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. (1/4)^2
1/16
Find simple interest then look for the answer that is a little bigger
(sum of bases)(height) / 2
______ |m-n|

2. 2n+1 - 2n+3 - 2n+5
Odd
12.5%
(total A) / (total B)
Gross Profit = Selling Price - Cost

3. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
Sum of digits is multiple of 3
22
y2 - y1 / x2 - x1
Sum of digits is multiple of 3 - last two digits multiple of 4.

4. gcd(m,n)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
n! / (n - r)!
83.3%
______ |m-n|

5. How to check whether a number is a multiple of 4.
always try to factor
4/3 TT r ^3
1.7
Last two digits are multiple of 4 or the number can be divided by 2 twice.

6. The number of ways independent events can occur together.
gcd(m,n)*lcm(m,n) = mn
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
D or E
P(E)P(F)

7. To determine multiple-event probability where each individual event must occur in a certain way.
Number is a multiple of 3 and 2
Figure out the probability for each individual event. Multiply the individual probabilities together.
P(E)P(F)
Immediately UNFACTOR or vice versa

8. What to do with equations that have fractions
(x-n(n)y-n)
The probability of an event occurring plus the probability of the event not occurring = 1
Immediately try factoring/simplifying when possible
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

9. 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?
s Sq. rt (x^r)
2 steps
14 liters
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

10. Number added or deleted
Sum of digits is multiple of 3 - last two digits multiple of 4.
(# of favorable outcomes) / (# of possible outcomes)
If the outcome of one event affects the outcome of the other event.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

11. 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)
p/100 = is/of
(total A) / (total B)
The probability of an event occurring plus the probability of the event not occurring = 1

12. Average Rate: Average speed
Group 1 + Group 2 + Neither - Both = Total
4/3 TT r ^3
(total distance) / (total time)
p/100 = is/of

13. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
347
P(E) + P(F) - P(E and F)
22
Even

14. Inscribed Angle - Minor Arc
Minor arc = 2(inscribed angle)
always try to factor
Figure out the probability for each individual event. Multiply the individual probabilities together.
P(E) + P(F) - P(E and F)

15. Sum of consecutive numbers
P(E)P(F)
2 steps
sum = (average)(number of terms)
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.

16. When you see an equation in factored form in a question?
(# of favorable outcomes) / (# of possible outcomes)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
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.
Immediately UNFACTOR or vice versa

17. 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.
The probability of an event occurring plus the probability of the event not occurring = 1
(# of favorable outcomes) / (# of possible outcomes)
Even
Organize into a grid.

18. How to check for a prime number.

19. How to check whether a number is a multiple of 3.
14 liters
Sum of digits is multiple of 3
principle (interest rate - in decimal form) (time - in years)
Principal (1 + interest/number times compounded)^(t)(n)

20. Price sold for by retailer (after markup)
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.
Any multiplication involving an even number creates an even product.
P(E) + P(F) - P(E and F)
market value

21. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
$11 - 025
principle (interest rate - in decimal form) (time - in years)
always try to factor
347

22. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
Immediately UNFACTOR or vice versa
(n-1)!
Immediately try factoring/simplifying when possible
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

23. Compound interest rule
4/3 TT r ^3
Immediately UNFACTOR or vice versa
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

24. Quadratic formula
-b +- sq. rt(b^2 - 4ac) / 2a
$11 - 025
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.

25. Properties of 0
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Exterior angle d is equal to the sum of the two remote interior angles a and b
Even
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

26. Sq. rt(3)
1.7
Organize into a grid.
(n-1)!
(total A) / (total B)

27. What does the Sum of the angles in a Regular Polygon formula look like?
180(n-2)
market value
s Sq. rt (x^r)
Immediately UNFACTOR or vice versa

28. Intersecting Sets
| A union B| = |A| + |B| - |A intersect 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
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.
(# of favorable outcomes) / (# of possible outcomes)

29. Percent Formula
Balancing
p/100 = is/of
16.6%
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

30. Set Problems formula
Any multiplication involving an even number creates an even product.
(x-n(n)y-n)
P(E) + P(F) - P(E and F)
1st Rule of Probability: Basic Rule is what?

31. The average of consecutive numbers
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Purchase price
Organize into a grid.
always try to factor

32. 45-45-90 triangle basic lengths of sides
The amount after deductions
x - x - x(sq. rt 2)
1.4
Odd numbers only have ___________

33. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
$11 - 025
at least 3 steps
The probability of event occurring is...
P(E)P(F)

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
______ |m-n|
(# of favorable outcomes) / (# of possible outcomes)
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
Balancing

35. Sq. rt(2)
Even
(amount of change) / (original amount)
2 steps
1.4

36. Odd Factors
Odd numbers only have ___________
(total distance) / (total time)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
4/3 TT r ^3

37. 3^3 x 4^3 = ?
Immediately try factoring/simplifying when possible
p/100 = is/of
12^3
16.6%

38. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
market value
The total amount before any deductions
Exterior angle d is equal to the sum of the two remote interior angles a and b
D or E

39. Volume of a sphere
(n-1)!
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.
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.
4/3 TT r ^3

40. Indistinguishable events how to find the number of permutations

41. Permutations: Order Matters
16.6%
n! / (n - r)!
always try to factor
Sum of digits is multiple of 3

42. In general - difficult questions require how many steps to solve?
Minor arc = 2(inscribed angle)
at least 3 steps
The probability of event occurring is...
Sum of digits is multiple of 3

43. Multiples of 3
3-4-5 - 5-12-13 - 9-12-15
22
3 - 6 - 9 - 12
1.7

44. 2nd Rule of Probability: P(E) = 1 - P(not E)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
| A union B| = |A| + |B| - |A intersect B|
12.5%
The probability of an event occurring plus the probability of the event not occurring = 1

45. How do you multiply roots together.
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
market value
Principal (1 + interest/number times compounded)^(t)(n)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

46. Three triangle length patterns
x(sq. rt 3) - x - 2x
3-4-5 - 5-12-13 - 9-12-15
The total amount before any deductions
Number is a multiple of 3 and 2

47. Always try to factor
(n-1)!
12^3
Even
always try to factor

48. 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?
Find all prime factors
Minor arc = 2(inscribed angle)
Even

49. 3rd Rule of Probability: Conditional Probability
Group 1 + Group 2 + Neither - Both = Total
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
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

50. 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
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.
2 steps
$11 - 025
180(n-2)