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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 for a prime number.

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2. Always try to factor
y2 - y1 / x2 - x1
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.
Sum of digits is multiple of 3
always try to factor

3. 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.
P(event NOT occurring) = 1 - P(event occurring)
(n-1)!
The amount after deductions

4. How do you multiply roots together.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
(# of favorable outcomes) / (# of possible outcomes)
A = P(1 + r) ^n
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.

5. How to check whether a number is a multiple of 4.
p/100 = is/of
Any multiplication involving an even number creates an even product.
Exterior angle d is equal to the sum of the two remote interior angles a and b
Last two digits are multiple of 4 or the number can be divided by 2 twice.

6. gcd(m,n)*lcm(m,n)
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.
gcd(m,n)*lcm(m,n) = mn
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.

7. 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.
P(E) + P(F) - P(E and 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)
s Sq. rt (x^r)

8. 0! = ?
1
The amount after deductions
(total A) / (total B)
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.

9. To determine the number of integers less than 5000 that are evenly divisible by 15...?
Purchase price
83.3%
Divide 4999 by 15 => 333 integers
1.7

10. 4th rule of Probability
Sum of digits is multiple of 3
(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)
Immediately UNFACTOR or vice versa

11. Multiples of 3
3 - 6 - 9 - 12
The probability of an event occurring plus the probability of the event not occurring = 1
3-4-5 - 5-12-13 - 9-12-15
P(E) + P(F) - P(E and F)

12. 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?
12.5%
1.4
P(E)P(F)
0.15n + 0.08(5) = 0.1(n+5)

13. Inscribed Angle - Minor Arc
Minor arc = 2(inscribed angle)
| A union B| = |A| + |B| - |A intersect B|
83.3%
P(E) + P(F) - P(E and F)

14. Set Problems formula
(x-n(n)y-n)
83.3%
Odd
market value

15. 5/6 = what %
83.3%
22
Principal (1 + interest/number times compounded)^(t)(n)
(n-1)!

16. Average Rate: Average A per B
1
sum = (average)(number of terms)
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 A) / (total B)

17. Intersecting Sets
| A union B| = |A| + |B| - |A intersect B|
1
Find simple interest then look for the answer that is a little bigger
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.

18. 30-60-90 triangle basic lengths of sides
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
sum = (average)(number of terms)
x(sq. rt 3) - x - 2x
Gross Profit = Selling Price - Cost

19. 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.
p/100 = is/of
Sum of digits is multiple of 3 - last two digits multiple of 4.
1.7

20. 2n - 2n+2 - 2n+4
y2 - y1 / x2 - x1
Even
Gross Profit = Selling Price - Cost
gcd(m,n)*lcm(m,n) = mn

21. How to check whether number is multiple of 9
Any multiplication involving an even number creates an even product.
16.6%
Sum of digits is multiple of 9
Even

22. 1/6 = what %
(total A) / (total B)
P(E) + P(F) - P(E and F)
(total distance) / (total time)
16.6%

23. Three triangle length patterns
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)
3-4-5 - 5-12-13 - 9-12-15
If the outcome of one event affects the outcome of the other event.
p/100 = is/of

24. Probability and Geometry.
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
180(n-2)
The probability of an event occurring plus the probability of the event not occurring = 1
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

25. When you see an equation in factored form in a question?
Immediately UNFACTOR or vice versa
gcd(m,n)*lcm(m,n) = mn
Any multiplication involving an even number creates an even product.
1st Rule of Probability: Basic Rule is what?

26. Combined Events: E and F
x - x - x(sq. rt 2)
Immediately try factoring/simplifying when possible
at least 3 steps
P(E)P(F)

27. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
gcd(m,n)*lcm(m,n) = mn
always try to factor
$11 - 025
______ |m-n|

28. The number of outcomes that result in A divided by the total number of possible outcomes.
market value
Any multiplication involving an even number creates an even product.
Organize into a grid.
The probability of event occurring is...

29. 2nd Rule of Probability: P(E) = 1 - P(not E)
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 an event occurring plus the probability of the event not occurring = 1
n! / (n - r)!
A = P(1 + r) ^n

30. How to find all divisors of a number
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.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Find all prime factors

31. 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
(total A) / (total B)
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.
Any multiplication involving an even number creates an even product.
Figure out the probability for each individual event. Multiply the individual probabilities together.

32. The number of ways independent events can occur together.
Gross Profit = Selling Price - Cost
Exterior angle d is equal to the sum of the two remote interior angles a and b
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
______ |m-n|

33. Sum of consecutive numbers
sum = (average)(number of terms)
(total distance) / (total time)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
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

34. What does the Sum of the angles in a Regular Polygon formula look like?
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.
180(n-2)
(# of favorable outcomes) / (# of possible outcomes)

35. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
Sum of digits is multiple of 3
principle (interest rate - in decimal form) (time - in years)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
(total A) / (total B)

36. Compound interest rule
Number is a multiple of 3 and 2
Any multiplication involving an even number creates an even product.
Find simple interest then look for the answer that is a little bigger
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

37. 3rd Rule of Probability: Conditional Probability
12^3
180(n-2)
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.
gcd(m,n)*lcm(m,n) = mn

38. In general - difficult questions require how many steps to solve?
1
1.4
at least 3 steps
Immediately try factoring/simplifying when possible

39. 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.
principle (interest rate - in decimal form) (time - in years)
If the outcome of one event affects the outcome of the other event.
2 steps

40. How to check whether a number is a multiple of 6
| A union B| = |A| + |B| - |A intersect B|
Divide 4999 by 15 => 333 integers
Balancing
Number is a multiple of 3 and 2

41. Average Rate: Average speed
gcd(m,n)*lcm(m,n) = mn
-b +- sq. rt(b^2 - 4ac) / 2a
(total distance) / (total time)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

42. Price purchased for by wholesaler
347
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.
Exterior angle d is equal to the sum of the two remote interior angles a and b
Purchase price

43. 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
1.7
Principal (1 + interest/number times compounded)^(t)(n)
Balancing
P(E) + P(F) - P(E and F)

44. Sq. rt(2)
$11 - 025
4/3 TT r ^3
1.4
The probability of an event occurring plus the probability of the event not occurring = 1

45. How to find the slope.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
(total distance) / (total time)
y2 - y1 / x2 - x1
Exterior angle d is equal to the sum of the two remote interior angles a and b

46. x^r/s = ?
s Sq. rt (x^r)
______ |m-n|
market value
1.7

47. Sq. rt(3)
14 liters
Minor arc = 2(inscribed angle)
x - x - x(sq. rt 2)
1.7

48. Odd and Even rule.
4/3 TT r ^3
(sum of bases)(height) / 2
Organize into a grid.
Any multiplication involving an even number creates an even product.

49. Trial Problems: look at the probability of NOT OCCURRING
P(event NOT occurring) = 1 - P(event occurring)
Group 1 + Group 2 + Neither - Both = Total
3-4-5 - 5-12-13 - 9-12-15
0.15n + 0.08(5) = 0.1(n+5)

50. 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.
83.3%
180(n-2)
1st Rule of Probability: Basic Rule is what?
| A union B| = |A| + |B| - |A intersect B|