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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. How to find all divisors of a number
Find all prime factors
______ |m-n|
(total A) / (total B)
(n-1)!

2. Percent increase = ?
Purchase price
x - x - x(sq. rt 2)
(sum of bases)(height) / 2
(amount of change) / (original amount)

3. How to check whether a number is a multiple of 6
Number is a multiple of 3 and 2
D or E
(# of favorable outcomes) / (# of possible outcomes)
Divide 4999 by 15 => 333 integers

4. Sq. rt(2)
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
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.
1.4
(# of favorable outcomes) / (# of possible outcomes)

5. How do you multiply roots together.
14 liters
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
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.

6. How to check whether a number is a multiple of 12.
14 liters
Exterior angle d is equal to the sum of the two remote interior angles a and b
gcd(m,n)*lcm(m,n) = mn
Sum of digits is multiple of 3 - last two digits multiple of 4.

7. Triangle abc with d on the outside with a line. What does d = ?
If the outcome of one event affects the outcome of the other event.
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
| A union B| = |A| + |B| - |A intersect B|
Exterior angle d is equal to the sum of the two remote interior angles a and b

8. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
principle (interest rate - in decimal form) (time - in years)
y2 - y1 / x2 - x1
347
Group 1 + Group 2 + Neither - Both = Total

9. 2n+1 - 2n+3 - 2n+5
Odd
22
180(n-2)
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

10. Combined Events: E or F
gcd(m,n)*lcm(m,n) = mn
P(E) + P(F) - P(E and F)
12^3
2 steps

11. x^r/s = ?
s Sq. rt (x^r)
(x-n(n)y-n)
1 - P(E)
Odd numbers only have ___________

12. Quadratic formula
1 - P(E)
16.6%
(n-1)!
-b +- sq. rt(b^2 - 4ac) / 2a

13. When you see an equation in factored form in a question?
A = P(1 + r) ^n
p/100 = is/of
Immediately UNFACTOR or vice versa
Immediately try factoring/simplifying when possible

14. What does the Sum of the angles in a Regular Polygon formula look like?
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)
180(n-2)
3-4-5 - 5-12-13 - 9-12-15
(total A) / (total B)

15. 2nd Rule of Probability: P(E) = 1 - P(not E)
P(E) + P(F) - P(E and F)
The probability of an event occurring plus the probability of the event not occurring = 1
1.7
gcd(m,n)*lcm(m,n) = mn

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?
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Minor arc = 2(inscribed angle)
14 liters
Sum of digits is multiple of 9

17. Price sold for by retailer (after markup)
market value
Principal (1 + interest/number times compounded)^(t)(n)
Immediately UNFACTOR or vice versa
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.

18. How to check whether a number is a multiple of 3.
1.4
Sum of digits is multiple of 3
sum = (average)(number of terms)
2 steps

19. gcd(m,n)*lcm(m,n)
Gross Profit = Selling Price - Cost
gcd(m,n)*lcm(m,n) = mn
(# of favorable outcomes) / (# of possible outcomes)
Even

20. 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
1
P(event NOT occurring) = 1 - P(event occurring)
The amount after deductions

21. Net
x(sq. rt 3) - x - 2x
$11 - 025
The amount after deductions
180(n-2)

22. Set Problems formula
(x-n(n)y-n)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Immediately UNFACTOR or vice versa
-b +- sq. rt(b^2 - 4ac) / 2a

23. Odd and Even rule.
Sum of digits is multiple of 9
(# of favorable outcomes) / (# of possible outcomes)
0.15n + 0.08(5) = 0.1(n+5)
Any multiplication involving an even number creates an even product.

24. 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.
Organize into a grid.
The amount after deductions
______ |m-n|
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

25. 4th rule of Probability
347
Balancing
always try to factor
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)

26. 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.
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
Balancing
The probability of an event occurring plus the probability of the event not occurring = 1

27. Volume of a sphere
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)
Minor arc = 2(inscribed angle)
______ |m-n|
4/3 TT r ^3

28. Simple probability
(# of favorable outcomes) / (# of possible outcomes)
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
4/3 TT r ^3
Odd

29. Percent Formula
p/100 = is/of
Balancing
Principal (1 + interest/number times compounded)^(t)(n)
1/16

30. 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
principle (interest rate - in decimal form) (time - in years)
D or E
22

31. How to check whether a number is a multiple of 4.
Purchase price
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Gross Profit = Selling Price - Cost
1st Rule of Probability: Basic Rule is what?

32. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
sum = (average)(number of terms)
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 number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
A = P(1 + r) ^n

33. Compound interest rule
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
(total A) / (total B)
Find simple interest then look for the answer that is a little bigger
principle (interest rate - in decimal form) (time - in years)

34. Formula for Mixed Group problems (involving Both/Neither)
Group 1 + Group 2 + Neither - Both = Total
P(E) + P(F) - P(E and F)
83.3%
12.5%

35. Indistinguishable events how to find the number of permutations

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36. Sum of consecutive numbers
sum = (average)(number of terms)
0.15n + 0.08(5) = 0.1(n+5)
gcd(m,n)*lcm(m,n) = mn
______ |m-n|

37. Three triangle length patterns
180(n-2)
3-4-5 - 5-12-13 - 9-12-15
4/3 TT r ^3
1.4

38. 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.
347
$11 - 025
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?

39. To determine the number of integers less than 5000 that are evenly divisible by 15...?
Divide 4999 by 15 => 333 integers
The amount after deductions
Sum of digits is multiple of 3 - last two digits multiple of 4.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

40. Price purchased for by wholesaler
1/16
Purchase price
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.

41. Dependent events: When are two events said to be dependent events?
12^3
3 - 6 - 9 - 12
16.6%
If the outcome of one event affects the outcome of the other event.

42. 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
Immediately try factoring/simplifying when possible
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.
n! / (n - r)!
Purchase price

43. Multiples of 3
Find all prime factors
p/100 = is/of
(total distance) / (total time)
3 - 6 - 9 - 12

44. 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?
Number is a multiple of 3 and 2
0.15n + 0.08(5) = 0.1(n+5)
The probability of event occurring is...
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.

45. Average Rate: Average A per B
0.15n + 0.08(5) = 0.1(n+5)
83.3%
Number is a multiple of 3 and 2
(total A) / (total B)

46. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
at least 3 steps
p/100 = is/of
(x-n(n)y-n)
22

47. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
P(E)P(F)
$11 - 025
3-4-5 - 5-12-13 - 9-12-15
Balancing

48. What to do with equations that have fractions
Immediately try factoring/simplifying when possible
y2 - y1 / x2 - x1
0.15n + 0.08(5) = 0.1(n+5)
(amount of change) / (original amount)

49. gcd(m,n)
______ |m-n|
The probability of event occurring is...
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any 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)

50. In general - medium questions require how many steps to solve?
Odd
gcd(m,n)*lcm(m,n) = mn
Odd numbers only have ___________
2 steps