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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 find all divisors of a number
The amount after deductions
Find all prime factors
market value
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

2. 1/6 = 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%
(n-1)!
n! / (n - r)!

3. 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?
at least 3 steps
1
0.15n + 0.08(5) = 0.1(n+5)
Gross Profit = Selling Price - Cost

4. 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.
Organize into a grid.
12^3
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)
always try to factor

5. 30-60-90 triangle basic lengths of sides
x(sq. rt 3) - x - 2x
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)
y2 - y1 / x2 - x1
1.7

6. Compound interest rule
Find simple interest then look for the answer that is a little bigger
Minor arc = 2(inscribed angle)
The amount after deductions
16.6%

7. Odd and Even rule.
22
Any multiplication involving an even number creates an even product.
Gross Profit = Selling Price - Cost
A = P(1 + r) ^n

8. Combined Events: E and F
(sum of bases)(height) / 2
1
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
P(E)P(F)

9. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
D or E
3 - 6 - 9 - 12
Any multiplication involving an even number creates an even product.
Find all prime factors

10. Quadratic formula
-b +- sq. rt(b^2 - 4ac) / 2a
at least 3 steps
market value
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

11. Set Problems formula
(x-n(n)y-n)
Odd
22
(total A) / (total B)

12. How to check for a prime number.

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13. 45-45-90 triangle basic lengths of sides
$11 - 025
x - x - x(sq. rt 2)
Purchase price
(total distance) / (total time)

14. How to check whether a number is a multiple of 12.
Sum of digits is multiple of 3 - last two digits multiple of 4.
Immediately UNFACTOR or vice versa
x - x - x(sq. rt 2)
2 steps

15. 3^3 x 4^3 = ?
Immediately UNFACTOR or vice versa
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
12^3
Find all prime factors

16. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
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.
A = P(1 + r) ^n
(total A) / (total B)
Any multiplication involving an even number creates an even product.

17. Sq. rt(2)
12.5%
1.4
P(E) + P(F) - P(E and F)
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.

18. How to find the slope.
1 - P(E)
Exterior angle d is equal to the sum of the two remote interior angles a and b
D or E
y2 - y1 / x2 - x1

19. How do you multiply roots together.
16.6%
Find all prime factors
always try to factor
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

20. 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 3
principle (interest rate - in decimal form) (time - in years)
Balancing
Even

21. How to check whether a number is a multiple of 4.
sum = (average)(number of terms)
Purchase price
Last two digits are multiple of 4 or the number can be divided by 2 twice.
market value

22. The number of ways independent events can occur together.
Find simple interest then look for the answer that is a little bigger
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Figure out the probability for each individual event. Multiply the individual probabilities together.
(sum of bases)(height) / 2

23. Compound interest formula
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Principal (1 + interest/number times compounded)^(t)(n)
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
x - x - x(sq. rt 2)

24. How to check whether number is multiple of 9
at least 3 steps
Sum of digits is multiple of 9
Organize into a grid.
Group 1 + Group 2 + Neither - Both = Total

25. 0! = ?
Find all prime factors
x(sq. rt 3) - x - 2x
(amount of change) / (original amount)
1

26. The number of outcomes that result in A divided by the total number of possible outcomes.
The probability of event occurring is...
______ |m-n|
Immediately try factoring/simplifying when possible
Any multiplication involving an even number creates an even product.

27. Multiples of 3
P(event NOT occurring) = 1 - P(event occurring)
3 - 6 - 9 - 12
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.
x(sq. rt 3) - x - 2x

28. Triangle abc with d on the outside with a line. What does d = ?
14 liters
Last two digits are multiple of 4 or the number can be divided by 2 twice.
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.
Exterior angle d is equal to the sum of the two remote interior angles a and b

29. Simple probability
12.5%
1.4
22
(# of favorable outcomes) / (# of possible outcomes)

30. What does the Sum of the angles in a Regular Polygon formula look like?
sum = (average)(number of terms)
180(n-2)
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.
Exterior angle d is equal to the sum of the two remote interior angles a and b

31. Permutations: Order Matters
n! / (n - r)!
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.
(total A) / (total B)
principle (interest rate - in decimal form) (time - in years)

32. To determine multiple-event probability where each individual event must occur in a certain way.
1 - P(E)
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
Figure out the probability for each individual event. Multiply the individual probabilities together.

33. (1/4)^2
1/16
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
P(E)P(F)
The total amount before any deductions

34. Work problem rule
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.
Find all prime factors
P(E)P(F)

35. Combined Events: E or F
1.7
P(E) + P(F) - P(E and F)
always try to factor
0.15n + 0.08(5) = 0.1(n+5)

36. Average Rate: Average A per B
A = P(1 + r) ^n
P(E) + P(F) - P(E and F)
(total A) / (total B)
Organize into a grid.

37. gcd(m,n)*lcm(m,n)
The total amount before any deductions
3 - 6 - 9 - 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.
gcd(m,n)*lcm(m,n) = mn

38. Gross Profit formula
1st Rule of Probability: Basic Rule is what?
The amount after deductions
Gross Profit = Selling Price - Cost
16.6%

39. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
x - x - x(sq. rt 2)
(total A) / (total B)
(n-1)!
Number is a multiple of 3 and 2

40. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
Figure out the probability for each individual event. Multiply the individual probabilities together.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
3-4-5 - 5-12-13 - 9-12-15
4/3 TT r ^3

41. Prime Factorization to find Greatest Common Factor
principle (interest rate - in decimal form) (time - in years)
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
| A union B| = |A| + |B| - |A intersect B|
Divide 4999 by 15 => 333 integers

42. 3rd Rule of Probability: Conditional Probability
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.
x(sq. rt 3) - x - 2x
P(event NOT occurring) = 1 - P(event occurring)
s Sq. rt (x^r)

43. Volume of a sphere
The probability of event occurring is...
4/3 TT r ^3
Odd numbers only have ___________
180(n-2)

44. Number added or deleted
p/100 = is/of
The probability of an event occurring plus the probability of the event not occurring = 1
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.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

45. What to do with equations that have fractions
gcd(m,n)*lcm(m,n) = mn
Odd
12^3
Immediately try factoring/simplifying when possible

46. Three triangle length patterns
$11 - 025
3-4-5 - 5-12-13 - 9-12-15
Divide 4999 by 15 => 333 integers
12.5%

47. 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
Number is a multiple of 3 and 2
Balancing
12^3
(total A) / (total B)

48. 5/6 = what %
always try to factor
83.3%
1.4
x(sq. rt 3) - x - 2x

49. Price sold for by retailer (after markup)
3-4-5 - 5-12-13 - 9-12-15
Sum of digits is multiple of 9
market value
x(sq. rt 3) - x - 2x

50. 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?
Find simple interest then look for the answer that is a little bigger
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
14 liters
Any multiplication involving an even number creates an even product.