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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. 30-60-90 triangle basic lengths of sides
12^3
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
x(sq. rt 3) - x - 2x
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.

2. What to do with equations that have fractions
(total distance) / (total time)
Immediately try factoring/simplifying when possible
Organize into a grid.
Minor arc = 2(inscribed angle)

3. Combined Events: E or F
Purchase price
P(E) + P(F) - P(E and F)
The amount after deductions
12.5%

4. How to check whether a number is a multiple of 3.
Figure out the probability for each individual event. Multiply the individual probabilities together.
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
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.
Sum of digits is multiple of 3

5. 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
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)
4/3 TT r ^3
The probability of an event occurring plus the probability of the event not occurring = 1
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.

6. How to find the slope.
180(n-2)
y2 - y1 / x2 - x1
gcd(m,n)*lcm(m,n) = mn
The total amount before any deductions

7. Formula for area of a Trapezoid
Find all prime factors
Minor arc = 2(inscribed angle)
(sum of bases)(height) / 2
s Sq. rt (x^r)

8. How to check for a prime number.

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9. Simple probability
(total distance) / (total time)
(# of favorable outcomes) / (# of possible outcomes)
3-4-5 - 5-12-13 - 9-12-15
Find simple interest then look for the answer that is a little bigger

10. Volume of a sphere
Odd
3-4-5 - 5-12-13 - 9-12-15
4/3 TT r ^3
1.7

11. The number of ways independent events can occur together.
______ |m-n|
Sum of digits is multiple of 3
2 steps
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

12. Sq. rt(2)
0.15n + 0.08(5) = 0.1(n+5)
Any multiplication involving an even number creates an even product.
(# of favorable outcomes) / (# of possible outcomes)
1.4

13. To determine multiple-event probability where each individual event must occur in a certain way.
Even
Figure out the probability for each individual event. Multiply the individual probabilities together.
1st Rule of Probability: Basic Rule is what?
D or E

14. In general - difficult questions require how many steps to solve?
P(E) + P(F) - P(E and F)
Number is a multiple of 3 and 2
If the outcome of one event affects the outcome of the other event.
at least 3 steps

15. Prime Factorization to find Greatest Common Factor
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
(x-n(n)y-n)
Sum of digits is multiple of 3 - last two digits multiple of 4.
P(E)P(F)

16. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
x - x - x(sq. rt 2)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
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)
Figure out the probability for each individual event. Multiply the individual probabilities together.

17. Trial Problems: look at the probability of NOT OCCURRING
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.
1.7
(n-1)!

18. Average Rate: Average speed
Gross Profit = Selling Price - Cost
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Any multiplication involving an even number creates an even product.
(total distance) / (total time)

19. Combined Events: Not E = P(not E) = ?
1 - P(E)
p/100 = is/of
(total distance) / (total time)
3 - 6 - 9 - 12

20. Number added or deleted
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
180(n-2)
4/3 TT r ^3
sum = (average)(number of terms)

21. 45-45-90 triangle basic lengths of sides
Odd
P(event NOT occurring) = 1 - P(event occurring)
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)
x - x - x(sq. rt 2)

22. Odd and Even rule.
at least 3 steps
Any multiplication involving an even number creates an even product.
______ |m-n|
| A union B| = |A| + |B| - |A intersect B|

23. Sq. rt(3)
(n-1)!
1.7
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Odd

24. Net
The amount after deductions
16.6%
Exterior angle d is equal to the sum of the two remote interior angles a and b
12.5%

25. Indistinguishable events how to find the number of permutations

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26. 5/6 = what %
3-4-5 - 5-12-13 - 9-12-15
83.3%
P(E) + P(F) - P(E and F)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

27. 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.
Find all prime factors
12^3
4/3 TT r ^3
1st Rule of Probability: Basic Rule is what?

28. How to find all divisors of a number
D or E
Find all prime factors
1st Rule of Probability: Basic Rule is what?
principle (interest rate - in decimal form) (time - in years)

29. Work problem rule
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
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.
1.4
-b +- sq. rt(b^2 - 4ac) / 2a

30. 0! = ?
180(n-2)
1
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Sum of digits is multiple of 3 - last two digits multiple of 4.

31. 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.
Figure out the probability for each individual event. Multiply the individual probabilities together.
principle (interest rate - in decimal form) (time - in years)
(x-n(n)y-n)
Organize into a grid.

32. 2n+1 - 2n+3 - 2n+5
Odd
p/100 = is/of
Find all prime factors
If the outcome of one event affects the outcome of the other event.

33. (1/4)^2
The probability of event occurring is...
Any multiplication involving an even number creates an even product.
2 steps
1/16

34. 1/6 = what %
sum = (average)(number of terms)
16.6%
Figure out the probability for each individual event. Multiply the individual probabilities together.
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

35. gcd(m,n)*lcm(m,n)
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.
gcd(m,n)*lcm(m,n) = mn
16.6%
Gross Profit = Selling Price - Cost

36. The number of outcomes that result in A divided by the total number 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.
3-4-5 - 5-12-13 - 9-12-15
The probability of event occurring is...
sum = (average)(number of terms)

37. Price purchased for by wholesaler
Minor arc = 2(inscribed angle)
______ |m-n|
(amount of change) / (original amount)
Purchase price

38. Triangle abc with d on the outside with a line. What does d = ?
$11 - 025
3-4-5 - 5-12-13 - 9-12-15
Exterior angle d is equal to the sum of the two remote interior angles a and b
y2 - y1 / x2 - x1

39. How do you multiply roots together.
(total A) / (total B)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Find simple interest then look for the answer that is a little bigger
P(event NOT occurring) = 1 - P(event occurring)

40. Always try to factor
P(event NOT occurring) = 1 - P(event occurring)
always try to factor
(x-n(n)y-n)
Gross Profit = Selling Price - Cost

41. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
principle (interest rate - in decimal form) (time - in years)
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
Sum of digits is multiple of 3 - last two digits multiple of 4.
$11 - 025

42. To determine the number of integers less than 5000 that are evenly divisible by 15...?
Divide 4999 by 15 => 333 integers
Last two digits are multiple of 4 or the number can be divided by 2 twice.
The probability of event occurring is...
n! / (n - r)!

43. Three triangle length patterns
n! / (n - r)!
3-4-5 - 5-12-13 - 9-12-15
A = P(1 + r) ^n
1 - P(E)

44. Combined Events: E and F
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
p/100 = is/of
at least 3 steps
P(E)P(F)

45. Average Rate: Average A per 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
(total A) / (total B)
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 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)

46. Gross
4/3 TT r ^3
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
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.
The total amount before any deductions

47. Percent increase = ?
1st Rule of Probability: Basic Rule is what?
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
| A union B| = |A| + |B| - |A intersect B|
(amount of change) / (original amount)

48. Multiples of 3
2 steps
3 - 6 - 9 - 12
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
Number is a multiple of 3 and 2

49. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
p/100 = is/of
Last two digits are multiple of 4 or the number can be divided by 2 twice.
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.
347

50. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
1
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.
$11 - 025