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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 purchased for by wholesaler
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.
Purchase price
22

2. Three triangle length patterns
3-4-5 - 5-12-13 - 9-12-15
Immediately UNFACTOR or vice versa
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.
market value

3. The number of outcomes that result in A divided by the total number of possible outcomes.
(amount of change) / (original amount)
The amount after deductions
The total amount before any deductions
The probability of event occurring is...

4. 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
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
Purchase price
22

5. In general - difficult questions require how many steps to solve?
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.
Even
The probability of event occurring is...
at least 3 steps

6. Average Rate: Average speed
Even
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.
Immediately try factoring/simplifying when possible
(total distance) / (total time)

7. Combined Events: E and F
P(E)P(F)
market value
Immediately try factoring/simplifying when possible
Exterior angle d is equal to the sum of the two remote interior angles a and b

8. Formula for area of a Trapezoid
y2 - y1 / x2 - x1
(sum of bases)(height) / 2
Find simple interest then look for the answer that is a little bigger
P(E) + P(F) - P(E and F)

9. 3rd Rule of Probability: Conditional Probability
A = P(1 + r) ^n
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. 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
(n-1)!

10. 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 union B| = |A| + |B| - |A intersect B|
0.15n + 0.08(5) = 0.1(n+5)
1
gcd(m,n)*lcm(m,n) = mn

11. To determine the number of integers less than 5000 that are evenly divisible by 15...?
3 - 6 - 9 - 12
1st Rule of Probability: Basic Rule is what?
Divide 4999 by 15 => 333 integers
Last two digits are multiple of 4 or the number can be divided by 2 twice.

12. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
Find all prime factors
(n-1)!
Find simple interest then look for the answer that is a little bigger
Gross Profit = Selling Price - Cost

13. The number of ways independent events can occur together.
Balancing
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
(x-n(n)y-n)
The probability of an event occurring plus the probability of the event not occurring = 1

14. Sum of consecutive numbers
Figure out the probability for each individual event. Multiply the individual probabilities together.
The probability of event occurring is...
sum = (average)(number of terms)
1

15. How to check whether number is multiple of 9
Sum of digits is multiple of 9
P(event NOT occurring) = 1 - P(event occurring)
______ |m-n|
Divide 4999 by 15 => 333 integers

16. Always try to factor
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
(sum of bases)(height) / 2
The probability of event occurring is...
always try to factor

17. How to check whether a number is a multiple of 4.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
1
(n-1)!
1/16

18. Percent increase = ?
always try to factor
180(n-2)
The amount after deductions
(amount of change) / (original amount)

19. Sq. rt(3)
______ |m-n|
1
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.
1.7

20. Number added or deleted
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
1/16
3-4-5 - 5-12-13 - 9-12-15
347

21. Simple probability
(# of favorable outcomes) / (# of possible outcomes)
Divide 4999 by 15 => 333 integers
Sum of digits is multiple of 9
(total A) / (total B)

22. Gross
The total amount before any deductions
(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
Odd

23. How to check whether a number is a multiple of 12.
gcd(m,n)*lcm(m,n) = mn
Sum of digits is multiple of 3 - last two digits multiple of 4.
Sum of digits is multiple of 3
$11 - 025

24. gcd(m,n)*lcm(m,n)
gcd(m,n)*lcm(m,n) = mn
at least 3 steps
Divide 4999 by 15 => 333 integers
Immediately UNFACTOR or vice versa

25. 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?
1 - P(E)
14 liters
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

26. Volume of a sphere
at least 3 steps
4/3 TT r ^3
Organize into a grid.
p/100 = is/of

27. 1/8 = what %
(total distance) / (total time)
Gross Profit = Selling Price - Cost
12.5%
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

28. 30-60-90 triangle basic lengths of sides
1.4
1st Rule of Probability: Basic Rule is what?
gcd(m,n)*lcm(m,n) = mn
x(sq. rt 3) - x - 2x

29. Formula for Mixed Group problems (involving Both/Neither)
Group 1 + Group 2 + Neither - Both = Total
P(E) + P(F) - P(E and F)
4/3 TT r ^3
Exterior angle d is equal to the sum of the two remote interior angles a and b

30. x^r/s = ?
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)
s Sq. rt (x^r)
347
n! / (n - r)!

31. How to check whether a number is a multiple of 3.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
A = P(1 + r) ^n
Purchase price
Sum of digits is multiple of 3

32. How to check whether a number is a multiple of 6
Any multiplication involving an even number creates an even product.
$11 - 025
Number is a multiple of 3 and 2
0.15n + 0.08(5) = 0.1(n+5)

33. Dependent events: When are two events said to be dependent events?
3-4-5 - 5-12-13 - 9-12-15
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.
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
If the outcome of one event affects the outcome of the other event.

34. Combined Events: Not E = P(not E) = ?
Principal (1 + interest/number times compounded)^(t)(n)
1 - P(E)
(total distance) / (total time)
sum = (average)(number of terms)

35. Indistinguishable events how to find the number of permutations

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36. Trial Problems: look at the probability of NOT OCCURRING
Group 1 + Group 2 + Neither - Both = Total
1/16
-b +- sq. rt(b^2 - 4ac) / 2a
P(event NOT occurring) = 1 - P(event occurring)

37. Average Rate: Average A per B
22
(total A) / (total B)
Divide 4999 by 15 => 333 integers
Purchase price

38. 45-45-90 triangle basic lengths of sides
180(n-2)
x - x - x(sq. rt 2)
x(sq. rt 3) - x - 2x
principle (interest rate - in decimal form) (time - in years)

39. 2n+1 - 2n+3 - 2n+5
Odd
P(E)P(F)
The probability of event occurring is...
Immediately UNFACTOR or vice versa

40. Multiples of 3
3 - 6 - 9 - 12
principle (interest rate - in decimal form) (time - in years)
Find simple interest then look for the answer that is a little bigger
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

41. Percent Formula
p/100 = is/of
Sum of digits is multiple of 3 - last two digits multiple of 4.
(amount of change) / (original amount)
Gross Profit = Selling Price - Cost

42. Net
Even
The amount after deductions
x(sq. rt 3) - x - 2x
at least 3 steps

43. Permutations: Order Matters
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.
347
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
n! / (n - r)!

44. When you see an equation in factored form in a question?
| A union B| = |A| + |B| - |A intersect B|
Even
Immediately UNFACTOR or vice versa
x(sq. rt 3) - x - 2x

45. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
$11 - 025
x(sq. rt 3) - x - 2x
Divide 4999 by 15 => 333 integers
Find all prime factors

46. 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
347
The amount after deductions
Even

47. The average of consecutive numbers
83.3%
Principal (1 + interest/number times compounded)^(t)(n)
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 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.

48. Price sold for by retailer (after markup)
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.
market value
(total distance) / (total time)
-b +- sq. rt(b^2 - 4ac) / 2a

49. How to check for a prime number.

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50. 3^3 x 4^3 = ?
The probability of an event occurring plus the probability of the event not occurring = 1
sum = (average)(number of terms)
22
12^3