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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. Sum of consecutive numbers
sum = (average)(number of terms)
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
Odd
3 - 6 - 9 - 12

2. How to check whether a number is a multiple of 3.
22
1.4
Sum of digits is multiple of 3
Organize into a grid.

3. 4th rule of Probability
Exterior angle d is equal to the sum of the two remote interior angles a and b
Odd numbers only have ___________
Number is a multiple of 3 and 2
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)

4. Number added or deleted
(n-1)!
14 liters
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
x(sq. rt 3) - x - 2x

5. 3^3 x 4^3 = ?
Immediately UNFACTOR or vice versa
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
12^3
14 liters

6. Quadratic formula
(amount of change) / (original amount)
P(E)P(F)
P(event NOT occurring) = 1 - P(event occurring)
-b +- sq. rt(b^2 - 4ac) / 2a

7. 5/6 = what %
83.3%
12^3
347
gcd(m,n)*lcm(m,n) = mn

8. 2n+1 - 2n+3 - 2n+5
1.4
Organize into a grid.
Odd
p/100 = is/of

9. Average Rate: Average speed
(total distance) / (total time)
0.15n + 0.08(5) = 0.1(n+5)
The total amount before any deductions
P(E)P(F)

10. 0! = ?
$11 - 025
1
22
(x-n(n)y-n)

11. Trial Problems: look at the probability of NOT OCCURRING
The probability of an event occurring plus the probability of the event not occurring = 1
Purchase price
P(event NOT occurring) = 1 - P(event occurring)
1

12. Work problem rule
Sum of digits is multiple of 9
(sum of bases)(height) / 2
always try to factor
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.

13. The average of consecutive numbers
always try to factor
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
0.15n + 0.08(5) = 0.1(n+5)
Sum of digits is multiple of 3 - last two digits multiple of 4.

14. Dependent events: When are two events said to be dependent events?
P(E)P(F)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
The probability of event occurring is...
If the outcome of one event affects the outcome of the other event.

15. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
s Sq. rt (x^r)
2 steps
principle (interest rate - in decimal form) (time - in years)
Divide 4999 by 15 => 333 integers

16. The number of outcomes that result in A divided by the total number of possible outcomes.
1.4
The probability of event occurring is...
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.

17. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
12.5%
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
(sum of bases)(height) / 2
Sum of digits is multiple of 9

18. 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
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Even
(x-n(n)y-n)

19. Compound interest formula
The probability of an event occurring plus the probability of the event not occurring = 1
Find simple interest then look for the answer that is a little bigger
Principal (1 + interest/number times compounded)^(t)(n)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

20. Percent increase = ?
P(event NOT occurring) = 1 - P(event occurring)
y2 - y1 / x2 - x1
P(E)P(F)
(amount of change) / (original amount)

21. Three triangle length patterns
always try to factor
0.15n + 0.08(5) = 0.1(n+5)
3 - 6 - 9 - 12
3-4-5 - 5-12-13 - 9-12-15

22. 3rd Rule of Probability: Conditional Probability
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.
p/100 = is/of
s Sq. rt (x^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.

23. Multiples of 3
x - x - x(sq. rt 2)
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
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

24. 1/6 = what %
Find simple interest then look for the answer that is a little bigger
16.6%
Balancing
83.3%

25. Intersecting Sets
347
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
(n-1)!
| A union B| = |A| + |B| - |A intersect B|

26. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
A = P(1 + r) ^n
4/3 TT r ^3
The probability of an event occurring plus the probability of the event not occurring = 1
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

27. Price sold for by retailer (after markup)
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 = P(1 + r) ^n
market value
0.15n + 0.08(5) = 0.1(n+5)

28. 45-45-90 triangle basic lengths of sides
1st Rule of Probability: Basic Rule is what?
x - x - x(sq. rt 2)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
The amount after deductions

29. Percent Formula
p/100 = is/of
| A union B| = |A| + |B| - |A intersect B|
always try to factor
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.

30. gcd(m,n)
3-4-5 - 5-12-13 - 9-12-15
1.4
22
______ |m-n|

31. Odd Factors
n! / (n - r)!
principle (interest rate - in decimal form) (time - in years)
Odd numbers only have ___________
2 steps

32. How to check for a prime number.

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33. How to check whether a number is a multiple of 4.
1
Any multiplication involving an even number creates an even product.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
y2 - y1 / x2 - x1

34. 1/8 = what %
1st Rule of Probability: Basic Rule is what?
12.5%
P(E)P(F)
Principal (1 + interest/number times compounded)^(t)(n)

35. 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.
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
Group 1 + Group 2 + Neither - Both = Total
1st Rule of Probability: Basic Rule is what?

36. Odd and Even rule.
Any multiplication involving an even number creates an even product.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
at least 3 steps
Find simple interest then look for the answer that is a little bigger

37. Multiplication principle
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.
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
1
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)

38. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
$11 - 025
Balancing
0.15n + 0.08(5) = 0.1(n+5)
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

39. In general - medium questions require how many steps to solve?
1
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)
2 steps
1.7

40. (1/4)^2
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.
-b +- sq. rt(b^2 - 4ac) / 2a
The total amount before any deductions
1/16

41. In general - difficult questions require how many steps to solve?
Number is a multiple of 3 and 2
16.6%
at least 3 steps
Sum of digits is multiple of 3

42. How to find the slope.
Immediately UNFACTOR or vice versa
y2 - y1 / x2 - x1
If the outcome of one event affects the outcome of the other event.
16.6%

43. Formula for Mixed Group problems (involving Both/Neither)
Group 1 + Group 2 + Neither - Both = Total
Gross Profit = Selling Price - Cost
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
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

44. Permutations: Order Matters
Odd numbers only have ___________
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
(# of favorable outcomes) / (# of possible outcomes)
n! / (n - r)!

45. 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
Odd numbers only have ___________
Odd
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

46. Prime Factorization to find Greatest Common Factor
1 - P(E)
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
n! / (n - r)!
The probability of event occurring is...

47. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
D or E
Group 1 + Group 2 + Neither - Both = Total
Sum of digits is multiple of 3
Sum of digits is multiple of 3 - last two digits multiple of 4.

48. Probability and Geometry.
Any multiplication involving an even number creates an even product.
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
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 number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

49. 30-60-90 triangle basic lengths of sides
x(sq. rt 3) - x - 2x
The total amount before any deductions
P(E) + P(F) - P(E and F)
always try to factor

50. Formula for area of a Trapezoid
(sum of bases)(height) / 2
______ |m-n|
market value
(total distance) / (total time)