Test your basic knowledge |

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. 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)
4/3 TT r ^3
Sum of digits is multiple of 9
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

2. How to find the slope.
y2 - y1 / x2 - x1
Group 1 + Group 2 + Neither - Both = Total
(n-1)!
The probability of event occurring is...

3. How to check whether a number is a multiple of 4.
Sum of digits is multiple of 9
Last two digits are multiple of 4 or the number can be divided by 2 twice.
1.4
principle (interest rate - in decimal form) (time - in years)

4. Gross
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
n! / (n - r)!
Balancing
The total amount before any deductions

5. Combined Events: E and F
Principal (1 + interest/number times compounded)^(t)(n)
P(E)P(F)
1.7
D or E

6. How to check whether a number is a multiple of 3.
Sum of digits is multiple of 3
Balancing
1.7
The amount after deductions

7. How to check for a prime number.

8. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
Divide 4999 by 15 => 333 integers
$11 - 025
The amount after deductions
1st Rule of Probability: Basic Rule is what?

9. 45-45-90 triangle basic lengths of sides
x - x - x(sq. rt 2)
The amount after deductions
The total amount before any deductions
0.15n + 0.08(5) = 0.1(n+5)

10. x^r/s = ?
(x-n(n)y-n)
1.7
s Sq. rt (x^r)
Exterior angle d is equal to the sum of the two remote interior angles a and b

11. (1/4)^2
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
1/16
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
Find all prime factors

12. Always try to factor
Group 1 + Group 2 + Neither - Both = Total
Last two digits are multiple of 4 or the number can be divided by 2 twice.
always try to factor
Even

13. 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.
gcd(m,n)*lcm(m,n) = mn
Sum of digits is multiple of 9
2 steps

14. Price purchased for by wholesaler
Purchase price
Divide 4999 by 15 => 333 integers
1 - P(E)
(total A) / (total B)

15. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
x - x - x(sq. rt 2)
83.3%
347
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. What does the Sum of the angles in a Regular Polygon formula look like?
The probability of an event occurring plus the probability of the event not occurring = 1
s Sq. rt (x^r)
180(n-2)
3-4-5 - 5-12-13 - 9-12-15

17. Prime Factorization to find Greatest Common Factor
P(E)P(F)
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)
x(sq. rt 3) - x - 2x

18. The number of outcomes that result in A divided by the total number of possible outcomes.
s Sq. rt (x^r)
The probability of event occurring is...
1 - P(E)
1.4

19. Percent increase = ?
(amount of change) / (original amount)
P(event NOT occurring) = 1 - P(event occurring)
1
Last two digits are multiple of 4 or the number can be divided by 2 twice.

20. Average Rate: Average A per B
Sum of digits is multiple of 3
(total A) / (total B)
P(event NOT occurring) = 1 - P(event occurring)
If the outcome of one event affects the outcome of the other event.

21. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
22
(total A) / (total B)
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.
p/100 = is/of

22. Gross Profit formula
Find all prime factors
Minor arc = 2(inscribed angle)
Gross Profit = Selling Price - Cost
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

23. In general - difficult questions require how many steps to solve?
22
The amount after deductions
at least 3 steps
Gross Profit = Selling Price - Cost

24. How do you multiply roots together.
Group 1 + Group 2 + Neither - Both = Total
Immediately try factoring/simplifying when possible
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
P(E) + P(F) - P(E and F)

25. gcd(m,n)*lcm(m,n)
gcd(m,n)*lcm(m,n) = mn
180(n-2)
Minor arc = 2(inscribed angle)
Sum of digits is multiple of 3

26. Dependent events: When are two events said to be dependent events?
-b +- sq. rt(b^2 - 4ac) / 2a
If the outcome of one event affects the outcome of the other event.
Exterior angle d is equal to the sum of the two remote interior angles a and b
The amount after deductions

27. Multiples of 3
3 - 6 - 9 - 12
14 liters
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.

28. When you see an equation in factored form in a question?
Sum of digits is multiple of 3 - last two digits multiple of 4.
P(E) + P(F) - P(E and F)
Immediately UNFACTOR or vice versa
Any multiplication involving an even number creates an even product.

29. Volume of a sphere
A = P(1 + r) ^n
4/3 TT r ^3
1.4
16.6%

30. Three triangle length patterns
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Sum of digits is multiple of 3
Number is a multiple of 3 and 2
3-4-5 - 5-12-13 - 9-12-15

31. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
(x-n(n)y-n)
3 - 6 - 9 - 12
22
(n-1)!

32. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
always try to factor
Principal (1 + interest/number times compounded)^(t)(n)
A = P(1 + r) ^n
$11 - 025

33. Average Rate: Average speed
$11 - 025
(total distance) / (total time)
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
always try to factor

34. 0! = ?
Principal (1 + interest/number times compounded)^(t)(n)
Immediately UNFACTOR or vice versa
1
Last two digits are multiple of 4 or the number can be divided by 2 twice.

35. Compound interest formula
1st Rule of Probability: Basic Rule is what?
Principal (1 + interest/number times compounded)^(t)(n)
83.3%
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.

36. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Immediately try factoring/simplifying when possible
Figure out the probability for each individual event. Multiply the individual probabilities together.
Sum of digits is multiple of 3 - last two digits multiple of 4.

37. In general - medium questions require how many steps to solve?
at least 3 steps
(amount of change) / (original amount)
2 steps
Figure out the probability for each individual event. Multiply the individual probabilities together.

38. Simple probability
The total amount before any deductions
180(n-2)
(n-1)!
(# of favorable outcomes) / (# of possible outcomes)

39. 2n - 2n+2 - 2n+4
14 liters
s Sq. rt (x^r)
y2 - y1 / x2 - x1
Even

40. What to do with equations that have fractions
at least 3 steps
Principal (1 + interest/number times compounded)^(t)(n)
Immediately try factoring/simplifying when possible
p/100 = is/of

41. 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
(n-1)!
Organize into a grid.
D or E

42. Combined Events: Not E = P(not E) = ?
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.
180(n-2)
1 - P(E)
12.5%

43. Formula for Mixed Group problems (involving Both/Neither)
P(event NOT occurring) = 1 - P(event occurring)
1 - P(E)
Number is a multiple of 3 and 2
Group 1 + Group 2 + Neither - Both = Total

44. Quadratic formula
-b +- sq. rt(b^2 - 4ac) / 2a
22
0.15n + 0.08(5) = 0.1(n+5)
x - x - x(sq. rt 2)

45. Trial Problems: look at the probability of NOT OCCURRING
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
P(event NOT occurring) = 1 - P(event occurring)
Purchase price
The total amount before any deductions

46. 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
1 - P(E)
The total amount before any deductions
| A union B| = |A| + |B| - |A intersect B|

47. 30-60-90 triangle basic lengths of sides
x - x - x(sq. rt 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
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
x(sq. rt 3) - x - 2x

48. Set Problems formula
x - x - x(sq. rt 2)
(x-n(n)y-n)
n! / (n - r)!
1/16

49. How to check whether a number is a multiple of 12.
1
The total amount before any deductions
Sum of digits is multiple of 3 - last two digits multiple of 4.
3 - 6 - 9 - 12

50. 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
______ |m-n|
principle (interest rate - in decimal form) (time - in years)
1.7