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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. Multiplication principle
22
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
______ |m-n|
Immediately try factoring/simplifying when possible

2. How to find the slope.
y2 - y1 / x2 - x1
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Principal (1 + interest/number times compounded)^(t)(n)

3. How to check whether a number is a multiple of 12.
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.
1.7
Sum of digits is multiple of 3 - last two digits multiple of 4.
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. Multiples of 3
| A union B| = |A| + |B| - |A intersect B|
1st Rule of Probability: Basic Rule is what?
The probability of an event occurring plus the probability of the event not occurring = 1
3 - 6 - 9 - 12

5. Sum of consecutive numbers
sum = (average)(number of terms)
x - x - x(sq. rt 2)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
83.3%

6. How to check whether a number is a multiple of 3.
Sum of digits is multiple of 9
Minor arc = 2(inscribed angle)
Sum of digits is multiple of 3
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.

7. 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
Sum of digits is multiple of 9
(x-n(n)y-n)
(total distance) / (total time)

8. How to check whether a number is a multiple of 6
1st Rule of Probability: Basic Rule is what?
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Number is a multiple of 3 and 2
| A union B| = |A| + |B| - |A intersect B|

9. In general - difficult questions require how many steps to solve?
16.6%
Divide 4999 by 15 => 333 integers
at least 3 steps
12.5%

10. 5/6 = what %
gcd(m,n)*lcm(m,n) = mn
83.3%
P(E) + P(F) - P(E and F)
(sum of bases)(height) / 2

11. How to find all divisors of a number
Find all prime factors
12^3
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.
(n-1)!

12. Gross Profit formula
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
1.4
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Gross Profit = Selling Price - Cost

13. Triangle abc with d on the outside with a line. What does d = ?
P(event NOT occurring) = 1 - P(event occurring)
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.
Exterior angle d is equal to the sum of the two remote interior angles a and b
y2 - y1 / x2 - x1

14. Indistinguishable events how to find the number of permutations

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15. 1/8 = what %
| A union B| = |A| + |B| - |A intersect B|
If the outcome of one event affects the outcome of the other event.
Sum of digits is multiple of 3
12.5%

16. Odd and Even rule.
at least 3 steps
Any multiplication involving an even number creates an even product.
D or E
12.5%

17. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
(total distance) / (total time)
A = P(1 + r) ^n
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Purchase price

18. 30-60-90 triangle basic lengths of sides
p/100 = is/of
x(sq. rt 3) - x - 2x
P(E)P(F)
Sum of digits is multiple of 9

19. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
Number is a multiple of 3 and 2
Last two digits are multiple of 4 or the number can be divided by 2 twice.
market value
$11 - 025

20. 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?
1
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
1.4
0.15n + 0.08(5) = 0.1(n+5)

21. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
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
22
1.7

22. What does the Sum of the angles in a Regular Polygon formula look like?
Principal (1 + interest/number times compounded)^(t)(n)
-b +- sq. rt(b^2 - 4ac) / 2a
1/16
180(n-2)

23. To determine the number of integers less than 5000 that are evenly divisible by 15...?
Figure out the probability for each individual event. Multiply the individual probabilities together.
Divide 4999 by 15 => 333 integers
1.7
Sum of digits is multiple of 3 - last two digits multiple of 4.

24. Number added or deleted
x - x - x(sq. rt 2)
3-4-5 - 5-12-13 - 9-12-15
The amount after deductions
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

25. Dependent events: When are two events said to be dependent events?
1
3-4-5 - 5-12-13 - 9-12-15
P(event NOT occurring) = 1 - P(event occurring)
If the outcome of one event affects the outcome of the other event.

26. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
always try to factor
(x-n(n)y-n)
principle (interest rate - in decimal form) (time - in years)
Immediately try factoring/simplifying when possible

27. 3^3 x 4^3 = ?
4/3 TT r ^3
12^3
1 - P(E)
Find simple interest then look for the answer that is a little bigger

28. Formula for area of a Trapezoid
If the outcome of one event affects the outcome of the other event.
(sum of bases)(height) / 2
The probability of event occurring is...
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

29. How to check for a prime number.

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30. 1/6 = what %
Group 1 + Group 2 + Neither - Both = Total
(sum of bases)(height) / 2
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
16.6%

31. Intersecting Sets
Sum of digits is multiple of 3
| A union B| = |A| + |B| - |A intersect B|
The total amount before any deductions
-b +- sq. rt(b^2 - 4ac) / 2a

32. Net
(total A) / (total B)
The amount after deductions
12^3
1.7

33. Prime Factorization to find Greatest Common Factor
1.7
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 total amount before any deductions
12^3

34. Permutations: Order Matters
1
n! / (n - r)!
always try to factor
(total distance) / (total time)

35. 2n - 2n+2 - 2n+4
3 - 6 - 9 - 12
The probability of an event occurring plus the probability of the event not occurring = 1
Even
0.15n + 0.08(5) = 0.1(n+5)

36. What to do with equations that have fractions
22
Sum of digits is multiple of 9
Immediately try factoring/simplifying when possible
1

37. The number of ways independent events can occur together.
n! / (n - r)!
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
D or E
The probability of event occurring is...

38. How to check whether number is multiple of 9
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
Sum of digits is multiple of 9
x(sq. rt 3) - x - 2x
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.

39. gcd(m,n)*lcm(m,n)
Exterior angle d is equal to the sum of the two remote interior angles a and b
Any multiplication involving an even number creates an even product.
gcd(m,n)*lcm(m,n) = mn
1st Rule of Probability: Basic Rule is what?

40. gcd(m,n)
______ |m-n|
(sum of bases)(height) / 2
Group 1 + Group 2 + Neither - Both = Total
Find all prime factors

41. Trial Problems: look at the probability of NOT OCCURRING
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.
Odd
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
P(event NOT occurring) = 1 - P(event occurring)

42. 0! = ?
Purchase price
1
gcd(m,n)*lcm(m,n) = mn
Any multiplication involving an even number creates an even product.

43. Always try to factor
Balancing
Odd numbers only have ___________
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.
always try to factor

44. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
347
Purchase price
P(E) + P(F) - P(E and F)
3-4-5 - 5-12-13 - 9-12-15

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
always try to factor
Balancing
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
The probability of an event occurring plus the probability of the event not occurring = 1

46. In general - medium questions require how many steps to solve?
Principal (1 + interest/number times compounded)^(t)(n)
2 steps
P(E) + P(F) - P(E and F)
12^3

47. 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
market value
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.
3-4-5 - 5-12-13 - 9-12-15
Number is a multiple of 3 and 2

48. Odd Factors
3-4-5 - 5-12-13 - 9-12-15
Odd numbers only have ___________
Purchase price
1.4

49. Quadratic formula
-b +- sq. rt(b^2 - 4ac) / 2a
1/16
180(n-2)
at least 3 steps

50. Percent Formula
1st Rule of Probability: Basic Rule is what?
p/100 = is/of
| A union B| = |A| + |B| - |A intersect B|
Minor arc = 2(inscribed angle)