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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. When you see an equation in factored form in a question?
Sum of digits is multiple of 3 - last two digits multiple of 4.
Immediately UNFACTOR or vice versa
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.
Number is a multiple of 3 and 2

2. 5/6 = what %
2 steps
83.3%
P(E)P(F)
180(n-2)

3. 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?
0.15n + 0.08(5) = 0.1(n+5)
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
16.6%
Divide 4999 by 15 => 333 integers

4. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
A = P(1 + r) ^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)
$11 - 025
14 liters

5. The number of ways independent events can occur together.
Exterior angle d is equal to the sum of the two remote interior angles a and b
always try to factor
D or E
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

6. How to check whether number is multiple of 9
Exterior angle d is equal to the sum of the two remote interior angles 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
Sum of digits is multiple of 9
(sum of bases)(height) / 2

7. Percent increase = ?
(amount of change) / (original amount)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
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
2 steps

8. Dependent events: When are two events said to be dependent events?
180(n-2)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Find all prime factors
If the outcome of one event affects the outcome of the other event.

9. Price sold for by retailer (after markup)
market value
Sum of digits is multiple of 3
Principal (1 + interest/number times compounded)^(t)(n)
Odd

10. How do you multiply roots together.
y2 - y1 / x2 - x1
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
p/100 = is/of
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

11. Permutations: Order Matters
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
P(event NOT occurring) = 1 - P(event occurring)
n! / (n - r)!
Exterior angle d is equal to the sum of the two remote interior angles a and b

12. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
P(E)P(F)
(total distance) / (total time)
D or E
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)

13. The number of outcomes that result in A divided by the total number of possible outcomes.
The probability of event occurring is...
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Purchase price
1 - P(E)

14. 3^3 x 4^3 = ?
12^3
(sum of bases)(height) / 2
(total distance) / (total time)
A = P(1 + r) ^n

15. How to check whether a number is a multiple of 4.
(sum of bases)(height) / 2
Last two digits are multiple of 4 or the number can be divided by 2 twice.
The probability of an event occurring plus the probability of the event not occurring = 1
Number is a multiple of 3 and 2

16. 3rd Rule of Probability: Conditional Probability
D or E
(# of favorable outcomes) / (# of possible outcomes)
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.
Sum of digits is multiple of 3

17. 0! = ?
83.3%
The probability of an event occurring plus the probability of the event not occurring = 1
1
market value

18. 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
Minor arc = 2(inscribed angle)
Immediately UNFACTOR or vice versa
Balancing
1

19. gcd(m,n)*lcm(m,n)
gcd(m,n)*lcm(m,n) = mn
s Sq. rt (x^r)
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
principle (interest rate - in decimal form) (time - in years)

20. 1/6 = what %
16.6%
P(event NOT occurring) = 1 - P(event occurring)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
3-4-5 - 5-12-13 - 9-12-15

21. 2n+1 - 2n+3 - 2n+5
0.15n + 0.08(5) = 0.1(n+5)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Odd
The probability of event occurring is...

22. 2n - 2n+2 - 2n+4
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Odd
Even
$11 - 025

23. 2nd Rule of Probability: P(E) = 1 - P(not E)
1.7
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.
$11 - 025

24. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
Minor arc = 2(inscribed angle)
1.4
180(n-2)
principle (interest rate - in decimal form) (time - in years)

25. Quadratic formula
$11 - 025
4/3 TT r ^3
-b +- sq. rt(b^2 - 4ac) / 2a
Even

26. What does the Sum of the angles in a Regular Polygon formula look like?
180(n-2)
(total A) / (total B)
principle (interest rate - in decimal form) (time - in years)
0.15n + 0.08(5) = 0.1(n+5)

27. The average of consecutive numbers
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
(n-1)!
x - x - x(sq. rt 2)
Immediately UNFACTOR or vice versa

28. Combined Events: E or F
p/100 = is/of
P(E) + P(F) - P(E and F)
-b +- sq. rt(b^2 - 4ac) / 2a
P(event NOT occurring) = 1 - P(event occurring)

29. How to find all divisors of a number
0.15n + 0.08(5) = 0.1(n+5)
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 all prime factors
Last two digits are multiple of 4 or the number can be divided by 2 twice.

30. Formula for Mixed Group problems (involving Both/Neither)
3-4-5 - 5-12-13 - 9-12-15
Minor arc = 2(inscribed angle)
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)
Group 1 + Group 2 + Neither - Both = Total

31. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
22
P(E)P(F)
2 steps
83.3%

32. x^r/s = ?
s Sq. rt (x^r)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
P(event NOT occurring) = 1 - P(event occurring)
1.7

33. Gross
1.7
The total amount before any deductions
22
(n-1)!

34. Volume of a sphere
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Gross Profit = Selling Price - Cost
4/3 TT r ^3
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)

35. Intersecting Sets
(total A) / (total B)
| A union B| = |A| + |B| - |A intersect B|
always try to factor
s Sq. rt (x^r)

36. Gross Profit formula
1.4
(# of favorable outcomes) / (# of possible outcomes)
Gross Profit = Selling Price - Cost
Even

37. 45-45-90 triangle basic lengths of sides
x - x - x(sq. rt 2)
4/3 TT r ^3
(amount of change) / (original amount)
Odd numbers only have ___________

38. Set Problems formula
1.7
3 - 6 - 9 - 12
(x-n(n)y-n)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

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.
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
sum = (average)(number of terms)
P(E) + P(F) - P(E and F)
Organize into a grid.

40. Trial Problems: look at the probability of NOT OCCURRING
Number is a multiple of 3 and 2
P(event NOT occurring) = 1 - P(event occurring)
P(E) + P(F) - P(E and F)
Last two digits are multiple of 4 or the number can be divided by 2 twice.

41. To determine the number of integers less than 5000 that are evenly divisible by 15...?
principle (interest rate - in decimal form) (time - in years)
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.
Divide 4999 by 15 => 333 integers

42. gcd(m,n)
2 steps
3-4-5 - 5-12-13 - 9-12-15
______ |m-n|
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

43. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
347
(n-1)!
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
0.15n + 0.08(5) = 0.1(n+5)

44. Indistinguishable events how to find the number of permutations

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45. Sum of consecutive numbers
sum = (average)(number of terms)
12^3
Organize into a grid.
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

46. How to check for a prime number.

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47. To determine multiple-event probability where each individual event must occur in a certain way.
Odd numbers only have ___________
Figure out the probability for each individual event. Multiply the individual probabilities together.
Group 1 + Group 2 + Neither - Both = Total
-b +- sq. rt(b^2 - 4ac) / 2a

48. Price purchased for by wholesaler
D or 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
Purchase price
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

49. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
A = P(1 + r) ^n
Minor arc = 2(inscribed angle)
principle (interest rate - in decimal form) (time - in years)
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.

50. Properties of 0
P(event NOT occurring) = 1 - P(event occurring)
347
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.