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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. 45-45-90 triangle basic lengths of sides
Principal (1 + interest/number times compounded)^(t)(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
x - x - x(sq. rt 2)
gcd(m,n)*lcm(m,n) = mn

2. What to do with equations that have fractions
14 liters
P(event NOT occurring) = 1 - P(event occurring)
Immediately try factoring/simplifying when possible
D or E

3. Number added or deleted
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
3-4-5 - 5-12-13 - 9-12-15
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
347

4. Price sold for by retailer (after markup)
83.3%
market value
If the outcome of one event affects the outcome of the other event.
Odd numbers only have ___________

5. Triangle abc with d on the outside with a line. What does d = ?
Exterior angle d is equal to the sum of the two remote interior angles a and b
14 liters
n! / (n - r)!
x - x - x(sq. rt 2)

6. The number of outcomes that result in A divided by the total number of possible outcomes.
The probability of an event occurring plus the probability of the event not occurring = 1
0.15n + 0.08(5) = 0.1(n+5)
The probability of event occurring is...
Any multiplication involving an even number creates an even product.

7. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
12.5%
(total A) / (total B)
22
principle (interest rate - in decimal form) (time - in years)

8. In general - difficult questions require how many steps to solve?
-b +- sq. rt(b^2 - 4ac) / 2a
P(E)P(F)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
at least 3 steps

9. Multiples of 3
Balancing
1 - P(E)
3 - 6 - 9 - 12
2 steps

10. Intersecting Sets
1 - P(E)
1/16
| A union B| = |A| + |B| - |A intersect B|
P(E) + P(F) - P(E and F)

11. Odd Factors
1
s Sq. rt (x^r)
Odd numbers only have ___________
(# of favorable outcomes) / (# of possible outcomes)

12. Multiplication principle
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.
(total distance) / (total time)
3 - 6 - 9 - 12
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

13. 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
p/100 = is/of
P(E)P(F)
0.15n + 0.08(5) = 0.1(n+5)

14. Trial Problems: look at the probability of NOT OCCURRING
1st Rule of Probability: Basic Rule is what?
Sum of digits is multiple of 3 - last two digits multiple of 4.
Find simple interest then look for the answer that is a little bigger
P(event NOT occurring) = 1 - P(event occurring)

15. What does the Sum of the angles in a Regular Polygon formula look like?
180(n-2)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
y2 - y1 / x2 - x1
1.4

16. Formula for Mixed Group problems (involving Both/Neither)
1.7
Group 1 + Group 2 + Neither - Both = Total
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

17. gcd(m,n)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
______ |m-n|
at least 3 steps
The amount after deductions

18. 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
Find simple interest then look for the answer that is a little bigger
Immediately try factoring/simplifying when possible
Immediately UNFACTOR or vice versa

19. To determine the number of integers less than 5000 that are evenly divisible by 15...?
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.
Gross Profit = Selling Price - Cost
Divide 4999 by 15 => 333 integers
y2 - y1 / x2 - x1

20. 5/6 = what %
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
83.3%
A = P(1 + r) ^n
Organize into a grid.

21. Compound interest formula
Principal (1 + interest/number times compounded)^(t)(n)
Immediately UNFACTOR or vice versa
Even
Gross Profit = Selling Price - Cost

22. 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
16.6%
1 - P(E)
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 bases)(height) / 2

23. Combined Events: E and F
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
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.
y2 - y1 / x2 - x1
P(E)P(F)

24. Permutations: Order Matters
Number is a multiple of 3 and 2
principle (interest rate - in decimal form) (time - in years)
Exterior angle d is equal to the sum of the two remote interior angles a and b
n! / (n - r)!

25. Volume of a sphere
4/3 TT r ^3
Purchase price
14 liters
22

26. When you see an equation in factored form in a question?
Immediately UNFACTOR or vice versa
Number is a multiple of 3 and 2
(total distance) / (total time)
The probability of event occurring is...

27. Work problem rule
3-4-5 - 5-12-13 - 9-12-15
Find all prime factors
Purchase price
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.

28. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
$11 - 025
Balancing
1.4
Sum of digits is multiple of 3

29. Formula for area of a Trapezoid
(sum of bases)(height) / 2
(amount of change) / (original amount)
1/16
Sum of digits is multiple of 3

30. 2nd Rule of Probability: P(E) = 1 - P(not E)
Immediately try factoring/simplifying when possible
The probability of an event occurring plus the probability of the event not occurring = 1
If the outcome of one event affects the outcome of the other event.
y2 - y1 / x2 - x1

31. How do you multiply roots together.
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
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
principle (interest rate - in decimal form) (time - in years)

32. Price purchased for by wholesaler
Purchase price
Gross Profit = Selling Price - Cost
1/16
Odd

33. 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.
p/100 = is/of
$11 - 025
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.

34. 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.
Group 1 + Group 2 + Neither - Both = Total
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)
The total amount before any deductions

35. 30-60-90 triangle basic lengths of sides
4/3 TT r ^3
Even
-b +- sq. rt(b^2 - 4ac) / 2a
x(sq. rt 3) - x - 2x

36. Combined Events: E or F
market value
y2 - y1 / x2 - x1
P(E) + P(F) - P(E and F)
Minor arc = 2(inscribed angle)

37. 2n - 2n+2 - 2n+4
1 - P(E)
The total amount before any deductions
Even
4/3 TT r ^3

38. Properties of 0
83.3%
p/100 = is/of
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

39. Percent increase = ?
(# of favorable outcomes) / (# of possible outcomes)
(amount of change) / (original amount)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
______ |m-n|

40. 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
Principal (1 + interest/number times compounded)^(t)(n)
Even
Balancing
P(E)P(F)

41. 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.
P(event NOT occurring) = 1 - P(event occurring)
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.
1.7
Organize into a grid.

42. Average Rate: Average speed
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.
(total distance) / (total time)
-b +- sq. rt(b^2 - 4ac) / 2a
(amount of change) / (original amount)

43. x^r/s = ?
x - x - x(sq. rt 2)
Purchase price
(x-n(n)y-n)
s Sq. rt (x^r)

44. 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)
at least 3 steps
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
12.5%

45. 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?
A = P(1 + r) ^n
0.15n + 0.08(5) = 0.1(n+5)
1.4
16.6%

46. To determine multiple-event probability where each individual event must occur in a certain way.
Figure out the probability for each individual event. Multiply the individual probabilities together.
p/100 = is/of
Find simple interest then look for the answer that is a little bigger
1 - P(E)

47. Average Rate: Average A per B
Odd
(total A) / (total B)
P(event NOT occurring) = 1 - P(event occurring)
Number is a multiple of 3 and 2

48. 1/6 = what %
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
always try to factor
P(E) + P(F) - P(E and F)
16.6%

49. 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.
1st Rule of Probability: Basic Rule is what?
Gross Profit = Selling Price - Cost
always try to factor
y2 - y1 / x2 - x1

50. Combined Events: Not E = P(not E) = ?
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.
(total A) / (total B)
1 - P(E)
Minor arc = 2(inscribed angle)