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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. 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 probability of event occurring is...
Balancing
3 - 6 - 9 - 12
Exterior angle d is equal to the sum of the two remote interior angles a and b

2. 2nd Rule of Probability: P(E) = 1 - P(not E)
The amount after deductions
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
The probability of an event occurring plus the probability of the event not occurring = 1
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

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.
3-4-5 - 5-12-13 - 9-12-15
1st Rule of Probability: Basic Rule is what?
D or E
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

4. Set Problems formula
(amount of change) / (original amount)
(x-n(n)y-n)
12^3
always try to factor

5. Number added or deleted
Exterior angle d is equal to the sum of the two remote interior angles a and b
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
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.

6. Simple probability
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
(# of favorable outcomes) / (# of possible outcomes)
Any multiplication involving an even number creates an even product.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

7. (1/4)^2
Purchase price
(sum of bases)(height) / 2
1/16
Sum of digits is multiple of 3

8. 30-60-90 triangle basic lengths of sides
Immediately UNFACTOR or vice versa
x(sq. rt 3) - x - 2x
1/16
Sum of digits is multiple of 3 - last two digits multiple of 4.

9. 0! = ?
1
Sum of digits is multiple of 9
P(E) + P(F) - P(E and F)
n! / (n - r)!

10. gcd(m,n)
______ |m-n|
3 - 6 - 9 - 12
0.15n + 0.08(5) = 0.1(n+5)
n! / (n - r)!

11. Inscribed Angle - Minor Arc
P(event NOT occurring) = 1 - P(event occurring)
Odd
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
Minor arc = 2(inscribed angle)

12. How to find all divisors of a number
2 steps
Balancing
Immediately try factoring/simplifying when possible
Find all prime factors

13. 5/6 = what %
Organize into a grid.
83.3%
(sum of bases)(height) / 2
y2 - y1 / x2 - x1

14. 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
1/16
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.
Immediately UNFACTOR or vice versa
Balancing

15. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
347
P(E)P(F)
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)
1/16

16. Work problem rule
Figure out the probability for each individual event. Multiply the individual probabilities together.
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.
Any multiplication involving an even number creates an even product.
Odd

17. Multiples of 3
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
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.
3 - 6 - 9 - 12
347

18. To determine the number of integers less than 5000 that are evenly divisible by 15...?
12.5%
P(E)P(F)
Divide 4999 by 15 => 333 integers
Find simple interest then look for the answer that is a little bigger

19. Sum of consecutive numbers
Immediately UNFACTOR or vice versa
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Sum of digits is multiple of 3 - last two digits multiple of 4.
sum = (average)(number of terms)

20. The average of consecutive numbers
22
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
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
1st Rule of Probability: Basic Rule is what?

21. Price sold for by retailer (after markup)
Group 1 + Group 2 + Neither - Both = Total
market value
at least 3 steps
1st Rule of Probability: Basic Rule is what?

22. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
22
(# of favorable outcomes) / (# of possible outcomes)
16.6%
Last two digits are multiple of 4 or the number can be divided by 2 twice.

23. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
y2 - y1 / x2 - x1
P(event NOT occurring) = 1 - P(event occurring)
(x-n(n)y-n)
(n-1)!

24. Formula for Mixed Group problems (involving Both/Neither)
$11 - 025
Even
12.5%
Group 1 + Group 2 + Neither - Both = Total

25. Combined Events: E and F
principle (interest rate - in decimal form) (time - in years)
P(E)P(F)
Immediately UNFACTOR or vice versa
P(event NOT occurring) = 1 - P(event occurring)

26. Intersecting Sets
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
P(event NOT occurring) = 1 - P(event occurring)
Find simple interest then look for the answer that is a little bigger
| A union B| = |A| + |B| - |A intersect B|

27. How to check for a prime number.

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28. In general - difficult 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)
| A union B| = |A| + |B| - |A intersect B|
at least 3 steps
-b +- sq. rt(b^2 - 4ac) / 2a

29. Gross Profit formula
Odd
n! / (n - r)!
16.6%
Gross Profit = Selling Price - Cost

30. Price purchased for by wholesaler
Purchase price
(x-n(n)y-n)
The probability of an event occurring plus the probability of the event not occurring = 1
2 steps

31. Probability and Geometry.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
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 = (average)(number of terms)
Find all prime factors

32. How to check whether a number is a multiple of 6
Number is a multiple of 3 and 2
P(E) + P(F) - P(E and F)
P(event NOT occurring) = 1 - P(event occurring)
22

33. 1/8 = what %
12.5%
Odd numbers only have ___________
The probability of event occurring is...
Minor arc = 2(inscribed angle)

34. 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
1/16
Last two digits are multiple of 4 or the number can be divided by 2 twice.
2 steps

35. How to check whether number is multiple of 9
(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.
Group 1 + Group 2 + Neither - Both = Total
Sum of digits is multiple of 9

36. Indistinguishable events how to find the number of permutations

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37. Three triangle length patterns
(sum of bases)(height) / 2
sum = (average)(number of terms)
P(E) + P(F) - P(E and F)
3-4-5 - 5-12-13 - 9-12-15

38. Percent Formula
p/100 = is/of
Purchase price
1.4
x(sq. rt 3) - x - 2x

39. How to check whether a number is a multiple of 12.
347
1st Rule of Probability: Basic Rule is what?
Sum of digits is multiple of 3 - last two digits multiple of 4.
s Sq. rt (x^r)

40. Average Rate: Average speed
0.15n + 0.08(5) = 0.1(n+5)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
(total distance) / (total time)
The probability of an event occurring plus the probability of the event not occurring = 1

41. 3rd Rule of Probability: Conditional Probability
1st Rule of Probability: Basic Rule is what?
The amount after deductions
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.
Sum of digits is multiple of 9

42. Combined Events: Not E = P(not E) = ?
Principal (1 + interest/number times compounded)^(t)(n)
1 - P(E)
1st Rule of Probability: Basic Rule is what?
If the outcome of one event affects the outcome of the other event.

43. gcd(m,n)*lcm(m,n)
1/16
-b +- sq. rt(b^2 - 4ac) / 2a
1st Rule of Probability: Basic Rule is what?
gcd(m,n)*lcm(m,n) = mn

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)
(sum of bases)(height) / 2
P(event NOT occurring) = 1 - P(event occurring)
at least 3 steps

45. Odd Factors
(total distance) / (total time)
Odd numbers only have ___________
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
______ |m-n|

46. Triangle abc with d on the outside with a line. What does d = ?
1/16
Sum of digits is multiple of 3
Exterior angle d is equal to the sum of the two remote interior angles a and b
$11 - 025

47. Formula for area of a Trapezoid
s Sq. rt (x^r)
Principal (1 + interest/number times compounded)^(t)(n)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
(sum of bases)(height) / 2

48. Permutations: Order Matters
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
Immediately UNFACTOR or vice versa
n! / (n - r)!
1 - P(E)

49. 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?
0.15n + 0.08(5) = 0.1(n+5)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
If the outcome of one event affects the outcome of the other event.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

50. Quadratic formula
-b +- sq. rt(b^2 - 4ac) / 2a
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)
Find simple interest then look for the answer that is a little bigger
180(n-2)