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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. 2n+1 - 2n+3 - 2n+5
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Odd
n! / (n - r)!
16.6%

2. How to check whether a number is a multiple of 12.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
83.3%
always try to factor
Sum of digits is multiple of 3 - last two digits multiple of 4.

3. 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.
(total distance) / (total time)
Gross Profit = Selling Price - Cost
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

4. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
$11 - 025
Find simple interest then look for the answer that is a little bigger
(total A) / (total B)
3 - 6 - 9 - 12

5. Properties of 0
Sum of digits is multiple of 9
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
-b +- sq. rt(b^2 - 4ac) / 2a
12^3

6. 2n - 2n+2 - 2n+4
16.6%
1
Even
Divide 4999 by 15 => 333 integers

7. Simple probability
The probability of an event occurring plus the probability of the event not occurring = 1
The amount after deductions
(# of favorable outcomes) / (# of possible outcomes)
Number is a multiple of 3 and 2

8. Intersecting Sets
| A union B| = |A| + |B| - |A intersect B|
The probability of event occurring is...
principle (interest rate - in decimal form) (time - in years)
(# of favorable outcomes) / (# of possible outcomes)

9. Sq. rt(2)
Divide 4999 by 15 => 333 integers
P(E)P(F)
1.4
Sum of digits is multiple of 3 - last two digits multiple of 4.

10. What does the Sum of the angles in a Regular Polygon formula look like?
180(n-2)
$11 - 025
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)
22

11. Price sold for by retailer (after markup)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
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.
market value
Sum of digits is multiple of 3

12. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
The probability of event occurring is...
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
Sum of digits is multiple of 3
A = P(1 + r) ^n

13. Probability and Geometry.
1
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
(n-1)!

14. Average Rate: Average speed
(sum of bases)(height) / 2
14 liters
(total distance) / (total time)
Divide 4999 by 15 => 333 integers

15. Percent increase = ?
The amount after deductions
1
Sum of digits is multiple of 3
(amount of change) / (original amount)

16. 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
0.15n + 0.08(5) = 0.1(n+5)
market value
Principal (1 + interest/number times compounded)^(t)(n)

17. In general - medium questions require how many steps to solve?
Immediately try factoring/simplifying when possible
180(n-2)
2 steps
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.

18. gcd(m,n)
______ |m-n|
The probability of event occurring is...
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

19. Formula for Mixed Group problems (involving Both/Neither)
(# of favorable outcomes) / (# of possible outcomes)
Group 1 + Group 2 + Neither - Both = Total
1/16
Find all prime factors

20. Formula for area of a Trapezoid
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
0.15n + 0.08(5) = 0.1(n+5)
Any multiplication involving an even number creates an even product.
(sum of bases)(height) / 2

21. How to find all divisors of a number
A = P(1 + r) ^n
Number is a multiple of 3 and 2
Find all prime factors
2 steps

22. In general - difficult questions require how many steps to solve?
(total distance) / (total time)
D or E
at least 3 steps
Odd numbers only have ___________

23. 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.
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.
-b +- sq. rt(b^2 - 4ac) / 2a
4/3 TT r ^3
Organize into a grid.

24. Compound interest formula
Principal (1 + interest/number times compounded)^(t)(n)
Find simple interest then look for the answer that is a little bigger
The probability of event occurring is...
$11 - 025

25. How to check for a prime number.

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26. Combined Events: E or F
(total A) / (total B)
Odd numbers only have ___________
P(E) + P(F) - P(E and F)
s Sq. rt (x^r)

27. 3^3 x 4^3 = ?
22
at least 3 steps
-b +- sq. rt(b^2 - 4ac) / 2a
12^3

28. To determine the number of integers less than 5000 that are evenly divisible by 15...?
3-4-5 - 5-12-13 - 9-12-15
(# of favorable outcomes) / (# of possible outcomes)
Divide 4999 by 15 => 333 integers
(sum of bases)(height) / 2

29. Triangle abc with d on the outside with a line. What does d = ?
principle (interest rate - in decimal form) (time - in years)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Exterior angle d is equal to the sum of the two remote interior angles a and b
3-4-5 - 5-12-13 - 9-12-15

30. How to check whether number is multiple of 9
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Any multiplication involving an even number creates an even product.
The probability of an event occurring plus the probability of the event not occurring = 1
Sum of digits is multiple of 9

31. Price purchased for by wholesaler
D or E
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.
Purchase price

32. 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
180(n-2)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Balancing

33. 30-60-90 triangle basic lengths of sides
x(sq. rt 3) - x - 2x
P(E) + P(F) - P(E and F)
(total A) / (total B)
1.7

34. 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
(# of favorable outcomes) / (# of possible outcomes)
Find all prime factors
If the outcome of one event affects the outcome of the other event.
Balancing

35. x^r/s = ?
16.6%
Sum of digits is multiple of 3 - last two digits multiple of 4.
s Sq. rt (x^r)
always try to factor

36. 1/8 = what %
(# of favorable outcomes) / (# of possible outcomes)
1 - P(E)
12.5%
1

37. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
at least 3 steps
1
3 - 6 - 9 - 12
22

38. 0! = ?
Minor arc = 2(inscribed angle)
Find simple interest then look for the answer that is a little bigger
1
market value

39. Percent Formula
16.6%
(amount of change) / (original amount)
-b +- sq. rt(b^2 - 4ac) / 2a
p/100 = is/of

40. 4th rule of Probability
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
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)
x(sq. rt 3) - x - 2x
Odd

41. Net
P(E)P(F)
The amount after deductions
x - x - x(sq. rt 2)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

42. How to check whether a number is a multiple of 4.
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.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
(n-1)!
Immediately try factoring/simplifying when possible

43. Volume of a sphere
Even
always try to factor
4/3 TT r ^3
The total amount before any deductions

44. When you see an equation in factored form in a question?
0.15n + 0.08(5) = 0.1(n+5)
P(event NOT occurring) = 1 - P(event occurring)
Immediately UNFACTOR or vice versa
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

45. (1/4)^2
If the outcome of one event affects the outcome of the other event.
Immediately try factoring/simplifying when possible
The probability of event occurring is...
1/16

46. 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
P(event NOT occurring) = 1 - P(event occurring)
1.7
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.
$11 - 025

47. Always try to factor
The probability of event occurring is...
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
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.
always try to factor

48. The number of outcomes that result in A divided by the total number of possible outcomes.
22
______ |m-n|
p/100 = is/of
The probability of event occurring is...

49. Compound interest 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.
Find simple interest then look for the answer that is a little bigger
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
market value

50. Sq. rt(3)
(amount of change) / (original amount)
Immediately try factoring/simplifying when possible
(# of favorable outcomes) / (# of possible outcomes)
1.7

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GMAT Quantitative General

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