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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. gcd(m,n)*lcm(m,n)
(# of favorable outcomes) / (# of possible outcomes)
gcd(m,n)*lcm(m,n) = mn
x(sq. rt 3) - x - 2x
16.6%

2. How to check whether number is multiple of 9
Sum of digits is multiple of 9
(total distance) / (total time)
market value
Odd numbers only have ___________

3. How to check whether a number is a multiple of 6
Number is a multiple of 3 and 2
1.7
A = P(1 + r) ^n
Sum of digits is multiple of 3 - last two digits multiple of 4.

4. Formula for area of a Trapezoid
D or E
(sum of bases)(height) / 2
Sum of digits is multiple of 9
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

5. Trial Problems: look at the probability of NOT OCCURRING
2 steps
P(event NOT occurring) = 1 - P(event occurring)
Any multiplication involving an even number creates an even product.
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

6. Average Rate: Average A per B
Find all prime factors
(total A) / (total B)
4/3 TT r ^3
The probability of event occurring is...

7. 0! = ?
1
-b +- sq. rt(b^2 - 4ac) / 2a
Figure out the probability for each individual event. Multiply the individual probabilities together.
(sum of bases)(height) / 2

8. Compound interest 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.
Find simple interest then look for the answer that is a little bigger
16.6%
Immediately try factoring/simplifying when possible

9. Formula for Mixed Group problems (involving Both/Neither)
$11 - 025
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.
1/16
Group 1 + Group 2 + Neither - Both = Total

10. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
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
Number is a multiple of 3 and 2
A = P(1 + r) ^n

11. Prime Factorization to find Greatest Common Factor
1.4
x - x - x(sq. rt 2)
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
180(n-2)

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

13. Net
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 amount after deductions
14 liters
(total A) / (total B)

14. What to do with equations that have fractions
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
Immediately try factoring/simplifying when possible
Immediately UNFACTOR or vice versa

15. Simple probability
$11 - 025
(# of favorable outcomes) / (# of possible outcomes)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Figure out the probability for each individual event. Multiply the individual probabilities together.

16. Combined Events: E and F
D or E
P(E)P(F)
______ |m-n|
p/100 = is/of

17. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
(n-1)!
1/16
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Last two digits are multiple of 4 or the number can be divided by 2 twice.

18. Triangle abc with d on the outside with a line. What does d = ?
P(E) + P(F) - P(E and F)
Exterior angle d is equal to the sum of the two remote interior angles a and b
Gross Profit = Selling Price - Cost
always try to factor

19. Multiples of 3
n! / (n - r)!
-b +- sq. rt(b^2 - 4ac) / 2a
3 - 6 - 9 - 12
83.3%

20. x^r/s = ?
Sum of digits is multiple of 9
s Sq. rt (x^r)
Divide 4999 by 15 => 333 integers
1

21. Number added or deleted
347
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
(x-n(n)y-n)
180(n-2)

22. How do you multiply roots together.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Any multiplication involving an even number creates an even product.
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)
Even

23. Compound interest formula
1
p/100 = is/of
y2 - y1 / x2 - x1
Principal (1 + interest/number times compounded)^(t)(n)

24. Combined Events: Not E = P(not E) = ?
-b +- sq. rt(b^2 - 4ac) / 2a
The amount after deductions
1 - P(E)
Organize into a grid.

25. Price sold for by retailer (after markup)
16.6%
4/3 TT r ^3
market value
22

26. How to check whether a number is a multiple of 3.
Odd
Sum of digits is multiple of 3
12.5%
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.

27. Price purchased for by wholesaler
Purchase price
Odd
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.
Any multiplication involving an even number creates an even product.

28. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
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)
Immediately UNFACTOR or vice versa
Sum of digits is multiple of 3
principle (interest rate - in decimal form) (time - in years)

29. In general - medium questions require how many steps to solve?
Odd
Principal (1 + interest/number times compounded)^(t)(n)
2 steps
principle (interest rate - in decimal form) (time - in years)

30. Multiplication principle
-b +- sq. rt(b^2 - 4ac) / 2a
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
Even
Odd numbers only have ___________

31. Work problem rule
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.
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.
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.
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. How to check for a prime number.

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33. 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.
Group 1 + Group 2 + Neither - Both = Total
Number is a multiple of 3 and 2
Organize into a grid.
1st Rule of Probability: Basic Rule is what?

34. 45-45-90 triangle basic lengths of sides
x - x - x(sq. rt 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.
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.
Purchase price

35. 2nd Rule of Probability: P(E) = 1 - P(not E)
A = P(1 + r) ^n
0.15n + 0.08(5) = 0.1(n+5)
The probability of an event occurring plus the probability of the event not occurring = 1
sum = (average)(number of terms)

36. How to find the slope.
347
y2 - y1 / x2 - x1
D or E
2 steps

37. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
$11 - 025
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
22

38. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
Organize into a grid.
y2 - y1 / x2 - x1
Balancing
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

39. Average Rate: Average speed
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
(total distance) / (total time)
2 steps

40. 3rd Rule of Probability: Conditional Probability
Principal (1 + interest/number times compounded)^(t)(n)
1.7
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(event NOT occurring) = 1 - P(event occurring)

41. To determine the number of integers less than 5000 that are evenly divisible by 15...?
Divide 4999 by 15 => 333 integers
| A union B| = |A| + |B| - |A intersect B|
4/3 TT r ^3
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.

42. To determine multiple-event probability where each individual event must occur in a certain way.
3 - 6 - 9 - 12
The total amount before any deductions
0.15n + 0.08(5) = 0.1(n+5)
Figure out the probability for each individual event. Multiply the individual probabilities together.

43. 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
Odd numbers only have ___________
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
P(E) + P(F) - P(E and 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. Probability and Geometry.
83.3%
3-4-5 - 5-12-13 - 9-12-15
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
Balancing

45. The number of ways independent events can occur together.
Sum of digits is multiple of 3
Odd
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

46. (1/4)^2
Any multiplication involving an even number creates an even product.
3-4-5 - 5-12-13 - 9-12-15
1/16
The amount after deductions

47. Gross Profit formula
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.
Divide 4999 by 15 => 333 integers
Gross Profit = Selling Price - Cost
1 - P(E)

48. 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
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Sum of digits is multiple of 3 - last two digits multiple of 4.
The total amount before any deductions
Balancing

49. Inscribed Angle - Minor Arc
Minor arc = 2(inscribed angle)
Immediately try factoring/simplifying when possible
22
12^3

50. Always try to factor
A = P(1 + r) ^n
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
always try to factor
Sum of digits is multiple of 3 - last two digits multiple of 4.