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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. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
1.7
(n-1)!
83.3%
(total A) / (total B)

2. 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.
n! / (n - r)!
p/100 = is/of
Minor arc = 2(inscribed angle)
Organize into a grid.

3. Compound interest formula
D or E
Principal (1 + interest/number times compounded)^(t)(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
3-4-5 - 5-12-13 - 9-12-15

4. Inscribed Angle - Minor Arc
Minor arc = 2(inscribed angle)
347
D or E
12.5%

5. gcd(m,n)*lcm(m,n)
x - x - x(sq. rt 2)
If the outcome of one event affects the outcome of the other event.
The probability of event occurring is...
gcd(m,n)*lcm(m,n) = mn

6. How to check whether a number is a multiple of 3.
s Sq. rt (x^r)
Sum of digits is multiple of 3
Minor arc = 2(inscribed angle)
3 - 6 - 9 - 12

7. 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.
1st Rule of Probability: Basic Rule is what?
D or E
| A union B| = |A| + |B| - |A intersect B|
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

8. What does the Sum of the angles in a Regular Polygon formula look like?
gcd(m,n)*lcm(m,n) = mn
at least 3 steps
22
180(n-2)

9. Number added or deleted
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Figure out the probability for each individual event. Multiply the individual probabilities together.
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.
(amount of change) / (original amount)

10. How to check whether number is multiple of 9
-b +- sq. rt(b^2 - 4ac) / 2a
Find simple interest then look for the answer that is a little bigger
Sum of digits is multiple of 9
P(event NOT occurring) = 1 - P(event occurring)

11. 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?
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
Immediately UNFACTOR or vice versa
0.15n + 0.08(5) = 0.1(n+5)
Group 1 + Group 2 + Neither - Both = Total

12. When you see an equation in factored form in a question?
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.
P(E) + P(F) - P(E and F)
1st Rule of Probability: Basic Rule is what?
Immediately UNFACTOR or vice versa

13. 30-60-90 triangle basic lengths of sides
(total distance) / (total time)
1/16
Purchase price
x(sq. rt 3) - x - 2x

14. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
gcd(m,n)*lcm(m,n) = mn
Odd
A = P(1 + r) ^n
Gross Profit = Selling Price - Cost

15. Intersecting Sets
| A union B| = |A| + |B| - |A intersect B|
Immediately UNFACTOR or vice versa
P(event NOT occurring) = 1 - P(event occurring)
The probability of an event occurring plus the probability of the event not occurring = 1

16. In general - difficult questions require how many steps to solve?
Odd
3 - 6 - 9 - 12
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
at least 3 steps

17. Formula for area of a Trapezoid
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.
Organize into a grid.
(sum of bases)(height) / 2
Immediately try factoring/simplifying when possible

18. 1/8 = what %
12.5%
Sum of digits is multiple of 3 - last two digits multiple of 4.
Immediately UNFACTOR or vice versa
principle (interest rate - in decimal form) (time - in years)

19. How to check whether a number is a multiple of 6
Number is a multiple of 3 and 2
3 - 6 - 9 - 12
$11 - 025
Group 1 + Group 2 + Neither - Both = Total

20. Gross
The total amount before any deductions
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
1st Rule of Probability: Basic Rule is what?
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

21. Prime Factorization to find Greatest Common Factor
83.3%
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
Find simple interest then look for the answer that is a little bigger
(x-n(n)y-n)

22. Odd and Even rule.
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
D or E
Any multiplication involving an even number creates an even product.
Sum of digits is multiple of 9

23. 45-45-90 triangle basic lengths of sides
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
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
gcd(m,n)*lcm(m,n) = mn

24. Sum of consecutive numbers
Sum of digits is multiple of 3
sum = (average)(number of terms)
-b +- sq. rt(b^2 - 4ac) / 2a
1.7

25. Permutations: Order Matters
x - x - x(sq. rt 2)
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 A AND event B occurring is the probability of event A times the probability of event B - given that A has already occurred.
n! / (n - r)!

26. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
347
Balancing
x(sq. rt 3) - x - 2x
12.5%

27. Three triangle length patterns
The amount after 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)
3-4-5 - 5-12-13 - 9-12-15
Any multiplication involving an even number creates an even product.

28. What to do with equations that have fractions
Immediately try factoring/simplifying when possible
-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
(# of favorable outcomes) / (# of possible outcomes)

29. x^r/s = ?
1.4
(# of favorable outcomes) / (# of possible outcomes)
Principal (1 + interest/number times compounded)^(t)(n)
s Sq. rt (x^r)

30. Quadratic formula
-b +- sq. rt(b^2 - 4ac) / 2a
4/3 TT r ^3
Sum of digits is multiple of 3
Find simple interest then look for the answer that is a little bigger

31. How do you multiply roots together.
14 liters
A = P(1 + r) ^n
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
3-4-5 - 5-12-13 - 9-12-15

32. 1/6 = what %
16.6%
347
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
12^3

33. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
$11 - 025
12^3
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 total amount before any deductions

34. Average Rate: Average A per B
1 - P(E)
market value
(total A) / (total B)
Odd numbers only have ___________

35. The number of outcomes that result in A divided by the total number of possible outcomes.
at least 3 steps
Even
The probability of event occurring is...
3 - 6 - 9 - 12

36. Combined Events: Not E = P(not E) = ?
1/16
Figure out the probability for each individual event. Multiply the individual probabilities together.
(sum of bases)(height) / 2
1 - P(E)

37. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
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.
D or E
x(sq. rt 3) - x - 2x
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

38. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
12^3
Immediately UNFACTOR or vice versa
principle (interest rate - in decimal form) (time - in years)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

39. 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
The total amount before any deductions
Last two digits are multiple of 4 or the number can be divided by 2 twice.
always try to factor
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.

40. Price purchased for by wholesaler
Purchase price
at least 3 steps
Group 1 + Group 2 + Neither - Both = Total
Odd numbers only have ___________

41. Sq. rt(3)
y2 - y1 / x2 - x1
1.7
Sum of digits is multiple of 3
A = P(1 + r) ^n

42. Volume of a sphere
Odd
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
4/3 TT r ^3
always try to factor

43. Formula for Mixed Group problems (involving Both/Neither)
1.4
16.6%
Group 1 + Group 2 + Neither - Both = Total
1/16

44. Compound interest rule
The total amount before any deductions
Number is a multiple of 3 and 2
1
Find simple interest then look for the answer that is a little bigger

45. 5/6 = what %
Find simple interest then look for the answer that is a little bigger
at least 3 steps
(amount of change) / (original amount)
83.3%

46. Net
14 liters
The amount after deductions
x(sq. rt 3) - x - 2x
Immediately UNFACTOR or vice versa

47. Multiples of 3
Odd numbers only have ___________
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
3 - 6 - 9 - 12
Immediately try factoring/simplifying when possible

48. 2n+1 - 2n+3 - 2n+5
(# of favorable outcomes) / (# of possible outcomes)
Odd
principle (interest rate - in decimal form) (time - in years)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

49. How to check whether a number is a multiple of 4.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
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
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.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

50. (1/4)^2
1/16
Group 1 + Group 2 + Neither - Both = Total
12^3
22

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GMAT Quantitative General

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