Algebra

Question 1

(x+y)^2 - (x-y)^2

Answer 1

4xy

Question 2

(x+y+z)^2

Answer 2

x^2 + y^2 + z^2 + 2(xy + xz + yz)

Question 3

x^3 + y^3

Answer 3

(x+y)(x^2 + y^2 - xy)

Question 4

x^3 - y^3

Answer 4

(x-y)(x^2 +y^2 +xy)

Question 5

T or F. a^n - b^n is always divisible by a- b

Answer 5

T

Question 6

a^n - b^n is divisible by a+b if

Answer 6

n is even

Question 7

a^n + b^n is divisible by a+b if

Answer 7

n is odd

Question 8

How do you express negative exponents ?

Answer 8

reciprocal of the inside base and turn negative to positive exponent

Question 9

T or F. if 0^x = 0 = 0^y , x is equal to y

Answer 9

False. 0^4 = 0 = 0^3 but 4 ≠ 3

Question 10

How do you express exponential growth formula?

Answer 10

y(t) = y(0).k^t

Question 11

T or F. In GMAT, you should always subtract or divide two inequalities

Answer 11

F. You should never

Question 12

If 0< G < 1 then how does G^n compare to G (if n is odd/even positive integer)

Answer 12

G^n is less than original G

Question 13

If 0< G < 1 then how does G^n compare to G (if n is odd/even negative integer)

Answer 13

G^n is larger than original G

Question 14

If -1< G < 0 then how does G^n compare to G (if n is odd/even positive integer)

Answer 14

G^n is larger than original G

Question 15

If -1< G < 0 then how does G^n compare to G (if n is odd/even negative integer)

Answer 15

G^n is larger than original G (if n is even)

G^n is smaller than original G (if n is odd)

Question 16

T or F. If both sides are known to be negative, you can’t flip the inequalities sign when you square

Answer 16

False. You can flip the sign.

Ex: -4 < - 3 then 16 > 9

Question 17

T or F. If both sides are known to be positive, you don’t flip the inequalities sign when you square

Answer 17

True.

Question 18

T or F. If one side is positive and one side is negative, the inequality sign stays when you square

Answer 18

False.

it may or may not

Question 19

T or F. If the signs are unclear, then you cannot square

Answer 19

True.

Question 20

If x < y, then how does 1/x compare to 1/y when x and y are both positive or both negative?

Answer 20

1/x > 1/y (flip the sign)

Question 21

If x < y, then how does 1/x compare to 1/y when x is negative and y is positive?

Answer 21

1/x < 1/y

Question 22

T or F. If you don’t know the sign of x or y, you can still take the reciprocals.

Answer 22

False.

Question 23

if |x| > a then:

Answer 23

x > a or x < -a

Question 24

if |x| < a then:

Answer 24

-a < x < a

Question 25

If |A| = |B| then

Answer 25

``` A = B or A = - B ```

Question 26

What is the equation expression for directional proportionality?

Answer 26

y(1)/ x(1) = y(2)/ x(2)

Question 27

What is the equation expression for inverse proportionality?

Answer 27

y(1) . x(1) = y(2) . x(2)

Question 28

When 0< G < 1, G^n < G if

Answer 28

n is positive integer

Question 29

When 0< G < 1, G^n > G if

Answer 29

n is negative integer

Question 30

When -1 < G < 0, G^n < G if

Answer 30

n is odd negative integer

Question 31

When -1< G< 0, G^n > G if

Answer 31

n is positive integer or | n is negative even integer

Question 32

square root of 2

Answer 32

about 1.4

Question 33

square root of 3

Answer 33

about 1.7

Question 34

square root of 5

Answer 34

around 2.25

Question 35

square root of 121

Answer 35

11

Question 36

square root of 144

Answer 36

12

Question 37

13^2

Answer 37

169

Question 38

square root of 196

Answer 38

14

Question 39

square root of 225

Answer 39

15

Question 40

square root of 256

Answer 40

16

Question 41

square root of 625

Answer 41

25

Question 42

G^n < G when

Answer 42

0< G < 1 | -1 < G < 0 if n is negative odd

Question 43

G^n > G when

Answer 43

n is negative for 0< G < 1 n is negative even for -1< G < 0 n is positive for -1< G < 0

Question 44

T or F. Any positive proper fraction raised to a power between 0 and 1 will result in a number larger than the original fraction.

Answer 44

T (problem #3 p. 125 Manhattan)

Question 45

T or F. Any positive proper fraction raised to a power greater than 1 will result in a number larger than the original fraction.

Answer 45

F.

Question 46

How do you translate "The retailer has less than twice as many radios as clocks in inventory" in math expression?

Answer 46

r < 2c

Question 47

How do we know a quadratic function has a solution or not?

Answer 47

if the discriminant (b^2 - 4ac) < 0, = 0 or > 0

Question 48

If the discriminant is greater than zero, then how many solutions are there?

Answer 48

two

Question 49

If the discriminant is equal to zero, then how many solutions are there?

Answer 49

one solution

Question 50

If the discriminant is less than zero, then how many solutions are there?

Answer 50

no solution

Question 51

The answer (A) in data sufficiency is?

Answer 51

Statement (1) alone is sufficient, but statement (2) is not

Question 52

The answer (B) in data sufficiency is?

Answer 52

Statement (2) alone is sufficient, but statement (1) is not

Question 53

The answer (C) in data sufficiency is?

Answer 53

Both statement together are sufficient, but neither statement alone is sufficient

Question 54

The answer (D) in data sufficiency is?

Answer 54

EACH statement ALONE is sufficient

Question 55

The answer (E) in data sufficiency is?

Answer 55

Statement (1) and (2) TOGETHER are NOT sufficient.

Question 56

The trick to translate fractional exponent of a number to a root

Answer 56

denominator OUT | numerator IN

Question 57

The trick to translate a root to fraction exponent

Answer 57

in NUMERATOR | out DENOMINATOR

Question 58

Can absolute value result in negative number?

Answer 58

NO. its results are always greater than 0

Question 59

x^0 = ?

Answer 59

1

Question 60

0^x = ?

Answer 60

0

Question 61

proper fraction

Answer 61

a fraction between 0 and 1

Question 62

How do you express proper fraction with decimals with exponents? Ex: (0.6)^2 (0.5)^4 (0.1)^5

Answer 62

The decimals move to the left in accordance with the value of exponent after exponent non-zero digits. Ex: (0.6)^2= 0.36 (0. 5)^2 = 0.0625 (0. 1)^5 = 0.00001

Question 63

what is the value of 0^0 ?

Answer 63

undefined

Question 64

T or F. There is no solution for the even root of a negative number

Answer 64

T

Question 65

What does x^2 - x < 0 imply?

Answer 65

x^2 < x, so 0 < x < 1

Question 66

square root of 324

Answer 66

18

Question 67

square root of 289

Answer 67

17

Question 68

19^2

Answer 68

361

Question 69

What is the vertex (x,y) of equation: | a(x-h)^2 + k = 0

Answer 69

(h,k)

Question 70

T or F. Any two points the same distance from the origin along perpendicular lines will have the opposite coordinates from one another - if one point is (a,b), the other will be (b,a)

Answer 70

True.

Question 71

T or F. In x-y plane, the quadrants is upper shaded area if the inequality is equal to or greater (>=)

Answer 71

True.

Question 72

T or F. In x-y plane, the quadrants is below shaded area if the inequality is equal to or less (=

Answer 72

True.