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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. Dependent events: When are two events said to be dependent events?
A = P(1 + r) ^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
(n-1)!
If the outcome of one event affects the outcome of the other event.

2. Simple probability
Principal (1 + interest/number times compounded)^(t)(n)
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)
P(event NOT occurring) = 1 - P(event occurring)
(# of favorable outcomes) / (# of possible outcomes)

3. Volume of a sphere
3 - 6 - 9 - 12
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
Organize into a grid.
4/3 TT r ^3

4. Three triangle length patterns
at least 3 steps
Figure out the probability for each individual event. Multiply the individual probabilities together.
sum = (average)(number of terms)
3-4-5 - 5-12-13 - 9-12-15

5. Average Rate: Average speed
(total distance) / (total time)
P(event NOT occurring) = 1 - P(event occurring)
(x-n(n)y-n)
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)

6. How do you multiply roots together.
(x-n(n)y-n)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Odd
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

7. 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)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
(# of favorable outcomes) / (# of possible outcomes)
Figure out the probability for each individual event. Multiply the individual probabilities together.

8. When you see an equation in factored form in a question?
Immediately UNFACTOR or vice versa
83.3%
16.6%
Sum of digits is multiple of 3 - last two digits multiple of 4.

9. Properties of 0
Immediately try factoring/simplifying when possible
(x-n(n)y-n)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
p/100 = is/of

10. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
sum = (average)(number of terms)
22
| A union B| = |A| + |B| - |A intersect B|
1st Rule of Probability: Basic Rule is what?

11. How to check for a prime number.

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12. How to find the slope.
y2 - y1 / x2 - x1
Odd numbers only have ___________
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
P(E)P(F)

13. Percent increase = ?
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.
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.
P(E)P(F)
(amount of change) / (original amount)

14. Trial Problems: look at the probability of NOT OCCURRING
gcd(m,n)*lcm(m,n) = mn
1.4
y2 - y1 / x2 - x1
P(event NOT occurring) = 1 - P(event occurring)

15. To determine the number of integers less than 5000 that are evenly divisible by 15...?
Divide 4999 by 15 => 333 integers
x - x - x(sq. rt 2)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
12^3

16. Percent Formula
Number is a multiple of 3 and 2
p/100 = is/of
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.
Principal (1 + interest/number times compounded)^(t)(n)

17. 1/6 = what %
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(event NOT occurring) = 1 - P(event occurring)
14 liters
16.6%

18. To determine multiple-event probability where each individual event must occur in a certain way.
sum = (average)(number of terms)
The probability of an event occurring plus the probability of the event not occurring = 1
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.

19. How to find all divisors of a number
Find all prime factors
The probability of event occurring is...
Sum of digits is multiple of 9
x - x - x(sq. rt 2)

20. Gross Profit formula
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Gross Profit = Selling Price - Cost
The amount after deductions
The total amount before any deductions

21. 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.
(# of favorable outcomes) / (# of possible outcomes)
(n-1)!
Organize into a grid.
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.

22. Number added or deleted
(# of favorable outcomes) / (# of possible outcomes)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
1.7
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.

23. Multiplication principle
D or E
Immediately UNFACTOR or vice versa
-b +- sq. rt(b^2 - 4ac) / 2a
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

24. 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.
Exterior angle d is equal to the sum of the two remote interior angles a and b
1st Rule of Probability: Basic Rule is what?
12^3
D or E

25. How to check whether a number is a multiple of 3.
D or E
Gross Profit = Selling Price - Cost
Sum of digits is multiple of 3
The probability of an event occurring plus the probability of the event not occurring = 1

26. 30-60-90 triangle basic lengths of sides
x(sq. rt 3) - x - 2x
Sum of digits is multiple of 3 - last two digits multiple of 4.
The amount after deductions
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

27. In general - difficult questions require how many steps to solve?
(x-n(n)y-n)
at least 3 steps
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.
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

28. Sq. rt(2)
Principal (1 + interest/number times compounded)^(t)(n)
14 liters
1.4
market value

29. Price sold for by retailer (after markup)
Sum of digits is multiple of 3
P(event NOT occurring) = 1 - P(event occurring)
(amount of change) / (original amount)
market value

30. Combined Events: E and F
3 - 6 - 9 - 12
Immediately UNFACTOR or vice versa
Purchase price
P(E)P(F)

31. Formula for Mixed Group problems (involving Both/Neither)
1.7
Exterior angle d is equal to the sum of the two remote interior angles a and b
P(E) + P(F) - P(E and F)
Group 1 + Group 2 + Neither - Both = Total

32. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
The amount after deductions
The probability of an event occurring plus the probability of the event not occurring = 1
$11 - 025
(sum of bases)(height) / 2

33. Gross
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
The total amount before any deductions
The probability of event occurring is...

34. Sum of consecutive numbers
market value
p/100 = is/of
sum = (average)(number of terms)
The probability of an event occurring plus the probability of the event not occurring = 1

35. 1/8 = what %
12.5%
16.6%
22
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)

36. Odd and Even rule.
Sum of digits is multiple of 3 - last two digits multiple of 4.
sum = (average)(number of terms)
3 - 6 - 9 - 12
Any multiplication involving an even number creates an even product.

37. 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
x(sq. rt 3) - x - 2x
3-4-5 - 5-12-13 - 9-12-15
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.
347

38. Compound interest formula
Principal (1 + interest/number times compounded)^(t)(n)
Odd
principle (interest rate - in decimal form) (time - in years)
-b +- sq. rt(b^2 - 4ac) / 2a

39. Always try to factor
always try to factor
Exterior angle d is equal to the sum of the two remote interior angles a and b
(total distance) / (total time)
Find all prime factors

40. Combined Events: Not E = 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
Odd
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.
1 - P(E)

41. 3rd Rule of Probability: Conditional Probability
P(E)P(F)
4/3 TT r ^3
12.5%
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.

42. 2n+1 - 2n+3 - 2n+5
12.5%
1/16
(n-1)!
Odd

43. The number of ways independent events can occur together.
Balancing
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
s Sq. rt (x^r)
Find simple interest then look for the answer that is a little bigger

44. Prime Factorization to find Greatest Common Factor
Find simple interest then look for the answer that is a little bigger
gcd(m,n)*lcm(m,n) = mn
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 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

45. How to check whether a number is a multiple of 12.
Sum of digits is multiple of 3 - last two digits multiple of 4.
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.
Even
P(E)P(F)

46. 0! = ?
(x-n(n)y-n)
1
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

47. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
D or E
Figure out the probability for each individual event. Multiply the individual probabilities together.
$11 - 025
2 steps

48. Combined Events: E or F
12.5%
4/3 TT r ^3
sum = (average)(number of terms)
P(E) + P(F) - P(E and F)

49. How to check whether a number is a multiple of 6
Number is a multiple of 3 and 2
market value
Even
22

50. 3^3 x 4^3 = ?
1/16
12^3
The total amount before any deductions
P(event NOT occurring) = 1 - P(event occurring)