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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. Trial Problems: look at the probability of NOT OCCURRING
Purchase price
180(n-2)
1.7
P(event NOT occurring) = 1 - P(event occurring)

2. Inscribed Angle - Minor Arc
$11 - 025
Find all prime factors
P(event NOT occurring) = 1 - P(event occurring)
Minor arc = 2(inscribed angle)

3. 1/8 = what %
always try to factor
83.3%
4/3 TT r ^3
12.5%

4. Always try to factor
Gross Profit = Selling Price - Cost
1
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
always try to factor

5. Gross Profit formula
Exterior angle d is equal to the sum of the two remote interior angles a and b
Immediately UNFACTOR or vice versa
Gross Profit = Selling Price - Cost
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.

6. 2nd Rule of Probability: P(E) = 1 - P(not E)
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 an event occurring plus the probability of the event not occurring = 1
(# of favorable outcomes) / (# of possible outcomes)
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.

7. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
$11 - 025
P(E) + P(F) - P(E and F)
1.4
2 steps

8. gcd(m,n)
______ |m-n|
2 steps
Divide 4999 by 15 => 333 integers
Group 1 + Group 2 + Neither - Both = Total

9. 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.
Immediately try factoring/simplifying when possible
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.

10. 5/6 = what %
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
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
83.3%
A = P(1 + r) ^n

11. Three triangle length patterns
1/16
s Sq. rt (x^r)
3-4-5 - 5-12-13 - 9-12-15
Find simple interest then look for the answer that is a little bigger

12. 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
$11 - 025
Balancing
12^3
If the outcome of one event affects the outcome of the other event.

13. How to find all divisors of a 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)
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.
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.
Find all prime factors

14. Set Problems formula
The amount after deductions
(x-n(n)y-n)
Any multiplication involving an even number creates an even product.
P(E)P(F)

15. 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.
Find simple interest then look for the answer that is a little bigger
Organize into a grid.
Immediately UNFACTOR or vice versa
(n-1)!

16. How to check whether a number is a multiple of 3.
1 - P(E)
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.
3-4-5 - 5-12-13 - 9-12-15
Sum of digits is multiple of 3

17. Sq. rt(2)
83.3%
22
(n-1)!
1.4

18. How to check for a prime number.

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19. 1/6 = what %
market value
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
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)
16.6%

20. (1/4)^2
1/16
principle (interest rate - in decimal form) (time - in years)
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 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)

21. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
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.
Divide 4999 by 15 => 333 integers
principle (interest rate - in decimal form) (time - in years)
22

22. Prime Factorization to find Greatest Common Factor
Group 1 + Group 2 + Neither - Both = Total
16.6%
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
| A union B| = |A| + |B| - |A intersect B|

23. 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?
Gross Profit = Selling Price - Cost
1
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

24. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Minor arc = 2(inscribed angle)
347
(n-1)!

25. Multiplication principle
22
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
P(event NOT occurring) = 1 - P(event occurring)
(n-1)!

26. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
at least 3 steps
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
A = P(1 + r) ^n
p/100 = is/of

27. Net
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
s Sq. rt (x^r)
The amount after deductions
1 - P(E)

28. Average Rate: Average A per B
P(event NOT occurring) = 1 - P(event occurring)
12^3
16.6%
(total A) / (total B)

29. 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)
Number is a multiple of 3 and 2
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
gcd(m,n)*lcm(m,n) = mn

30. 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?
180(n-2)
2 steps
14 liters
0.15n + 0.08(5) = 0.1(n+5)

31. Formula for area of a Trapezoid
(sum of bases)(height) / 2
Gross Profit = Selling Price - Cost
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
D or E

32. Compound interest rule
Find simple interest then look for the answer that is a little bigger
Figure out the probability for each individual event. Multiply the individual probabilities together.
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.
s Sq. rt (x^r)

33. When you see an equation in factored form in a question?
1.4
P(E)P(F)
Immediately UNFACTOR or vice versa
-b +- sq. rt(b^2 - 4ac) / 2a

34. Sq. rt(3)
(# of favorable outcomes) / (# of possible outcomes)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
1.7
Principal (1 + interest/number times compounded)^(t)(n)

35. How to check whether a number is a multiple of 12.
Sum of digits is multiple of 3 - last two digits multiple of 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.
12^3
1/16

36. Combined Events: Not E = P(not E) = ?
Organize into a grid.
12^3
sum = (average)(number of terms)
1 - P(E)

37. Gross
The probability of event occurring is...
sum = (average)(number of terms)
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)
The total amount before any deductions

38. How to check whether a number is a multiple of 6
sum = (average)(number of terms)
Number is a multiple of 3 and 2
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

39. What to do with equations that have fractions
The probability of event occurring is...
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
1st Rule of Probability: Basic Rule is what?

40. 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
1.4
sum = (average)(number of terms)
Gross Profit = Selling Price - Cost

41. Probability and Geometry.
180(n-2)
1.4
3-4-5 - 5-12-13 - 9-12-15
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

42. 3^3 x 4^3 = ?
Figure out the probability for each individual event. Multiply the individual probabilities together.
Even
12^3
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)

43. Triangle abc with d on the outside with a line. What does d = ?
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Any multiplication involving an even number creates an even product.
Organize into a grid.
Exterior angle d is equal to the sum of the two remote interior angles a and b

44. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
Principal (1 + interest/number times compounded)^(t)(n)
D or E
P(event NOT occurring) = 1 - P(event occurring)
1

45. 30-60-90 triangle basic lengths of sides
If the outcome of one event affects the outcome of the other event.
x(sq. rt 3) - x - 2x
2 steps
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

46. How to check whether number is multiple of 9
Figure out the probability for each individual event. Multiply the individual probabilities together.
Sum of digits is multiple of 9
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
$11 - 025

47. Permutations: Order Matters
(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.
The probability of an event occurring plus the probability of the event not occurring = 1
n! / (n - r)!

48. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
347
Group 1 + Group 2 + Neither - Both = Total
4/3 TT r ^3
83.3%

49. The number of outcomes that result in A divided by the total number of possible outcomes.
The probability of event occurring is...
12^3
P(event NOT occurring) = 1 - P(event occurring)
x - x - x(sq. rt 2)

50. The average of consecutive numbers
Immediately UNFACTOR or vice versa
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
market value
3 - 6 - 9 - 12