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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. 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)
at least 3 steps
Even
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

2. When you see an equation in factored form in a question?
Immediately UNFACTOR or vice versa
Sum of digits is multiple of 3 - last two digits multiple of 4.
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)

3. 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.
1.4
Organize into a grid.
Divide 4999 by 15 => 333 integers
D or E

4. 3^3 x 4^3 = ?
12^3
Principal (1 + interest/number times compounded)^(t)(n)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
3 - 6 - 9 - 12

5. Volume of a sphere
n! / (n - r)!
sum = (average)(number of terms)
P(E)P(F)
4/3 TT r ^3

6. How to check whether a number is a multiple of 6
market value
sum = (average)(number of terms)
Number is a multiple of 3 and 2
The probability of event occurring is...

7. Work problem rule
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 3 - last two digits multiple of 4.
1.7
______ |m-n|

8. Odd Factors
D or E
Odd numbers only have ___________
2 steps
1.7

9. To determine the number of integers less than 5000 that are evenly divisible by 15...?
Divide 4999 by 15 => 333 integers
(total A) / (total B)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

10. Percent increase = ?
(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.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
(amount of change) / (original amount)

11. Simple probability
12^3
(# of favorable outcomes) / (# of possible outcomes)
22
1/16

12. Intersecting Sets
12.5%
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
(n-1)!
| A union B| = |A| + |B| - |A intersect B|

13. Prime Factorization to find Greatest Common Factor
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.
Balancing
2 steps
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

14. Average Rate: Average speed
(total distance) / (total time)
Principal (1 + interest/number times compounded)^(t)(n)
at least 3 steps
Group 1 + Group 2 + Neither - Both = Total

15. Percent Formula
4/3 TT r ^3
1st Rule of Probability: Basic Rule is what?
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.
p/100 = is/of

16. What to do with equations that have fractions
Immediately try factoring/simplifying when possible
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
P(event NOT occurring) = 1 - P(event occurring)
(# of favorable outcomes) / (# of possible outcomes)

17. 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.
Number is a multiple of 3 and 2
(total A) / (total B)
Any multiplication involving an even number creates an even product.

18. Permutations: Order Matters
12.5%
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.
(# of favorable outcomes) / (# of possible outcomes)
n! / (n - r)!

19. Sum of consecutive numbers
n! / (n - r)!
Any multiplication involving an even number creates an even product.
4/3 TT r ^3
sum = (average)(number of terms)

20. Indistinguishable events how to find the number of permutations

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21. Combined Events: Not E = P(not E) = ?
The probability of an event occurring plus the probability of the event not occurring = 1
347
Organize into a grid.
1 - P(E)

22. 45-45-90 triangle basic lengths of sides
x - x - x(sq. rt 2)
A = P(1 + r) ^n
Immediately try factoring/simplifying when possible
at least 3 steps

23. gcd(m,n)*lcm(m,n)
4/3 TT r ^3
1.7
gcd(m,n)*lcm(m,n) = mn
If the outcome of one event affects the outcome of the other event.

24. 1/6 = what %
(total A) / (total B)
83.3%
Exterior angle d is equal to the sum of the two remote interior angles a and b
16.6%

25. Gross Profit formula
The probability of event occurring is...
Find simple interest then look for the answer that is a little bigger
Gross Profit = Selling Price - Cost
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. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
The total amount before any deductions
P(E)P(F)
principle (interest rate - in decimal form) (time - in years)
$11 - 025

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

28. 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
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
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

29. Formula for area of a Trapezoid
(sum of bases)(height) / 2
If the outcome of one event affects the outcome of the other event.
180(n-2)
The probability of event occurring is...

30. 5/6 = what %
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.
at least 3 steps
The probability of an event occurring plus the probability of the event not occurring = 1
83.3%

31. Triangle abc with d on the outside with a line. What does d = ?
Balancing
Exterior angle d is equal to the sum of the two remote interior angles a and b
(sum of bases)(height) / 2
The amount after deductions

32. Price sold for by retailer (after markup)
Group 1 + Group 2 + Neither - Both = Total
Odd numbers only have ___________
market value
22

33. 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 - P(E)
D or E
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.
always try to factor

34. Odd and Even rule.
Immediately UNFACTOR or vice versa
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.
Any multiplication involving an even number creates an even product.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

35. How to check whether number is multiple of 9
Sum of digits is multiple of 9
-b +- sq. rt(b^2 - 4ac) / 2a
12.5%
(amount of change) / (original amount)

36. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
A = P(1 + r) ^n
1st Rule of Probability: Basic Rule is what?
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
14 liters

37. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
22
3 - 6 - 9 - 12
The probability of event occurring is...
Find all prime factors

38. The number of outcomes that result in A divided by the total number of possible outcomes.
Number is a multiple of 3 and 2
The probability of event occurring is...
The total amount before any deductions
______ |m-n|

39. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
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.
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)
D or E
Any multiplication involving an even number creates an even product.

40. Price purchased for by wholesaler
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
Balancing
Purchase price

41. How to check for a prime number.

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42. Multiplication principle
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 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)
Figure out the probability for each individual event. Multiply the individual probabilities together.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

43. Combined Events: E and F
$11 - 025
Any multiplication involving an even number creates an even product.
P(E)P(F)
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.

44. 30-60-90 triangle basic lengths of sides
Group 1 + Group 2 + Neither - Both = Total
market value
x(sq. rt 3) - x - 2x
12.5%

45. 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?
Principal (1 + interest/number times compounded)^(t)(n)
(sum of bases)(height) / 2
Figure out the probability for each individual event. Multiply the individual probabilities together.
0.15n + 0.08(5) = 0.1(n+5)

46. Compound interest formula
3-4-5 - 5-12-13 - 9-12-15
Principal (1 + interest/number times compounded)^(t)(n)
y2 - y1 / x2 - x1
4/3 TT r ^3

47. x^r/s = ?
s Sq. rt (x^r)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
180(n-2)
x(sq. rt 3) - x - 2x

48. 2n+1 - 2n+3 - 2n+5
Odd
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|
Organize into a grid.

49. How to find all divisors of a number
0.15n + 0.08(5) = 0.1(n+5)
P(E) + P(F) - P(E and F)
D or E
Find all prime factors

50. Probability and Geometry.
The amount after deductions
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
principle (interest rate - in decimal form) (time - in years)
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.