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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. Properties of 0
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Even
Balancing
16.6%

2. Net
always try to factor
The amount after deductions
Exterior angle d is equal to the sum of the two remote interior angles a and b
4/3 TT r ^3

3. How to find the slope.
y2 - y1 / x2 - x1
x - x - x(sq. rt 2)
(sum of bases)(height) / 2
p/100 = is/of

4. Gross
Number is a multiple of 3 and 2
Sum of digits is multiple of 3 - last two digits multiple of 4.
The total amount before any deductions
The probability of event occurring is...

5. When you see an equation in factored form in a question?
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Immediately UNFACTOR or vice versa
Even
(n-1)!

6. Number added or deleted
n! / (n - r)!
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Number is a multiple of 3 and 2
3 - 6 - 9 - 12

7. Work problem rule
1.7
14 liters
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.
(amount of change) / (original amount)

8. To determine multiple-event probability where each individual event must occur in a certain way.
gcd(m,n)*lcm(m,n) = mn
Any multiplication involving an even number creates an even product.
Figure out the probability for each individual event. Multiply the individual probabilities together.
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.

9. Intersecting Sets
| A union B| = |A| + |B| - |A intersect B|
1 - P(E)
-b +- sq. rt(b^2 - 4ac) / 2a
at least 3 steps

10. 5/6 = what %
P(event NOT occurring) = 1 - P(event occurring)
market value
83.3%
Organize into a grid.

11. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
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
Last two digits are multiple of 4 or the number can be divided by 2 twice.
22
D or E

12. Price sold for by retailer (after markup)
Even
market value
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
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

13. 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)
(total A) / (total B)
The amount after deductions
22

14. Odd and Even rule.
Any multiplication involving an even number creates an even product.
Find all prime factors
x(sq. rt 3) - x - 2x
p/100 = is/of

15. 3^3 x 4^3 = ?
Odd numbers only have ___________
12^3
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.
Odd

16. Three triangle length patterns
3-4-5 - 5-12-13 - 9-12-15
A = P(1 + r) ^n
sum = (average)(number of terms)
Even

17. 0! = ?
Immediately try factoring/simplifying when possible
1
(total A) / (total B)
12^3

18. Percent increase = ?
n! / (n - r)!
D or E
(amount of change) / (original amount)
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.

19. In general - medium questions require how many steps to solve?
3 - 6 - 9 - 12
market value
The probability of an event occurring plus the probability of the event not occurring = 1
2 steps

20. How do you multiply roots together.
Divide 4999 by 15 => 333 integers
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
14 liters
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

21. gcd(m,n)
(x-n(n)y-n)
(total distance) / (total time)
1 - P(E)
______ |m-n|

22. 2nd Rule of Probability: P(E) = 1 - P(not E)
(sum of bases)(height) / 2
The probability of an event occurring plus the probability of the event not occurring = 1
(total distance) / (total time)
Any multiplication involving an even number creates an even product.

23. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
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.
(n-1)!
Last two digits are multiple of 4 or the number can be divided by 2 twice.
3 - 6 - 9 - 12

24. Odd Factors
Purchase price
347
Odd numbers only have ___________
(x-n(n)y-n)

25. How to check whether number is multiple of 9
-b +- sq. rt(b^2 - 4ac) / 2a
(amount of change) / (original amount)
Sum of digits is multiple of 9
Last two digits are multiple of 4 or the number can be divided by 2 twice.

26. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
$11 - 025
Odd numbers only have ___________
-b +- sq. rt(b^2 - 4ac) / 2a
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.

27. The average of consecutive numbers
Find simple interest then look for the answer that is a little bigger
1/16
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)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

28. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
Divide 4999 by 15 => 333 integers
D or E
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
Find simple interest then look for the answer that is a little bigger

29. Average Rate: Average A per B
(total A) / (total B)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
If the outcome of one event affects the outcome of the other event.
P(E) + P(F) - P(E and F)

30. 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
12^3
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.
0.15n + 0.08(5) = 0.1(n+5)

31. x^r/s = ?
12^3
$11 - 025
s Sq. rt (x^r)
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

32. 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. 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.
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.
1 - P(E)
Minor arc = 2(inscribed angle)

33. What does the Sum of the angles in a Regular Polygon formula look like?
Purchase price
180(n-2)
Number is a multiple of 3 and 2
Balancing

34. Triangle abc with d on the outside with a line. What does d = ?
1st Rule of Probability: Basic Rule is what?
A = P(1 + r) ^n
D or E
Exterior angle d is equal to the sum of the two remote interior angles a and b

35. 45-45-90 triangle basic lengths of sides
Sum of digits is multiple of 3
D or E
14 liters
x - x - x(sq. rt 2)

36. 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.
at least 3 steps
1.4
180(n-2)
Organize into a grid.

37. Compound interest rule
Exterior angle d is equal to the sum of the two remote interior angles a and b
Find simple interest then look for the answer that is a little bigger
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
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

38. Permutations: Order Matters
0.15n + 0.08(5) = 0.1(n+5)
Find simple interest then look for the answer that is a little bigger
n! / (n - r)!
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

39. Price purchased for by wholesaler
Immediately try factoring/simplifying when possible
Purchase price
(sum of bases)(height) / 2
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)

40. The number of outcomes that result in A divided by the total number of possible outcomes.
P(E) + P(F) - P(E and F)
16.6%
gcd(m,n)*lcm(m,n) = mn
The probability of event occurring is...

41. Always try to factor
Odd numbers only have ___________
Find simple interest then look for the answer that is a little bigger
always try to factor
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.

42. To determine the number of integers less than 5000 that are evenly divisible by 15...?
Find simple interest then look for the answer that is a little bigger
Divide 4999 by 15 => 333 integers
-b +- sq. rt(b^2 - 4ac) / 2a
Last two digits are multiple of 4 or the number can be divided by 2 twice.

43. 30-60-90 triangle basic lengths of sides
Immediately UNFACTOR or vice versa
The probability of event occurring is...
x(sq. rt 3) - x - 2x
3 - 6 - 9 - 12

44. Multiples of 3
(total A) / (total B)
14 liters
180(n-2)
3 - 6 - 9 - 12

45. Compound interest formula
3 - 6 - 9 - 12
Sum of digits is multiple of 9
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.
Principal (1 + interest/number times compounded)^(t)(n)

46. How to check whether a number is a multiple of 12.
Sum of digits is multiple of 3 - last two digits multiple of 4.
16.6%
sum = (average)(number of terms)
2 steps

47. Trial Problems: look at the probability of NOT OCCURRING
Last two digits are multiple of 4 or the number can be divided by 2 twice.
(n-1)!
Divide 4999 by 15 => 333 integers
P(event NOT occurring) = 1 - P(event occurring)

48. Average Rate: Average speed
1.7
4/3 TT r ^3
D or E
(total distance) / (total time)

49. 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
$11 - 025
Sum of digits is multiple of 3 - last two digits multiple of 4.
Any multiplication involving an even number creates an even product.
Balancing

50. Simple probability
83.3%
The probability of an event occurring plus the probability of the event not occurring = 1
1/16
(# of favorable outcomes) / (# of possible outcomes)