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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. Average Rate: Average speed
1 - P(E)
Find simple interest then look for the answer that is a little bigger
(total distance) / (total time)
$11 - 025

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

3. Sq. rt(2)
1.4
Immediately try factoring/simplifying when possible
D or E
(x-n(n)y-n)

4. Prime Factorization to find Greatest Common Factor
1/16
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
3-4-5 - 5-12-13 - 9-12-15
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

5. Formula for area of a Trapezoid
(sum of bases)(height) / 2
1/16
Balancing
Find simple interest then look for the answer that is a little bigger

6. Inscribed Angle - Minor Arc
Principal (1 + interest/number times compounded)^(t)(n)
Minor arc = 2(inscribed angle)
(total A) / (total B)
x(sq. rt 3) - x - 2x

7. Combined Events: E or F
P(E) + P(F) - P(E and F)
Sum of digits is multiple of 3
2 steps
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

8. Indistinguishable events how to find the number of permutations

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9. 1/6 = what %
16.6%
1.4
A = P(1 + r) ^n
(amount of change) / (original amount)

10. 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?
y2 - y1 / x2 - x1
14 liters
Principal (1 + interest/number times compounded)^(t)(n)
1.7

11. 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
Odd
Balancing
n! / (n - r)!
22

12. How to check whether a number is a multiple of 3.
sum = (average)(number of terms)
If the outcome of one event affects the outcome of the other event.
s Sq. rt (x^r)
Sum of digits is multiple of 3

13. Intersecting Sets
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
| A union B| = |A| + |B| - |A intersect B|
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 number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

14. How to check whether a number is a multiple of 12.
Sum of digits is multiple of 3 - last two digits multiple of 4.
(total A) / (total B)
Minor arc = 2(inscribed angle)
(# of favorable outcomes) / (# of possible outcomes)

15. Triangle abc with d on the outside with a line. What does d = ?
The probability of an event occurring plus the probability of the event not occurring = 1
x(sq. rt 3) - x - 2x
If the outcome of one event affects the outcome of the other event.
Exterior angle d is equal to the sum of the two remote interior angles a and b

16. Percent increase = ?
12^3
3-4-5 - 5-12-13 - 9-12-15
always try to factor
(amount of change) / (original amount)

17. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
D or E
1st Rule of Probability: Basic Rule is what?
-b +- sq. rt(b^2 - 4ac) / 2a
Find all prime factors

18. Sum of consecutive numbers
P(E) + P(F) - P(E and F)
sum = (average)(number of terms)
Purchase price
principle (interest rate - in decimal form) (time - in years)

19. 30-60-90 triangle basic lengths of sides
Even
x(sq. rt 3) - x - 2x
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
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

20. 2nd Rule of Probability: P(E) = 1 - P(not E)
x(sq. rt 3) - x - 2x
1st Rule of Probability: Basic Rule is what?
p/100 = is/of
The probability of an event occurring plus the probability of the event not occurring = 1

21. The average of consecutive numbers
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
(total A) / (total B)
y2 - y1 / x2 - x1
Immediately UNFACTOR or vice versa

22. 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.
Immediately UNFACTOR or vice versa
Organize into a grid.
The amount after deductions
x(sq. rt 3) - x - 2x

23. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
market value
(n-1)!
Number is a multiple of 3 and 2
P(E)P(F)

24. 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)
Any multiplication involving an even number creates an even product.
at least 3 steps
______ |m-n|

25. How to check for a prime number.

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26. Sq. rt(3)
1.4
p/100 = is/of
1.7
16.6%

27. gcd(m,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.
______ |m-n|
Sum of digits is multiple of 9
(x-n(n)y-n)

28. 5/6 = what %
(total A) / (total B)
83.3%
Sum of digits is multiple of 3
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.

29. 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?
P(E)P(F)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
0.15n + 0.08(5) = 0.1(n+5)
Minor arc = 2(inscribed angle)

30. Compound interest rule
market value
Find simple interest then look for the answer that is a little bigger
1/16
1 - P(E)

31. Probability and Geometry.
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
4/3 TT r ^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
3-4-5 - 5-12-13 - 9-12-15

32. 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.
sum = (average)(number of terms)
The probability of event occurring is...
x - x - x(sq. rt 2)
1st Rule of Probability: Basic Rule is what?

33. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
Even
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
$11 - 025
3-4-5 - 5-12-13 - 9-12-15

34. Odd Factors
Purchase price
Even
P(E)P(F)
Odd numbers only have ___________

35. Always try to factor
$11 - 025
sum = (average)(number of terms)
always try to factor
p/100 = is/of

36. Number added or deleted
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.
Sum of digits is multiple of 3 - last two digits multiple of 4.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Principal (1 + interest/number times compounded)^(t)(n)

37. 3^3 x 4^3 = ?
(total A) / (total B)
1/16
(sum of bases)(height) / 2
12^3

38. 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
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Sum of digits is multiple of 3 - last two digits multiple of 4.

39. 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
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Organize into a grid.

40. Price sold for by retailer (after markup)
3-4-5 - 5-12-13 - 9-12-15
Gross Profit = Selling Price - Cost
market value
3 - 6 - 9 - 12

41. Compound interest formula
Figure out the probability for each individual event. Multiply the individual probabilities together.
Principal (1 + interest/number times compounded)^(t)(n)
(n-1)!
Balancing

42. In general - difficult questions require how many steps to solve?
Balancing
at least 3 steps
x - x - x(sq. rt 2)
-b +- sq. rt(b^2 - 4ac) / 2a

43. Gross
Number is a multiple of 3 and 2
Minor arc = 2(inscribed angle)
The total amount before any deductions
Odd numbers only have ___________

44. Price purchased for by wholesaler
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
Group 1 + Group 2 + Neither - Both = Total
Purchase price
y2 - y1 / x2 - x1

45. 4th rule of Probability
______ |m-n|
Sum of digits is multiple of 3 - last two digits multiple of 4.
Sum of digits is multiple of 3
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)

46. Gross Profit formula
Divide 4999 by 15 => 333 integers
Odd numbers only have ___________
3 - 6 - 9 - 12
Gross Profit = Selling Price - Cost

47. Combined Events: Not E = P(not E) = ?
n! / (n - r)!
1 - P(E)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
0.15n + 0.08(5) = 0.1(n+5)

48. What does the Sum of the angles in a Regular Polygon formula look like?
Divide 4999 by 15 => 333 integers
83.3%
180(n-2)
principle (interest rate - in decimal form) (time - in years)

49. How do you multiply roots together.
3-4-5 - 5-12-13 - 9-12-15
Find all prime factors
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Immediately UNFACTOR or vice versa

50. Average Rate: Average A per 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.
-b +- sq. rt(b^2 - 4ac) / 2a
P(E) + P(F) - P(E and F)
(total A) / (total B)