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. Price purchased for by wholesaler
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.
always try to factor
A = P(1 + r) ^n
Purchase price

2. Multiplication principle
D or E
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
83.3%
principle (interest rate - in decimal form) (time - in years)

3. Properties of 0
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
1
1/16
always try to factor

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
______ |m-n|
Balancing
1 - P(E)
3 - 6 - 9 - 12

5. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
sum = (average)(number of terms)
14 liters
1.7
347

6. How to check whether a number is a multiple of 6
n! / (n - r)!
Number is a multiple of 3 and 2
Organize into a grid.
Divide 4999 by 15 => 333 integers

7. Sq. rt(2)
1.4
Find simple interest then look for the answer that is a little bigger
3 - 6 - 9 - 12
p/100 = is/of

8. Volume of a sphere
(x-n(n)y-n)
Immediately UNFACTOR or vice versa
Gross Profit = Selling Price - Cost
4/3 TT r ^3

9. 1/8 = what %
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
4/3 TT r ^3
12.5%
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

10. How to find all divisors of a number
Find all prime factors
Figure out the probability for each individual event. Multiply the individual probabilities together.
p/100 = is/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

11. How do you multiply roots together.
2 steps
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
gcd(m,n)*lcm(m,n) = mn
Number is a multiple of 3 and 2

12. 30-60-90 triangle basic lengths of sides
(total distance) / (total time)
(x-n(n)y-n)
p/100 = is/of
x(sq. rt 3) - x - 2x

13. The average of consecutive numbers
22
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 3 - last two digits multiple of 4.
D or E

14. Three triangle length patterns
3-4-5 - 5-12-13 - 9-12-15
$11 - 025
347
y2 - y1 / x2 - x1

15. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
Principal (1 + interest/number times compounded)^(t)(n)
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)
gcd(m,n)*lcm(m,n) = mn

16. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
sum = (average)(number of terms)
D or E
n! / (n - r)!
market value

17. (1/4)^2
3 - 6 - 9 - 12
1/16
180(n-2)
16.6%

18. Percent Formula
The probability of event occurring is...
(total distance) / (total time)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
p/100 = is/of

19. Simple probability
Organize into a grid.
16.6%
(# of favorable outcomes) / (# of possible outcomes)
$11 - 025

20. Formula for Mixed Group problems (involving Both/Neither)
Immediately UNFACTOR or vice versa
| A union B| = |A| + |B| - |A intersect B|
Exterior angle d is equal to the sum of the two remote interior angles a and b
Group 1 + Group 2 + Neither - Both = Total

21. The number of outcomes that result in A divided by the total number of possible outcomes.
The total amount before any deductions
3 - 6 - 9 - 12
The probability of event occurring is...
y2 - y1 / x2 - x1

22. Average Rate: Average A per B
(total A) / (total B)
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 digits is multiple of 3 - last two digits multiple of 4.
Purchase price

23. Percent increase = ?
(total A) / (total B)
(amount of change) / (original amount)
sum = (average)(number of terms)
0.15n + 0.08(5) = 0.1(n+5)

24. 3^3 x 4^3 = ?
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.
If the outcome of one event affects the outcome of the other event.
at least 3 steps
12^3

25. Indistinguishable events how to find the number of permutations

26. Intersecting Sets
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.
| A union B| = |A| + |B| - |A intersect B|
3-4-5 - 5-12-13 - 9-12-15
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

27. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
Immediately try factoring/simplifying when possible
22
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
(amount of change) / (original amount)

28. Formula for area of a Trapezoid
The amount after deductions
(sum of bases)(height) / 2
12.5%
(total distance) / (total time)

29. Triangle abc with d on the outside with a line. What does d = ?
x - x - x(sq. rt 2)
16.6%
Exterior angle d is equal to the sum of the two remote interior angles a and b
3 - 6 - 9 - 12

30. Quadratic formula
1.7
The probability of an event occurring plus the probability of the event not occurring = 1
y2 - y1 / x2 - x1
-b +- sq. rt(b^2 - 4ac) / 2a

31. How to check whether number is multiple of 9
(amount of change) / (original amount)
______ |m-n|
Sum of digits is multiple of 9
Sum of digits is multiple of 3

32. Dependent events: When are two events said to be dependent events?
Group 1 + Group 2 + Neither - Both = Total
If the outcome of one event affects the outcome of the other event.
0.15n + 0.08(5) = 0.1(n+5)
n! / (n - r)!

33. Combined Events: E or F
(sum of bases)(height) / 2
P(E) + P(F) - P(E and F)
Exterior angle d is equal to the sum of the two remote interior angles a and b
at least 3 steps

34. Average Rate: Average speed
12.5%
0.15n + 0.08(5) = 0.1(n+5)
2 steps
(total distance) / (total time)

35. 45-45-90 triangle basic lengths of sides
x - x - x(sq. rt 2)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
P(event NOT occurring) = 1 - P(event occurring)
1.4

36. 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
Divide 4999 by 15 => 333 integers
Purchase price
Minor arc = 2(inscribed angle)
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.

37. 2n - 2n+2 - 2n+4
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.
Even
Immediately try factoring/simplifying when possible
principle (interest rate - in decimal form) (time - in years)

38. When you see an equation in factored form in a question?
The probability of event occurring is...
Immediately UNFACTOR or vice versa
1.7
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

39. Set Problems formula
(x-n(n)y-n)
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.
Group 1 + Group 2 + Neither - Both = Total
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.

40. 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?
(total A) / (total B)
Group 1 + Group 2 + Neither - Both = Total
0.15n + 0.08(5) = 0.1(n+5)
Sum of digits is multiple of 9

41. Compound interest formula
Principal (1 + interest/number times compounded)^(t)(n)
n! / (n - r)!
Find all prime factors
Divide 4999 by 15 => 333 integers

42. The number of ways independent events can occur together.
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
A = P(1 + r) ^n
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

43. Trial Problems: look at the probability of NOT OCCURRING
P(event NOT occurring) = 1 - P(event occurring)
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%
The total amount before any deductions

44. Multiples of 3
Last two digits are multiple of 4 or the number can be divided by 2 twice.
P(E)P(F)
3 - 6 - 9 - 12
principle (interest rate - in decimal form) (time - in years)

45. 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
Balancing
Figure out the probability for each individual event. Multiply the individual probabilities together.
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.

46. Combined Events: E and F
P(E)P(F)
D or E
If the outcome of one event affects the outcome of the other event.
347

47. 2nd Rule of Probability: P(E) = 1 - P(not E)
$11 - 025
The probability of an event occurring plus the probability of the event not occurring = 1
always try to factor
The total amount before any deductions

48. How to check whether a number is a multiple of 3.
Sum of digits is multiple of 3
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)
0.15n + 0.08(5) = 0.1(n+5)

49. Inscribed Angle - Minor Arc
4/3 TT r ^3
Minor arc = 2(inscribed angle)
principle (interest rate - in decimal form) (time - in years)
If the outcome of one event affects the outcome of the other event.

50. How to check whether a number is a multiple of 4.
x(sq. rt 3) - x - 2x
Last two digits are multiple of 4 or the number can be divided by 2 twice.
-b +- sq. rt(b^2 - 4ac) / 2a
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.