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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. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
16.6%
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.
347
| A union B| = |A| + |B| - |A intersect B|

2. gcd(m,n)
______ |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.
principle (interest rate - in decimal form) (time - in years)
12^3

3. Always try to factor
always try to factor
| A union B| = |A| + |B| - |A intersect B|
P(E) + P(F) - P(E and F)
Any multiplication involving an even number creates an even product.

4. 2n+1 - 2n+3 - 2n+5
1
Divide 4999 by 15 => 333 integers
Odd
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.

5. Sq. rt(2)
Balancing
market value
(total A) / (total B)
1.4

6. 4th rule of Probability
(total distance) / (total time)
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)
Principal (1 + interest/number times compounded)^(t)(n)
P(E)P(F)

7. Prime Factorization to find Greatest Common Factor
Purchase price
Group 1 + Group 2 + Neither - Both = Total
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)

8. Average Rate: Average speed
(total distance) / (total time)
1 - P(E)
A = P(1 + r) ^n
4/3 TT r ^3

9. Properties of 0
Group 1 + Group 2 + Neither - Both = Total
s Sq. rt (x^r)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
at least 3 steps

10. To determine multiple-event probability where each individual event must occur in a certain way.
Sum of digits is multiple of 3 - last two digits multiple of 4.
(sum of bases)(height) / 2
22
Figure out the probability for each individual event. Multiply the individual probabilities together.

11. 5/6 = what %
83.3%
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
(n-1)!
n! / (n - r)!

12. Combined Events: Not E = P(not 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.
Minor arc = 2(inscribed angle)
1 - P(E)
x(sq. rt 3) - x - 2x

13. How to check whether a number is a multiple of 3.
s Sq. rt (x^r)
Divide 4999 by 15 => 333 integers
Balancing
Sum of digits is multiple of 3

14. Combined Events: E or F
(# of favorable outcomes) / (# of possible outcomes)
2 steps
0.15n + 0.08(5) = 0.1(n+5)
P(E) + P(F) - P(E and F)

15. 2nd Rule of Probability: P(E) = 1 - P(not E)
Gross Profit = Selling Price - Cost
p/100 = is/of
The probability of an event occurring plus the probability of the event not occurring = 1
D or E

16. 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?
(x-n(n)y-n)
16.6%
P(E)P(F)
14 liters

17. Probability and Geometry.
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
4/3 TT r ^3
Group 1 + Group 2 + Neither - Both = Total
Find simple interest then look for the answer that is a little bigger

18. gcd(m,n)*lcm(m,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
If the outcome of one event affects the outcome of the other event.
market value
gcd(m,n)*lcm(m,n) = mn

19. 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
(n-1)!
Exterior angle d is equal to the sum of the two remote interior angles a and b
Sum of digits is multiple of 9

20. Trial Problems: look at the probability of NOT OCCURRING
P(event NOT occurring) = 1 - P(event occurring)
P(E) + P(F) - P(E and F)
The total amount before any deductions
The probability of event occurring is...

21. How do you multiply roots together.
gcd(m,n)*lcm(m,n) = mn
(total distance) / (total time)
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)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

22. The average of consecutive numbers
1 - P(E)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
s Sq. rt (x^r)
Group 1 + Group 2 + Neither - Both = Total

23. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
0.15n + 0.08(5) = 0.1(n+5)
3-4-5 - 5-12-13 - 9-12-15
(n-1)!
1 - P(E)

24. Work problem rule
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
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.
P(E)P(F)

25. How to check for a prime number.

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26. Intersecting Sets
1
14 liters
| A union B| = |A| + |B| - |A intersect B|
Organize into a grid.

27. How to check whether a number is a multiple of 6
3 - 6 - 9 - 12
Group 1 + Group 2 + Neither - Both = Total
Number is a multiple of 3 and 2
sum = (average)(number of terms)

28. Gross
Figure out the probability for each individual event. Multiply the individual probabilities together.
Organize into a grid.
The total amount before any deductions
1/16

29. Permutations: Order Matters
347
n! / (n - r)!
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.

30. Compound interest rule
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
$11 - 025
Find simple interest then look for the answer that is a little bigger
A = P(1 + r) ^n

31. Dependent events: When are two events said to be dependent events?
If the outcome of one event affects the outcome of the other event.
Any multiplication involving an even number creates an even product.
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.
Organize into a grid.

32. The number of outcomes that result in A divided by the total number of possible outcomes.
The probability of event occurring is...
347
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.
P(E)P(F)

33. Combined Events: E and F
Principal (1 + interest/number times compounded)^(t)(n)
P(E)P(F)
s Sq. rt (x^r)
The probability of event occurring is...

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
Balancing
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
(total distance) / (total time)
Figure out the probability for each individual event. Multiply the individual probabilities together.

35. Simple probability
(# of favorable outcomes) / (# of possible outcomes)
D or E
s Sq. rt (x^r)
(total distance) / (total time)

36. Sq. rt(3)
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
1.7
(sum of bases)(height) / 2
A = P(1 + r) ^n

37. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
Purchase price
22
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
principle (interest rate - in decimal form) (time - in years)

38. Number added or deleted
Immediately try factoring/simplifying when possible
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
(x-n(n)y-n)
D or E

39. 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.
(total A) / (total B)
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)
Organize into a grid.
Gross Profit = Selling Price - Cost

40. How to check whether a number is a multiple of 4.
Odd
-b +- sq. rt(b^2 - 4ac) / 2a
(n-1)!
Last two digits are multiple of 4 or the number can be divided by 2 twice.

41. 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?
16.6%
0.15n + 0.08(5) = 0.1(n+5)
Immediately UNFACTOR or vice versa
x - x - x(sq. rt 2)

42. Inscribed Angle - Minor Arc
If the outcome of one event affects the outcome of the other event.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Minor arc = 2(inscribed angle)
(n-1)!

43. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
n! / (n - r)!
A = P(1 + r) ^n
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
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.

44. Triangle abc with d on the outside with a line. What does d = ?
Number is a multiple of 3 and 2
Immediately UNFACTOR or vice versa
Balancing
Exterior angle d is equal to the sum of the two remote interior angles a and b

45. How to check whether a number is a multiple of 12.
s Sq. rt (x^r)
Sum of digits is multiple of 3 - last two digits multiple of 4.
gcd(m,n)*lcm(m,n) = mn
n! / (n - r)!

46. Price purchased for by wholesaler
(# of favorable outcomes) / (# of possible outcomes)
p/100 = is/of
Purchase price
If the outcome of one event affects the outcome of the other event.

47. 45-45-90 triangle basic lengths of sides
1st Rule of Probability: Basic Rule is what?
x - x - x(sq. rt 2)
at least 3 steps
Figure out the probability for each individual event. Multiply the individual probabilities together.

48. Odd and Even rule.
Any multiplication involving an even number creates an even product.
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.
Exterior angle d is equal to the sum of the two remote interior angles a and b
Sum of digits is multiple of 3 - last two digits multiple of 4.

49. How to check whether number is multiple of 9
P(E) + P(F) - P(E and F)
Sum of digits is multiple of 9
| A union B| = |A| + |B| - |A intersect B|
Principal (1 + interest/number times compounded)^(t)(n)

50. 3^3 x 4^3 = ?
Gross Profit = Selling Price - Cost
12^3
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
x(sq. rt 3) - x - 2x