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. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
The probability of an event occurring plus the probability of the event not occurring = 1
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.
market value
22

2. Properties of 0
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
1 - P(E)
s Sq. rt (x^r)

3. Simple 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)
Find simple interest then look for the answer that is a little bigger
(# of favorable outcomes) / (# of possible outcomes)
The total amount before any deductions

4. The number of outcomes that result in A divided by the total number of possible outcomes.
The probability of event occurring is...
347
sum = (average)(number of terms)
16.6%

5. x^r/s = ?
The total amount before any deductions
(n-1)!
s Sq. rt (x^r)
-b +- sq. rt(b^2 - 4ac) / 2a

6. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
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.
347
y2 - y1 / x2 - x1
Gross Profit = Selling Price - Cost

7. Compound interest formula
Organize into a grid.
Find simple interest then look for the answer that is a little bigger
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Principal (1 + interest/number times compounded)^(t)(n)

8. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
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 an event occurring plus the probability of the event not occurring = 1
x - x - x(sq. rt 2)
principle (interest rate - in decimal form) (time - in years)

9. How to find all divisors of a number
-b +- sq. rt(b^2 - 4ac) / 2a
(total A) / (total B)
n! / (n - r)!
Find all prime factors

10. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
180(n-2)
Any multiplication involving an even number creates an even product.
$11 - 025
p/100 = is/of

11. Combined Events: E and F
P(E)P(F)
Divide 4999 by 15 => 333 integers
The total amount before any deductions
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. Sq. rt(2)
1st Rule of Probability: Basic Rule is what?
Immediately try factoring/simplifying when possible
12.5%
1.4

13. What does the Sum of the angles in a Regular Polygon formula look like?
(sum of bases)(height) / 2
180(n-2)
1 - P(E)
22

14. Combined Events: E or F
P(E) + P(F) - P(E and F)
(total A) / (total B)
y2 - y1 / x2 - x1
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

15. Triangle abc with d on the outside with a line. What does d = ?
Sum of digits is multiple of 3 - last two digits multiple of 4.
(# of favorable outcomes) / (# of possible outcomes)
Exterior angle d is equal to the sum of the two remote interior angles a and b
The amount after deductions

16. Three triangle length patterns
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Purchase price
Any multiplication involving an even number creates an even product.
3-4-5 - 5-12-13 - 9-12-15

17. Compound interest rule
Find simple interest then look for the answer that is a little bigger
(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.
$11 - 025

18. gcd(m,n)*lcm(m,n)
Sum of digits is multiple of 3 - last two digits multiple of 4.
gcd(m,n)*lcm(m,n) = mn
(amount of change) / (original amount)
Organize into a grid.

19. Multiplication principle
1 - P(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
p/100 = is/of
D or E

20. 5/6 = what %
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.
market value
83.3%
(total distance) / (total time)

21. 2nd Rule of Probability: P(E) = 1 - P(not E)
(amount of change) / (original amount)
1/16
The probability of an event occurring plus the probability of the event not occurring = 1
at least 3 steps

22. Average Rate: Average speed
Divide 4999 by 15 => 333 integers
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)
Immediately UNFACTOR or vice versa

23. 45-45-90 triangle basic lengths of sides
3-4-5 - 5-12-13 - 9-12-15
4/3 TT r ^3
D or E
x - x - x(sq. rt 2)

24. Formula for area of a Trapezoid
12^3
347
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
(sum of bases)(height) / 2

25. Work problem rule
y2 - y1 / x2 - x1
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.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
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. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
D or E
y2 - y1 / x2 - x1
(total A) / (total B)
A = P(1 + r) ^n

27. Set Problems formula
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
180(n-2)
(x-n(n)y-n)
Divide 4999 by 15 => 333 integers

28. 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?
3 - 6 - 9 - 12
22
y2 - y1 / x2 - x1
0.15n + 0.08(5) = 0.1(n+5)

29. How to check whether number is multiple of 9
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
347
always try to factor
Sum of digits is multiple of 9

30. 3rd Rule of Probability: Conditional Probability
83.3%
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.
347
The probability of event occurring is...

31. The number of ways independent events can occur together.
1.4
y2 - y1 / x2 - x1
1 - P(E)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

32. How to check whether a number is a multiple of 6
Number is a multiple of 3 and 2
market value
| A union B| = |A| + |B| - |A intersect B|
4/3 TT r ^3

33. Net
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.
-b +- sq. rt(b^2 - 4ac) / 2a
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.
The amount after deductions

34. 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)
16.6%
Sum of digits is multiple of 3 - last two digits multiple of 4.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

35. 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
x - x - x(sq. rt 2)
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.
(sum of bases)(height) / 2
Find simple interest then look for the answer that is a little bigger

36. In general - medium questions require how many steps to solve?
2 steps
The total amount before any deductions
347
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.

37. Average Rate: Average A per B
$11 - 025
(total A) / (total B)
-b +- sq. rt(b^2 - 4ac) / 2a
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

38. Price purchased for by wholesaler
Figure out the probability for each individual event. Multiply the individual probabilities together.
(x-n(n)y-n)
Purchase price
p/100 = is/of

39. Multiples of 3
3 - 6 - 9 - 12
83.3%
at least 3 steps
x(sq. rt 3) - x - 2x

40. 3^3 x 4^3 = ?
1
-b +- sq. rt(b^2 - 4ac) / 2a
12^3
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.

41. gcd(m,n)
If the outcome of one event affects the outcome of the other event.
Purchase price
______ |m-n|
1

42. (1/4)^2
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
1st Rule of Probability: Basic Rule is what?
always try to factor
1/16

43. Intersecting Sets
| A union B| = |A| + |B| - |A intersect B|
Balancing
sum = (average)(number of terms)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

44. Dependent events: When are two events said to be dependent events?
at least 3 steps
always try to factor
If the outcome of one event affects the outcome of the other event.
Find simple interest then look for the answer that is a little bigger

45. Gross Profit formula
1st Rule of Probability: Basic Rule is what?
Sum of digits is multiple of 3 - last two digits multiple of 4.
1.7
Gross Profit = Selling Price - Cost

46. Volume of a sphere
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
4/3 TT r ^3
(x-n(n)y-n)
y2 - y1 / x2 - x1

47. 1/8 = what %
1.4
Sum of digits is multiple of 3
12.5%
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

48. How do you multiply roots together.
180(n-2)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
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.
A = P(1 + r) ^n

49. 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
1st Rule of Probability: Basic Rule is what?
Balancing
Number is a multiple of 3 and 2
Sum of digits is multiple of 9

50. Trial Problems: look at the probability of NOT OCCURRING
Immediately try factoring/simplifying when possible
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
347
P(event NOT occurring) = 1 - P(event occurring)