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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. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
1 - P(E)
$11 - 025
Last two digits are multiple of 4 or the number can be divided by 2 twice.
(sum of bases)(height) / 2

2. Properties of 0
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
sum = (average)(number of terms)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

3. Intersecting Sets
4/3 TT r ^3
| A union B| = |A| + |B| - |A intersect B|
Sum of digits is multiple of 9
gcd(m,n)*lcm(m,n) = mn

4. Inscribed Angle - Minor Arc
(sum of bases)(height) / 2
p/100 = is/of
Minor arc = 2(inscribed angle)
180(n-2)

5. Formula for Mixed Group problems (involving Both/Neither)
Odd
Group 1 + Group 2 + Neither - Both = Total
Odd numbers only have ___________
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

6. 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)
1.7
1
A = P(1 + r) ^n

7. Work problem rule
P(E) + P(F) - P(E and F)
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.
Find simple interest then look for the answer that is a little bigger
gcd(m,n)*lcm(m,n) = mn

8. How to find the slope.
347
1.7
y2 - y1 / x2 - x1
P(event NOT occurring) = 1 - P(event occurring)

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.
16.6%
______ |m-n|
A = P(1 + r) ^n

10. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
A = P(1 + r) ^n
22
Immediately try factoring/simplifying when possible

11. 2n - 2n+2 - 2n+4
(x-n(n)y-n)
s Sq. rt (x^r)
D or E
Even

12. The number of ways independent events can occur together.
n! / (n - r)!
Exterior angle d is equal to the sum of the two remote interior angles a and b
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

13. How do you multiply roots together.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Sum of digits is multiple of 3
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
12^3

14. Probability and Geometry.
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 total amount before any deductions
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
P(E) + P(F) - P(E and F)

15. 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?
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)
y2 - y1 / x2 - x1
0.15n + 0.08(5) = 0.1(n+5)

16. In general - medium questions require how many steps to solve?
Exterior angle d is equal to the sum of the two remote interior angles a and b
2 steps
(# of favorable outcomes) / (# of possible outcomes)
1

17. 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
3 - 6 - 9 - 12
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
1.4

18. (1/4)^2
1/16
1st Rule of Probability: Basic Rule is what?
Odd numbers only have ___________
Last two digits are multiple of 4 or the number can be divided by 2 twice.

19. Multiples of 3
3 - 6 - 9 - 12
(total distance) / (total time)
$11 - 025
A = P(1 + r) ^n

20. 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.
y2 - y1 / x2 - x1
83.3%
16.6%
Organize into a grid.

21. 1/6 = what %
1
16.6%
P(E) + P(F) - P(E and F)
-b +- sq. rt(b^2 - 4ac) / 2a

22. Combined Events: Not E = P(not E) = ?
1 - P(E)
Odd numbers only have ___________
1
3 - 6 - 9 - 12

23. 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
(# of favorable outcomes) / (# of possible outcomes)
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.
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.
180(n-2)

24. Odd Factors
at least 3 steps
| A union B| = |A| + |B| - |A intersect B|
Odd numbers only have ___________
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

25. Sum of consecutive numbers
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
(sum of bases)(height) / 2
always try to factor
sum = (average)(number of terms)

26. Set Problems formula
principle (interest rate - in decimal form) (time - in years)
(# of favorable outcomes) / (# of possible outcomes)
(x-n(n)y-n)
The probability of an event occurring plus the probability of the event not occurring = 1

27. 1/8 = what %
The amount after deductions
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
12.5%
(# of favorable outcomes) / (# of possible outcomes)

28. Gross
Sum of digits is multiple of 9
Last two digits are multiple of 4 or the number can be divided by 2 twice.
The total amount before any deductions
Principal (1 + interest/number times compounded)^(t)(n)

29. 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
1.7
Even
Purchase price

30. Dependent events: When are two events said to be dependent events?
Group 1 + Group 2 + Neither - Both = Total
If the outcome of one event affects the outcome of the other event.
| A union B| = |A| + |B| - |A intersect B|
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.

31. Sq. rt(2)
1.4
Divide 4999 by 15 => 333 integers
(# of favorable outcomes) / (# of possible outcomes)
Any multiplication involving an even number creates an even product.

32. 0! = ?
Last two digits are multiple of 4 or the number can be divided by 2 twice.
market value
1
(n-1)!

33. gcd(m,n)*lcm(m,n)
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
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Any multiplication involving an even number creates an even product.

34. Triangle abc with d on the outside with a line. What does d = ?
principle (interest rate - in decimal form) (time - in years)
Exterior angle d is equal to the sum of the two remote interior angles a and b
Divide 4999 by 15 => 333 integers
16.6%

35. 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?
2 steps
Sum of digits is multiple of 3 - last two digits multiple of 4.
83.3%
0.15n + 0.08(5) = 0.1(n+5)

36. 5/6 = what %
83.3%
4/3 TT r ^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

37. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
always try to factor
(n-1)!
347
n! / (n - r)!

38. Number added or deleted
12^3
Odd numbers only have ___________
3 - 6 - 9 - 12
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

39. When you see an equation in factored form in a question?
P(event NOT occurring) = 1 - P(event occurring)
Sum of digits is multiple of 3 - last two digits multiple of 4.
Immediately UNFACTOR or vice versa
Even

40. Average Rate: Average A per B
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.
(total A) / (total B)
12.5%
1 - P(E)

41. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
22
The amount after deductions
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.
(amount of change) / (original amount)

42. Quadratic formula
-b +- sq. rt(b^2 - 4ac) / 2a
Purchase price
always try to factor
347

43. 3^3 x 4^3 = ?
Find all prime factors
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.
(sum of bases)(height) / 2
12^3

44. Sq. rt(3)
x(sq. rt 3) - x - 2x
$11 - 025
1.7
1.4

45. Net
347
The amount after deductions
12^3
gcd(m,n)*lcm(m,n) = mn

46. gcd(m,n)
______ |m-n|
(sum of bases)(height) / 2
Exterior angle d is equal to the sum of the two remote interior angles a and b
Find all prime factors

47. What to do with equations that have fractions
Gross Profit = Selling Price - Cost
at least 3 steps
Immediately try factoring/simplifying when possible
Organize into a grid.

48. To determine multiple-event probability where each individual event must occur in a certain way.
market value
Even
Figure out the probability for each individual event. Multiply the individual probabilities together.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

49. x^r/s = ?
22
The amount after deductions
s Sq. rt (x^r)
Balancing

50. How to check whether a number is a multiple of 12.
Find all prime factors
(amount of change) / (original amount)
Sum of digits is multiple of 3 - last two digits multiple of 4.
Even