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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. 45-45-90 triangle basic lengths of sides
x - x - x(sq. rt 2)
Exterior angle d is equal to the sum of the two remote interior angles a and b
Divide 4999 by 15 => 333 integers
Group 1 + Group 2 + Neither - Both = Total

2. 0! = ?
Organize into a grid.
1
(total A) / (total B)
Find all prime factors

3. Triangle abc with d on the outside with a line. What does d = ?
22
market value
The probability of event occurring is...
Exterior angle d is equal to the sum of the two remote interior angles a and b

4. 1/6 = what %
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.
16.6%
Any multiplication involving an even number creates an even product.
Find all prime factors

5. (1/4)^2
Organize into a grid.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
1/16
Sum of digits is multiple of 9

6. Simple probability
Find all prime factors
(# of favorable outcomes) / (# of possible outcomes)
The probability of event occurring is...
market value

7. 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.
Group 1 + Group 2 + Neither - Both = Total
1st Rule of Probability: Basic Rule is what?
Last two digits are multiple of 4 or the number can be divided by 2 twice.
347

8. What does the Sum of the angles in a Regular Polygon formula look like?
x(sq. rt 3) - x - 2x
180(n-2)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Principal (1 + interest/number times compounded)^(t)(n)

9. gcd(m,n)
n! / (n - r)!
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.
______ |m-n|
(amount of change) / (original amount)

10. How to check whether a number is a multiple of 3.
Exterior angle d is equal to the sum of the two remote interior angles a and b
Sum of digits is multiple of 3
A = P(1 + r) ^n
Immediately UNFACTOR or vice versa

11. Prime Factorization to find Greatest Common Factor
Gross Profit = Selling Price - Cost
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
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)
Divide 4999 by 15 => 333 integers

12. To determine the number of integers less than 5000 that are evenly divisible by 15...?
Sum of digits is multiple of 3
$11 - 025
Divide 4999 by 15 => 333 integers
y2 - y1 / x2 - x1

13. Percent Formula
p/100 = is/of
(total A) / (total B)
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.
16.6%

14. Dependent events: When are two events said to be dependent events?
Minor arc = 2(inscribed angle)
0.15n + 0.08(5) = 0.1(n+5)
If the outcome of one event affects the outcome of the other event.
principle (interest rate - in decimal form) (time - in years)

15. In general - medium questions require how many steps to solve?
4/3 TT r ^3
Even
Find simple interest then look for the answer that is a little bigger
2 steps

16. Sq. rt(2)
Find simple interest then look for the answer that is a little bigger
(# of favorable outcomes) / (# of possible outcomes)
p/100 = is/of
1.4

17. Multiples of 3
(# of favorable outcomes) / (# of possible outcomes)
P(event NOT occurring) = 1 - P(event occurring)
3 - 6 - 9 - 12
P(E) + P(F) - P(E and F)

18. Sq. rt(3)
Gross Profit = Selling Price - Cost
83.3%
1.7
Group 1 + Group 2 + Neither - Both = Total

19. Properties of 0
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
-b +- sq. rt(b^2 - 4ac) / 2a
2 steps
3-4-5 - 5-12-13 - 9-12-15

20. How do you multiply roots together.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
gcd(m,n)*lcm(m,n) = mn
16.6%
Number is a multiple of 3 and 2

21. Sum of consecutive numbers
3 - 6 - 9 - 12
Exterior angle d is equal to the sum of the two remote interior angles a and b
sum = (average)(number of terms)
x(sq. rt 3) - x - 2x

22. 5/6 = what %
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.
16.6%
83.3%
Number is a multiple of 3 and 2

23. 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?
x - x - x(sq. rt 2)
347
n! / (n - r)!
14 liters

24. 2n - 2n+2 - 2n+4
Even
1/16
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
The probability of an event occurring plus the probability of the event not occurring = 1

25. Intersecting Sets
Sum of digits is multiple of 3
3 - 6 - 9 - 12
| A union B| = |A| + |B| - |A intersect B|
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

26. Formula for area of a Trapezoid
1.4
(sum of bases)(height) / 2
______ |m-n|
x(sq. rt 3) - x - 2x

27. When you see an equation in factored form in a question?
A = P(1 + r) ^n
-b +- sq. rt(b^2 - 4ac) / 2a
Minor arc = 2(inscribed angle)
Immediately UNFACTOR or vice versa

28. Inscribed Angle - Minor Arc
$11 - 025
Minor arc = 2(inscribed angle)
Immediately try factoring/simplifying when possible
Exterior angle d is equal to the sum of the two remote interior angles a and b

29. 3^3 x 4^3 = ?
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 average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
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.
12^3

30. 2nd Rule of Probability: P(E) = 1 - P(not E)
(total A) / (total B)
The probability of an event occurring plus the probability of the event not occurring = 1
Organize into a grid.
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

31. How to find the slope.
y2 - y1 / x2 - x1
Odd numbers only have ___________
The amount after deductions
83.3%

32. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
A = P(1 + r) ^n
0.15n + 0.08(5) = 0.1(n+5)
The probability of event occurring is...
The total amount before any deductions

33. Odd 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.
x - x - x(sq. rt 2)
(# of favorable outcomes) / (# of possible outcomes)
Odd numbers only have ___________

34. Odd and Even rule.
(amount of change) / (original amount)
Any multiplication involving an even number creates an even product.
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.

35. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
Group 1 + Group 2 + Neither - Both = Total
Last two digits are multiple of 4 or the number can be divided by 2 twice.
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

36. Indistinguishable events how to find the number of permutations

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37. Percent increase = ?
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
1 - P(E)
180(n-2)
(amount of change) / (original amount)

38. 30-60-90 triangle basic lengths of sides
1 - P(E)
Immediately try factoring/simplifying when possible
16.6%
x(sq. rt 3) - x - 2x

39. Price sold for by retailer (after markup)
Minor arc = 2(inscribed angle)
3-4-5 - 5-12-13 - 9-12-15
Principal (1 + interest/number times compounded)^(t)(n)
market value

40. Gross
Number is a multiple of 3 and 2
The total amount before any deductions
(# of favorable outcomes) / (# of possible outcomes)
$11 - 025

41. Volume of a sphere
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
4/3 TT r ^3
2 steps

42. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
(# of favorable outcomes) / (# of possible outcomes)
Odd numbers only have ___________
(n-1)!
Last two digits are multiple of 4 or the number can be divided by 2 twice.

43. Combined Events: Not E = P(not E) = ?
1/16
1 - P(E)
Group 1 + Group 2 + Neither - Both = Total
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

44. How to find all divisors of a number
2 steps
Minor arc = 2(inscribed angle)
Find all prime factors
P(event NOT occurring) = 1 - P(event occurring)

45. How to check whether a number is a multiple of 4.
x - x - x(sq. rt 2)
Purchase price
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Odd numbers only have ___________

46. What to do with equations that have fractions
83.3%
Immediately try factoring/simplifying when possible
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Sum of digits is multiple of 9

47. In general - difficult questions require how many steps to solve?
3 - 6 - 9 - 12
1.7
at least 3 steps
Organize into a grid.

48. Price purchased for by wholesaler
Purchase price
3-4-5 - 5-12-13 - 9-12-15
D or E
(total distance) / (total time)

49. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
Sum of digits is multiple of 3 - last two digits multiple of 4.
Odd numbers only have ___________
Any multiplication involving an even number creates an even product.
$11 - 025

50. The number of outcomes that result in A divided by the total number of possible outcomes.
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.
Number is a multiple of 3 and 2
The probability of event occurring is...