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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. How to check whether a number is a multiple of 12.
Sum of digits is multiple of 3 - last two digits multiple of 4.
Sum of digits is multiple of 3
principle (interest rate - in decimal form) (time - in years)
Minor arc = 2(inscribed angle)

2. Intersecting Sets
market value
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
| A union B| = |A| + |B| - |A intersect B|

3. In general - medium questions require how many steps to solve?
Sum of digits is multiple of 9
1.4
Immediately UNFACTOR or vice versa
2 steps

4. gcd(m,n)
______ |m-n|
If the outcome of one event affects the outcome of the other event.
P(E) + P(F) - P(E and F)
12^3

5. Formula for Mixed Group problems (involving Both/Neither)
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.
Group 1 + Group 2 + Neither - Both = Total
| A union B| = |A| + |B| - |A intersect B|
The amount after deductions

6. Combined Events: Not E = P(not E) = ?
n! / (n - r)!
1 - P(E)
(# of favorable outcomes) / (# of possible outcomes)
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

7. 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?
(# of favorable outcomes) / (# of possible outcomes)
0.15n + 0.08(5) = 0.1(n+5)
s Sq. rt (x^r)
gcd(m,n)*lcm(m,n) = mn

8. When you see an equation in factored form in a question?
Immediately UNFACTOR or vice versa
p/100 = is/of
sum = (average)(number of terms)
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?
1.7
p/100 = is/of
14 liters
market value

10. 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
The probability of event occurring is...
If the outcome of one event affects the outcome of the other event.
(x-n(n)y-n)
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.

11. Inscribed Angle - Minor Arc
3-4-5 - 5-12-13 - 9-12-15
(amount of change) / (original amount)
Balancing
Minor arc = 2(inscribed angle)

12. Volume of a sphere
P(event NOT occurring) = 1 - P(event occurring)
Sum of digits is multiple of 9
P(E)P(F)
4/3 TT r ^3

13. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
$11 - 025
Find simple interest then look for the answer that is a little bigger
Figure out the probability for each individual event. Multiply the individual probabilities together.
12.5%

14. To determine the number of integers less than 5000 that are evenly divisible by 15...?
Divide 4999 by 15 => 333 integers
p/100 = is/of
1
1.4

15. Properties of 0
(x-n(n)y-n)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
83.3%
Even

16. Odd Factors
P(E)P(F)
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.
Odd numbers only have ___________
p/100 = is/of

17. Indistinguishable events how to find the number of permutations

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18. Prime Factorization to find Greatest Common Factor
Sum of digits is multiple of 3 - last two digits multiple of 4.
12.5%
x - x - x(sq. rt 2)
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

19. Net
D or E
The amount after deductions
Sum of digits is multiple of 3 - last two digits multiple of 4.
y2 - y1 / x2 - x1

20. Multiples of 3
P(E)P(F)
Find all prime factors
3 - 6 - 9 - 12
Balancing

21. 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.
Sum of digits is multiple of 9
y2 - y1 / x2 - x1
Immediately try factoring/simplifying when possible

22. How to find all divisors of a number
Find all prime factors
Immediately try factoring/simplifying when possible
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.
Sum of digits is multiple of 9

23. Trial Problems: look at the probability of NOT OCCURRING
P(event NOT occurring) = 1 - P(event occurring)
14 liters
The total amount before any deductions
Immediately try factoring/simplifying when possible

24. Sum of consecutive numbers
1st Rule of Probability: Basic Rule is what?
-b +- sq. rt(b^2 - 4ac) / 2a
principle (interest rate - in decimal form) (time - in years)
sum = (average)(number of terms)

25. What to do with equations that have fractions
Immediately try factoring/simplifying when possible
always try to factor
Balancing
Immediately UNFACTOR or vice versa

26. Dependent events: When are two events said to be dependent events?
The total amount before any deductions
If the outcome of one event affects the outcome of the other event.
22
D or E

27. 1/6 = what %
$11 - 025
16.6%
12^3
(total distance) / (total time)

28. Percent increase = ?
(amount of change) / (original amount)
1.4
market value
Organize into a grid.

29. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
Group 1 + Group 2 + Neither - Both = Total
always try to factor
principle (interest rate - in decimal form) (time - in years)
p/100 = is/of

30. Gross
Odd
The total amount before any deductions
always try to factor
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

31. Sq. rt(3)
1.7
Odd numbers only have ___________
The amount after deductions
(x-n(n)y-n)

32. How to check whether number is multiple of 9
Sum of digits is multiple of 9
n! / (n - r)!
Divide 4999 by 15 => 333 integers
-b +- sq. rt(b^2 - 4ac) / 2a

33. Price sold for by retailer (after markup)
1/16
market value
1st Rule of Probability: Basic Rule is what?
1.7

34. Formula for area of a Trapezoid
(sum of bases)(height) / 2
gcd(m,n)*lcm(m,n) = mn
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Immediately UNFACTOR or vice versa

35. 0! = ?
______ |m-n|
principle (interest rate - in decimal form) (time - in years)
P(E) + P(F) - P(E and F)
1

36. Combined Events: E or F
1st Rule of Probability: Basic Rule is what?
1
P(E) + P(F) - P(E and F)
12^3

37. Always try to factor
always try to factor
______ |m-n|
1st Rule of Probability: Basic Rule is what?
14 liters

38. 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.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
1st Rule of Probability: Basic Rule is what?
n! / (n - r)!
(total distance) / (total time)

39. Combined Events: E and F
A = P(1 + r) ^n
y2 - y1 / x2 - x1
s Sq. rt (x^r)
P(E)P(F)

40. How do you multiply roots together.
p/100 = is/of
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
D or E
1.7

41. Average Rate: Average A per B
3 - 6 - 9 - 12
market value
(total A) / (total B)
(# of favorable outcomes) / (# of possible outcomes)

42. Number added or deleted
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
s Sq. rt (x^r)
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)
Gross Profit = Selling Price - Cost

43. 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.
Divide 4999 by 15 => 333 integers
sum = (average)(number of terms)
Odd numbers only have ___________

44. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
0.15n + 0.08(5) = 0.1(n+5)
347
sum = (average)(number of terms)
1/16

45. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
P(E) + P(F) - P(E and F)
D or E
principle (interest rate - in decimal form) (time - in years)
The probability of an event occurring plus the probability of the event not occurring = 1

46. Price purchased for by wholesaler
A = P(1 + r) ^n
D or E
Purchase price
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. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
Balancing
$11 - 025
(n-1)!
P(event NOT occurring) = 1 - P(event occurring)

48. 2n - 2n+2 - 2n+4
83.3%
D or E
at least 3 steps
Even

49. 4th rule of Probability
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)
sum = (average)(number of terms)
14 liters

50. Multiplication principle
16.6%
12.5%
(total distance) / (total time)
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