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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. Percent Formula
83.3%
x(sq. rt 3) - x - 2x
p/100 = is/of
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.

2. 30-60-90 triangle basic lengths of sides
P(E)P(F)
Divide 4999 by 15 => 333 integers
Minor arc = 2(inscribed angle)
x(sq. rt 3) - x - 2x

3. 3rd Rule of Probability: Conditional Probability
3-4-5 - 5-12-13 - 9-12-15
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)
Immediately try factoring/simplifying when possible
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.

4. 1/6 = what %
16.6%
14 liters
0.15n + 0.08(5) = 0.1(n+5)
Figure out the probability for each individual event. Multiply the individual probabilities together.

5. Volume of a sphere
4/3 TT r ^3
Sum of digits is multiple of 3 - last two digits multiple of 4.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
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

6. Gross
0.15n + 0.08(5) = 0.1(n+5)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
12.5%
The total amount before any deductions

7. To determine multiple-event probability where each individual event must occur in a certain way.
Minor arc = 2(inscribed angle)
2 steps
Figure out the probability for each individual event. Multiply the individual probabilities together.
Balancing

8. 1/8 = what %
P(E)P(F)
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
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.
12.5%

9. Prime Factorization to find Greatest Common Factor
A = P(1 + r) ^n
Minor arc = 2(inscribed angle)
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
principle (interest rate - in decimal form) (time - in years)

10. gcd(m,n)
(total A) / (total B)
y2 - y1 / x2 - x1
83.3%
______ |m-n|

11. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
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)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
D or E
x(sq. rt 3) - x - 2x

12. Set Problems formula
(x-n(n)y-n)
P(event NOT occurring) = 1 - P(event occurring)
always try to factor
Minor arc = 2(inscribed angle)

13. Combined Events: E and F
(total distance) / (total time)
Organize into a grid.
P(E)P(F)
Purchase price

14. Price sold for by retailer (after markup)
market value
(sum of bases)(height) / 2
Principal (1 + interest/number times compounded)^(t)(n)
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.

15. 45-45-90 triangle basic lengths of sides
n! / (n - r)!
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)
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.

16. The number of ways independent events can occur together.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
180(n-2)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
at least 3 steps

17. Combined Events: Not E = P(not E) = ?
Immediately UNFACTOR or vice versa
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
(sum of bases)(height) / 2
1 - P(E)

18. Triangle abc with d on the outside with a line. What does d = ?
12^3
Exterior angle d is equal to the sum of the two remote interior angles a and b
Number is a multiple of 3 and 2
P(E)P(F)

19. Properties of 0
p/100 = is/of
sum = (average)(number of terms)
Balancing
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

20. Odd and Even rule.
x - x - x(sq. rt 2)
Find all prime factors
Any multiplication involving an even number creates an even product.
12.5%

21. Formula for Mixed Group problems (involving Both/Neither)
Any multiplication involving an even number creates an even product.
Balancing
Group 1 + Group 2 + Neither - Both = Total
Odd

22. Inscribed Angle - Minor Arc
2 steps
Minor arc = 2(inscribed angle)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
22

23. 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. 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.
x - x - x(sq. rt 2)
sum = (average)(number of terms)
Balancing

24. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
0.15n + 0.08(5) = 0.1(n+5)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
principle (interest rate - in decimal form) (time - in years)
y2 - y1 / x2 - x1

25. Always try to factor
2 steps
always try to factor
gcd(m,n)*lcm(m,n) = mn
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

26. How to check whether number is multiple of 9
Sum of digits is multiple of 9
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.
83.3%

27. 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
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Exterior angle d is equal to the sum of the two remote interior angles a and b
Minor arc = 2(inscribed angle)

28. How to find the slope.
1/16
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
y2 - y1 / x2 - x1
Organize into a grid.

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.
1st Rule of Probability: Basic Rule is what?
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Odd numbers only have ___________

30. 3^3 x 4^3 = ?
12^3
14 liters
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)
Purchase price

31. 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
The amount after deductions
1.4
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.

32. How to check whether a number is a multiple of 12.
Sum of digits is multiple of 3 - last two digits multiple of 4.
p/100 = is/of
Divide 4999 by 15 => 333 integers
x - x - x(sq. rt 2)

33. (1/4)^2
The probability of an event occurring plus the probability of the event not occurring = 1
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
1/16
n! / (n - r)!

34. 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.
Immediately try factoring/simplifying when possible
P(event NOT occurring) = 1 - P(event occurring)
1st Rule of Probability: Basic Rule is what?
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.

35. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
3 - 6 - 9 - 12
2 steps
22
-b +- sq. rt(b^2 - 4ac) / 2a

36. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
14 liters
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
(n-1)!
(total distance) / (total time)

37. Quadratic formula
-b +- sq. rt(b^2 - 4ac) / 2a
principle (interest rate - in decimal form) (time - in years)
always try to factor
sum = (average)(number of terms)

38. To determine the number of integers less than 5000 that are evenly divisible by 15...?
Principal (1 + interest/number times compounded)^(t)(n)
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.
83.3%
Divide 4999 by 15 => 333 integers

39. Probability and Geometry.
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
n! / (n - r)!
Find simple interest then look for the answer that is a little bigger

40. When you see an equation in factored form in a question?
Immediately UNFACTOR or vice versa
Even
3 - 6 - 9 - 12
16.6%

41. How to check for a prime number.

42. Indistinguishable events how to find the number of permutations

43. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
P(event NOT occurring) = 1 - P(event occurring)
347
1st Rule of Probability: Basic Rule is what?
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.

44. Compound interest formula
Principal (1 + interest/number times compounded)^(t)(n)
The amount after deductions
3-4-5 - 5-12-13 - 9-12-15
1 - P(E)

45. Price purchased for by wholesaler
Purchase price
(amount of change) / (original amount)
A = P(1 + r) ^n
| A union B| = |A| + |B| - |A intersect B|

46. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
Balancing
Sum of digits is multiple of 3
A = P(1 + r) ^n
2 steps

47. What to do with equations that have fractions
12.5%
The probability of an event occurring plus the probability of the event not occurring = 1
(n-1)!
Immediately try factoring/simplifying when possible

48. Dependent events: When are two events said to be dependent events?
The total amount before any deductions
If the outcome of one event affects the outcome of the other event.
P(E) + P(F) - P(E and F)
14 liters

49. Intersecting Sets
| A union B| = |A| + |B| - |A intersect 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.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

50. 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)
(total A) / (total B)
1.7
347