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. Percent increase = ?
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Organize into a grid.
(amount of change) / (original amount)
n! / (n - r)!

2. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
83.3%
22
Sum of digits is multiple of 3
market value

3. Three triangle length patterns
A = P(1 + r) ^n
If the outcome of one event affects the outcome of the other event.
3-4-5 - 5-12-13 - 9-12-15
Minor arc = 2(inscribed angle)

4. Multiplication principle
(total distance) / (total time)
Immediately try factoring/simplifying when possible
x(sq. rt 3) - x - 2x
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

5. Probability and Geometry.
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
Immediately UNFACTOR or vice versa
P(E) + P(F) - P(E and F)
Odd

6. 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?
P(E) + P(F) - P(E and F)
The probability of an event occurring plus the probability of the event not occurring = 1
principle (interest rate - in decimal form) (time - in years)
0.15n + 0.08(5) = 0.1(n+5)

7. Trial Problems: look at the probability of NOT OCCURRING
Figure out the probability for each individual event. Multiply the individual probabilities together.
p/100 = is/of
(n-1)!
P(event NOT occurring) = 1 - P(event occurring)

8. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
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.
A = P(1 + r) ^n
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
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.

9. 0! = ?
Organize into a grid.
The probability of event occurring is...
1
P(event NOT occurring) = 1 - P(event occurring)

10. Compound interest formula
If the outcome of one event affects the outcome of the other event.
Principal (1 + interest/number times compounded)^(t)(n)
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
12.5%

11. Permutations: Order Matters
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
n! / (n - r)!
The total amount before any deductions

12. How to find the slope.
Organize into a grid.
y2 - y1 / x2 - x1
0.15n + 0.08(5) = 0.1(n+5)
1

13. gcd(m,n)
83.3%
______ |m-n|
y2 - y1 / x2 - x1
1 - P(E)

14. What does the Sum of the angles in a Regular Polygon formula look like?
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
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)
-b +- sq. rt(b^2 - 4ac) / 2a
180(n-2)

15. Always try to factor
0.15n + 0.08(5) = 0.1(n+5)
gcd(m,n)*lcm(m,n) = mn
always try to factor
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

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.
| A union B| = |A| + |B| - |A intersect B|
market value
Immediately UNFACTOR or vice versa

17. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
3-4-5 - 5-12-13 - 9-12-15
(n-1)!
Divide 4999 by 15 => 333 integers
D or E

18. How do you multiply roots together.
Any multiplication involving an even number creates an even product.
The total amount before any deductions
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

19. Price purchased for by wholesaler
Gross Profit = Selling Price - Cost
Purchase price
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.
If the outcome of one event affects the outcome of the other event.

20. How to check whether a number is a multiple of 6
Find all prime factors
Number is a multiple of 3 and 2
(sum of bases)(height) / 2
(x-n(n)y-n)

21. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
Gross Profit = Selling Price - Cost
Odd numbers only have ___________
A = P(1 + r) ^n
(n-1)!

22. When you see an equation in factored form in a question?
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Immediately UNFACTOR or vice versa
A = P(1 + r) ^n
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

23. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
2 steps
0.15n + 0.08(5) = 0.1(n+5)
347
market value

24. Compound interest rule
1 - P(E)
(amount of change) / (original amount)
347
Find simple interest then look for the answer that is a little bigger

25. Odd Factors
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)
Odd numbers only have ___________
(amount of change) / (original amount)
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.

26. 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.
The probability of event occurring is...
P(event NOT occurring) = 1 - P(event occurring)
Sum of digits is multiple of 9

27. In general - difficult questions require how many steps to solve?
Divide 4999 by 15 => 333 integers
(n-1)!
Exterior angle d is equal to the sum of the two remote interior angles a and b
at least 3 steps

28. 30-60-90 triangle basic lengths of sides
y2 - y1 / x2 - x1
The total amount before any deductions
x(sq. rt 3) - x - 2x
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)

29. Combined Events: E and F
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
Find simple interest then look for the answer that is a little bigger
(n-1)!
P(E)P(F)

30. Odd and Even rule.
P(event NOT occurring) = 1 - P(event occurring)
1
Divide 4999 by 15 => 333 integers
Any multiplication involving an even number creates an even product.

31. 2nd Rule of Probability: P(E) = 1 - P(not E)
Principal (1 + interest/number times compounded)^(t)(n)
The probability of an event occurring plus the probability of the event not occurring = 1
3-4-5 - 5-12-13 - 9-12-15
Divide 4999 by 15 => 333 integers

32. 4th rule of Probability
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Sum of digits is multiple of 9
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

33. Net
D or E
Group 1 + Group 2 + Neither - Both = Total
The amount after deductions
Odd

34. 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
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Balancing
83.3%
(n-1)!

35. Price sold for by retailer (after markup)
market value
Sum of digits is multiple of 3
-b +- sq. rt(b^2 - 4ac) / 2a
| A union B| = |A| + |B| - |A intersect B|

36. To determine the number of integers less than 5000 that are evenly divisible by 15...?
1
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
1/16

37. Some GMAT word problems involve groups with distinct 'either/or' categories (male/female - blue collar/white collar - etc.) The key is to do what with the information? 1. Find total number of possible outcomes. 2. Find the number of desired outcomes.
(x-n(n)y-n)
at least 3 steps
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Organize into a grid.

38. In general - medium questions require how many steps to solve?
2 steps
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.
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.
Sum of digits is multiple of 9

39. Volume of a sphere
The total amount before any deductions
12^3
Organize into a grid.
4/3 TT r ^3

40. Sq. rt(3)
1.4
1.7
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)
3-4-5 - 5-12-13 - 9-12-15

41. Combined Events: E or F
gcd(m,n)*lcm(m,n) = mn
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
P(E) + P(F) - P(E and F)
(n-1)!

42. x^r/s = ?
s Sq. rt (x^r)
Sum of digits is multiple of 9
sum = (average)(number of terms)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

43. Simple probability
(# of favorable outcomes) / (# of possible outcomes)
Sum of digits is multiple of 9
Organize into a grid.
Gross Profit = Selling Price - Cost

44. Properties of 0
Minor arc = 2(inscribed angle)
1
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 integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

45. (1/4)^2
1/16
always try to factor
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Minor arc = 2(inscribed angle)

46. Percent Formula
Sum of digits is multiple of 3 - last two digits multiple of 4.
p/100 = is/of
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
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

47. Quadratic formula
-b +- sq. rt(b^2 - 4ac) / 2a
P(E)P(F)
Find simple interest then look for the answer that is a little bigger
| A union B| = |A| + |B| - |A intersect B|

48. Sum of consecutive numbers
sum = (average)(number of terms)
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.
12.5%
Principal (1 + interest/number times compounded)^(t)(n)

49. Work problem rule
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.
Find simple interest then look for the answer that is a little bigger
(x-n(n)y-n)
Even

50. 45-45-90 triangle basic lengths of sides
(n-1)!
x - x - x(sq. rt 2)
14 liters
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.