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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 check whether a number is a multiple of 12.
Sum of digits is multiple of 3 - last two digits multiple of 4.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
______ |m-n|
Number is a multiple of 3 and 2

2. Volume of a sphere
s Sq. rt (x^r)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Any multiplication involving an even number creates an even product.
4/3 TT r ^3

3. How do you multiply roots together.
n! / (n - r)!
The probability of event occurring is...
at least 3 steps
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

4. Average Rate: Average speed
347
(total distance) / (total time)
s Sq. rt (x^r)
Any multiplication involving an even number creates an even product.

5. 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.
-b +- sq. rt(b^2 - 4ac) / 2a
Purchase price

6. How to check whether a number is a multiple of 3.
x - x - x(sq. rt 2)
at least 3 steps
Sum of digits is multiple of 3
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

7. Inscribed Angle - Minor Arc
Minor arc = 2(inscribed angle)
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.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
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.

8. To determine the number of integers less than 5000 that are evenly divisible by 15...?
Divide 4999 by 15 => 333 integers
A = P(1 + r) ^n
Group 1 + Group 2 + Neither - Both = Total
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

9. When you see an equation in factored form in a question?
P(event NOT occurring) = 1 - P(event occurring)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Immediately UNFACTOR or vice versa
y2 - y1 / x2 - x1

10. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
Sum of digits is multiple of 9
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.
principle (interest rate - in decimal form) (time - in years)
Any multiplication involving an even number creates an even product.

11. In general - difficult questions require how many steps to solve?
Odd numbers only have ___________
at least 3 steps
The amount after deductions
Find simple interest then look for the answer that is a little bigger

12. 2nd Rule of Probability: P(E) = 1 - P(not E)
The probability of an event occurring plus the probability of the event not occurring = 1
Gross Profit = Selling Price - Cost
s Sq. rt (x^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.

13. (1/4)^2
(n-1)!
Minor arc = 2(inscribed angle)
1/16
The probability of event occurring is...

14. Dependent events: When are two events said to be dependent events?
| A union B| = |A| + |B| - |A intersect B|
Find all prime factors
If the outcome of one event affects the outcome of the other event.
Immediately try factoring/simplifying when possible

15. Gross
180(n-2)
The total amount before any deductions
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

16. Indistinguishable events how to find the number of permutations

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17. Sq. rt(2)
1.4
If the outcome of one event affects the outcome of the other event.
1st Rule of Probability: Basic Rule is what?
The probability of an event occurring plus the probability of the event not occurring = 1

18. x^r/s = ?
s Sq. rt (x^r)
Number is a multiple of 3 and 2
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
16.6%

19. Three triangle length patterns
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.
The total amount before any deductions
3-4-5 - 5-12-13 - 9-12-15
1.7

20. Always try to factor
P(E) + P(F) - P(E and F)
16.6%
Find all prime factors
always try to factor

21. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
347
-b +- sq. rt(b^2 - 4ac) / 2a
______ |m-n|

22. What does the Sum of the angles in a Regular Polygon formula look like?
n! / (n - r)!
at least 3 steps
1 - P(E)
180(n-2)

23. How to find all divisors of a number
Find all prime factors
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
Odd
Purchase price

24. Quadratic formula
(sum of bases)(height) / 2
Immediately try factoring/simplifying when possible
Immediately UNFACTOR or vice versa
-b +- sq. rt(b^2 - 4ac) / 2a

25. The number of ways independent events can occur together.
at least 3 steps
Immediately UNFACTOR or vice versa
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.

26. 2n - 2n+2 - 2n+4
Figure out the probability for each individual event. Multiply the individual probabilities together.
x(sq. rt 3) - x - 2x
180(n-2)
Even

27. 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
gcd(m,n)*lcm(m,n) = mn
(x-n(n)y-n)
principle (interest rate - in decimal form) (time - in years)

28. Set Problems formula
(x-n(n)y-n)
12.5%
0.15n + 0.08(5) = 0.1(n+5)
Group 1 + Group 2 + Neither - Both = Total

29. gcd(m,n)*lcm(m,n)
Sum of digits is multiple of 3 - last two digits multiple of 4.
principle (interest rate - in decimal form) (time - in years)
(total A) / (total B)
gcd(m,n)*lcm(m,n) = mn

30. 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
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.
180(n-2)
The probability of an event occurring plus the probability of the event not occurring = 1
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)

31. 1/8 = 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
12.5%
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.
at least 3 steps

32. 1/6 = what %
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Find simple interest then look for the answer that is a little bigger
16.6%
83.3%

33. 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.
1st Rule of Probability: Basic Rule is what?
Find all prime factors
x - x - x(sq. rt 2)

34. gcd(m,n)
Odd numbers only have ___________
Immediately UNFACTOR or vice versa
1st Rule of Probability: Basic Rule is what?
______ |m-n|

35. How to check for a prime number.

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36. 3^3 x 4^3 = ?
12^3
If the outcome of one event affects the outcome of the other event.
s Sq. rt (x^r)
Find simple interest then look for the answer that is a little bigger

37. Triangle abc with d on the outside with a line. What does d = ?
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. 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 3
Exterior angle d is equal to the sum of the two remote interior angles a and b

38. Price purchased for by wholesaler
Purchase price
347
Find all prime factors
y2 - y1 / x2 - x1

39. Combined Events: E and F
1/16
Sum of digits is multiple of 3
Organize into a grid.
P(E)P(F)

40. 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.
(sum of bases)(height) / 2
1st Rule of Probability: Basic Rule is what?
16.6%
Figure out the probability for each individual event. Multiply the individual probabilities together.

41. Compound interest formula
Principal (1 + interest/number times compounded)^(t)(n)
(total A) / (total B)
(x-n(n)y-n)
Purchase price

42. Net
1st Rule of Probability: Basic Rule is what?
1.4
0.15n + 0.08(5) = 0.1(n+5)
The amount after deductions

43. Probability and Geometry.
Even
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
x - x - x(sq. rt 2)
0.15n + 0.08(5) = 0.1(n+5)

44. 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?
Organize into a grid.
14 liters
Balancing
0.15n + 0.08(5) = 0.1(n+5)

45. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
gcd(m,n)*lcm(m,n) = mn
A = P(1 + r) ^n
Divide 4999 by 15 => 333 integers
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

46. Prime Factorization to find Greatest Common Factor
P(E) + P(F) - P(E and F)
Divide 4999 by 15 => 333 integers
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
180(n-2)

47. 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.
Purchase price
P(E)P(F)
1.4

48. 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
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
sum = (average)(number of terms)
The probability of an event occurring plus the probability of the event not occurring = 1

49. 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.
gcd(m,n)*lcm(m,n) = mn
Organize into a grid.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Find simple interest then look for the answer that is a little bigger

50. Intersecting Sets
p/100 = is/of
3 - 6 - 9 - 12
P(E) + P(F) - P(E and F)
| A union B| = |A| + |B| - |A intersect B|