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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. Probability and Geometry.
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
(n-1)!
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.
$11 - 025

2. How to check whether number is multiple of 9
x(sq. rt 3) - x - 2x
Sum of digits is multiple of 9
Immediately UNFACTOR or vice versa
1 - P(E)

3. 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.
Group 1 + Group 2 + Neither - Both = Total
Find simple interest then look for the answer that is a little bigger
Organize into a grid.
Odd

4. Percent increase = ?
(x-n(n)y-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
(amount of change) / (original amount)
Any multiplication involving an even number creates an even product.

5. gcd(m,n)
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.
______ |m-n|
The amount after deductions
The probability of event occurring is...

6. 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
Find simple interest then look for the answer that is a little bigger
2 steps
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.

7. Simple probability
(# of favorable outcomes) / (# of possible outcomes)
1.7
1st Rule of Probability: Basic Rule is what?
Sum of digits is multiple of 3

8. Formula for area of a Trapezoid
(sum of bases)(height) / 2
The probability of event occurring is...
A = P(1 + r) ^n
D or E

9. Compound interest formula
Principal (1 + interest/number times compounded)^(t)(n)
1.7
x - x - x(sq. rt 2)
22

10. (1/4)^2
Last two digits are multiple of 4 or the number can be divided by 2 twice.
1/16
(# of favorable outcomes) / (# of possible outcomes)
12.5%

11. How to check for a prime number.

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12. Odd and Even rule.
Balancing
Any multiplication involving an even number creates an even product.
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?

13. What does the Sum of the angles in a Regular Polygon formula look like?
180(n-2)
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
347
Find simple interest then look for the answer that is a little bigger

14. Compound interest rule
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
1 - P(E)
Find simple interest then look for the answer that is a little bigger
______ |m-n|

15. 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.
market value
The probability of an event occurring plus the probability of the event not occurring = 1
P(event NOT occurring) = 1 - P(event occurring)

16. Percent Formula
p/100 = is/of
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
347
1 - P(E)

17. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
83.3%
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
(n-1)!
gcd(m,n)*lcm(m,n) = mn

18. How to find all divisors of a number
gcd(m,n)*lcm(m,n) = mn
16.6%
Find all prime factors
Immediately try factoring/simplifying when possible

19. Triangle abc with d on the outside with a line. What does d = ?
0.15n + 0.08(5) = 0.1(n+5)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Exterior angle d is equal to the sum of the two remote interior angles a and b
Group 1 + Group 2 + Neither - Both = Total

20. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
(# of favorable outcomes) / (# of possible outcomes)
347
(x-n(n)y-n)
market value

21. 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 9
(# of favorable outcomes) / (# of possible outcomes)
The total amount before any deductions
$11 - 025

22. Combined Events: E or F
4/3 TT r ^3
n! / (n - r)!
-b +- sq. rt(b^2 - 4ac) / 2a
P(E) + P(F) - P(E and F)

23. Work problem rule
Sum of digits is multiple of 9
Figure out the probability for each individual event. Multiply the individual probabilities together.
Number is a multiple of 3 and 2
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.

24. How to check whether a number is a multiple of 4.
347
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.
p/100 = is/of

25. 2nd Rule of Probability: P(E) = 1 - P(not E)
Balancing
The probability of an event occurring plus the probability of the event not occurring = 1
12^3
Principal (1 + interest/number times compounded)^(t)(n)

26. Number added or deleted
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
The amount after deductions
The total amount before any deductions
principle (interest rate - in decimal form) (time - in years)

27. gcd(m,n)*lcm(m,n)
gcd(m,n)*lcm(m,n) = mn
Last two digits are multiple of 4 or the number can be divided by 2 twice.
(total distance) / (total time)
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

28. Three triangle length patterns
Principal (1 + interest/number times compounded)^(t)(n)
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.
3-4-5 - 5-12-13 - 9-12-15
Minor arc = 2(inscribed angle)

29. Set Problems formula
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
market value
(x-n(n)y-n)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

30. Quadratic formula
347
-b +- sq. rt(b^2 - 4ac) / 2a
Immediately UNFACTOR or vice versa
P(event NOT occurring) = 1 - P(event occurring)

31. How to check whether a number is a multiple of 12.
(# of favorable outcomes) / (# of possible outcomes)
Sum of digits is multiple of 3 - last two digits multiple of 4.
1.7
Sum of digits is multiple of 9

32. Properties of 0
14 liters
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Exterior angle d is equal to the sum of the two remote interior angles a and b

33. 3^3 x 4^3 = ?
Sum of digits is multiple of 9
12^3
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
x(sq. rt 3) - x - 2x

34. 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.
2 steps
12^3
1st Rule of Probability: Basic Rule is what?
(# of favorable outcomes) / (# of possible outcomes)

35. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
Purchase price
Balancing
A = P(1 + r) ^n
14 liters

36. Inscribed Angle - Minor Arc
(sum of bases)(height) / 2
A = P(1 + r) ^n
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
Minor arc = 2(inscribed angle)

37. Combined Events: E and F
Last two digits are multiple of 4 or the number can be divided by 2 twice.
(amount of change) / (original amount)
P(E)P(F)
Any multiplication involving an even number creates an even product.

38. Sq. rt(2)
1.4
3-4-5 - 5-12-13 - 9-12-15
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)
22

39. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
22
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Gross Profit = Selling Price - Cost
The probability of an event occurring plus the probability of the event not occurring = 1

40. Volume of a sphere
at least 3 steps
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.
4/3 TT r ^3
0.15n + 0.08(5) = 0.1(n+5)

41. Indistinguishable events how to find the number of permutations

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42. 30-60-90 triangle basic lengths of sides
(total distance) / (total time)
Sum of digits is multiple of 3 - last two digits multiple of 4.
x(sq. rt 3) - x - 2x
at least 3 steps

43. 2n - 2n+2 - 2n+4
gcd(m,n)*lcm(m,n) = mn
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
| A union B| = |A| + |B| - |A intersect B|
Even

44. Price purchased for by wholesaler
at least 3 steps
(sum of bases)(height) / 2
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Purchase price

45. Always try to factor
Minor arc = 2(inscribed angle)
always try to factor
market value
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.

46. The number of outcomes that result in A divided by the total number of possible outcomes.
Figure out the probability for each individual event. Multiply the individual probabilities together.
The probability of event occurring is...
y2 - y1 / x2 - x1
n! / (n - r)!

47. Dependent events: When are two events said to be dependent events?
market value
| A union B| = |A| + |B| - |A intersect B|
If the outcome of one event affects the outcome of the other event.
1

48. The number of ways independent events can occur together.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
gcd(m,n)*lcm(m,n) = mn
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.
Any multiplication involving an even number creates an even product.

49. 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?
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
0.15n + 0.08(5) = 0.1(n+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.
Odd

50. Prime Factorization to find Greatest Common Factor
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
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.
D or E