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. 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
A = P(1 + r) ^n
Immediately try factoring/simplifying when possible
Minor arc = 2(inscribed angle)
Balancing

2. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
Last two digits are multiple of 4 or the number can be divided by 2 twice.
(n-1)!
347
P(E) + P(F) - P(E and F)

3. Sq. rt(3)
12^3
Find simple interest then look for the answer that is a little bigger
22
1.7

4. Percent increase = ?
Minor arc = 2(inscribed angle)
Immediately UNFACTOR or vice versa
market value
(amount of change) / (original amount)

5. Triangle abc with d on the outside with a line. What does d = ?
Group 1 + Group 2 + Neither - Both = Total
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.
12.5%
Exterior angle d is equal to the sum of the two remote interior angles a and b

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?
3-4-5 - 5-12-13 - 9-12-15
A = P(1 + r) ^n
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
0.15n + 0.08(5) = 0.1(n+5)

7. Volume of a sphere
Group 1 + Group 2 + Neither - Both = Total
12.5%
3 - 6 - 9 - 12
4/3 TT r ^3

8. gcd(m,n)
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.
12.5%
______ |m-n|
Odd numbers only have ___________

9. Price sold for by retailer (after markup)
market value
Sum of digits is multiple of 3
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)
A = P(1 + r) ^n

10. 1/8 = what %
12.5%
1.7
Principal (1 + interest/number times compounded)^(t)(n)
n! / (n - r)!

11. 2nd Rule of Probability: P(E) = 1 - P(not E)
The probability of an event occurring plus the probability of the event not occurring = 1
16.6%
Even
1 - P(E)

12. Formula for area of a Trapezoid
always try to factor
Minor arc = 2(inscribed angle)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
(sum of bases)(height) / 2

13. Probability and Geometry.
(total distance) / (total time)
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
Any multiplication involving an even number creates an even product.
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)

14. How to check whether a number is a multiple of 6
Number is a multiple of 3 and 2
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Exterior angle d is equal to the sum of the two remote interior angles a and b
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.

15. Number added or deleted
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
(sum of bases)(height) / 2
always try to factor
| A union B| = |A| + |B| - |A intersect B|

16. Permutations: Order Matters
n! / (n - r)!
The probability of event occurring is...
The amount after deductions
347

17. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
Divide 4999 by 15 => 333 integers
2 steps
A = P(1 + r) ^n
y2 - y1 / x2 - x1

18. 4th rule of Probability
A = P(1 + r) ^n
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)
at least 3 steps
(# of favorable outcomes) / (# of possible outcomes)

19. Indistinguishable events how to find the number of permutations

20. Work problem rule
at least 3 steps
D or E
3-4-5 - 5-12-13 - 9-12-15
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.

21. Intersecting Sets
Gross Profit = Selling Price - Cost
| A union B| = |A| + |B| - |A intersect B|
(n-1)!
Figure out the probability for each individual event. Multiply the individual probabilities together.

22. Properties of 0
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
1.4
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)
Figure out the probability for each individual event. Multiply the individual probabilities together.

23. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
1.7
(n-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.
D or E

24. How to check whether number is multiple of 9
y2 - y1 / x2 - x1
x(sq. rt 3) - x - 2x
s Sq. rt (x^r)
Sum of digits is multiple of 9

25. How to find the slope.
sum = (average)(number of terms)
always try to factor
(amount of change) / (original amount)
y2 - y1 / x2 - x1

26. Net
(total A) / (total B)
Minor arc = 2(inscribed angle)
1.7
The amount after deductions

27. (1/4)^2
Purchase price
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.
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

28. Gross Profit formula
Balancing
Sum of digits is multiple of 3
market value
Gross Profit = Selling Price - Cost

29. When you see an equation in factored form in a question?
The amount after deductions
Immediately UNFACTOR or vice versa
83.3%
Sum of digits is multiple of 3 - last two digits multiple of 4.

30. Compound interest rule
Find simple interest then look for the answer that is a little bigger
14 liters
Odd numbers only have ___________
______ |m-n|

31. Odd 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.
4/3 TT r ^3
Odd numbers only have ___________
Purchase price

32. 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?
| A union B| = |A| + |B| - |A intersect B|
14 liters
p/100 = is/of
Exterior angle d is equal to the sum of the two remote interior angles a and b

33. 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.
(x-n(n)y-n)
22
1st Rule of Probability: Basic Rule is what?
Find all prime factors

34. How to check whether a number is a multiple of 4.
s Sq. rt (x^r)
The total amount before any deductions
P(E)P(F)
Last two digits are multiple of 4 or the number can be divided by 2 twice.

35. Odd and Even rule.
Any multiplication involving an even number creates an even product.
1.4
16.6%
Even

36. The number of outcomes that result in A divided by the total number of possible outcomes.
The probability of event occurring is...
Sum of digits is multiple of 3 - last two digits multiple of 4.
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.
Balancing

37. Combined Events: E or F
Organize into a grid.
P(E) + P(F) - P(E and F)
at least 3 steps
Number is a multiple of 3 and 2

38. Multiples of 3
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
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
1st Rule of Probability: Basic Rule is what?
3 - 6 - 9 - 12

39. Always try to factor
always try to factor
at least 3 steps
Last two digits are multiple of 4 or the number can be divided by 2 twice.
16.6%

40. Inscribed Angle - Minor Arc
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
180(n-2)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Minor arc = 2(inscribed angle)

41. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
1.7
12.5%
22
The probability of an event occurring plus the probability of the event not occurring = 1

42. 3^3 x 4^3 = ?
P(E)P(F)
Purchase price
12^3
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

43. To determine multiple-event probability where each individual event must occur in a certain way.
Immediately try factoring/simplifying when possible
s Sq. rt (x^r)
P(event NOT occurring) = 1 - P(event occurring)
Figure out the probability for each individual event. Multiply the individual probabilities together.

44. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
Immediately UNFACTOR or vice versa
(n-1)!
p/100 = is/of
P(E)P(F)

45. Combined Events: E and F
P(E)P(F)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
x - x - x(sq. rt 2)
1st Rule of Probability: Basic Rule is what?

46. Multiplication principle
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
Exterior angle d is equal to the sum of the two remote interior angles a and b
Find all prime factors
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

47. Sq. rt(2)
(# of favorable outcomes) / (# of possible outcomes)
1/16
1.4
-b +- sq. rt(b^2 - 4ac) / 2a

48. 5/6 = what %
x(sq. rt 3) - x - 2x
83.3%
1.7
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.

49. 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
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
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)
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.

50. 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.
Minor arc = 2(inscribed angle)
n! / (n - r)!
Organize into a grid.
1st Rule of Probability: Basic Rule is what?