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. In general - difficult questions require how many steps to solve?
at least 3 steps
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.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
347

2. (1/4)^2
Any multiplication involving an even number creates an even product.
P(E) + P(F) - P(E and F)
-b +- sq. rt(b^2 - 4ac) / 2a
1/16

3. 1/8 = what %
12.5%
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.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Group 1 + Group 2 + Neither - Both = Total

4. Triangle abc with d on the outside with a line. What does d = ?
Group 1 + Group 2 + Neither - Both = Total
1/16
Exterior angle d is equal to the sum of the two remote interior angles a and b
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

5. Multiples of 3
Last two digits are multiple of 4 or the number can be divided by 2 twice.
| A union B| = |A| + |B| - |A intersect B|
3 - 6 - 9 - 12
y2 - y1 / x2 - x1

6. How to check whether a number is a multiple of 4.
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.
(total distance) / (total time)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
The amount after deductions

7. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
2 steps
at least 3 steps
Find simple interest then look for the answer that is a little bigger

8. Percent increase = ?
1
12^3
gcd(m,n)*lcm(m,n) = mn
(amount of change) / (original amount)

9. x^r/s = ?
Odd
s Sq. rt (x^r)
Sum of digits is multiple of 3
Group 1 + Group 2 + Neither - Both = Total

10. How to check whether a number is a multiple of 3.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Gross Profit = Selling Price - Cost
Sum of digits is multiple of 3
3 - 6 - 9 - 12

11. Sum of consecutive numbers
4/3 TT r ^3
sum = (average)(number of terms)
D or E
22

12. How to check whether number is multiple of 9
Sum of digits is multiple of 9
Find all prime factors
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.
Group 1 + Group 2 + Neither - Both = Total

13. Intersecting Sets
(sum of bases)(height) / 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.
| A union B| = |A| + |B| - |A intersect B|
P(E) + P(F) - P(E and F)

14. 3rd Rule of Probability: Conditional Probability
D or E
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.
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.
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)
347
(sum of bases)(height) / 2
Immediately UNFACTOR or vice versa
principle (interest rate - in decimal form) (time - in years)

16. Combined Events: E or F
Odd
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
83.3%

17. Dependent events: When are two events said to be dependent events?
If the outcome of one event affects the outcome of the other event.
P(E)P(F)
Exterior angle d is equal to the sum of the two remote interior angles a and b
Odd numbers only have ___________

18. How to find all divisors of a number
Find all prime factors
y2 - y1 / x2 - x1
347
Immediately try factoring/simplifying when possible

19. 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
1
P(event NOT occurring) = 1 - P(event occurring)
Odd

20. Sq. rt(2)
(x-n(n)y-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
(amount of change) / (original amount)
1.4

21. Probability and Geometry.
Figure out the probability for each individual event. Multiply the individual probabilities together.
Exterior angle d is equal to the sum of the two remote interior angles a and b
Find simple interest then look for the answer that is a little bigger
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

22. Price sold for by retailer (after markup)
market value
12.5%
14 liters
x - x - x(sq. rt 2)

23. Three triangle length patterns
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)
22
3-4-5 - 5-12-13 - 9-12-15
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

24. Volume of a sphere
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
Organize into a grid.
Sum of digits is multiple of 9
4/3 TT r ^3

25. 2n - 2n+2 - 2n+4
Even
22
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.
n! / (n - r)!

26. 2nd Rule of Probability: P(E) = 1 - P(not E)
D or E
Divide 4999 by 15 => 333 integers
The probability of an event occurring plus the probability of the event not occurring = 1
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

27. Sq. rt(3)
83.3%
Principal (1 + interest/number times compounded)^(t)(n)
1.7
347

28. To determine multiple-event probability where each individual event must occur in a certain way.
Exterior angle d is equal to the sum of the two remote interior angles a and b
Figure out the probability for each individual event. Multiply the individual probabilities together.
12.5%
Immediately try factoring/simplifying when possible

29. 45-45-90 triangle basic lengths of sides
x - x - x(sq. rt 2)
market value
Find all prime factors
14 liters

30. Compound interest rule
Number is a multiple of 3 and 2
Find simple interest then look for the answer that is a little bigger
Sum of digits is multiple of 9
16.6%

31. The number of outcomes that result in A divided by the total number of possible outcomes.
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
Odd
Minor arc = 2(inscribed angle)
The probability of event occurring is...

32. Gross Profit formula
Even
Gross Profit = Selling Price - Cost
x - x - x(sq. rt 2)
1.4

33. gcd(m,n)*lcm(m,n)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
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.
gcd(m,n)*lcm(m,n) = mn
3 - 6 - 9 - 12

34. How to check whether a number is a multiple of 12.
Sum of digits is multiple of 3 - last two digits multiple of 4.
(amount of change) / (original amount)
83.3%
Number is a multiple of 3 and 2

35. What does the Sum of the angles in a Regular Polygon formula look like?
Organize into a grid.
2 steps
180(n-2)
| A union B| = |A| + |B| - |A intersect B|

36. gcd(m,n)
______ |m-n|
Immediately UNFACTOR or vice versa
180(n-2)
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

37. Multiplication principle
0.15n + 0.08(5) = 0.1(n+5)
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.
sum = (average)(number of terms)

38. Average Rate: Average A per B
at least 3 steps
4/3 TT r ^3
| A union B| = |A| + |B| - |A intersect B|
(total A) / (total B)

39. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
Immediately UNFACTOR or vice versa
16.6%
$11 - 025
-b +- sq. rt(b^2 - 4ac) / 2a

40. 5/6 = what %
(sum of bases)(height) / 2
3-4-5 - 5-12-13 - 9-12-15
12^3
83.3%

41. 4th rule of Probability
s Sq. rt (x^r)
Odd numbers only have ___________
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)
Any multiplication involving an even number creates an even product.

42. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
22
(# of favorable outcomes) / (# of possible outcomes)
Minor arc = 2(inscribed angle)
market value

43. Percent Formula
3 - 6 - 9 - 12
p/100 = is/of
Purchase price
at least 3 steps

44. Trial Problems: look at the probability of NOT OCCURRING
P(event NOT occurring) = 1 - P(event occurring)
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
180(n-2)

45. The average of consecutive numbers
22
1
1/16
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

46. 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?
2 steps
0.15n + 0.08(5) = 0.1(n+5)
1 - P(E)

47. 1/6 = what %
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
22
16.6%
P(event NOT occurring) = 1 - P(event occurring)

48. The number of ways independent events can occur together.
Sum of digits is multiple of 3
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.
always try to factor

49. 0! = ?
1
x(sq. rt 3) - x - 2x
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.
Odd numbers only have ___________

50. To determine the number of integers less than 5000 that are evenly divisible by 15...?
principle (interest rate - in decimal form) (time - in years)
at least 3 steps
Divide 4999 by 15 => 333 integers
3-4-5 - 5-12-13 - 9-12-15