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. Sq. rt(3)
14 liters
1.7
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
p/100 = is/of

2. Gross
3-4-5 - 5-12-13 - 9-12-15
The total amount before any deductions
Sum of digits is multiple of 3
Odd numbers only have ___________

3. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
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.
D or E
(sum of bases)(height) / 2
Find all prime factors

4. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
The probability of event occurring is...
(n-1)!
P(event NOT occurring) = 1 - P(event occurring)
p/100 = is/of

5. 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.
P(event NOT occurring) = 1 - P(event occurring)
______ |m-n|
Minor arc = 2(inscribed angle)
Organize into a grid.

6. 4th rule of Probability
always try to factor
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)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
s Sq. rt (x^r)

7. Combined Events: E or F
Immediately UNFACTOR or vice versa
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.
(total A) / (total B)
P(E) + P(F) - P(E and F)

8. When you see an equation in factored form in a question?
Immediately UNFACTOR or vice versa
Number is a multiple of 3 and 2
If the outcome of one event affects the outcome of the other event.
12^3

9. Volume of a sphere
P(event NOT occurring) = 1 - P(event occurring)
4/3 TT r ^3
x(sq. rt 3) - x - 2x
(amount of change) / (original amount)

10. x^r/s = ?
P(E) + P(F) - P(E and F)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
s Sq. rt (x^r)
y2 - y1 / x2 - x1

11. Number added or deleted
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Even
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.

12. Formula for Mixed Group problems (involving Both/Neither)
12.5%
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
always try to factor
Group 1 + Group 2 + Neither - Both = Total

13. Gross Profit formula
Even
y2 - y1 / x2 - x1
Balancing
Gross Profit = Selling Price - Cost

14. (1/4)^2
Number is a multiple of 3 and 2
Balancing
Organize into a grid.
1/16

15. What to do with equations that have fractions
22
Immediately try factoring/simplifying when possible
Balancing
Number is a multiple of 3 and 2

16. 45-45-90 triangle basic lengths of sides
x - x - x(sq. rt 2)
Principal (1 + interest/number times compounded)^(t)(n)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
P(event NOT occurring) = 1 - P(event occurring)

17. Permutations: Order Matters
gcd(m,n)*lcm(m,n) = mn
n! / (n - r)!
4/3 TT r ^3
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

18. Combined Events: Not E = P(not E) = ?
always try to factor
1 - P(E)
347
P(event NOT occurring) = 1 - P(event occurring)

19. Three triangle length patterns
3-4-5 - 5-12-13 - 9-12-15
Immediately try factoring/simplifying when possible
(sum of bases)(height) / 2
180(n-2)

20. 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
0.15n + 0.08(5) = 0.1(n+5)
If the outcome of one event affects the outcome of the other event.
p/100 = is/of

21. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
3 - 6 - 9 - 12
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
347
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

22. Compound interest rule
(n-1)!
Sum of digits is multiple of 9
Number is a multiple of 3 and 2
Find simple interest then look for the answer that is a little bigger

23. 1/6 = what %
Number is a multiple of 3 and 2
2 steps
16.6%
1.7

24. 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?
0.15n + 0.08(5) = 0.1(n+5)
(x-n(n)y-n)
1.4
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.

25. Quadratic formula
-b +- sq. rt(b^2 - 4ac) / 2a
1.4
(sum of bases)(height) / 2
(total distance) / (total time)

26. The number of outcomes that result in A divided by the total number of possible outcomes.
The probability of event occurring is...
x(sq. rt 3) - x - 2x
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.
180(n-2)

27. 3rd Rule of Probability: Conditional Probability
sum = (average)(number of terms)
$11 - 025
principle (interest rate - in decimal form) (time - in years)
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. 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.
12^3
P(E) + P(F) - P(E and F)
22

29. How to check whether number is multiple of 9
s Sq. rt (x^r)
Sum of digits is multiple of 9
Purchase price
Odd numbers only have ___________

30. 2n - 2n+2 - 2n+4
Even
1.4
(n-1)!
Find simple interest then look for the answer that is a little bigger

31. How to check whether a number is a multiple of 3.
180(n-2)
1.4
Sum of digits is multiple of 3
1/16

32. 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.
1st Rule of Probability: Basic Rule is what?
The amount after deductions
Odd
______ |m-n|

33. 2n+1 - 2n+3 - 2n+5
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.
s Sq. rt (x^r)
3-4-5 - 5-12-13 - 9-12-15
Odd

34. In general - difficult questions require how many steps to solve?
Last two digits are multiple of 4 or the number can be divided by 2 twice.
at least 3 steps
Odd numbers only have ___________
always try to factor

35. 2nd Rule of Probability: P(E) = 1 - P(not E)
2 steps
always try to factor
The probability of an event occurring plus the probability of the event not occurring = 1
Exterior angle d is equal to the sum of the two remote interior angles a and b

36. Formula for area of a Trapezoid
-b +- sq. rt(b^2 - 4ac) / 2a
1
(sum of bases)(height) / 2
D or E

37. Properties of 0
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
180(n-2)
$11 - 025
Odd

38. How to find all divisors of a number
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Find all prime factors
3-4-5 - 5-12-13 - 9-12-15
(n-1)!

39. 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
(x-n(n)y-n)
3-4-5 - 5-12-13 - 9-12-15
Balancing
12.5%

40. Always try to factor
Exterior angle d is equal to the sum of the two remote interior angles a and b
Organize into a grid.
always try to factor
p/100 = is/of

41. Net
14 liters
1st Rule of Probability: Basic Rule is what?
The amount after deductions
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

42. Set Problems formula
1/16
1.4
Gross Profit = Selling Price - Cost
(x-n(n)y-n)

43. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
$11 - 025
x - x - x(sq. rt 2)
Find simple interest then look for the answer that is a little bigger
4/3 TT r ^3

44. Odd and Even rule.
14 liters
Any multiplication involving an even number creates an even product.
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

45. In general - medium questions require how many steps to solve?
The probability of event occurring is...
2 steps
If the outcome of one event affects the outcome of the other event.
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

46. Sq. rt(2)
347
1.4
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

47. Price sold for by retailer (after markup)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
market value
always try to factor
Gross Profit = Selling Price - Cost

48. How do you multiply roots together.
Sum of digits is multiple of 9
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
Immediately UNFACTOR or vice versa
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

49. How to find the slope.
y2 - y1 / x2 - x1
347
P(event NOT occurring) = 1 - P(event occurring)
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.

50. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
Exterior angle d is equal to the sum of the two remote interior angles a and b
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
3 - 6 - 9 - 12
principle (interest rate - in decimal form) (time - in years)