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GMAT Quantitative General

Subjects : gmat, math

Instructions:

Answer 50 questions in 15 minutes.
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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. gcd(m,n)
16.6%
(total distance) / (total time)
______ |m-n|
$11 - 025

2. When you see an equation in factored form in a question?
x(sq. rt 3) - x - 2x
p/100 = is/of
y2 - y1 / x2 - x1
Immediately UNFACTOR or vice versa

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.
sum = (average)(number of terms)
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.
The probability of event occurring is...
Organize into a grid.

4. Inscribed Angle - Minor Arc
P(E)P(F)
Group 1 + Group 2 + Neither - Both = Total
Minor arc = 2(inscribed angle)
The probability of event occurring is...

5. Probability and Geometry.
Balancing
Sum of digits is multiple 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
gcd(m,n)*lcm(m,n) = mn

6. x^r/s = ?
1st Rule of Probability: Basic Rule is what?
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
s Sq. rt (x^r)
Sum of digits is multiple of 3 - last two digits multiple of 4.

7. 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?
(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
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.
14 liters

8. 45-45-90 triangle basic lengths of sides
Minor arc = 2(inscribed angle)
180(n-2)
(x-n(n)y-n)
x - x - x(sq. rt 2)

9. How to check whether number is multiple of 9
Sum of digits is multiple of 3 - last two digits multiple of 4.
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.
D or E
Sum of digits is multiple of 9

10. 1/8 = what %
Purchase price
p/100 = is/of
The amount after deductions
12.5%

11. Sq. rt(2)
1.4
x(sq. rt 3) - x - 2x
always try to factor
2 steps

12. How to check whether a number is a multiple of 3.
Sum of digits is multiple of 3
Minor arc = 2(inscribed angle)
2 steps
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.

13. Permutations: Order Matters
Immediately UNFACTOR or vice versa
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
always try to factor
n! / (n - r)!

14. gcd(m,n)*lcm(m,n)
0.15n + 0.08(5) = 0.1(n+5)
gcd(m,n)*lcm(m,n) = mn
Divide 4999 by 15 => 333 integers
1/16

15. Indistinguishable events how to find the number of permutations
4/3 TT r ^3
If the outcome of one event affects the outcome of the other event.
(sum of bases)(height) / 2
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.

16. Always try to factor
Immediately UNFACTOR or vice versa
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
always try to factor
14 liters

17. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
4/3 TT r ^3
$11 - 025
______ |m-n|
D or E

18. 2n - 2n+2 - 2n+4
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.
Even
Organize into a grid.
P(E) + P(F) - P(E and F)

19. 2n+1 - 2n+3 - 2n+5
22
Odd
(total A) / (total B)
Minor arc = 2(inscribed angle)

20. Quadratic formula
Principal (1 + interest/number times compounded)^(t)(n)
| A union B| = |A| + |B| - |A intersect B|
-b +- sq. rt(b^2 - 4ac) / 2a
Sum of digits is multiple of 9

21. 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?
s Sq. rt (x^r)
0.15n + 0.08(5) = 0.1(n+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.
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.

22. Odd and Even rule.
(# of favorable outcomes) / (# of possible outcomes)
always try to factor
A = P(1 + r) ^n
Any multiplication involving an even number creates an even product.

23. How to check whether a number is a multiple of 12.
347
Immediately try factoring/simplifying when possible
Sum of digits is multiple of 3 - last two digits multiple of 4.
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.

24. 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.
Balancing
1.4
always try to factor

25. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
A = P(1 + r) ^n
Sum of digits is multiple of 9
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
If the outcome of one event affects the outcome of the other event.

26. Simple probability
Purchase price
12^3
(# of favorable outcomes) / (# of possible outcomes)
4/3 TT r ^3

27. 3^3 x 4^3 = ?
Sum of digits is multiple of 9
s Sq. rt (x^r)
Immediately try factoring/simplifying when possible
12^3

28. 0! = ?
1
Last two digits are multiple of 4 or the number can be divided by 2 twice.
1 - P(E)
y2 - y1 / x2 - x1

29. 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.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Organize into a grid.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

30. Gross
at least 3 steps
The total amount before any deductions
| A union B| = |A| + |B| - |A intersect B|
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

31. Multiplication principle
The probability of event occurring is...
12^3
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
Balancing

32. How to check whether a number is a multiple of 6
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.
Number is a multiple of 3 and 2
(total distance) / (total time)
Even

33. Trial Problems: look at the probability of NOT OCCURRING
P(event NOT occurring) = 1 - P(event occurring)
(sum of bases)(height) / 2
market value
1st Rule of Probability: Basic Rule is what?

34. Sum of consecutive numbers
sum = (average)(number of terms)
83.3%
347
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.

35. Price purchased for by wholesaler
gcd(m,n)*lcm(m,n) = mn
Purchase price
Sum of digits is multiple of 9
347

36. Odd Factors
Odd numbers only have ___________
12^3
Divide 4999 by 15 => 333 integers
1st Rule of Probability: Basic Rule is what?

37. Average Rate: Average speed
Divide 4999 by 15 => 333 integers
The amount after deductions
(total distance) / (total time)
Last two digits are multiple of 4 or the number can be divided by 2 twice.

38. Properties of 0
22
Minor arc = 2(inscribed angle)
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
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

39. To determine the number of integers less than 5000 that are evenly divisible by 15...?
(# of favorable outcomes) / (# of possible outcomes)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Divide 4999 by 15 => 333 integers
The amount after deductions

40. Net
(# of favorable outcomes) / (# of possible outcomes)
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 amount after deductions
| A union B| = |A| + |B| - |A intersect B|

41. Sq. rt(3)
at least 3 steps
Number is a multiple of 3 and 2
1.7
Exterior angle d is equal to the sum of the two remote interior angles a and b

42. Price sold for by retailer (after markup)
Any multiplication involving an even number creates an even product.
1/16
(total A) / (total B)
market value

43. In general - difficult questions require how many steps to solve?
x(sq. rt 3) - x - 2x
at least 3 steps
Organize into a grid.
(total A) / (total B)

44. 3rd Rule of Probability: Conditional Probability
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.
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
If the outcome of one event affects the outcome of the other event.
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.

45. Formula for area of a Trapezoid
1
(sum of bases)(height) / 2
Immediately try factoring/simplifying when possible
12^3

46. What does the Sum of the angles in a Regular Polygon formula look like?
180(n-2)
Find simple interest then look for the answer that is a little bigger
at least 3 steps
(# of favorable outcomes) / (# of possible outcomes)

47. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
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.
12.5%
P(E) + P(F) - P(E and F)
$11 - 025

48. Formula for Mixed Group problems (involving Both/Neither)
gcd(m,n)*lcm(m,n) = mn
If the outcome of one event affects the outcome of the other event.
Group 1 + Group 2 + Neither - Both = Total
y2 - y1 / x2 - x1

49. 30-60-90 triangle basic lengths of sides
The total amount before any deductions
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)
x(sq. rt 3) - x - 2x
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.

50. Gross Profit formula
P(E)P(F)
Figure out the probability for each individual event. Multiply the individual probabilities together.
Gross Profit = Selling Price - Cost
$11 - 025

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