Test your basic knowledge |

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 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?
Balancing
14 liters
0.15n + 0.08(5) = 0.1(n+5)
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

2. 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.
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
Odd numbers only have ___________
(n-1)!

3. In general - difficult questions require how many steps to solve?
3-4-5 - 5-12-13 - 9-12-15
Find simple interest then look for the answer that is a little bigger
1 - P(E)
at least 3 steps

4. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
$11 - 025
p/100 = is/of
P(E) + P(F) - P(E and F)
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.

5. How do you multiply roots together.
16.6%
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
always try to factor
y2 - y1 / x2 - x1

6. How to check whether a number is a multiple of 6
x(sq. rt 3) - x - 2x
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Number is a multiple of 3 and 2
1.4

7. The number of ways independent events can occur together.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
180(n-2)
Balancing
x(sq. rt 3) - x - 2x

8. 5/6 = what %
Purchase price
83.3%
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
| A union B| = |A| + |B| - |A intersect B|

9. Average Rate: Average A per B
Sum of digits is multiple of 3
(total A) / (total B)
347
| A union B| = |A| + |B| - |A intersect B|

10. x^r/s = ?
s Sq. rt (x^r)
always try to factor
12.5%
Figure out the probability for each individual event. Multiply the individual probabilities together.

11. What to do with equations that have fractions
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
at least 3 steps
Immediately try factoring/simplifying when possible
-b +- sq. rt(b^2 - 4ac) / 2a

12. 2n - 2n+2 - 2n+4
2 steps
Even
P(E)P(F)
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)

13. Always try to factor
always try to factor
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
______ |m-n|
x - x - x(sq. rt 2)

14. Odd and Even rule.
Any multiplication involving an even number creates an even product.
Sum of digits is multiple of 9
Immediately UNFACTOR or vice versa
______ |m-n|

15. Percent Formula
Even
Odd numbers only have ___________
p/100 = is/of
-b +- sq. rt(b^2 - 4ac) / 2a

16. Formula for area of a Trapezoid
2 steps
| A union B| = |A| + |B| - |A intersect B|
always try to factor
(sum of bases)(height) / 2

17. Intersecting Sets
| A union B| = |A| + |B| - |A intersect B|
Find simple interest then look for the answer that is a little bigger
(# of favorable outcomes) / (# of possible outcomes)
1.4

18. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
P(E)P(F)
(total distance) / (total time)
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.
(n-1)!

19. Compound interest rule
Find simple interest then look for the answer that is a little bigger
3-4-5 - 5-12-13 - 9-12-15
p/100 = is/of
(n-1)!

20. To determine multiple-event probability where each individual event must occur in a certain way.
Figure out the probability for each individual event. Multiply the individual probabilities together.
3-4-5 - 5-12-13 - 9-12-15
Balancing
Find simple interest then look for the answer that is a little bigger

21. 3rd Rule of Probability: Conditional Probability
y2 - y1 / x2 - x1
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)
2 steps
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. Price purchased for by wholesaler
1.7
principle (interest rate - in decimal form) (time - in years)
x - x - x(sq. rt 2)
Purchase price

23. Simple probability
n! / (n - r)!
gcd(m,n)*lcm(m,n) = mn
always try to factor
(# of favorable outcomes) / (# of possible outcomes)

24. Volume of a sphere
(amount of change) / (original amount)
Divide 4999 by 15 => 333 integers
4/3 TT r ^3
Principal (1 + interest/number times compounded)^(t)(n)

25. Trial Problems: look at the probability of NOT OCCURRING
______ |m-n|
22
1 - P(E)
P(event NOT occurring) = 1 - P(event occurring)

26. 3^3 x 4^3 = ?
12.5%
1/16
12^3
Number is a multiple of 3 and 2

27. Multiples of 3
x(sq. rt 3) - x - 2x
3 - 6 - 9 - 12
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
______ |m-n|

28. How to find all divisors of a number
P(E) + P(F) - P(E and F)
Find all prime factors
Immediately try factoring/simplifying when possible
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

29. Probability and Geometry.
y2 - y1 / x2 - x1
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.
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
The amount after deductions

30. 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)
(n-1)!
Immediately try factoring/simplifying when possible
x - x - x(sq. rt 2)

31. How to check whether a number is a multiple of 4.
The probability of an event occurring plus the probability of the event not occurring = 1
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
Last two digits are multiple of 4 or the number can be divided by 2 twice.
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.

32. Inscribed Angle - Minor Arc
Minor arc = 2(inscribed angle)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
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.
Find all prime factors

33. Gross
gcd(m,n)*lcm(m,n) = mn
1
p/100 = is/of
The total amount before any deductions

34. The number of outcomes that result in A divided by the total number of possible outcomes.
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
The probability of event occurring is...
______ |m-n|
14 liters

35. 45-45-90 triangle basic lengths of sides
Odd numbers only have ___________
Sum of digits is multiple of 3 - last two digits multiple of 4.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
x - x - x(sq. rt 2)

36. Formula for Mixed Group problems (involving Both/Neither)
Group 1 + Group 2 + Neither - Both = Total
347
-b +- sq. rt(b^2 - 4ac) / 2a
Exterior angle d is equal to the sum of the two remote interior angles a and b

37. Percent increase = ?
(n-1)!
Immediately try factoring/simplifying when possible
(amount of change) / (original amount)
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

38. Three triangle length patterns
3-4-5 - 5-12-13 - 9-12-15
Principal (1 + interest/number times compounded)^(t)(n)
principle (interest rate - in decimal form) (time - in years)
Sum of digits is multiple of 9

39. Combined Events: Not E = P(not E) = ?
The probability of an event occurring plus the probability of the event not occurring = 1
1.7
1 - P(E)
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.

40. 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
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
D or E
1.4
Balancing

41. How to find the slope.
y2 - y1 / x2 - x1
(amount of change) / (original amount)
at least 3 steps
gcd(m,n)*lcm(m,n) = mn

42. Gross Profit formula
n! / (n - r)!
Gross Profit = Selling Price - Cost
1/16
14 liters

43. How to check whether a number is a multiple of 3.
$11 - 025
0.15n + 0.08(5) = 0.1(n+5)
Sum of digits is multiple of 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.

44. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
1/16
gcd(m,n)*lcm(m,n) = mn
A = P(1 + r) ^n
The amount after deductions

45. 30-60-90 triangle basic lengths of sides
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.
Sum of digits is multiple of 3
Immediately try factoring/simplifying when possible
x(sq. rt 3) - x - 2x

46. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest 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.
x - x - x(sq. rt 2)
Find simple interest then look for the answer that is a little bigger
principle (interest rate - in decimal form) (time - in years)

47. 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.
Figure out the probability for each individual event. Multiply the individual probabilities together.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
p/100 = is/of

48. Combined Events: E or F
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)
y2 - y1 / x2 - x1
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(E) + P(F) - P(E and F)

49. Prime Factorization to find Greatest Common Factor
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
Gross Profit = Selling Price - Cost
A = P(1 + r) ^n
The probability of an event occurring plus the probability of the event not occurring = 1

50. Quadratic formula
market value
1st Rule of Probability: Basic Rule is what?
-b +- sq. rt(b^2 - 4ac) / 2a
(n-1)!