 4 or the number can be divided by 2 twice.

13. Always try to factor
always try to factor
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.
Minor arc = 2(inscribed angle)
Any multiplication involving an even number creates an even product.

14. How to check whether number is multiple of 9
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Sum of digits is multiple of 9
1/16
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.

15. 3rd Rule of Probability: Conditional Probability
Divide 4999 by 15 => 333 integers
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
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.
Last two digits are multiple of 4 or the number can be divided by 2 twice.

16. 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
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
y2 - y1 / x2 - x1

17. Volume of a sphere
P(E)P(F)
Even
1.7
4/3 TT r ^3

18. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
D or E
1st Rule of Probability: Basic Rule is what?
Divide 4999 by 15 => 333 integers
180(n-2)

19. 2n+1 - 2n+3 - 2n+5
(total A) / (total B)
2 steps
If the outcome of one event affects the outcome of the other event.
Odd

20. 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?
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.
s Sq. rt (x^r)
347

21. Quadratic formula
-b +- sq. rt(b^2 - 4ac) / 2a
83.3%
D or E
Group 1 + Group 2 + Neither - Both = Total

22. Sq. rt(2)
1.4
Purchase price
Minor arc = 2(inscribed angle)
The total amount before any deductions

23. Price sold for by retailer (after markup)
market value
(total A) / (total B)
A = P(1 + r) ^n
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

24. 0! = ?
1
Immediately try factoring/simplifying when possible
14 liters
347

25. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
22
x(sq. rt 3) - x - 2x
P(E) + P(F) - P(E and F)
sum = (average)(number of terms)

26. 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.
p/100 = is/of
Gross Profit = Selling Price - Cost
Group 1 + Group 2 + Neither - Both = Total

27. Gross
y2 - y1 / x2 - x1
1 - P(E)
The total amount before any deductions
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

28. 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
(n-1)!
Last two digits are multiple of 4 or the number can be divided by 2 twice.
347

29. 1/8 = what %
(x-n(n)y-n)
12.5%
(total A) / (total B)
Find all prime factors

30. Combined Events: E and F
P(E)P(F)
Exterior angle d is equal to the sum of the two remote interior angles a and b
1st Rule of Probability: Basic Rule is what?
(n-1)!

31. Formula for area of a Trapezoid
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 of bases)(height) / 2
(amount of change) / (original amount)
Odd numbers only have ___________

32. Indistinguishable events how to find the number of permutations

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33. Dependent events: When are two events said to be dependent events?
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
-b +- sq. rt(b^2 - 4ac) / 2a
If the outcome of one event affects the outcome of the other event.
(total A) / (total B)

34. Inscribed Angle - Minor Arc
4/3 TT r ^3
Minor arc = 2(inscribed angle)
P(event NOT occurring) = 1 - P(event occurring)
D or E

35. What to do with equations that have fractions
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
principle (interest rate - in decimal form) (time - in years)
Immediately try factoring/simplifying when possible
P(E)P(F)

36. The number of outcomes that result in A divided by the total number of possible outcomes.
$11 - 025
The probability of event occurring is...
(# of favorable outcomes) / (# of possible outcomes)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

37. Compound interest formula
Principal (1 + interest/number times compounded)^(t)(n)
1st Rule of Probability: Basic Rule is what?
3-4-5 - 5-12-13 - 9-12-15
P(E)P(F)

38. Trial Problems: look at the probability of NOT OCCURRING
Last two digits are multiple of 4 or the number can be divided by 2 twice.
P(event NOT occurring) = 1 - P(event occurring)
(x-n(n)y-n)
The total amount before any deductions

39. Multiplication principle
always try to factor
Find all prime factors
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

40. What does the Sum of the angles in a Regular Polygon formula look like?
1st Rule of Probability: Basic Rule is what?
180(n-2)
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)

41. Combined Events: Not E = P(not E) = ?
A = P(1 + r) ^n
1 - P(E)
Balancing
12^3

42. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
Organize into a grid.
Principal (1 + interest/number times compounded)^(t)(n)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
principle (interest rate - in decimal form) (time - in years)

43. When you see an equation in factored form in a question?
y2 - y1 / x2 - x1
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
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.
Immediately UNFACTOR or vice versa

44. 3^3 x 4^3 = ?
1
12^3
p/100 = is/of
Sum of digits is multiple of 9

45. 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?
Divide 4999 by 15 => 333 integers
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.
Any multiplication involving an even number creates an even product.
0.15n + 0.08(5) = 0.1(n+5)

46. 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
1.7
1
Balancing
at least 3 steps

47. In general - difficult questions require how many steps to solve?
Even
s Sq. rt (x^r)
If the outcome of one event affects the outcome of the other event.
at least 3 steps

48. The average of consecutive numbers
Immediately try factoring/simplifying when possible
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.
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

49. (1/4)^2
Figure out the probability for each individual event. Multiply the individual probabilities together.
12.5%
1/16
Organize into a grid.

50. Multiples of 3
Immediately UNFACTOR or vice versa
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
3 - 6 - 9 - 12
1.7