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GMAT Quantitative General

Subjects : gmat, math

Instructions:

Answer 50 questions in 15 minutes.
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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. 5/6 = what %
83.3%
Odd numbers only have ___________
1 - P(E)
2 steps

2. How to find the slope.
at least 3 steps
______ |m-n|
Organize into a grid.
y2 - y1 / x2 - x1

3. 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.
The probability of an event occurring plus the probability of the event not occurring = 1
4/3 TT r ^3
1st Rule of Probability: Basic Rule is what?
| A union B| = |A| + |B| - |A intersect B|

4. 3^3 x 4^3 = ?
12^3
x(sq. rt 3) - x - 2x
principle (interest rate - in decimal form) (time - in years)
1.7

5. Set Problems formula
Odd numbers only have ___________
Purchase price
16.6%
(x-n(n)y-n)

6. Sum of consecutive numbers
$11 - 025
sum = (average)(number of terms)
______ |m-n|
s Sq. rt (x^r)

7. Three triangle length patterns
The probability of event occurring is...
3-4-5 - 5-12-13 - 9-12-15
Find simple interest then look for the answer that is a little bigger
12.5%

8. Combined Events: Not E = P(not E) = ?
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)
1 - P(E)
Group 1 + Group 2 + Neither - Both = Total
market value

9. 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?
P(event NOT occurring) = 1 - P(event occurring)
14 liters
The amount after deductions
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

10. Formula for Mixed Group problems (involving Both/Neither)
Group 1 + Group 2 + Neither - Both = Total
| A union B| = |A| + |B| - |A intersect B|
gcd(m,n)*lcm(m,n) = mn
Minor arc = 2(inscribed angle)

11. Price purchased for by wholesaler
sum = (average)(number of terms)
2 steps
Purchase price
p/100 = is/of

12. Work problem rule
P(event NOT occurring) = 1 - P(event occurring)
1.4
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.
Divide 4999 by 15 => 333 integers

13. Probability and Geometry.
The total amount before any deductions
Even
Last two digits are multiple of 4 or the number can be divided by 2 twice.
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

14. Inscribed Angle - Minor Arc
-b +- sq. rt(b^2 - 4ac) / 2a
Minor arc = 2(inscribed angle)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
3-4-5 - 5-12-13 - 9-12-15

15. How to check whether a number is a multiple of 12.
3-4-5 - 5-12-13 - 9-12-15
1st Rule of Probability: Basic Rule is what?
P(event NOT occurring) = 1 - P(event occurring)
Sum of digits is multiple of 3 - last two digits multiple of 4.

16. Triangle abc with d on the outside with a line. What does d = ?
The probability of event occurring is...
(amount of change) / (original amount)
Exterior angle d is equal to the sum of the two remote interior angles a and b
(total A) / (total B)

17. What to do with equations that have fractions
Immediately try factoring/simplifying when possible
(# of favorable outcomes) / (# of possible outcomes)
sum = (average)(number of terms)
Number is a multiple of 3 and 2

18. Sq. rt(3)
s Sq. rt (x^r)
P(event NOT occurring) = 1 - P(event occurring)
1.7
principle (interest rate - in decimal form) (time - in years)

19. Trial Problems: look at the probability of NOT OCCURRING
P(event NOT occurring) = 1 - P(event occurring)
1
Organize into a grid.
Sum of digits is multiple of 3

20. Multiples of 3
3 - 6 - 9 - 12
The probability of event occurring is...
Odd numbers only have ___________
Purchase price

21. 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)
Immediately UNFACTOR or vice versa
Purchase price
Balancing

22. gcd(m,n)*lcm(m,n)
(x-n(n)y-n)
gcd(m,n)*lcm(m,n) = mn
x(sq. rt 3) - x - 2x
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

23. To determine the number of integers less than 5000 that are evenly divisible by 15...?
Divide 4999 by 15 => 333 integers
s Sq. rt (x^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.
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

24. The number of ways independent events can occur together.
22
Sum of digits is multiple of 9
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
x(sq. rt 3) - x - 2x

25. 30-60-90 triangle basic lengths of sides
Find simple interest then look for the answer that is a little bigger
The probability of event occurring is...
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.
x(sq. rt 3) - x - 2x

26. gcd(m,n)
4/3 TT r ^3
______ |m-n|
(n-1)!
x - x - x(sq. rt 2)

27. Average Rate: Average A per B
Purchase price
22
The total amount before any deductions
(total A) / (total B)

28. 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
$11 - 025
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
(total A) / (total B)
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.

29. Percent Formula
(x-n(n)y-n)
y2 - y1 / x2 - x1
p/100 = is/of
The probability of event occurring is...

30. Compound interest formula
Find all prime factors
Figure out the probability for each individual event. Multiply the individual probabilities together.
1 - P(E)
Principal (1 + interest/number times compounded)^(t)(n)

31. Formula for area of a Trapezoid
Find simple interest then look for the answer that is a little bigger
Sum of digits is multiple of 3
Divide 4999 by 15 => 333 integers
(sum of bases)(height) / 2

32. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
Even
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
(n-1)!
1 - P(E)

33. 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?
Odd
Figure out the probability for each individual event. Multiply the individual probabilities together.
0.15n + 0.08(5) = 0.1(n+5)
always try to factor

34. 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)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
The total amount before any deductions
(n-1)!

35. Combined Events: E and F
Divide 4999 by 15 => 333 integers
(amount of change) / (original amount)
P(E)P(F)
Gross Profit = Selling Price - Cost

36. Sq. rt(2)
Organize into a grid.
Immediately try factoring/simplifying when possible
1.4
1

37. Gross Profit formula
If the outcome of one event affects the outcome of the other event.
Gross Profit = Selling Price - Cost
Organize into a grid.
12^3

38. 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
D or E
______ |m-n|
A = P(1 + r) ^n

39. 4th rule of Probability
Odd
always try to factor
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(sq. rt 3) - x - 2x

40. How to check whether a number is a multiple of 6
Number is a multiple of 3 and 2
1.4
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
(amount of change) / (original amount)

41. 45-45-90 triangle basic lengths of sides
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 digits is multiple of 3 - last two digits multiple of 4.
x - x - x(sq. rt 2)
y2 - y1 / x2 - x1

42. x^r/s = ?
s Sq. rt (x^r)
The amount after deductions
Even
The total amount before any deductions

43. 0! = ?
Odd numbers only have ___________
1
D or E
3-4-5 - 5-12-13 - 9-12-15

44. How to find all divisors of a number
The probability of an event occurring plus the probability of the event not occurring = 1
Find all prime factors
______ |m-n|
y2 - y1 / x2 - x1

45. How to check for a prime number.

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46. Odd and Even rule.
2 steps
always try to factor
Any multiplication involving an even number creates an even product.
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

47. Average Rate: Average speed
(total distance) / (total time)
market value
(# of favorable outcomes) / (# of possible outcomes)
Sum of digits is multiple of 9

48. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
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.
A = P(1 + r) ^n
Number is a multiple of 3 and 2

49. In general - medium questions require how many steps to solve?
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
2 steps
Find all prime factors
Immediately try factoring/simplifying when possible

50. Price sold for by retailer (after markup)
(total distance) / (total time)
(sum of bases)(height) / 2
market value
1.4

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GMAT Quantitative General

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