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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. Price sold for by retailer (after markup)
A = P(1 + r) ^n
$11 - 025
market value
Find all prime factors

2. gcd(m,n)*lcm(m,n)
Find all prime factors
Divide 4999 by 15 => 333 integers
gcd(m,n)*lcm(m,n) = mn
(amount of change) / (original amount)

3. Multiplication principle
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
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
347
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

4. Compound interest rule
Divide 4999 by 15 => 333 integers
P(E) + P(F) - P(E and F)
x(sq. rt 3) - x - 2x
Find simple interest then look for the answer that is a little bigger

5. Inscribed Angle - Minor Arc
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.
Minor arc = 2(inscribed angle)
Organize into a grid.
D or E

6. Percent increase = ?
(amount of change) / (original amount)
Sum of digits is multiple of 3 - last two digits multiple of 4.
Immediately try factoring/simplifying when possible
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. Trial Problems: look at the probability of NOT OCCURRING
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Immediately try factoring/simplifying when possible
P(event NOT occurring) = 1 - P(event occurring)
3 - 6 - 9 - 12

8. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
(amount of change) / (original amount)
$11 - 025
______ |m-n|
| A union B| = |A| + |B| - |A intersect B|

9. Set Problems formula
4/3 TT r ^3
(x-n(n)y-n)
(total distance) / (total time)
3-4-5 - 5-12-13 - 9-12-15

10. Work problem rule
Any multiplication involving an even number creates an even product.
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.
(amount of change) / (original amount)
Balancing

11. 1/8 = what %
12.5%
Gross Profit = Selling Price - Cost
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Immediately UNFACTOR or vice versa

12. 1/6 = what %
1/16
16.6%
(sum of bases)(height) / 2
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

13. Formula for area of a Trapezoid
Balancing
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 bases)(height) / 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.

14. 3^3 x 4^3 = ?
12^3
The total amount before any deductions
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! / (n - r)!

15. Intersecting Sets
| A union B| = |A| + |B| - |A intersect B|
3 - 6 - 9 - 12
Immediately UNFACTOR or vice versa
at least 3 steps

16. How to check whether number is multiple of 9
Sum of digits is multiple of 9
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
at least 3 steps
(total A) / (total B)

17. To determine the number of integers less than 5000 that are evenly divisible by 15...?
Divide 4999 by 15 => 333 integers
| A union B| = |A| + |B| - |A intersect B|
Immediately UNFACTOR or vice versa
Balancing

18. Price purchased for by wholesaler
180(n-2)
Purchase price
Organize into a grid.
Sum of digits is multiple of 9

19. 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
Any multiplication involving an even number creates an even product.
Odd numbers only have ___________
Sum of digits is multiple of 3 - last two digits multiple of 4.

20. Gross Profit formula
Gross Profit = Selling Price - Cost
3 - 6 - 9 - 12
P(E)P(F)
The probability of event occurring is...

21. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
(n-1)!
1 - P(E)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
-b +- sq. rt(b^2 - 4ac) / 2a

22. Permutations: Order Matters
n! / (n - r)!
Odd
______ |m-n|
(n-1)!

23. How to check whether a number is a multiple of 3.
1.4
P(E)P(F)
Principal (1 + interest/number times compounded)^(t)(n)
Sum of digits is multiple of 3

24. How do you multiply roots together.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
at least 3 steps
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.
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

25. To determine multiple-event probability where each individual event must occur in a certain way.
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)
Figure out the probability for each individual event. Multiply the individual probabilities together.
(amount of change) / (original amount)

26. 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
p/100 = is/of
| A union B| = |A| + |B| - |A intersect B|
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
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.

27. Triangle abc with d on the outside with a line. What does d = ?
at least 3 steps
The total amount before any deductions
Exterior angle d is equal to the sum of the two remote interior angles a and b
Principal (1 + interest/number times compounded)^(t)(n)

28. 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
The amount after deductions
Immediately try factoring/simplifying when possible
Balancing
| A union B| = |A| + |B| - |A intersect B|

29. 5/6 = what %
83.3%
The probability of an event occurring plus the probability of the event not occurring = 1
12.5%
Sum of digits is multiple of 9

30. 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?
1.4
0.15n + 0.08(5) = 0.1(n+5)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
P(E) + P(F) - P(E and F)

31. 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
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.
at least 3 steps
83.3%

32. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
347
$11 - 025
Sum of digits is multiple of 3
-b +- sq. rt(b^2 - 4ac) / 2a

33. How to find the slope.
y2 - y1 / x2 - x1
(amount of change) / (original amount)
(total distance) / (total time)
P(E) + P(F) - P(E and F)

34. Number added or deleted
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Group 1 + Group 2 + Neither - Both = Total
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Sum of digits is multiple of 3

35. Gross
1st Rule of Probability: Basic Rule is what?
The total amount before any deductions
Any multiplication involving an even number creates an even product.
4/3 TT r ^3

36. Odd and Even rule.
Number is a multiple of 3 and 2
Divide 4999 by 15 => 333 integers
p/100 = is/of
Any multiplication involving an even number creates an even product.

37. 3rd Rule of Probability: Conditional Probability
Divide 4999 by 15 => 333 integers
Figure out the probability for each individual event. Multiply the individual probabilities together.
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.
s Sq. rt (x^r)

38. What to do with equations that have fractions
$11 - 025
12^3
14 liters
Immediately try factoring/simplifying when possible

39. How to check whether a number is a multiple of 12.
-b +- sq. rt(b^2 - 4ac) / 2a
Sum of digits is multiple of 3 - last two digits multiple of 4.
(sum of bases)(height) / 2
Find all prime factors

40. Formula for Mixed Group problems (involving Both/Neither)
12.5%
Odd
Odd numbers only have ___________
Group 1 + Group 2 + Neither - Both = Total

41. Percent Formula
p/100 = is/of
s Sq. rt (x^r)
-b +- sq. rt(b^2 - 4ac) / 2a
16.6%

42. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
D or E
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
If the outcome of one event affects the outcome of the other event.
Figure out the probability for each individual event. Multiply the individual probabilities together.

43. Net
347
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
The probability of an event occurring plus the probability of the event not occurring = 1
The amount after deductions

44. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
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.
1.4
A = P(1 + r) ^n
1.7

45. Combined Events: E or F
Purchase price
Immediately try factoring/simplifying when possible
Gross Profit = Selling Price - Cost
P(E) + P(F) - P(E and F)

46. 30-60-90 triangle basic lengths of sides
x(sq. rt 3) - x - 2x
12^3
Principal (1 + interest/number times compounded)^(t)(n)
Odd numbers only have ___________

47. Average Rate: Average A per B
(total A) / (total B)
Group 1 + Group 2 + Neither - Both = Total
1.4
3 - 6 - 9 - 12

48. Indistinguishable events how to find the number of permutations

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49. When you see an equation in factored form in a question?
Immediately UNFACTOR or vice versa
1st Rule of Probability: Basic Rule is what?
market value
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

50. How to find all divisors of a number
Find all prime factors
(x-n(n)y-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
Balancing