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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 number is multiple of 9
1/16
Find all prime factors
______ |m-n|
Sum of digits is multiple of 9

2. Intersecting Sets
3-4-5 - 5-12-13 - 9-12-15
(n-1)!
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
| A union B| = |A| + |B| - |A intersect B|

3. 3^3 x 4^3 = ?
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.
$11 - 025
12^3

4. Sum of consecutive numbers
sum = (average)(number of terms)
The probability of an event occurring plus the probability of the event not occurring = 1
12^3
3-4-5 - 5-12-13 - 9-12-15

5. 2n+1 - 2n+3 - 2n+5
Odd
14 liters
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.
1st Rule of Probability: Basic Rule is what?

6. gcd(m,n)
-b +- sq. rt(b^2 - 4ac) / 2a
Number is a multiple of 3 and 2
at least 3 steps
______ |m-n|

7. Triangle abc with d on the outside with a line. What does d = ?
-b +- sq. rt(b^2 - 4ac) / 2a
Exterior angle d is equal to the sum of the two remote interior angles a and b
Balancing
Divide 4999 by 15 => 333 integers

8. In general - medium questions require how many steps to solve?
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
2 steps
83.3%
Even

9. Multiplication principle
(sum of bases)(height) / 2
83.3%
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
A = P(1 + r) ^n

10. Inscribed Angle - Minor Arc
Minor arc = 2(inscribed angle)
3 - 6 - 9 - 12
1
2 steps

11. How to check whether a number is a multiple of 3.
Sum of digits is multiple of 3
Number is a multiple of 3 and 2
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
180(n-2)

12. What to do with equations that have fractions
Find simple interest then look for the answer that is a little bigger
Group 1 + Group 2 + Neither - Both = Total
Immediately try factoring/simplifying when possible
x(sq. rt 3) - x - 2x

13. How to check whether a number is a multiple of 6
1/16
p/100 = is/of
Number is a multiple of 3 and 2
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

14. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
12.5%
22
Exterior angle d is equal to the sum of the two remote interior angles a and b
(amount of change) / (original amount)

15. Percent increase = ?
always try to factor
Immediately try factoring/simplifying when possible
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
(amount of change) / (original amount)

16. Number added or deleted
1.7
Odd numbers only have ___________
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)

17. Price purchased for by wholesaler
4/3 TT r ^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
Purchase price
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

18. Average Rate: Average A per B
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
If the outcome of one event affects the outcome of the other event.
P(event NOT occurring) = 1 - P(event occurring)
(total A) / (total B)

19. When you see an equation in factored form in a question?
(x-n(n)y-n)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
(total A) / (total B)
Immediately UNFACTOR or vice versa

20. Volume of a sphere
4/3 TT r ^3
Sum of digits is multiple of 3 - last two digits multiple of 4.
2 steps
12^3

21. Formula for Mixed Group problems (involving Both/Neither)
180(n-2)
Group 1 + Group 2 + Neither - Both = Total
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Balancing

22. Work problem rule
______ |m-n|
Principal (1 + interest/number times compounded)^(t)(n)
1.7
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.

23. The number of ways independent events can occur together.
Gross Profit = Selling Price - Cost
Balancing
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
P(E) + P(F) - P(E and F)

24. Odd and Even rule.
The amount after deductions
Any multiplication involving an even number creates an even product.
Purchase price
Immediately UNFACTOR or vice versa

25. 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.
A = P(1 + r) ^n
1
Immediately UNFACTOR or vice versa
Organize into a grid.

26. To determine multiple-event probability where each individual event must occur in a certain way.
s Sq. rt (x^r)
Organize into a grid.
sum = (average)(number of terms)
Figure out the probability for each individual event. Multiply the individual probabilities together.

27. How to find all divisors of a number
y2 - y1 / x2 - x1
p/100 = is/of
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
Find all prime factors

28. What does the Sum of the angles in a Regular Polygon formula look like?
Minor arc = 2(inscribed angle)
180(n-2)
Figure out the probability for each individual event. Multiply the individual probabilities together.
______ |m-n|

29. Sq. rt(3)
1.7
gcd(m,n)*lcm(m,n) = mn
A = P(1 + r) ^n
3-4-5 - 5-12-13 - 9-12-15

30. 3rd Rule of Probability: Conditional Probability
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.
(total A) / (total B)
| A union B| = |A| + |B| - |A intersect B|
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.

31. 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)
Minor arc = 2(inscribed angle)
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
3-4-5 - 5-12-13 - 9-12-15

32. 5/6 = what %
83.3%
Sum of digits is multiple of 9
Even
Immediately try factoring/simplifying when possible

33. Permutations: Order Matters
Odd numbers only have ___________
Find all prime factors
n! / (n - r)!
Balancing

34. Combined Events: E or F
sum = (average)(number of terms)
The amount after deductions
P(E) + P(F) - P(E and F)
Find simple interest then look for the answer that is a little bigger

35. How to find the slope.
always try to factor
y2 - y1 / x2 - x1
(n-1)!
Sum of digits is multiple of 9

36. How to check for a prime number.

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37. Prime Factorization to find Greatest Common Factor
principle (interest rate - in decimal form) (time - in years)
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
gcd(m,n)*lcm(m,n) = mn
-b +- sq. rt(b^2 - 4ac) / 2a

38. Always try to factor
(total A) / (total B)
always try to factor
Find all prime factors
1/16

39. Formula for area of a Trapezoid
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
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
(sum of bases)(height) / 2

40. 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
Even
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.
2 steps
| A union B| = |A| + |B| - |A intersect B|

41. 45-45-90 triangle basic lengths of sides
1
12.5%
x - x - x(sq. rt 2)
(# of favorable outcomes) / (# of possible outcomes)

42. Properties of 0
347
Group 1 + Group 2 + Neither - Both = Total
Minor arc = 2(inscribed angle)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

43. 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.
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.
14 liters
Immediately UNFACTOR or vice versa

44. Simple probability
Find simple interest then look for the answer that is a little bigger
(# of favorable outcomes) / (# of possible outcomes)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
1 - P(E)

45. Set Problems formula
2 steps
Principal (1 + interest/number times compounded)^(t)(n)
(total A) / (total B)
(x-n(n)y-n)

46. Average Rate: Average speed
(x-n(n)y-n)
12.5%
(total distance) / (total time)
16.6%

47. 2n - 2n+2 - 2n+4
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Exterior angle d is equal to the sum of the two remote interior angles a and b
Even
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

48. x^r/s = ?
market value
s Sq. rt (x^r)
Odd numbers only have ___________
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.

49. Odd Factors
Immediately UNFACTOR or vice versa
y2 - y1 / x2 - x1
Odd numbers only have ___________
Odd

50. To determine the number of integers less than 5000 that are evenly divisible by 15...?
22
Divide 4999 by 15 => 333 integers
D or E
14 liters